From c22a5fb5748e939c9e1f85e715f84a8b1abca929 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Thu, 19 Nov 2020 18:03:50 -0600
Subject: [PATCH 01/38] Sketch the design and implement the (line expansion +
 direct evaluation) case

---
 examples/boundary-layer.py | 199 +++++++++++++++++++++++++++
 pytential/qbx/__init__.py  | 274 ++++++++++++++++++++++++++++++++++++-
 pytential/qbx/fmm.py       | 123 ++++++++++++++++-
 3 files changed, 591 insertions(+), 5 deletions(-)
 create mode 100644 examples/boundary-layer.py

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
new file mode 100644
index 00000000..203488b0
--- /dev/null
+++ b/examples/boundary-layer.py
@@ -0,0 +1,199 @@
+# using LineTaylor for local expansion
+# must force direct evaluation because cannot translate from VolumeTaylor to LineTaylor
+
+enable_mayavi = 0
+if enable_mayavi:
+    from mayavi import mlab  # noqa
+
+import numpy as np
+import pyopencl as cl
+from sumpy.visualization import FieldPlotter
+from sumpy.kernel import one_kernel_2d, LaplaceKernel, HelmholtzKernel  # noqa
+
+from pytential import bind, sym
+
+from meshmode.mesh.generation import starfish, ellipse, drop # noqa
+from meshmode.mesh.refinement import RefinerWithoutAdjacency
+from meshmode.discretization.connection import (
+    make_refinement_connection, ChainedDiscretizationConnection,
+    L2ProjectionInverseDiscretizationConnection)
+
+target_order = 16
+qbx_order = 3
+coarse_nelements = 20
+mode_nr = 3
+n_refine_cycles = 4
+
+k = 3 + 50j
+
+from sumpy.expansion import ExpansionFactoryBase
+class VolumeMultipoleLineLocalTaylorExpansionFactory(ExpansionFactoryBase):
+    """Volume Taylor for multipole, line Taylor for local, to be used only with
+    direct evaluation.
+    """
+    def get_local_expansion_class(self, base_kernel):
+        from sumpy.expansion.local import LineTaylorLocalExpansion
+        return LineTaylorLocalExpansion
+
+    def get_multipole_expansion_class(self, base_kernel):
+        from sumpy.expansion.multipole import VolumeTaylorMultipoleExpansion
+        return VolumeTaylorMultipoleExpansion
+
+
+def main(curve_fn=starfish, visualize=True):
+    import logging
+    logging.basicConfig(level=logging.WARN)  # INFO for more progress info
+
+    cl_ctx = cl.create_some_context()
+    queue = cl.CommandQueue(cl_ctx)
+
+    from meshmode.mesh.generation import make_curve_mesh
+    base_mesh = make_curve_mesh(
+            curve_fn,
+            np.linspace(0, 1, coarse_nelements+1),
+            target_order)
+    refiner = RefinerWithoutAdjacency(base_mesh)
+
+    if k:
+        if k.imag:
+            kernel = HelmholtzKernel(2, allow_evanescent=True)
+        else:
+            kernel = HelmholtzKernel(2, allow_evanescent=False)
+        kernel_kwargs = {"k": sym.var("k")}
+    else:
+        kernel = LaplaceKernel(2)
+        kernel_kwargs = {}
+
+    from pytential.qbx import QBXLayerPotentialSource
+    from meshmode.array_context import PyOpenCLArrayContext
+    from meshmode.discretization import Discretization
+    from meshmode.discretization.poly_element import \
+            InterpolatoryQuadratureSimplexGroupFactory
+    from meshmode.dof_array import flatten
+
+    actx = PyOpenCLArrayContext(queue)
+    base_density_discr = Discretization(
+        actx, base_mesh,
+        InterpolatoryQuadratureSimplexGroupFactory(target_order))
+    previous_discr = base_density_discr
+
+    from pytential.qbx import QBXLayerPotentialAsymptotics
+    import sympy as sp
+    dist = sp.Symbol("dist")
+    k_sym = sp.Symbol("k")
+    expr = sp.exp(1j * k_sym * dist)
+    asmt = QBXLayerPotentialAsymptotics(2, kernel, expr=expr)
+    line_expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
+
+    def op(**kwargs):
+        kwargs.update(kernel_kwargs)
+        # op = sym.d_dx(sym.S(kernel, sym.var("sigma"), **kwargs))
+        # return sym.D(kernel, sym.var("sigma"), **kwargs)
+        return sym.S(kernel, sym.var("sigma"), **kwargs)
+
+    conns = []
+    ns = []
+    flds = []
+    flds_ref = []
+
+    for cycle in range(n_refine_cycles):
+        print(f"\nRefinement cycle {cycle+1}/{n_refine_cycles}")
+        refiner.refine_uniformly()
+        mesh = refiner.get_current_mesh()
+
+        pre_density_discr = Discretization(
+            actx, mesh,
+            InterpolatoryQuadratureSimplexGroupFactory(target_order))
+        conns.append(
+            make_refinement_connection(
+                actx, refiner, previous_discr,
+                InterpolatoryQuadratureSimplexGroupFactory(target_order)))
+        ns.append(pre_density_discr.ndofs)
+
+        qbx = QBXLayerPotentialSource(
+            pre_density_discr, 4*target_order, qbx_order,
+            fmm_order=False,
+            target_association_tolerance=0.005,
+            _target_asymptotics=asmt,
+            expansion_factory=line_expn_factory)
+
+        qbx_ref = QBXLayerPotentialSource(
+            pre_density_discr, 4*target_order, qbx_order,
+            fmm_order=False,
+            target_association_tolerance=0.005)
+
+        from pytential import GeometryCollection
+        places = GeometryCollection({"qbx": qbx}, auto_where="qbx")
+        places_ref = GeometryCollection({"qbx": qbx_ref}, auto_where="qbx")
+
+        density_discr = places.get_discretization("qbx")
+        assert density_discr is pre_density_discr
+        previous_discr = density_discr
+
+        from meshmode.dof_array import thaw
+        nodes = thaw(actx, density_discr.nodes())
+        angle = actx.np.arctan2(nodes[1], nodes[0])
+        sigma = actx.np.cos(mode_nr*angle)
+
+        if isinstance(kernel, HelmholtzKernel):
+            for i, elem in np.ndenumerate(sigma):
+                sigma[i] = elem.astype(np.complex128)
+            k_val = np.complex128(k)
+        else:
+            k_val = np.float64(k)
+
+        fld = bind(
+            places, op(source="qbx", qbx_forced_limit=-1))(
+                actx, sigma=sigma, k=k_val)
+        flds.append(fld)
+
+        fld_ref = bind(
+            places_ref, op(source="qbx", qbx_forced_limit=-1))(
+                actx, sigma=sigma, k=k_val)
+        flds_ref.append(fld_ref)
+
+    # everything onto the finest mesh
+    fs = []
+    fs_ref = []
+    for iexp in range(len(flds)):
+        conn = conns[iexp + 1:]
+        if conn:
+            total_conn = ChainedDiscretizationConnection(conn)
+            fs.append(actx.to_numpy(flatten(
+                total_conn(flds[iexp]))))
+            fs_ref.append(actx.to_numpy(flatten(
+                total_conn(flds_ref[iexp]))))
+        else:
+            fs.append(actx.to_numpy(flatten(
+                flds[iexp])))
+            fs_ref.append(actx.to_numpy(flatten(
+                flds_ref[iexp])))
+
+    from functools import partial
+    inorm = partial(np.linalg.norm, ord=np.inf)
+    last_diff = inorm(fs_ref[-1] - fs[-1]) / inorm(fs[-1])
+    print(f"Last diff = {last_diff}")
+
+    # total length of the boundary curve
+    arclen = bind(places, sym.integral(2, 1, operand=1, dofdesc="qbx"))(actx)
+
+    from pytools.convergence import EOCRecorder
+    eocrec = EOCRecorder()
+    eocrec_ref = EOCRecorder()
+    for iexp in range(len(fs) - 1):
+        eocrec.add_data_point(
+            arclen/ns[iexp],
+            inorm(fs[iexp] - fs[-1]) / inorm(fs[-1]))
+        eocrec_ref.add_data_point(
+            arclen/ns[iexp],
+            inorm(fs_ref[iexp] - fs_ref[-1]) / inorm(fs_ref[-1]))
+
+    print("\nQBX (without scaling):")
+    print(eocrec_ref)
+
+    print("\nTAQBX (with scaling):")
+    print(eocrec)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 4e3145a7..0c426ba6 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -28,6 +28,9 @@ from pytools import memoize_method, memoize_in
 from pytential.qbx.target_assoc import QBXTargetAssociationFailedException
 from pytential.source import LayerPotentialSourceBase
 
+import sumpy.symbolic as sym
+from sumpy.kernel import Kernel
+
 import pyopencl as cl
 
 import logging
@@ -37,6 +40,8 @@ logger = logging.getLogger(__name__)
 __doc__ = """
 .. autoclass:: QBXLayerPotentialSource
 
+.. autoclass:: QBXLayerPotentialAsymptotics
+
 .. autoclass:: QBXTargetAssociationFailedException
 """
 
@@ -83,6 +88,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             _from_sep_smaller_min_nsources_cumul=None,
             _tree_kind="adaptive",
             _use_target_specific_qbx=None,
+            _target_asymptotics=None,
             geometry_data_inspector=None,
             cost_model=None,
             fmm_backend="sumpy",
@@ -107,6 +113,10 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         :arg cost_model: Either *None* or an object implementing the
              :class:`~pytential.qbx.cost.AbstractQBXCostModel` interface, used for
              gathering modeled costs if provided (experimental)
+        :arg _target_asymptotics: Either *None* or an object implementing the
+             :class:`~pytential.qbx.QBXLayerPotentialAsymptotics` interface, used for
+             enabling TAQBX. It stores the asymptotic information about layer
+             potential of the "main" kernel (the one used for FMM).
         """
 
         # {{{ argument processing
@@ -206,6 +216,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 _from_sep_smaller_min_nsources_cumul
         self._tree_kind = _tree_kind
         self._use_target_specific_qbx = _use_target_specific_qbx
+        self._target_asymptotics = _target_asymptotics
         self.geometry_data_inspector = geometry_data_inspector
 
         if cost_model is None:
@@ -235,6 +246,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             _from_sep_smaller_crit=None,
             _tree_kind=None,
             _use_target_specific_qbx=_not_provided,
+            _target_asymptotics=_not_provided,
             geometry_data_inspector=None,
             cost_model=_not_provided,
             fmm_backend=None,
@@ -321,6 +333,10 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 _use_target_specific_qbx=(_use_target_specific_qbx
                     if _use_target_specific_qbx is not _not_provided
                     else self._use_target_specific_qbx),
+                _target_asymptotics=(
+                    self._target_asymptotics
+                    if _target_asymptotics is _not_provided
+                    else _target_asymptotics),
                 geometry_data_inspector=(
                     geometry_data_inspector or self.geometry_data_inspector),
                 cost_model=(
@@ -536,12 +552,24 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         if self.fmm_backend == "sumpy":
             from pytential.qbx.fmm import \
                     QBXSumpyExpansionWranglerCodeContainer
+
+            if self._target_asymptotics:
+                fmm_kernel_tascaled = \
+                    self._target_asymptotics.get_rescaled_kernel(local_expn_class)
+                taqbx_local_factory = partial(local_expn_class, fmm_kernel_tascaled)
+            else:
+                taqbx_local_factory = None
+
             return QBXSumpyExpansionWranglerCodeContainer(
                     self.cl_context,
                     fmm_mpole_factory, fmm_local_factory, qbx_local_factory,
-                    out_kernels)
+                    taqbx_local_factory, out_kernels)
 
         elif self.fmm_backend == "fmmlib":
+
+            if self._target_asymptotics:
+                raise ValueError("TAQBX is not implemented in fmmlib")
+
             from pytential.qbx.fmmlib import \
                     QBXFMMLibExpansionWranglerCodeContainer
             return QBXFMMLibExpansionWranglerCodeContainer(
@@ -688,8 +716,16 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         else:
             value_dtype = self.density_discr.real_dtype
 
-        from sumpy.qbx import LayerPotential
         from sumpy.expansion.local import LineTaylorLocalExpansion
+        if self._target_asymptotics:
+            if len(kernels) > 1:
+                raise ValueError("direct evaluation with asymptotic rescaling "
+                                 "only supports one output kernel at a time")
+            else:
+                kernels = [self._target_asymptotics.get_rescaled_kernel(
+                    LineTaylorLocalExpansion)]
+
+        from sumpy.qbx import LayerPotential
         return LayerPotential(self.cl_context,
                     [LineTaylorLocalExpansion(knl, self.qbx_order)
                         for knl in kernels],
@@ -705,8 +741,16 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         else:
             value_dtype = self.density_discr.real_dtype
 
-        from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         from sumpy.expansion.local import VolumeTaylorLocalExpansion
+        if self._target_asymptotics:
+            if len(kernels) > 1:
+                raise ValueError("direct evaluation with asymptotic rescaling "
+                                 "only supports one output kernel at a time")
+            else:
+                kernels = [self._target_asymptotics.get_rescaled_kernel(
+                    VolumeTaylorLocalExpansion)]
+
+        from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         return LayerPotentialOnTargetAndCenterSubset(
                 self.cl_context,
                 [VolumeTaylorLocalExpansion(knl, self.qbx_order)
@@ -882,8 +926,232 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
 # }}}
 
 
+# {{{ QBX layer potential asymptotics
+
+class AsymptoticallyRescaledKernel(Kernel):
+    """Extend the base kernel so that when asked by an expansion
+    factory, it replies with rescaled expression.
+    """
+    init_arg_names = ("base_kernel", "rescaled_expression")
+
+    def __init__(self, base_kernel, rescaled_expression):
+        """
+        :param rescaled_expression: A sympy expression that is directly
+        returned by get_expression to the expansion taker.
+        """
+        super().__init__(base_kernel.dim)
+        self.base_kernel = base_kernel
+        self.rescaled_expression = rescaled_expression
+
+    def __repr__(self):
+        return "AsymKnl%dD" % self.dim
+
+    @property
+    def is_complex_valued(self):
+        return self.base_kernel.is_complex_valued
+
+    def prepare_loopy_kernel(self, loopy_knl):
+        return self.base_kernel.prepare_loopy_kernel(loopy_knl)
+
+    def get_code_transformer(self):
+        return self.base_kernel.get_code_transformer()
+
+    def get_expression(self, scaled_dist_vec):
+        return self.rescaled_expression
+
+    def postprocess_at_source(self, expr, avec):
+        return self.base_kernel.postprocess_at_source(expr, avec)
+
+    def postprocess_at_target(self, expr, bvec):
+        return self.base_kernel.postprocess_at_target(expr, bvec)
+
+    def get_global_scaling_const(self):
+        return self.base_kernel.get_global_scaling_const()
+
+    def update_persistent_hash(self, key_hash, key_builder):
+        self.base_kernel.update_persistent_hash(key_hash, key_builder)
+        key_hash.update(str(self.rescaled_expression).encode("utf8"))
+
+    def get_args(self):
+        return self.base_kernel.get_args()
+
+    def get_source_args(self):
+        return self.base_kernel.get_source_args()
+
+    mapper_method = "map_asymptotically_rescaled_kernel"
+
+
+class QBXLayerPotentialAsymptotics:
+    """Asymptotic behavior of a layer potential near its source. The class
+    provides a symbolic description of the near-surface asymptotic behavior of
+    the layer potential and properly dispatch it to different expansion
+    classes.
+
+    The main use of this class is to make :class:`AsymptoticallyRescaledKernel`
+    objects. The rescaled kernels depend on expansion methods. This class tries
+    to isolate mathematical asymptotic expansions that depend solely on the
+    kernel and domain geometry.
+
+    .. attribute :: dim
+
+       The dimension of the ambient space.
+
+    .. attribute :: kernel
+
+       The potential kernel. A :class:`~sumpy.kernel.Kernel` object.
+
+    .. attribute :: expr
+
+       The asymptotic expansions. A scalar expression that depends on distance
+       from the boundary (denoted by the symbol "dist").
+
+    .. attribute :: geometric_order
+
+       Order of geometric approximation when computing the distance to
+       boundary.
+    """
+
+    def __init__(self, dim, kernel, expr, geometric_order=1):
+        self.dim = dim
+        self.kernel = kernel
+        self.expr = expr
+        self.geometric_order = geometric_order
+
+    @memoize_method
+    def get_taqbx_local_expansion(self, expn_class):
+        pass
+
+    @memoize_method
+    def get_rescaled_kernel(self, expn_class):
+        """Return a :mod:`sumpy` kernel with the rescaled expression.
+        """
+        resd_expr = self._get_rescaled_kernel_expr(expn_class)
+        base_kernel = self.kernel
+
+        return AsymptoticallyRescaledKernel(base_kernel, resd_expr)
+
+    @memoize_method
+    def _get_rescaled_kernel_expr(self, expn_class):
+        """Apply scaling to the kernel expression.
+        """
+        kernel_expr = self._get_kernel_expression_at_source(expn_class)
+        sym_map = self._get_symbol_map(expn_class)
+        expr_h = self._approximate_expr()
+        scaling = expr_h.subs(sym_map)
+        return kernel_expr / scaling
+
+    @memoize_method
+    def _approximate_expr(self):
+        """Transform the expression by approximating the distance with
+        geometric information known to the QBX routine.
+        """
+        normal, target, dist, rad = (
+            self._nvec, self._tvec, self._dist, self._radius)
+
+        if self.geometric_order == 1:
+            dist_approx = rad - normal.dot(target)
+        else:
+            # need curvature information for higher order approximations
+            raise NotImplementedError
+
+        return self.expr.subs(dist, dist_approx)
+
+    @memoize_method
+    def _get_symbol_map(self, expn_class):
+        """Get interpretation of ``nvec`` and ``tvec`` that depends on the
+        expansion class.
+        """
+        from sumpy.expansion.local import (
+            LineTaylorLocalExpansion, VolumeTaylorLocalExpansionBase)
+
+        bvec = sym.make_sym_vector("b", self.dim)
+
+        if issubclass(expn_class, LineTaylorLocalExpansion):
+            bvec_norm = sym.sqrt(bvec.dot(bvec))
+            sym_map = {
+                self._radius: bvec_norm
+            }
+
+            # self._nvec: bvec / bvec_norm
+            for lhs, rhs in zip(self._nvec, bvec):
+                sym_map[lhs] = rhs / bvec_norm
+
+            # self._tvec: sym.Symbol("tau") * bvec
+            for lhs, rhs in zip(self._tvec, bvec):
+                sym_map[lhs] = sym.Symbol("tau") * rhs
+
+        elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
+            sym_map = {
+                self._radius: sym.Symbol("rscale"),  # disk radius is used as rscale
+            }
+
+            # FIXME
+            # get the normal direction by connecting the expansion center with
+            # its associated source (point of tangency)
+            raise NotImplementedError
+
+            # self._tvec: bvec
+            for lhs, rhs in zip(self._tvec, bvec):
+                sym_map[lhs] = rhs
+
+        else:
+            raise ValueError("unsupported expansion class")
+
+        return sym_map
+
+    @memoize_method
+    def _get_kernel_expression_at_source(self, expn_class):
+        """Kernel expression used by ``coefficients_from_source``.
+        """
+        from sumpy.expansion.local import (
+            LineTaylorLocalExpansion, VolumeTaylorLocalExpansionBase)
+
+        avec = sym.make_sym_vector("a", self.dim)
+
+        if issubclass(expn_class, LineTaylorLocalExpansion):
+            tau = sym.Symbol("tau")
+            bvec = sym.make_sym_vector("b", self.dim)
+            avec_line = avec + tau*bvec
+            return self.kernel.get_expression(avec_line)
+        elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
+            return self.kernel.postprocess_at_source(
+                self.kernel.get_expression(avec), avec)
+        else:
+            raise ValueError("unsupported expansion class")
+
+    @property
+    def _dist(self):
+        """The distance of the target point from the boundary.
+        """
+        return sym.Symbol("dist")
+
+    @property
+    def _nvec(self):
+        """The unit normal vector obtained by normalizing the vector from the
+        QBX expansion center to the point of tangency.
+        """
+        return sym.make_sym_vector("nvec", self.dim)
+
+    @property
+    def _tvec(self):
+        """The vector from the QBX expansion center to the evaluation target
+        point.
+        """
+        return sym.make_sym_vector("tvec", self.dim)
+
+    @property
+    def _radius(self):
+        """Radius of the QBX disk, aka distance of the expansion center from
+        the boundary.
+        """
+        return sym.Symbol("radius")
+
+# }}}
+
+
 __all__ = (
         "QBXLayerPotentialSource",
+        "QBXLayerPotentialAsymptotics",
         "QBXTargetAssociationFailedException",
         )
 
diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index a58524b7..074444b7 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -51,22 +51,32 @@ __doc__ = """
 class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer):
     def __init__(self, cl_context,
             multipole_expansion_factory, local_expansion_factory,
-            qbx_local_expansion_factory, out_kernels):
+            qbx_local_expansion_factory, taqbx_local_expansion_factory, out_kernels):
         SumpyExpansionWranglerCodeContainer.__init__(self,
                 cl_context, multipole_expansion_factory, local_expansion_factory,
                 out_kernels)
 
         self.qbx_local_expansion_factory = qbx_local_expansion_factory
+        self.taqbx_local_expansion_factory = taqbx_local_expansion_factory
 
     @memoize_method
     def qbx_local_expansion(self, order):
         return self.qbx_local_expansion_factory(order, self.use_rscale)
 
+    @memoize_method
+    def target_asymptotic_qbx_local_expansion(self, order):
+        return self.taqbx_local_expansion_factory(order, self.use_rscale)
+
     @memoize_method
     def p2qbxl(self, order):
         return P2QBXLFromCSR(self.cl_context,
                 self.qbx_local_expansion(order))
 
+    @memoize_method
+    def p2taqbxl(self, order):
+        return P2QBXLFromCSR(self.cl_context,
+                self.taqbx_local_expansion(order))
+
     @memoize_method
     def m2qbxl(self, source_order, target_order):
         return M2QBXL(self.cl_context,
@@ -85,6 +95,12 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
                 self.qbx_local_expansion_factory(order),
                 self.out_kernels)
 
+    @memoize_method
+    def taqbxl2p(self, order):
+        return QBXL2P(self.cl_context,
+                self.taqbx_local_expansion_factory(order),
+                self.out_kernels)
+
     def get_wrangler(self, queue, geo_data, dtype,
             qbx_order, fmm_level_to_order,
             source_extra_kwargs={},
@@ -120,7 +136,7 @@ non_qbx_box_target_lists`),
     def __init__(self, code_container, queue, geo_data, dtype,
             qbx_order, fmm_level_to_order,
             source_extra_kwargs, kernel_extra_kwargs,
-            _use_target_specific_qbx=None):
+            _use_target_specific_qbx=None, _target_asymptotics=None):
         if _use_target_specific_qbx:
             raise ValueError("TSQBX is not implemented in sumpy")
 
@@ -132,6 +148,12 @@ non_qbx_box_target_lists`),
         self.geo_data = geo_data
         self.using_tsqbx = False
 
+        if _target_asymptotics:
+            self.using_taqbx = True
+            self.target_asymptotics = _target_asymptotics
+        else:
+            self.using_taqbx = False
+
     # {{{ data vector utilities
 
     def output_zeros(self):
@@ -204,6 +226,9 @@ non_qbx_box_target_lists`),
         local_exps = self.qbx_local_expansion_zeros()
         events = []
 
+        if self.using_taqbx:
+            return (local_exps, SumpyTimingFuture(self.queue, events))
+
         geo_data = self.geo_data
         if len(geo_data.global_qbx_centers()) == 0:
             return (local_exps, SumpyTimingFuture(self.queue, events))
@@ -238,6 +263,48 @@ non_qbx_box_target_lists`),
 
         return (result, SumpyTimingFuture(self.queue, events))
 
+    @log_process(logger)
+    def form_target_asymptotic_qbx_locals(self, src_weight_vecs):
+        ta_local_exps = self.qbx_local_expansion_zeros()
+        events = []
+
+        if not self.using_taqbx:
+            return (ta_local_exps, SumpyTimingFuture(self.queue, events))
+
+        geo_data = self.geo_data
+        if len(geo_data.global_qbx_centers()) == 0:
+            return (ta_local_exps, SumpyTimingFuture(self.queue, events))
+
+        traversal = geo_data.traversal()
+
+        starts = traversal.neighbor_source_boxes_starts
+        lists = traversal.neighbor_source_boxes_lists
+
+        kwargs = self.extra_kwargs.copy()
+        kwargs.update(self.box_source_list_kwargs())
+
+        p2taqbxl = self.code.p2taqbxl(self.qbx_order, self.target_asymptotics)
+
+        evt, (result,) = p2taqbxl(
+                self.queue,
+                global_qbx_centers=geo_data.global_qbx_centers(),
+                qbx_center_to_target_box=geo_data.qbx_center_to_target_box(),
+                qbx_centers=geo_data.flat_centers(),
+                qbx_expansion_radii=geo_data.flat_expansion_radii(),
+
+                source_box_starts=starts,
+                source_box_lists=lists,
+                strengths=src_weight_vecs,
+                qbx_expansions=ta_local_exps,
+
+                **kwargs)
+
+        events.append(evt)
+        assert ta_local_exps is result
+        result.add_event(evt)
+
+        return (result, SumpyTimingFuture(self.queue, events))
+
     @log_process(logger)
     def translate_box_multipoles_to_qbx_local(self, multipole_exps):
         qbx_expansions = self.qbx_local_expansion_zeros()
@@ -377,6 +444,45 @@ non_qbx_box_target_lists`),
     def eval_target_specific_qbx_locals(self, src_weight_vecs):
         return (self.full_output_zeros(), SumpyTimingFuture(self.queue, events=()))
 
+    @log_process(logger)
+    def eval_target_asymptotic_qbx_locals(self, taqbx_expansions):
+        pot = self.full_output_zeros()
+
+        geo_data = self.geo_data
+        events = []
+
+        if not self.using_taqbx:
+            return (pot, SumpyTimingFuture(self.queue, events))
+
+        if len(geo_data.global_qbx_centers()) == 0:
+            return (pot, SumpyTimingFuture(self.queue, events))
+
+        ctt = geo_data.center_to_tree_targets()
+
+        taqbxl2p = self.code.taqbxl2p(self.qbx_order)
+
+        evt, pot_res = taqbxl2p(
+            self.queue,
+            qbx_centers=geo_data.flat_centers(),
+            qbx_expansion_radii=geo_data.flat_expansion_radii(),
+
+            global_qbx_centers=geo_data.global_qbx_centers(),
+
+            center_to_targets_starts=ctt.starts,
+            center_to_targets_lists=ctt.lists,
+
+            targets=self.tree.targets,
+
+            taqbx_expansions=taqbx_expansions,
+            result=pot,
+
+            **self.kernel_extra_kwargs.copy())
+
+        for pot_i, pot_res_i in zip(pot, pot_res):
+            assert pot_i is pot_res_i
+
+        return (pot, SumpyTimingFuture(self.queue, events))
+
     # }}}
 
 # }}}
@@ -533,6 +639,7 @@ def drive_fmm(expansion_wrangler, src_weight_vecs, timing_data=None,
     # for the same interactions (directly evaluated portion of the potentials
     # via unified List 1).  Which one is used depends on the wrangler. If one of
     # them is unused the corresponding output entries will be zero.
+    # (TAQBX uses neither)
 
     qbx_expansions, timing_future = wrangler.form_global_qbx_locals(src_weight_vecs)
 
@@ -563,6 +670,18 @@ def drive_fmm(expansion_wrangler, src_weight_vecs, timing_data=None,
 
     recorder.add("eval_target_specific_qbx_locals", timing_future)
 
+    taqbx_expansions, timing_future = \
+        wrangler.form_target_asymptotic_qbx_locals(src_weight_vecs)
+
+    recorder.add("form_target_asymptotic_qbx_locals", timing_future)
+
+    ta_result, timing_future = \
+        wrangler.eval_target_asymptotic_qbx_locals(taqbx_expansions)
+
+    qbx_potentials = qbx_potentials + ta_result
+
+    recorder.add("eval_target_asymptotic_qbx_locals", timing_future)
+
     # }}}
 
     # {{{ reorder potentials
-- 
GitLab


From 38d74c57d9fcd2aa2313238d1b804140f282fed1 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Thu, 19 Nov 2020 18:49:33 -0600
Subject: [PATCH 02/38] Flake8 fixes

---
 examples/boundary-layer.py | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index 203488b0..022e2097 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -1,5 +1,5 @@
-# using LineTaylor for local expansion
-# must force direct evaluation because cannot translate from VolumeTaylor to LineTaylor
+# using LineTaylor for local expansion (must force direct evaluation because
+# cannot translate from VolumeTaylor to LineTaylor)
 
 enable_mayavi = 0
 if enable_mayavi:
@@ -7,7 +7,7 @@ if enable_mayavi:
 
 import numpy as np
 import pyopencl as cl
-from sumpy.visualization import FieldPlotter
+from sumpy.expansion import ExpansionFactoryBase
 from sumpy.kernel import one_kernel_2d, LaplaceKernel, HelmholtzKernel  # noqa
 
 from pytential import bind, sym
@@ -15,8 +15,7 @@ from pytential import bind, sym
 from meshmode.mesh.generation import starfish, ellipse, drop # noqa
 from meshmode.mesh.refinement import RefinerWithoutAdjacency
 from meshmode.discretization.connection import (
-    make_refinement_connection, ChainedDiscretizationConnection,
-    L2ProjectionInverseDiscretizationConnection)
+    make_refinement_connection, ChainedDiscretizationConnection)
 
 target_order = 16
 qbx_order = 3
@@ -26,7 +25,7 @@ n_refine_cycles = 4
 
 k = 3 + 50j
 
-from sumpy.expansion import ExpansionFactoryBase
+
 class VolumeMultipoleLineLocalTaylorExpansionFactory(ExpansionFactoryBase):
     """Volume Taylor for multipole, line Taylor for local, to be used only with
     direct evaluation.
-- 
GitLab


From 6f6a3307a5e2592bf6f3948aa2a95947dd452671 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Thu, 19 Nov 2020 19:10:34 -0600
Subject: [PATCH 03/38] Unbreak fmmlib

---
 pytential/qbx/fmmlib.py | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/pytential/qbx/fmmlib.py b/pytential/qbx/fmmlib.py
index 0075af11..8087782d 100644
--- a/pytential/qbx/fmmlib.py
+++ b/pytential/qbx/fmmlib.py
@@ -450,6 +450,16 @@ class QBXFMMLibExpansionWrangler(FMMLibExpansionWrangler):
 
     # }}}
 
+    @log_process(logger)
+    @return_timing_data
+    def form_target_asymptotic_qbx_locals(self, src_weight_vecs):
+        return self.qbx_local_expansion_zeros()
+
+    @log_process(logger)
+    @return_timing_data
+    def eval_target_asymptotic_qbx_locals(self, taqbx_expansions):
+        return self.full_output_zeros()
+
     @log_process(logger)
     @return_timing_data
     def translate_box_local_to_qbx_local(self, local_exps):
-- 
GitLab


From 7e89bbeabfe20cdbd9a26582cba61ae182e8ecce Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Thu, 19 Nov 2020 19:42:15 -0600
Subject: [PATCH 04/38] Not bothering with cost model for now

---
 pytential/qbx/fmm.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index 074444b7..67722248 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -673,14 +673,14 @@ def drive_fmm(expansion_wrangler, src_weight_vecs, timing_data=None,
     taqbx_expansions, timing_future = \
         wrangler.form_target_asymptotic_qbx_locals(src_weight_vecs)
 
-    recorder.add("form_target_asymptotic_qbx_locals", timing_future)
+    # recorder.add("form_target_asymptotic_qbx_locals", timing_future)
 
     ta_result, timing_future = \
         wrangler.eval_target_asymptotic_qbx_locals(taqbx_expansions)
 
     qbx_potentials = qbx_potentials + ta_result
 
-    recorder.add("eval_target_asymptotic_qbx_locals", timing_future)
+    # recorder.add("eval_target_asymptotic_qbx_locals", timing_future)
 
     # }}}
 
-- 
GitLab


From 206250c70b39537faac2a8fdb5ea5c31155ff6fa Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Thu, 19 Nov 2020 20:03:26 -0600
Subject: [PATCH 05/38] Fix cost model test

---
 test/test_cost_model.py | 22 +++++++++++++++++++++-
 1 file changed, 21 insertions(+), 1 deletion(-)

diff --git a/test/test_cost_model.py b/test/test_cost_model.py
index 1d9a2746..0b2de25f 100644
--- a/test/test_cost_model.py
+++ b/test/test_cost_model.py
@@ -483,7 +483,8 @@ def test_cost_model_metadata_gathering(ctx_factory):
 
 class ConstantOneQBXExpansionWrangler(ConstantOneExpansionWrangler):
 
-    def __init__(self, queue, geo_data, use_target_specific_qbx):
+    def __init__(self, queue, geo_data, use_target_specific_qbx,
+                 use_target_asymptotic_qbx=False):
         from pytential.qbx.utils import ToHostTransferredGeoDataWrapper
         geo_data = ToHostTransferredGeoDataWrapper(queue, geo_data)
 
@@ -493,6 +494,7 @@ class ConstantOneQBXExpansionWrangler(ConstantOneExpansionWrangler):
                 use_target_specific_qbx
                 # None means use by default if possible
                 or use_target_specific_qbx is None)
+        self.using_taqbx = use_target_asymptotic_qbx
 
         ConstantOneExpansionWrangler.__init__(self, geo_data.tree())
 
@@ -654,6 +656,24 @@ class ConstantOneQBXExpansionWrangler(ConstantOneExpansionWrangler):
 
         return pot, self.timing_future(ops)
 
+    def form_target_asymptotic_qbx_locals(self, src_weight_vecs):
+        ta_local_exps = self.qbx_local_expansion_zeros()
+        ops = 0
+
+        if not self.using_taqbx:
+            return ta_local_exps, self.timing_future(ops)
+
+        raise NotImplementedError
+
+    def eval_target_asymptotic_qbx_locals(self, taqbx_expansions):
+        pot = self.full_output_zeros()
+        ops = 0
+
+        if not self.using_taqbx:
+            return pot, self.timing_future(ops)
+
+        raise NotImplementedError
+
 # }}}
 
 
-- 
GitLab


From 6d441f1a0341cf7e4e9be1b8b1d06e7a27497c58 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Thu, 19 Nov 2020 20:15:47 -0600
Subject: [PATCH 06/38] Add docstring

---
 pytential/qbx/__init__.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 0c426ba6..6bb5ff11 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -40,6 +40,8 @@ logger = logging.getLogger(__name__)
 __doc__ = """
 .. autoclass:: QBXLayerPotentialSource
 
+.. autoclass:: AsymptoticallyRescaledKernel
+
 .. autoclass:: QBXLayerPotentialAsymptotics
 
 .. autoclass:: QBXTargetAssociationFailedException
-- 
GitLab


From 8c6fae50ac5bf7b61e4bc5e94605e4636bc255ee Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Thu, 19 Nov 2020 20:36:32 -0600
Subject: [PATCH 07/38] More compatibility fixes

---
 examples/boundary-layer.py |  2 --
 pytential/qbx/__init__.py  | 16 ++++++++++------
 pytential/qbx/fmm.py       |  4 ++++
 3 files changed, 14 insertions(+), 8 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index 022e2097..b330f64d 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -135,8 +135,6 @@ def main(curve_fn=starfish, visualize=True):
         sigma = actx.np.cos(mode_nr*angle)
 
         if isinstance(kernel, HelmholtzKernel):
-            for i, elem in np.ndenumerate(sigma):
-                sigma[i] = elem.astype(np.complex128)
             k_val = np.complex128(k)
         else:
             k_val = np.float64(k)
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 6bb5ff11..8e6a68d3 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -948,6 +948,9 @@ class AsymptoticallyRescaledKernel(Kernel):
     def __repr__(self):
         return "AsymKnl%dD" % self.dim
 
+    def __getinitargs__(self):
+        return (self.base_kernel, self.rescaled_expression)
+
     @property
     def is_complex_valued(self):
         return self.base_kernel.is_complex_valued
@@ -1069,7 +1072,7 @@ class QBXLayerPotentialAsymptotics:
         bvec = sym.make_sym_vector("b", self.dim)
 
         if issubclass(expn_class, LineTaylorLocalExpansion):
-            bvec_norm = sym.sqrt(bvec.dot(bvec))
+            bvec_norm = sym.sym.sqrt(bvec.dot(bvec))
             sym_map = {
                 self._radius: bvec_norm
             }
@@ -1080,11 +1083,12 @@ class QBXLayerPotentialAsymptotics:
 
             # self._tvec: sym.Symbol("tau") * bvec
             for lhs, rhs in zip(self._tvec, bvec):
-                sym_map[lhs] = sym.Symbol("tau") * rhs
+                sym_map[lhs] = sym.sym.Symbol("tau") * rhs
 
         elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
             sym_map = {
-                self._radius: sym.Symbol("rscale"),  # disk radius is used as rscale
+                # disk radius is used as rscale
+                self._radius: sym.sym.Symbol("rscale"),
             }
 
             # FIXME
@@ -1111,7 +1115,7 @@ class QBXLayerPotentialAsymptotics:
         avec = sym.make_sym_vector("a", self.dim)
 
         if issubclass(expn_class, LineTaylorLocalExpansion):
-            tau = sym.Symbol("tau")
+            tau = sym.sym.Symbol("tau")
             bvec = sym.make_sym_vector("b", self.dim)
             avec_line = avec + tau*bvec
             return self.kernel.get_expression(avec_line)
@@ -1125,7 +1129,7 @@ class QBXLayerPotentialAsymptotics:
     def _dist(self):
         """The distance of the target point from the boundary.
         """
-        return sym.Symbol("dist")
+        return sym.sym.Symbol("dist")
 
     @property
     def _nvec(self):
@@ -1146,7 +1150,7 @@ class QBXLayerPotentialAsymptotics:
         """Radius of the QBX disk, aka distance of the expansion center from
         the boundary.
         """
-        return sym.Symbol("radius")
+        return sym.sym.Symbol("radius")
 
 # }}}
 
diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index 67722248..6acaee42 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -63,6 +63,10 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
     def qbx_local_expansion(self, order):
         return self.qbx_local_expansion_factory(order, self.use_rscale)
 
+    @memoize_method
+    def taqbx_local_expansion(self, order):
+        return self.taqbx_local_expansion_factory(order, self.use_rscale)
+
     @memoize_method
     def target_asymptotic_qbx_local_expansion(self, order):
         return self.taqbx_local_expansion_factory(order, self.use_rscale)
-- 
GitLab


From 9e346417567aade2649e48b4d5c17c781f79164d Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Fri, 20 Nov 2020 08:59:52 -0600
Subject: [PATCH 08/38] actx.np.acos -> actx.np.arccos

---
 test/test_layer_pot_eigenvalues.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/test_layer_pot_eigenvalues.py b/test/test_layer_pot_eigenvalues.py
index 8ac492da..36d30b74 100644
--- a/test/test_layer_pot_eigenvalues.py
+++ b/test/test_layer_pot_eigenvalues.py
@@ -307,7 +307,7 @@ def test_sphere_eigenvalues(ctx_factory, mode_m, mode_n, qbx_order,
         density_discr = places.get_discretization(places.auto_source.geometry)
         nodes = thaw(actx, density_discr.nodes())
         r = actx.np.sqrt(nodes[0]*nodes[0] + nodes[1]*nodes[1] + nodes[2]*nodes[2])
-        phi = actx.np.acos(nodes[2]/r)
+        phi = actx.np.arccos(nodes[2]/r)
         theta = actx.np.arctan2(nodes[0], nodes[1])
 
         ymn = unflatten(actx, density_discr,
-- 
GitLab


From 23461c9f1cb8241b439e79c87b68574f514c801d Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Fri, 20 Nov 2020 09:32:53 -0600
Subject: [PATCH 09/38] Handle the case when norm is a dim-1 numpy array

---
 pytential/solve.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pytential/solve.py b/pytential/solve.py
index 3e25642d..1c157d5c 100644
--- a/pytential/solve.py
+++ b/pytential/solve.py
@@ -249,7 +249,7 @@ class ResidualPrinter:
         import sys
         if resid is not None:
             norm = np.sqrt(self.inner_product(resid, resid))
-            sys.stdout.write(f"IT {self.count:8d} {abs(norm):.8e}\n")
+            sys.stdout.write(f"IT {self.count:8d} {abs(float(norm)):.8e}\n")
         else:
             sys.stdout.write(f"IT {self.count:8d}\n")
         self.count += 1
-- 
GitLab


From 4a9fdbffecd4e49a8b38198aaa6e32435e89f559 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 23 Nov 2020 16:05:24 -0600
Subject: [PATCH 10/38] Revert changes to solve.py

---
 pytential/solve.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pytential/solve.py b/pytential/solve.py
index 1c157d5c..3e25642d 100644
--- a/pytential/solve.py
+++ b/pytential/solve.py
@@ -249,7 +249,7 @@ class ResidualPrinter:
         import sys
         if resid is not None:
             norm = np.sqrt(self.inner_product(resid, resid))
-            sys.stdout.write(f"IT {self.count:8d} {abs(float(norm)):.8e}\n")
+            sys.stdout.write(f"IT {self.count:8d} {abs(norm):.8e}\n")
         else:
             sys.stdout.write(f"IT {self.count:8d}\n")
         self.count += 1
-- 
GitLab


From 4ddb0f03a8bde08db1c279896fa4d266994ede15 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 23 Nov 2020 19:59:42 -0600
Subject: [PATCH 11/38] Implement TAQBX with volume Taylor expansion

---
 examples/boundary-layer.py | 135 +++++++++++++++++++++++++++----------
 pytential/qbx/__init__.py  |  66 ++++++++++++++----
 pytential/qbx/direct.py    |  37 +++++++++-
 3 files changed, 188 insertions(+), 50 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index b330f64d..c8d6b77d 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -1,5 +1,10 @@
-# using LineTaylor for local expansion (must force direct evaluation because
-# cannot translate from VolumeTaylor to LineTaylor)
+# Cases:
+# - "Line": use line Taylor expansion to compute on-surface.  Using LineTaylor
+#   for local expansion (must force direct evaluation because cannot translate
+#   from VolumeTaylor to LineTaylor)
+#
+# - "Volume": use volume Taylor expansion to compute anywhere.
+#
 
 enable_mayavi = 0
 if enable_mayavi:
@@ -39,10 +44,19 @@ class VolumeMultipoleLineLocalTaylorExpansionFactory(ExpansionFactoryBase):
         return VolumeTaylorMultipoleExpansion
 
 
-def main(curve_fn=starfish, visualize=True):
+def main(case="line", curve_fn=starfish, visualize=True):
     import logging
     logging.basicConfig(level=logging.WARN)  # INFO for more progress info
 
+    if case == "line":
+        fmm_order = False  # cannot use FMM here
+        expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
+    elif case == "volume":
+        fmm_order = False
+        expn_factory = None
+    else:
+        raise ValueError
+
     cl_ctx = cl.create_some_context()
     queue = cl.CommandQueue(cl_ctx)
 
@@ -53,6 +67,19 @@ def main(curve_fn=starfish, visualize=True):
             target_order)
     refiner = RefinerWithoutAdjacency(base_mesh)
 
+    if case == "volume":
+        from pytential.target import PointsTarget
+        if 1:
+            # in the volume
+            from sumpy.visualization import FieldPlotter
+            fplot = FieldPlotter(np.zeros(2), extent=2, npoints=100)
+            targets_dev = cl.array.to_device(queue, fplot.points)
+        else:
+            # near surface
+            target_mesh = make_curve_mesh(curve_fn, np.linspace(0, 1, 83), 1)
+            targets_dev = cl.array.to_device(
+                queue, np.ascontiguousarray(target_mesh.vertices))
+
     if k:
         if k.imag:
             kernel = HelmholtzKernel(2, allow_evanescent=True)
@@ -82,7 +109,6 @@ def main(curve_fn=starfish, visualize=True):
     k_sym = sp.Symbol("k")
     expr = sp.exp(1j * k_sym * dist)
     asmt = QBXLayerPotentialAsymptotics(2, kernel, expr=expr)
-    line_expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
 
     def op(**kwargs):
         kwargs.update(kernel_kwargs)
@@ -111,19 +137,30 @@ def main(curve_fn=starfish, visualize=True):
 
         qbx = QBXLayerPotentialSource(
             pre_density_discr, 4*target_order, qbx_order,
-            fmm_order=False,
+            fmm_order=fmm_order,
             target_association_tolerance=0.005,
             _target_asymptotics=asmt,
-            expansion_factory=line_expn_factory)
+            expansion_factory=expn_factory)
 
         qbx_ref = QBXLayerPotentialSource(
             pre_density_discr, 4*target_order, qbx_order,
-            fmm_order=False,
+            fmm_order=fmm_order,
             target_association_tolerance=0.005)
 
         from pytential import GeometryCollection
-        places = GeometryCollection({"qbx": qbx}, auto_where="qbx")
-        places_ref = GeometryCollection({"qbx": qbx_ref}, auto_where="qbx")
+
+        if case == "line":
+            places = GeometryCollection({"qbx": qbx}, auto_where="qbx")
+            places_ref = GeometryCollection({"qbx": qbx_ref}, auto_where="qbx")
+        elif case == "volume":
+            places = GeometryCollection({
+                "qbx": qbx, "targets": PointsTarget(targets_dev),
+            }, auto_where="qbx")
+            places_ref = GeometryCollection({
+                "qbx": qbx_ref, "targets": PointsTarget(targets_dev),
+            }, auto_where="qbx")
+        else:
+            raise ValueError
 
         density_discr = places.get_discretization("qbx")
         assert density_discr is pre_density_discr
@@ -139,32 +176,56 @@ def main(curve_fn=starfish, visualize=True):
         else:
             k_val = np.float64(k)
 
-        fld = bind(
-            places, op(source="qbx", qbx_forced_limit=-1))(
-                actx, sigma=sigma, k=k_val)
-        flds.append(fld)
-
-        fld_ref = bind(
-            places_ref, op(source="qbx", qbx_forced_limit=-1))(
-                actx, sigma=sigma, k=k_val)
-        flds_ref.append(fld_ref)
-
-    # everything onto the finest mesh
-    fs = []
-    fs_ref = []
-    for iexp in range(len(flds)):
-        conn = conns[iexp + 1:]
-        if conn:
-            total_conn = ChainedDiscretizationConnection(conn)
-            fs.append(actx.to_numpy(flatten(
-                total_conn(flds[iexp]))))
-            fs_ref.append(actx.to_numpy(flatten(
-                total_conn(flds_ref[iexp]))))
+        if case == "line":
+            fld = bind(
+                places, op(source="qbx", qbx_forced_limit=-1))(
+                    actx, sigma=sigma, k=k_val)
+            fld_ref = bind(
+                places_ref, op(source="qbx", qbx_forced_limit=-1))(
+                    actx, sigma=sigma, k=k_val)
+
+            # DoFArray
+            flds.append(fld)
+            flds_ref.append(fld_ref)
+
+        elif case == "volume":
+            fld = bind(places, op(
+                source="qbx", target="targets", qbx_forced_limit=None))(
+                    actx, sigma=sigma, k=k_val)
+            fld_ref = bind(places_ref, op(
+                source="qbx", target="targets", qbx_forced_limit=None))(
+                    actx, sigma=sigma, k=k_val)
+
+            # pyopencl Array
+            flds.append(fld.get())
+            flds_ref.append(fld_ref.get())
+
         else:
-            fs.append(actx.to_numpy(flatten(
-                flds[iexp])))
-            fs_ref.append(actx.to_numpy(flatten(
-                flds_ref[iexp])))
+            raise ValueError
+
+    # post-processing
+    if case == "line":
+        # everything onto the finest mesh
+        fs = []
+        fs_ref = []
+        for iexp in range(len(flds)):
+            conn = conns[iexp + 1:]
+            if conn:
+                total_conn = ChainedDiscretizationConnection(conn)
+                fs.append(actx.to_numpy(flatten(
+                    total_conn(flds[iexp]))))
+                fs_ref.append(actx.to_numpy(flatten(
+                    total_conn(flds_ref[iexp]))))
+            else:
+                fs.append(actx.to_numpy(flatten(
+                    flds[iexp])))
+                fs_ref.append(actx.to_numpy(flatten(
+                    flds_ref[iexp])))
+    elif case == "volume":
+        fs = flds
+        fs_ref = flds_ref
+    else:
+        raise ValueError
 
     from functools import partial
     inorm = partial(np.linalg.norm, ord=np.inf)
@@ -193,4 +254,8 @@ def main(curve_fn=starfish, visualize=True):
 
 
 if __name__ == "__main__":
-    main()
+    import sys
+    if len(sys.argv) > 1:
+        main(sys.argv[1])
+    else:
+        main()
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 8e6a68d3..a42b66ce 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -726,12 +726,16 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             else:
                 kernels = [self._target_asymptotics.get_rescaled_kernel(
                     LineTaylorLocalExpansion)]
+                sat = self._target_asymptotics.get_scaling_at_target(
+                    LineTaylorLocalExpansion)
+        else:
+            sat = None
 
         from sumpy.qbx import LayerPotential
         return LayerPotential(self.cl_context,
                     [LineTaylorLocalExpansion(knl, self.qbx_order)
                         for knl in kernels],
-                    value_dtypes=value_dtype)
+                    value_dtypes=value_dtype, scaling_at_target=sat)
 
     @memoize_method
     def get_lpot_applier_on_tgt_subset(self, kernels):
@@ -751,13 +755,17 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             else:
                 kernels = [self._target_asymptotics.get_rescaled_kernel(
                     VolumeTaylorLocalExpansion)]
+                sat = self._target_asymptotics.get_scaling_at_target(
+                    VolumeTaylorLocalExpansion)
+        else:
+            sat = None
 
         from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         return LayerPotentialOnTargetAndCenterSubset(
                 self.cl_context,
                 [VolumeTaylorLocalExpansion(knl, self.qbx_order)
                     for knl in kernels],
-                value_dtypes=value_dtype)
+                value_dtypes=value_dtype, scaling_at_target=sat)
 
     @memoize_method
     def get_qbx_target_numberer(self, dtype):
@@ -1008,7 +1016,10 @@ class QBXLayerPotentialAsymptotics:
     .. attribute :: expr
 
        The asymptotic expansions. A scalar expression that depends on distance
-       from the boundary (denoted by the symbol "dist").
+       from the boundary (denoted by the symbol "dist"), satisfying the
+       normalizing condition:
+
+         expr(dist=0) = 1
 
     .. attribute :: geometric_order
 
@@ -1036,13 +1047,39 @@ class QBXLayerPotentialAsymptotics:
         return AsymptoticallyRescaledKernel(base_kernel, resd_expr)
 
     @memoize_method
-    def _get_rescaled_kernel_expr(self, expn_class):
-        """Apply scaling to the kernel expression.
+    def get_scaling_at_target(self, expn_class):
+        """Target-dependent scaling expression, used for scaling back the
+        potential after summing up the expansion.
+        """
+        full_scaling = self._get_scaling_for_expansion(expn_class)
+
+        from sumpy.expansion.local import (
+            LineTaylorLocalExpansion, VolumeTaylorLocalExpansionBase)
+        if issubclass(expn_class, LineTaylorLocalExpansion):
+            sym_map = {sym.sym.Symbol("tau"): 1}  # target is at tau=1
+        elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
+            sym_map = {}
+        else:
+            raise ValueError("unsupported expansion class")
+
+        return full_scaling.subs(sym_map)
+
+    @memoize_method
+    def _get_scaling_for_expansion(self, expn_class):
+        """Target-dependent scaling expression, including the virtual variables
+        like "tau" for taking expansions.
         """
-        kernel_expr = self._get_kernel_expression_at_source(expn_class)
         sym_map = self._get_symbol_map(expn_class)
         expr_h = self._approximate_expr()
         scaling = expr_h.subs(sym_map)
+        return scaling
+
+    @memoize_method
+    def _get_rescaled_kernel_expr(self, expn_class):
+        """Apply scaling to the kernel expression.
+        """
+        kernel_expr = self._get_kernel_expression_at_source(expn_class)
+        scaling = self._get_scaling_for_expansion(expn_class)
         return kernel_expr / scaling
 
     @memoize_method
@@ -1072,6 +1109,9 @@ class QBXLayerPotentialAsymptotics:
         bvec = sym.make_sym_vector("b", self.dim)
 
         if issubclass(expn_class, LineTaylorLocalExpansion):
+            # in a line expansion, bvec is the normal, and the actual target is
+            # identified with tau.
+
             bvec_norm = sym.sym.sqrt(bvec.dot(bvec))
             sym_map = {
                 self._radius: bvec_norm
@@ -1091,10 +1131,11 @@ class QBXLayerPotentialAsymptotics:
                 self._radius: sym.sym.Symbol("rscale"),
             }
 
-            # FIXME
-            # get the normal direction by connecting the expansion center with
-            # its associated source (point of tangency)
-            raise NotImplementedError
+            # self._nvec: normal
+            normal = sym.make_sym_vector("normal", self.dim)
+            normal_norm = sym.sym.sqrt(normal.dot(normal))
+            for lhs, rhs in zip(self._nvec, normal):
+                sym_map[lhs] = rhs / normal_norm
 
             # self._tvec: bvec
             for lhs, rhs in zip(self._tvec, bvec):
@@ -1113,15 +1154,16 @@ class QBXLayerPotentialAsymptotics:
             LineTaylorLocalExpansion, VolumeTaylorLocalExpansionBase)
 
         avec = sym.make_sym_vector("a", self.dim)
+        bvec = sym.make_sym_vector("b", self.dim)
 
         if issubclass(expn_class, LineTaylorLocalExpansion):
             tau = sym.sym.Symbol("tau")
-            bvec = sym.make_sym_vector("b", self.dim)
             avec_line = avec + tau*bvec
             return self.kernel.get_expression(avec_line)
         elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
+            rad = avec + bvec
             return self.kernel.postprocess_at_source(
-                self.kernel.get_expression(avec), avec)
+                self.kernel.get_expression(rad), rad)
         else:
             raise ValueError("unsupported expansion class")
 
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 50e051db..50d1376f 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -33,6 +33,15 @@ from pytential.version import PYTENTIAL_KERNEL_VERSION
 class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
     default_name = "qbx_tgt_ctr_subset"
 
+    def __init__(self, ctx, expansions, strength_usage=None,
+                 value_dtypes=None, name=None, device=None,
+                 scaling_at_target=None):
+        super().__init__(ctx, expansions, strength_usage,
+                         value_dtypes, name, device, scaling_at_target)
+
+        if self._scaling_at_target:
+            self._vector_names.add("normal")  # needed for taqbx
+
     def get_cache_key(self):
         return super().get_cache_key() + (PYTENTIAL_KERNEL_VERSION,)
 
@@ -67,6 +76,28 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 shape="ntargets_total", order="C")
             for i in range(len(self.kernels))])
 
+        if self._scaling_at_target:
+            # using taqbx
+            # inject auxiliary insns for taqbx expansion
+            # SOURCE_FOR_CENTER_PARTICLE(i) = (i / 2)
+            taqbx_local_temp_insns = ["""
+            <> normal[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
+                    {dup=idim}
+            """]
+            sat = "sat * "
+            from sumpy.codegen import to_loopy_insns
+            sat_insns = to_loopy_insns(
+                [("sat", self._scaling_at_target)],
+                vector_names=self._vector_names,
+                pymbolic_expr_maps=[
+                    expn.kernel.get_code_transformer() for expn in self.expansions],
+                retain_names=["sat"],
+                complex_dtype=np.complex128)  # FIXME
+        else:
+            taqbx_local_temp_insns = []
+            sat = ""
+            sat_insns = []
+
         loopy_knl = lp.make_kernel([
             "{[itgt]: 0 <= itgt < ntargets}",
             "{[isrc]: 0 <= isrc < nsources}",
@@ -83,13 +114,13 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 <> b[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
                         {dup=idim}
                 <> rscale = expansion_radii[icenter]
-            """]
+            """] + taqbx_local_temp_insns + sat_insns
             + loopy_insns + kernel_exprs
             + ["""
-                result_{i}[itgt_overall] = knl_{i}_scaling * \
+                result_{i}[itgt_overall] = knl_{i}_scaling * {sat} \
                     simul_reduce(sum, isrc, pair_result_{i})  \
                         {{inames=itgt}}
-                """.format(i=iknl)
+                """.format(i=iknl, sat=sat)
                 for iknl in range(len(self.expansions))]
             + ["end"],
             arguments,
-- 
GitLab


From 7b9acc876dacf99eaecdd881cf848e8b33cb13a6 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 23 Nov 2020 21:56:36 -0600
Subject: [PATCH 12/38] Using radial scaling for each disk

---
 examples/boundary-layer.py | 10 +++++++---
 pytential/qbx/__init__.py  |  5 +++--
 pytential/qbx/direct.py    | 18 +++++++++++++-----
 pytential/qbx/fmm.py       |  6 ++++--
 4 files changed, 27 insertions(+), 12 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index c8d6b77d..5e8cfe5c 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -12,7 +12,7 @@ if enable_mayavi:
 
 import numpy as np
 import pyopencl as cl
-from sumpy.expansion import ExpansionFactoryBase
+from sumpy.expansion import ExpansionFactoryBase, VolumeTaylorExpansionFactory
 from sumpy.kernel import one_kernel_2d, LaplaceKernel, HelmholtzKernel  # noqa
 
 from pytential import bind, sym
@@ -52,8 +52,9 @@ def main(case="line", curve_fn=starfish, visualize=True):
         fmm_order = False  # cannot use FMM here
         expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
     elif case == "volume":
+        # fmm_order = False
         fmm_order = False
-        expn_factory = None
+        expn_factory = VolumeTaylorExpansionFactory()
     else:
         raise ValueError
 
@@ -142,10 +143,13 @@ def main(case="line", curve_fn=starfish, visualize=True):
             _target_asymptotics=asmt,
             expansion_factory=expn_factory)
 
+        # If expansion_factory is not set, default expansion is H2DLocal which
+        # yields comparable results to Taylor.
         qbx_ref = QBXLayerPotentialSource(
             pre_density_discr, 4*target_order, qbx_order,
             fmm_order=fmm_order,
-            target_association_tolerance=0.005)
+            target_association_tolerance=0.005,
+            expansion_factory=expn_factory)
 
         from pytential import GeometryCollection
 
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index a42b66ce..cd7ba54f 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -1163,9 +1163,10 @@ class QBXLayerPotentialAsymptotics:
         elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
             rad = avec + bvec
             return self.kernel.postprocess_at_source(
-                self.kernel.get_expression(rad), rad)
+                self.kernel.get_expression(rad), avec)
         else:
-            raise ValueError("unsupported expansion class")
+            raise ValueError(
+                f"unsupported expansion class for TAQBX: {expn_class.__name__}")
 
     @property
     def _dist(self):
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 50d1376f..785d512f 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -79,11 +79,19 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
         if self._scaling_at_target:
             # using taqbx
             # inject auxiliary insns for taqbx expansion
-            # SOURCE_FOR_CENTER_PARTICLE(i) = (i / 2)
-            taqbx_local_temp_insns = ["""
-            <> normal[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
-                    {dup=idim}
-            """]
+            if 1:
+                # just use bvec (as if boundary layer around the disk)
+                taqbx_local_temp_insns = ["""
+                <> normal[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
+                        {dup=idim}
+                """]
+            else:
+                # try to get point of tangency FIXME
+                # this is probably the wrong way (26000 sources, 1360 centers)
+                taqbx_local_temp_insns = ["""
+                <> normal[idim] = src[idim, icenter//2] - center[idim, icenter] \
+                        {dup=idim}
+                """]
             sat = "sat * "
             from sumpy.codegen import to_loopy_insns
             sat_insns = to_loopy_insns(
diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index 6acaee42..e0908950 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -109,13 +109,15 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
             qbx_order, fmm_level_to_order,
             source_extra_kwargs={},
             kernel_extra_kwargs=None,
-            _use_target_specific_qbx=False):
+            _use_target_specific_qbx=False,
+            _target_asymptotics=None):
         return QBXExpansionWrangler(self, queue, geo_data,
                 dtype,
                 qbx_order, fmm_level_to_order,
                 source_extra_kwargs,
                 kernel_extra_kwargs,
-                _use_target_specific_qbx)
+                _use_target_specific_qbx,
+                _target_asymptotics)
 
 
 class QBXExpansionWrangler(SumpyExpansionWrangler):
-- 
GitLab


From 8521fb1d6491a48069872548ead60904597fe8f9 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 23 Nov 2020 22:30:21 -0600
Subject: [PATCH 13/38] Fetch the proper nodes of tangency for qbx centers

---
 pytential/qbx/__init__.py |  9 ++++++++-
 pytential/qbx/direct.py   | 16 +++++++++++-----
 pytential/qbx/geometry.py | 16 ++++++++++++++++
 3 files changed, 35 insertions(+), 6 deletions(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index cd7ba54f..0c9d2c95 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -908,6 +908,13 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 for i, res_i in enumerate(output_for_each_kernel):
                     tgt_subset_kwargs[f"result_{i}"] = res_i
 
+                if self._target_asymptotics:
+                    taqbx_extra_kwargs = {
+                        "nodes_of_tangency": geo_data.flat_nodes()
+                    }
+                else:
+                    taqbx_extra_kwargs = {}
+
                 if qbx_tgt_count:
                     lpot_applier_on_tgt_subset(
                             queue,
@@ -918,7 +925,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                             strengths=[flat_strengths],
                             qbx_tgt_numbers=qbx_tgt_numbers,
                             qbx_center_numbers=qbx_center_numbers,
-                            **tgt_subset_kwargs)
+                            **tgt_subset_kwargs, **taqbx_extra_kwargs)
 
                 result = output_for_each_kernel[o.kernel_index]
                 if isinstance(target_discr, Discretization):
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 785d512f..acc73b32 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -79,20 +79,20 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
         if self._scaling_at_target:
             # using taqbx
             # inject auxiliary insns for taqbx expansion
-            if 1:
+            if 0:
                 # just use bvec (as if boundary layer around the disk)
                 taqbx_local_temp_insns = ["""
                 <> normal[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
                         {dup=idim}
                 """]
             else:
-                # try to get point of tangency FIXME
-                # this is probably the wrong way (26000 sources, 1360 centers)
                 taqbx_local_temp_insns = ["""
-                <> normal[idim] = src[idim, icenter//2] - center[idim, icenter] \
-                        {dup=idim}
+                <> normal[idim] = nodes_of_tangency[idim, icenter//2] - \
+                        center[idim, icenter] {dup=idim}
                 """]
+
             sat = "sat * "
+
             from sumpy.codegen import to_loopy_insns
             sat_insns = to_loopy_insns(
                 [("sat", self._scaling_at_target)],
@@ -101,6 +101,12 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                     expn.kernel.get_code_transformer() for expn in self.expansions],
                 retain_names=["sat"],
                 complex_dtype=np.complex128)  # FIXME
+
+            arguments += (
+                lp.GlobalArg("nodes_of_tangency", None,
+                    shape=(self.dim, "ncenters_total//2"), dim_tags="sep,C"),
+            )
+
         else:
             taqbx_local_temp_insns = []
             sat = ""
diff --git a/pytential/qbx/geometry.py b/pytential/qbx/geometry.py
index 417af6ac..889dc8ea 100644
--- a/pytential/qbx/geometry.py
+++ b/pytential/qbx/geometry.py
@@ -455,6 +455,22 @@ class QBXFMMGeometryData(FMMLibRotationDataInterface):
 
         return self.array_context.freeze(flatten(radii))
 
+    @memoize_method
+    def flat_nodes(self):
+        """Nodes associated with centers during QBX construction. Can be used
+        as points of tangency.
+
+            centers = nodes + sides * radii * normals
+        """
+        from pytential import bind, sym
+
+        nodes = bind(self.places, sym.nodes(
+                self.ambient_dim,
+                dofdesc=self.source_dd.to_stage1()).as_vector())(
+                    self.array_context)
+
+        return obj_array_vectorize(self.array_context.freeze, flatten(nodes))
+
     # }}}
 
     # {{{ target info
-- 
GitLab


From 0c550062e1e79d436780b5c60f17394f41b0e48f Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 24 Nov 2020 11:53:26 -0600
Subject: [PATCH 14/38] Fix caching of rescaled kernel, and rename tagent nodes
 for better readability

---
 examples/boundary-layer.py |  2 +-
 pytential/qbx/__init__.py  | 20 +++++++++++++++-----
 pytential/qbx/direct.py    |  6 +++---
 pytential/qbx/geometry.py  |  7 ++++---
 4 files changed, 23 insertions(+), 12 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index 5e8cfe5c..044faca4 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -33,7 +33,7 @@ k = 3 + 50j
 
 class VolumeMultipoleLineLocalTaylorExpansionFactory(ExpansionFactoryBase):
     """Volume Taylor for multipole, line Taylor for local, to be used only with
-    direct evaluation.
+    direct evaluation. Used by ``boundary-layer.py``
     """
     def get_local_expansion_class(self, base_kernel):
         from sumpy.expansion.local import LineTaylorLocalExpansion
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 0c9d2c95..ce57e1cb 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -910,7 +910,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
 
                 if self._target_asymptotics:
                     taqbx_extra_kwargs = {
-                        "nodes_of_tangency": geo_data.flat_nodes()
+                        "nodes_of_qbx_balls_tangency": geo_data.flat_stage1_nodes()
                     }
                 else:
                     taqbx_extra_kwargs = {}
@@ -953,12 +953,20 @@ class AsymptoticallyRescaledKernel(Kernel):
 
     def __init__(self, base_kernel, rescaled_expression):
         """
-        :param rescaled_expression: A sympy expression that is directly
-        returned by get_expression to the expansion taker.
+        :param rescaled_expression: A sympy/pymbolic expression.
+
+        The rescaled_expression is always stored as a pymbolic expression
+        internally for easy pickling.
         """
         super().__init__(base_kernel.dim)
         self.base_kernel = base_kernel
-        self.rescaled_expression = rescaled_expression
+
+        from pymbolic.primitives import Expression
+        if isinstance(rescaled_expression, Expression):
+            self.rescaled_expression = rescaled_expression
+        else:
+            from pymbolic.interop.sympy import SympyToPymbolicMapper
+            self.rescaled_expression = SympyToPymbolicMapper()(rescaled_expression)
 
     def __repr__(self):
         return "AsymKnl%dD" % self.dim
@@ -977,7 +985,9 @@ class AsymptoticallyRescaledKernel(Kernel):
         return self.base_kernel.get_code_transformer()
 
     def get_expression(self, scaled_dist_vec):
-        return self.rescaled_expression
+        from pymbolic.interop.sympy import PymbolicToSympyMapper
+        expr = PymbolicToSympyMapper()(self.rescaled_expression)
+        return expr
 
     def postprocess_at_source(self, expr, avec):
         return self.base_kernel.postprocess_at_source(expr, avec)
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index acc73b32..4e7c8a51 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -87,7 +87,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 """]
             else:
                 taqbx_local_temp_insns = ["""
-                <> normal[idim] = nodes_of_tangency[idim, icenter//2] - \
+                <> normal[idim] = nodes_of_qbx_balls_tangency[idim, icenter//2] - \
                         center[idim, icenter] {dup=idim}
                 """]
 
@@ -103,8 +103,8 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 complex_dtype=np.complex128)  # FIXME
 
             arguments += (
-                lp.GlobalArg("nodes_of_tangency", None,
-                    shape=(self.dim, "ncenters_total//2"), dim_tags="sep,C"),
+                lp.GlobalArg("nodes_of_qbx_balls_tangency", None,
+                    shape=(self.dim, "ncenters_total/2"), dim_tags="sep,C"),
             )
 
         else:
diff --git a/pytential/qbx/geometry.py b/pytential/qbx/geometry.py
index 889dc8ea..b19537b8 100644
--- a/pytential/qbx/geometry.py
+++ b/pytential/qbx/geometry.py
@@ -456,9 +456,10 @@ class QBXFMMGeometryData(FMMLibRotationDataInterface):
         return self.array_context.freeze(flatten(radii))
 
     @memoize_method
-    def flat_nodes(self):
-        """Nodes associated with centers during QBX construction. Can be used
-        as points of tangency.
+    def flat_stage1_nodes(self):
+        """Stage 1 nodes associated with centers during QBX construction. They
+        are the points of tangency between QBX expansion balls and the source
+        geometry.
 
             centers = nodes + sides * radii * normals
         """
-- 
GitLab


From 40def5a0ad231a19a36e6ee8c4810a3954ebafea Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 24 Nov 2020 12:01:59 -0600
Subject: [PATCH 15/38] Rebranding to qbmax (courteous to @inducer)

---
 pytential/qbx/__init__.py | 20 ++++++++---------
 pytential/qbx/direct.py   | 14 ++++++------
 pytential/qbx/fmm.py      | 46 +++++++++++++++++++--------------------
 pytential/qbx/fmmlib.py   |  2 +-
 4 files changed, 41 insertions(+), 41 deletions(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index ce57e1cb..d802f096 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -117,7 +117,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
              gathering modeled costs if provided (experimental)
         :arg _target_asymptotics: Either *None* or an object implementing the
              :class:`~pytential.qbx.QBXLayerPotentialAsymptotics` interface, used for
-             enabling TAQBX. It stores the asymptotic information about layer
+             enabling QBMAX. It stores the asymptotic information about layer
              potential of the "main" kernel (the one used for FMM).
         """
 
@@ -558,19 +558,19 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             if self._target_asymptotics:
                 fmm_kernel_tascaled = \
                     self._target_asymptotics.get_rescaled_kernel(local_expn_class)
-                taqbx_local_factory = partial(local_expn_class, fmm_kernel_tascaled)
+                qbmax_local_factory = partial(local_expn_class, fmm_kernel_tascaled)
             else:
-                taqbx_local_factory = None
+                qbmax_local_factory = None
 
             return QBXSumpyExpansionWranglerCodeContainer(
                     self.cl_context,
                     fmm_mpole_factory, fmm_local_factory, qbx_local_factory,
-                    taqbx_local_factory, out_kernels)
+                    qbmax_local_factory, out_kernels)
 
         elif self.fmm_backend == "fmmlib":
 
             if self._target_asymptotics:
-                raise ValueError("TAQBX is not implemented in fmmlib")
+                raise ValueError("QBMAX is not implemented in fmmlib")
 
             from pytential.qbx.fmmlib import \
                     QBXFMMLibExpansionWranglerCodeContainer
@@ -909,11 +909,11 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                     tgt_subset_kwargs[f"result_{i}"] = res_i
 
                 if self._target_asymptotics:
-                    taqbx_extra_kwargs = {
+                    qbmax_extra_kwargs = {
                         "nodes_of_qbx_balls_tangency": geo_data.flat_stage1_nodes()
                     }
                 else:
-                    taqbx_extra_kwargs = {}
+                    qbmax_extra_kwargs = {}
 
                 if qbx_tgt_count:
                     lpot_applier_on_tgt_subset(
@@ -925,7 +925,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                             strengths=[flat_strengths],
                             qbx_tgt_numbers=qbx_tgt_numbers,
                             qbx_center_numbers=qbx_center_numbers,
-                            **tgt_subset_kwargs, **taqbx_extra_kwargs)
+                            **tgt_subset_kwargs, **qbmax_extra_kwargs)
 
                 result = output_for_each_kernel[o.kernel_index]
                 if isinstance(target_discr, Discretization):
@@ -1051,7 +1051,7 @@ class QBXLayerPotentialAsymptotics:
         self.geometric_order = geometric_order
 
     @memoize_method
-    def get_taqbx_local_expansion(self, expn_class):
+    def get_qbmax_local_expansion(self, expn_class):
         pass
 
     @memoize_method
@@ -1183,7 +1183,7 @@ class QBXLayerPotentialAsymptotics:
                 self.kernel.get_expression(rad), avec)
         else:
             raise ValueError(
-                f"unsupported expansion class for TAQBX: {expn_class.__name__}")
+                f"unsupported expansion class for QBMAX: {expn_class.__name__}")
 
     @property
     def _dist(self):
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 4e7c8a51..2a42bb0b 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -40,7 +40,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                          value_dtypes, name, device, scaling_at_target)
 
         if self._scaling_at_target:
-            self._vector_names.add("normal")  # needed for taqbx
+            self._vector_names.add("normal")  # needed for qbmax
 
     def get_cache_key(self):
         return super().get_cache_key() + (PYTENTIAL_KERNEL_VERSION,)
@@ -77,16 +77,16 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
             for i in range(len(self.kernels))])
 
         if self._scaling_at_target:
-            # using taqbx
-            # inject auxiliary insns for taqbx expansion
+            # using qbmax
+            # inject auxiliary insns for qbmax expansion
             if 0:
                 # just use bvec (as if boundary layer around the disk)
-                taqbx_local_temp_insns = ["""
+                qbmax_local_temp_insns = ["""
                 <> normal[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
                         {dup=idim}
                 """]
             else:
-                taqbx_local_temp_insns = ["""
+                qbmax_local_temp_insns = ["""
                 <> normal[idim] = nodes_of_qbx_balls_tangency[idim, icenter//2] - \
                         center[idim, icenter] {dup=idim}
                 """]
@@ -108,7 +108,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
             )
 
         else:
-            taqbx_local_temp_insns = []
+            qbmax_local_temp_insns = []
             sat = ""
             sat_insns = []
 
@@ -128,7 +128,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 <> b[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
                         {dup=idim}
                 <> rscale = expansion_radii[icenter]
-            """] + taqbx_local_temp_insns + sat_insns
+            """] + qbmax_local_temp_insns + sat_insns
             + loopy_insns + kernel_exprs
             + ["""
                 result_{i}[itgt_overall] = knl_{i}_scaling * {sat} \
diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index e0908950..f8c99c0e 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -51,25 +51,25 @@ __doc__ = """
 class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer):
     def __init__(self, cl_context,
             multipole_expansion_factory, local_expansion_factory,
-            qbx_local_expansion_factory, taqbx_local_expansion_factory, out_kernels):
+            qbx_local_expansion_factory, qbmax_local_expansion_factory, out_kernels):
         SumpyExpansionWranglerCodeContainer.__init__(self,
                 cl_context, multipole_expansion_factory, local_expansion_factory,
                 out_kernels)
 
         self.qbx_local_expansion_factory = qbx_local_expansion_factory
-        self.taqbx_local_expansion_factory = taqbx_local_expansion_factory
+        self.qbmax_local_expansion_factory = qbmax_local_expansion_factory
 
     @memoize_method
     def qbx_local_expansion(self, order):
         return self.qbx_local_expansion_factory(order, self.use_rscale)
 
     @memoize_method
-    def taqbx_local_expansion(self, order):
-        return self.taqbx_local_expansion_factory(order, self.use_rscale)
+    def qbmax_local_expansion(self, order):
+        return self.qbmax_local_expansion_factory(order, self.use_rscale)
 
     @memoize_method
     def target_asymptotic_qbx_local_expansion(self, order):
-        return self.taqbx_local_expansion_factory(order, self.use_rscale)
+        return self.qbmax_local_expansion_factory(order, self.use_rscale)
 
     @memoize_method
     def p2qbxl(self, order):
@@ -77,9 +77,9 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
                 self.qbx_local_expansion(order))
 
     @memoize_method
-    def p2taqbxl(self, order):
+    def p2qbmaxl(self, order):
         return P2QBXLFromCSR(self.cl_context,
-                self.taqbx_local_expansion(order))
+                self.qbmax_local_expansion(order))
 
     @memoize_method
     def m2qbxl(self, source_order, target_order):
@@ -100,9 +100,9 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
                 self.out_kernels)
 
     @memoize_method
-    def taqbxl2p(self, order):
+    def qbmaxl2p(self, order):
         return QBXL2P(self.cl_context,
-                self.taqbx_local_expansion_factory(order),
+                self.qbmax_local_expansion_factory(order),
                 self.out_kernels)
 
     def get_wrangler(self, queue, geo_data, dtype,
@@ -155,10 +155,10 @@ non_qbx_box_target_lists`),
         self.using_tsqbx = False
 
         if _target_asymptotics:
-            self.using_taqbx = True
+            self.using_qbmax = True
             self.target_asymptotics = _target_asymptotics
         else:
-            self.using_taqbx = False
+            self.using_qbmax = False
 
     # {{{ data vector utilities
 
@@ -232,7 +232,7 @@ non_qbx_box_target_lists`),
         local_exps = self.qbx_local_expansion_zeros()
         events = []
 
-        if self.using_taqbx:
+        if self.using_qbmax:
             return (local_exps, SumpyTimingFuture(self.queue, events))
 
         geo_data = self.geo_data
@@ -274,7 +274,7 @@ non_qbx_box_target_lists`),
         ta_local_exps = self.qbx_local_expansion_zeros()
         events = []
 
-        if not self.using_taqbx:
+        if not self.using_qbmax:
             return (ta_local_exps, SumpyTimingFuture(self.queue, events))
 
         geo_data = self.geo_data
@@ -289,9 +289,9 @@ non_qbx_box_target_lists`),
         kwargs = self.extra_kwargs.copy()
         kwargs.update(self.box_source_list_kwargs())
 
-        p2taqbxl = self.code.p2taqbxl(self.qbx_order, self.target_asymptotics)
+        p2qbmaxl = self.code.p2qbmaxl(self.qbx_order, self.target_asymptotics)
 
-        evt, (result,) = p2taqbxl(
+        evt, (result,) = p2qbmaxl(
                 self.queue,
                 global_qbx_centers=geo_data.global_qbx_centers(),
                 qbx_center_to_target_box=geo_data.qbx_center_to_target_box(),
@@ -451,13 +451,13 @@ non_qbx_box_target_lists`),
         return (self.full_output_zeros(), SumpyTimingFuture(self.queue, events=()))
 
     @log_process(logger)
-    def eval_target_asymptotic_qbx_locals(self, taqbx_expansions):
+    def eval_target_asymptotic_qbx_locals(self, qbmax_expansions):
         pot = self.full_output_zeros()
 
         geo_data = self.geo_data
         events = []
 
-        if not self.using_taqbx:
+        if not self.using_qbmax:
             return (pot, SumpyTimingFuture(self.queue, events))
 
         if len(geo_data.global_qbx_centers()) == 0:
@@ -465,9 +465,9 @@ non_qbx_box_target_lists`),
 
         ctt = geo_data.center_to_tree_targets()
 
-        taqbxl2p = self.code.taqbxl2p(self.qbx_order)
+        qbmaxl2p = self.code.qbmaxl2p(self.qbx_order)
 
-        evt, pot_res = taqbxl2p(
+        evt, pot_res = qbmaxl2p(
             self.queue,
             qbx_centers=geo_data.flat_centers(),
             qbx_expansion_radii=geo_data.flat_expansion_radii(),
@@ -479,7 +479,7 @@ non_qbx_box_target_lists`),
 
             targets=self.tree.targets,
 
-            taqbx_expansions=taqbx_expansions,
+            qbmax_expansions=qbmax_expansions,
             result=pot,
 
             **self.kernel_extra_kwargs.copy())
@@ -645,7 +645,7 @@ def drive_fmm(expansion_wrangler, src_weight_vecs, timing_data=None,
     # for the same interactions (directly evaluated portion of the potentials
     # via unified List 1).  Which one is used depends on the wrangler. If one of
     # them is unused the corresponding output entries will be zero.
-    # (TAQBX uses neither)
+    # (QBMAX uses neither)
 
     qbx_expansions, timing_future = wrangler.form_global_qbx_locals(src_weight_vecs)
 
@@ -676,13 +676,13 @@ def drive_fmm(expansion_wrangler, src_weight_vecs, timing_data=None,
 
     recorder.add("eval_target_specific_qbx_locals", timing_future)
 
-    taqbx_expansions, timing_future = \
+    qbmax_expansions, timing_future = \
         wrangler.form_target_asymptotic_qbx_locals(src_weight_vecs)
 
     # recorder.add("form_target_asymptotic_qbx_locals", timing_future)
 
     ta_result, timing_future = \
-        wrangler.eval_target_asymptotic_qbx_locals(taqbx_expansions)
+        wrangler.eval_target_asymptotic_qbx_locals(qbmax_expansions)
 
     qbx_potentials = qbx_potentials + ta_result
 
diff --git a/pytential/qbx/fmmlib.py b/pytential/qbx/fmmlib.py
index 8087782d..b169a53a 100644
--- a/pytential/qbx/fmmlib.py
+++ b/pytential/qbx/fmmlib.py
@@ -457,7 +457,7 @@ class QBXFMMLibExpansionWrangler(FMMLibExpansionWrangler):
 
     @log_process(logger)
     @return_timing_data
-    def eval_target_asymptotic_qbx_locals(self, taqbx_expansions):
+    def eval_target_asymptotic_qbx_locals(self, qbmax_expansions):
         return self.full_output_zeros()
 
     @log_process(logger)
-- 
GitLab


From 47b5eaec2af7114519a1adfe6d28c18047ae95b7 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 24 Nov 2020 19:12:38 -0600
Subject: [PATCH 16/38] Temporarily switch requirements.txt to sumpy
 boundary-layer branch

---
 requirements.txt | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/requirements.txt b/requirements.txt
index 48627bae..b6bab311 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -8,5 +8,6 @@ git+https://github.com/inducer/islpy.git#egg=islpy
 git+https://github.com/inducer/loopy.git#egg=loopy
 git+https://github.com/inducer/boxtree.git#egg=boxtree
 git+https://github.com/inducer/meshmode.git#egg=meshmode
-git+https://github.com/inducer/sumpy.git#egg=sumpy
+# git+https://github.com/inducer/sumpy.git#egg=sumpy
+git+https://gitlab.tiker.net/inducer/sumpy.git@boundary-layer#egg=sumpy
 git+https://github.com/inducer/pyfmmlib.git#egg=pyfmmlib
-- 
GitLab


From 2520e5f359333a59814bdf05ddb153fede205625 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 30 Nov 2020 12:02:53 -0600
Subject: [PATCH 17/38] Refactor: combine scaling with the kernel

---
 pytential/qbx/__init__.py | 106 ++++++--------------------------------
 pytential/qbx/direct.py   |  70 ++++++++++++++++---------
 2 files changed, 61 insertions(+), 115 deletions(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index d802f096..8e71c9fe 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -29,7 +29,6 @@ from pytential.qbx.target_assoc import QBXTargetAssociationFailedException
 from pytential.source import LayerPotentialSourceBase
 
 import sumpy.symbolic as sym
-from sumpy.kernel import Kernel
 
 import pyopencl as cl
 
@@ -40,8 +39,6 @@ logger = logging.getLogger(__name__)
 __doc__ = """
 .. autoclass:: QBXLayerPotentialSource
 
-.. autoclass:: AsymptoticallyRescaledKernel
-
 .. autoclass:: QBXLayerPotentialAsymptotics
 
 .. autoclass:: QBXTargetAssociationFailedException
@@ -726,16 +723,12 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             else:
                 kernels = [self._target_asymptotics.get_rescaled_kernel(
                     LineTaylorLocalExpansion)]
-                sat = self._target_asymptotics.get_scaling_at_target(
-                    LineTaylorLocalExpansion)
-        else:
-            sat = None
 
         from sumpy.qbx import LayerPotential
-        return LayerPotential(self.cl_context,
-                    [LineTaylorLocalExpansion(knl, self.qbx_order)
-                        for knl in kernels],
-                    value_dtypes=value_dtype, scaling_at_target=sat)
+        return LayerPotential(
+            self.cl_context,
+            [LineTaylorLocalExpansion(knl, self.qbx_order) for knl in kernels],
+            value_dtypes=value_dtype)
 
     @memoize_method
     def get_lpot_applier_on_tgt_subset(self, kernels):
@@ -755,17 +748,12 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             else:
                 kernels = [self._target_asymptotics.get_rescaled_kernel(
                     VolumeTaylorLocalExpansion)]
-                sat = self._target_asymptotics.get_scaling_at_target(
-                    VolumeTaylorLocalExpansion)
-        else:
-            sat = None
 
         from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         return LayerPotentialOnTargetAndCenterSubset(
-                self.cl_context,
-                [VolumeTaylorLocalExpansion(knl, self.qbx_order)
-                    for knl in kernels],
-                value_dtypes=value_dtype, scaling_at_target=sat)
+            self.cl_context,
+            [VolumeTaylorLocalExpansion(knl, self.qbx_order) for knl in kernels],
+            value_dtypes=value_dtype)
 
     @memoize_method
     def get_qbx_target_numberer(self, dtype):
@@ -945,72 +933,6 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
 
 # {{{ QBX layer potential asymptotics
 
-class AsymptoticallyRescaledKernel(Kernel):
-    """Extend the base kernel so that when asked by an expansion
-    factory, it replies with rescaled expression.
-    """
-    init_arg_names = ("base_kernel", "rescaled_expression")
-
-    def __init__(self, base_kernel, rescaled_expression):
-        """
-        :param rescaled_expression: A sympy/pymbolic expression.
-
-        The rescaled_expression is always stored as a pymbolic expression
-        internally for easy pickling.
-        """
-        super().__init__(base_kernel.dim)
-        self.base_kernel = base_kernel
-
-        from pymbolic.primitives import Expression
-        if isinstance(rescaled_expression, Expression):
-            self.rescaled_expression = rescaled_expression
-        else:
-            from pymbolic.interop.sympy import SympyToPymbolicMapper
-            self.rescaled_expression = SympyToPymbolicMapper()(rescaled_expression)
-
-    def __repr__(self):
-        return "AsymKnl%dD" % self.dim
-
-    def __getinitargs__(self):
-        return (self.base_kernel, self.rescaled_expression)
-
-    @property
-    def is_complex_valued(self):
-        return self.base_kernel.is_complex_valued
-
-    def prepare_loopy_kernel(self, loopy_knl):
-        return self.base_kernel.prepare_loopy_kernel(loopy_knl)
-
-    def get_code_transformer(self):
-        return self.base_kernel.get_code_transformer()
-
-    def get_expression(self, scaled_dist_vec):
-        from pymbolic.interop.sympy import PymbolicToSympyMapper
-        expr = PymbolicToSympyMapper()(self.rescaled_expression)
-        return expr
-
-    def postprocess_at_source(self, expr, avec):
-        return self.base_kernel.postprocess_at_source(expr, avec)
-
-    def postprocess_at_target(self, expr, bvec):
-        return self.base_kernel.postprocess_at_target(expr, bvec)
-
-    def get_global_scaling_const(self):
-        return self.base_kernel.get_global_scaling_const()
-
-    def update_persistent_hash(self, key_hash, key_builder):
-        self.base_kernel.update_persistent_hash(key_hash, key_builder)
-        key_hash.update(str(self.rescaled_expression).encode("utf8"))
-
-    def get_args(self):
-        return self.base_kernel.get_args()
-
-    def get_source_args(self):
-        return self.base_kernel.get_source_args()
-
-    mapper_method = "map_asymptotically_rescaled_kernel"
-
-
 class QBXLayerPotentialAsymptotics:
     """Asymptotic behavior of a layer potential near its source. The class
     provides a symbolic description of the near-surface asymptotic behavior of
@@ -1050,21 +972,23 @@ class QBXLayerPotentialAsymptotics:
         self.expr = expr
         self.geometric_order = geometric_order
 
-    @memoize_method
-    def get_qbmax_local_expansion(self, expn_class):
-        pass
-
     @memoize_method
     def get_rescaled_kernel(self, expn_class):
         """Return a :mod:`sumpy` kernel with the rescaled expression.
         """
         resd_expr = self._get_rescaled_kernel_expr(expn_class)
         base_kernel = self.kernel
+        scaling = self._get_scaling_at_target(expn_class)
+
+        from pymbolic.interop.sympy import SympyToPymbolicMapper
+        resd_expr = SympyToPymbolicMapper()(resd_expr)
+        scaling = SympyToPymbolicMapper()(scaling)
 
-        return AsymptoticallyRescaledKernel(base_kernel, resd_expr)
+        from sumpy.kernel import AsymptoticallyRescaledKernel
+        return AsymptoticallyRescaledKernel(base_kernel, resd_expr, scaling)
 
     @memoize_method
-    def get_scaling_at_target(self, expn_class):
+    def _get_scaling_at_target(self, expn_class):
         """Target-dependent scaling expression, used for scaling back the
         potential after summing up the expansion.
         """
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 2a42bb0b..53fcd83b 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -34,21 +34,14 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
     default_name = "qbx_tgt_ctr_subset"
 
     def __init__(self, ctx, expansions, strength_usage=None,
-                 value_dtypes=None, name=None, device=None,
-                 scaling_at_target=None):
+                 value_dtypes=None, name=None, device=None):
         super().__init__(ctx, expansions, strength_usage,
-                         value_dtypes, name, device, scaling_at_target)
-
-        if self._scaling_at_target:
-            self._vector_names.add("normal")  # needed for qbmax
+                         value_dtypes, name, device)
 
     def get_cache_key(self):
         return super().get_cache_key() + (PYTENTIAL_KERNEL_VERSION,)
 
     def get_kernel(self):
-        loopy_insns, result_names = self.get_loopy_insns_and_result_names()
-        kernel_exprs = self.get_kernel_exprs(result_names)
-
         from sumpy.tools import gather_loopy_source_arguments
         arguments = (
             gather_loopy_source_arguments(self.kernels)
@@ -76,42 +69,71 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 shape="ntargets_total", order="C")
             for i in range(len(self.kernels))])
 
-        if self._scaling_at_target:
-            # using qbmax
+        sats = []
+        sat_insns_data = []
+        for iknl in range(len(self.expansions)):
+
+            from sumpy.expansion import ExpansionBase
+            if isinstance(self.expansions[iknl], ExpansionBase):
+                knl = self.expansions[iknl].kernel
+            else:
+                from sumpy.kernel import Kernel
+                assert isinstance(self.expansions[iknl], Kernel)
+                knl = self.expansions[iknl]
+
+            try:
+                sat_expr = knl.get_scaling_expression()
+            except AttributeError:
+                sat_expr = None
+
+            if sat_expr:
+                # inject the multiplicative scales of each output kernel
+                sats.append(f"sat_{iknl} * ")
+                sat_insns_data.append((f"sat_{iknl}", sat_expr))
+            else:
+                sats.append("")
+
+        if sat_insns_data:
             # inject auxiliary insns for qbmax expansion
             if 0:
                 # just use bvec (as if boundary layer around the disk)
                 qbmax_local_temp_insns = ["""
-                <> normal[idim] = tgt[idim, itgt_overall] - center[idim, icenter] \
-                        {dup=idim}
+                <> normal[idim] = tgt[idim, itgt_overall] - \
+                        center[idim, icenter] {dup=idim}
                 """]
             else:
                 qbmax_local_temp_insns = ["""
-                <> normal[idim] = nodes_of_qbx_balls_tangency[idim, icenter//2] - \
+                <> normal[idim] = \
+                        nodes_of_qbx_balls_tangency[idim, icenter//2] - \
                         center[idim, icenter] {dup=idim}
                 """]
 
-            sat = "sat * "
+                arguments += (
+                    lp.GlobalArg("nodes_of_qbx_balls_tangency", None,
+                        shape=(self.dim, "ncenters_total/2"), dim_tags="sep,C"),
+                )
+
+            # treat the injected "normal" as a vector during codegen
+            # must be before calling self.get_loopy_insns_and_result_names()
+            self._vector_names.add("normal")
 
             from sumpy.codegen import to_loopy_insns
             sat_insns = to_loopy_insns(
-                [("sat", self._scaling_at_target)],
+                sat_insns_data,
                 vector_names=self._vector_names,
                 pymbolic_expr_maps=[
                     expn.kernel.get_code_transformer() for expn in self.expansions],
-                retain_names=["sat"],
+                retain_names=[datpair[0] for datpair in sat_insns_data],
                 complex_dtype=np.complex128)  # FIXME
 
-            arguments += (
-                lp.GlobalArg("nodes_of_qbx_balls_tangency", None,
-                    shape=(self.dim, "ncenters_total/2"), dim_tags="sep,C"),
-            )
-
         else:
+            # no qbmax
             qbmax_local_temp_insns = []
-            sat = ""
             sat_insns = []
 
+        loopy_insns, result_names = self.get_loopy_insns_and_result_names()
+        kernel_exprs = self.get_kernel_exprs(result_names)
+
         loopy_knl = lp.make_kernel([
             "{[itgt]: 0 <= itgt < ntargets}",
             "{[isrc]: 0 <= isrc < nsources}",
@@ -134,7 +156,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 result_{i}[itgt_overall] = knl_{i}_scaling * {sat} \
                     simul_reduce(sum, isrc, pair_result_{i})  \
                         {{inames=itgt}}
-                """.format(i=iknl, sat=sat)
+                """.format(i=iknl, sat=sats[iknl])
                 for iknl in range(len(self.expansions))]
             + ["end"],
             arguments,
-- 
GitLab


From b08ea20e2bde044bfab5a6ca24ef2acda2455618 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 30 Nov 2020 16:20:32 -0600
Subject: [PATCH 18/38] Integrate with fmm

---
 examples/boundary-layer.py    |   2 +-
 pytential/qbx/__init__.py     |  16 +--
 pytential/qbx/fmm.py          |  51 ++++----
 pytential/qbx/interactions.py | 215 ++++++++++++++++++++++++++++++++++
 4 files changed, 247 insertions(+), 37 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index 044faca4..9226f797 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -53,7 +53,7 @@ def main(case="line", curve_fn=starfish, visualize=True):
         expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
     elif case == "volume":
         # fmm_order = False
-        fmm_order = False
+        fmm_order = 3
         expn_factory = VolumeTaylorExpansionFactory()
     else:
         raise ValueError
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 8e71c9fe..cf4c4dcf 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -560,9 +560,9 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 qbmax_local_factory = None
 
             return QBXSumpyExpansionWranglerCodeContainer(
-                    self.cl_context,
-                    fmm_mpole_factory, fmm_local_factory, qbx_local_factory,
-                    qbmax_local_factory, out_kernels)
+                self.cl_context,
+                fmm_mpole_factory, fmm_local_factory, qbx_local_factory, out_kernels,
+                _qbmax_local_expansion_factory=qbmax_local_factory)
 
         elif self.fmm_backend == "fmmlib":
 
@@ -939,10 +939,10 @@ class QBXLayerPotentialAsymptotics:
     the layer potential and properly dispatch it to different expansion
     classes.
 
-    The main use of this class is to make :class:`AsymptoticallyRescaledKernel`
-    objects. The rescaled kernels depend on expansion methods. This class tries
-    to isolate mathematical asymptotic expansions that depend solely on the
-    kernel and domain geometry.
+    The main use of this class is to make :class:
+    `sumpy.kernel.AsymptoticallyRescaledKernel` objects. The rescaled kernels
+    depend on expansion methods. This class tries to isolate mathematical
+    asymptotic expansions that depend solely on the kernel and domain geometry.
 
     .. attribute :: dim
 
@@ -1072,7 +1072,7 @@ class QBXLayerPotentialAsymptotics:
                 self._radius: sym.sym.Symbol("rscale"),
             }
 
-            # self._nvec: normal
+            # self._nvec: normal / norm(normal)
             normal = sym.make_sym_vector("normal", self.dim)
             normal_norm = sym.sym.sqrt(normal.dot(normal))
             for lhs, rhs in zip(self._nvec, normal):
diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index f8c99c0e..a81ad2ed 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -28,7 +28,8 @@ from sumpy.fmm import (SumpyExpansionWranglerCodeContainer,
         SumpyExpansionWrangler, level_to_rscale, SumpyTimingFuture)
 
 from pytools import memoize_method
-from pytential.qbx.interactions import P2QBXLFromCSR, M2QBXL, L2QBXL, QBXL2P
+from pytential.qbx.interactions import (P2QBXLFromCSR, P2QBMAXLFromCSR,
+                                        M2QBXL, L2QBXL, QBXL2P, QBMAXL2P)
 
 from boxtree.fmm import TimingRecorder
 from pytools import log_process, ProcessLogger
@@ -51,13 +52,14 @@ __doc__ = """
 class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer):
     def __init__(self, cl_context,
             multipole_expansion_factory, local_expansion_factory,
-            qbx_local_expansion_factory, qbmax_local_expansion_factory, out_kernels):
+            qbx_local_expansion_factory, out_kernels,
+            _qbmax_local_expansion_factory=None):
         SumpyExpansionWranglerCodeContainer.__init__(self,
                 cl_context, multipole_expansion_factory, local_expansion_factory,
                 out_kernels)
 
         self.qbx_local_expansion_factory = qbx_local_expansion_factory
-        self.qbmax_local_expansion_factory = qbmax_local_expansion_factory
+        self.qbmax_local_expansion_factory = _qbmax_local_expansion_factory
 
     @memoize_method
     def qbx_local_expansion(self, order):
@@ -67,10 +69,6 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
     def qbmax_local_expansion(self, order):
         return self.qbmax_local_expansion_factory(order, self.use_rscale)
 
-    @memoize_method
-    def target_asymptotic_qbx_local_expansion(self, order):
-        return self.qbmax_local_expansion_factory(order, self.use_rscale)
-
     @memoize_method
     def p2qbxl(self, order):
         return P2QBXLFromCSR(self.cl_context,
@@ -78,7 +76,7 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
 
     @memoize_method
     def p2qbmaxl(self, order):
-        return P2QBXLFromCSR(self.cl_context,
+        return P2QBMAXLFromCSR(self.cl_context,
                 self.qbmax_local_expansion(order))
 
     @memoize_method
@@ -101,7 +99,7 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
 
     @memoize_method
     def qbmaxl2p(self, order):
-        return QBXL2P(self.cl_context,
+        return QBMAXL2P(self.cl_context,
                 self.qbmax_local_expansion_factory(order),
                 self.out_kernels)
 
@@ -109,15 +107,13 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
             qbx_order, fmm_level_to_order,
             source_extra_kwargs={},
             kernel_extra_kwargs=None,
-            _use_target_specific_qbx=False,
-            _target_asymptotics=None):
+            _use_target_specific_qbx=False):
         return QBXExpansionWrangler(self, queue, geo_data,
                 dtype,
                 qbx_order, fmm_level_to_order,
                 source_extra_kwargs,
                 kernel_extra_kwargs,
-                _use_target_specific_qbx,
-                _target_asymptotics)
+                _use_target_specific_qbx)
 
 
 class QBXExpansionWrangler(SumpyExpansionWrangler):
@@ -142,7 +138,7 @@ non_qbx_box_target_lists`),
     def __init__(self, code_container, queue, geo_data, dtype,
             qbx_order, fmm_level_to_order,
             source_extra_kwargs, kernel_extra_kwargs,
-            _use_target_specific_qbx=None, _target_asymptotics=None):
+            _use_target_specific_qbx=None):
         if _use_target_specific_qbx:
             raise ValueError("TSQBX is not implemented in sumpy")
 
@@ -152,13 +148,10 @@ non_qbx_box_target_lists`),
 
         self.qbx_order = qbx_order
         self.geo_data = geo_data
-        self.using_tsqbx = False
 
-        if _target_asymptotics:
-            self.using_qbmax = True
-            self.target_asymptotics = _target_asymptotics
-        else:
-            self.using_qbmax = False
+    @property
+    def using_qbmax(self):
+        return self.code.qbmax_local_expansion_factory is not None
 
     # {{{ data vector utilities
 
@@ -270,7 +263,7 @@ non_qbx_box_target_lists`),
         return (result, SumpyTimingFuture(self.queue, events))
 
     @log_process(logger)
-    def form_target_asymptotic_qbx_locals(self, src_weight_vecs):
+    def form_qbmax_locals(self, src_weight_vecs):
         ta_local_exps = self.qbx_local_expansion_zeros()
         events = []
 
@@ -289,19 +282,20 @@ non_qbx_box_target_lists`),
         kwargs = self.extra_kwargs.copy()
         kwargs.update(self.box_source_list_kwargs())
 
-        p2qbmaxl = self.code.p2qbmaxl(self.qbx_order, self.target_asymptotics)
+        p2qbmaxl = self.code.p2qbmaxl(self.qbx_order)
 
         evt, (result,) = p2qbmaxl(
                 self.queue,
                 global_qbx_centers=geo_data.global_qbx_centers(),
                 qbx_center_to_target_box=geo_data.qbx_center_to_target_box(),
                 qbx_centers=geo_data.flat_centers(),
+                nodes_of_qbx_balls_tangency=geo_data.flat_stage1_nodes(),
                 qbx_expansion_radii=geo_data.flat_expansion_radii(),
 
                 source_box_starts=starts,
                 source_box_lists=lists,
                 strengths=src_weight_vecs,
-                qbx_expansions=ta_local_exps,
+                qbmax_expansions=ta_local_exps,
 
                 **kwargs)
 
@@ -451,7 +445,7 @@ non_qbx_box_target_lists`),
         return (self.full_output_zeros(), SumpyTimingFuture(self.queue, events=()))
 
     @log_process(logger)
-    def eval_target_asymptotic_qbx_locals(self, qbmax_expansions):
+    def eval_qbmax_locals(self, qbmax_expansions):
         pot = self.full_output_zeros()
 
         geo_data = self.geo_data
@@ -470,6 +464,7 @@ non_qbx_box_target_lists`),
         evt, pot_res = qbmaxl2p(
             self.queue,
             qbx_centers=geo_data.flat_centers(),
+            nodes_of_qbx_balls_tangency=geo_data.flat_stage1_nodes(),
             qbx_expansion_radii=geo_data.flat_expansion_radii(),
 
             global_qbx_centers=geo_data.global_qbx_centers(),
@@ -677,16 +672,16 @@ def drive_fmm(expansion_wrangler, src_weight_vecs, timing_data=None,
     recorder.add("eval_target_specific_qbx_locals", timing_future)
 
     qbmax_expansions, timing_future = \
-        wrangler.form_target_asymptotic_qbx_locals(src_weight_vecs)
+        wrangler.form_qbmax_locals(src_weight_vecs)
 
-    # recorder.add("form_target_asymptotic_qbx_locals", timing_future)
+    # recorder.add("form_qbmax_locals", timing_future)
 
     ta_result, timing_future = \
-        wrangler.eval_target_asymptotic_qbx_locals(qbmax_expansions)
+        wrangler.eval_qbmax_locals(qbmax_expansions)
 
     qbx_potentials = qbx_potentials + ta_result
 
-    # recorder.add("eval_target_asymptotic_qbx_locals", timing_future)
+    # recorder.add("eval_qbmax_locals", timing_future)
 
     # }}}
 
diff --git a/pytential/qbx/interactions.py b/pytential/qbx/interactions.py
index e8a13f51..6ddfc424 100644
--- a/pytential/qbx/interactions.py
+++ b/pytential/qbx/interactions.py
@@ -131,6 +131,114 @@ class P2QBXLFromCSR(P2EBase):
 # }}}
 
 
+# {{{ form qbmax expansions from points
+
+class P2QBMAXLFromCSR(P2EBase):
+    default_name = "p2qbmaxl_from_csr"
+
+    def get_cache_key(self):
+        return super().get_cache_key() + (PYTENTIAL_KERNEL_VERSION,)
+
+    def get_kernel(self):
+        ncoeffs = len(self.expansion)
+
+        # symbolic vector injected by qbmax
+        self._vector_names.add("normal")
+
+        from sumpy.tools import gather_loopy_source_arguments
+        arguments = (
+                [
+                    lp.GlobalArg("sources", None, shape=(self.dim, "nsources"),
+                        dim_tags="sep,c"),
+                    lp.GlobalArg("strengths", None, dim_tags="sep,c",
+                        shape="strength_count, nsources"),
+                    lp.GlobalArg("qbx_center_to_target_box",
+                        None, shape=None),
+                    lp.GlobalArg("source_box_starts,source_box_lists",
+                        None, shape=None),
+                    lp.GlobalArg("box_source_starts,box_source_counts_nonchild",
+                        None, shape=None),
+                    lp.GlobalArg("qbx_centers", None, shape="dim, ncenters",
+                        dim_tags="sep,c"),
+                    lp.GlobalArg("nodes_of_qbx_balls_tangency", None,
+                        shape=(self.dim, "ncenters/2"), dim_tags="sep,C"),
+                    lp.GlobalArg("qbx_expansion_radii", None, shape="ncenters"),
+                    lp.GlobalArg("qbmax_expansions", None,
+                        shape=("ncenters", ncoeffs)),
+                    lp.ValueArg("ncenters", np.int32),
+                    lp.ValueArg("nsources", np.int32),
+                    "..."
+                ] + gather_loopy_source_arguments([self.expansion]))
+
+        loopy_knl = lp.make_kernel(
+                [
+                    "{[itgt_center]: 0<=itgt_center<ntgt_centers}",
+                    "{[isrc_box]: isrc_box_start<=isrc_box<isrc_box_stop}",
+                    "{[isrc]: isrc_start<=isrc<isrc_end}",
+                    "{[idim]: 0<=idim<dim}",
+                    ],
+                ["""
+                for itgt_center
+                    <> tgt_icenter = global_qbx_centers[itgt_center]
+
+                    <> center[idim] = qbx_centers[idim, tgt_icenter] {dup=idim}
+                    <> rscale = qbx_expansion_radii[tgt_icenter]
+                    <> normal[idim] = \
+                            nodes_of_qbx_balls_tangency[idim, tgt_icenter//2] - \
+                            qbx_centers[idim, tgt_icenter] {dup=idim}
+
+                    <> itgt_box = qbx_center_to_target_box[tgt_icenter]
+
+                    <> isrc_box_start = source_box_starts[itgt_box]
+                    <> isrc_box_stop = source_box_starts[itgt_box+1]
+
+                    for isrc_box
+                        <> src_ibox = source_box_lists[isrc_box]
+                        <> isrc_start = box_source_starts[src_ibox]
+                        <> isrc_end = isrc_start+box_source_counts_nonchild[src_ibox]
+
+                        for isrc
+                            <> a[idim] = center[idim] - sources[idim, isrc] \
+                                    {dup=idim}
+                            """]
+                + self.get_loopy_instructions(isotropic_expansion=False) + ["""
+                        end
+                    end
+
+                    """] + [f"""
+                    qbmax_expansions[tgt_icenter, {i}] = \
+                            simul_reduce(sum, (isrc_box, isrc), \
+                                         {self.get_result_expr(i)}) \
+                            {{id_prefix=write_expn}}
+                    """ for i in range(ncoeffs)] + ["""
+
+                end
+                """],
+                arguments,
+                name=self.name, assumptions="ntgt_centers>=1",
+                silenced_warnings="write_race(write_expn*)",
+                fixed_parameters=dict(dim=self.dim,
+                    strength_count=self.strength_count),
+                lang_version=MOST_RECENT_LANGUAGE_VERSION)
+
+        loopy_knl = self.expansion.prepare_loopy_kernel(loopy_knl)
+        loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
+
+        return loopy_knl
+
+    @memoize_method
+    def get_optimized_kernel(self):
+        # FIXME
+        knl = self.get_kernel()
+        knl = lp.split_iname(knl, "itgt_center", 16, outer_tag="g.0")
+        return knl
+
+    def __call__(self, queue, **kwargs):
+        return self.get_cached_optimized_kernel()(queue, **kwargs)
+
+# }}}
+
+
 # {{{ translation from (likely, list 3) multipoles to qbx expansions
 
 class M2QBXL(E2EBase):
@@ -432,4 +540,111 @@ class QBXL2P(E2PBase):
 
 # }}}
 
+
+# {{{ evaluation of qbmax expansions
+
+class QBMAXL2P(E2PBase):
+    default_name = "qbmax_potential_from_local"
+
+    def get_cache_key(self):
+        return super().get_cache_key() + (PYTENTIAL_KERNEL_VERSION,)
+
+    def get_kernel(self):
+        ncoeffs = len(self.expansion)
+
+        self._vector_names.add("normal")
+        loopy_insns, result_names = self.get_loopy_insns_and_result_names()
+
+        # all output kernels share the same scaling at targets
+        sat_expr = self.expansion.kernel.get_scaling_expression()
+        sat = "sat * "
+
+        from sumpy.codegen import to_loopy_insns
+        sat_insns = to_loopy_insns(
+                [("sat", sat_expr)],
+                vector_names=self._vector_names,
+                pymbolic_expr_maps=[
+                    self.expansion.kernel.get_code_transformer()],
+                retain_names=["sat"],
+                complex_dtype=np.complex128)  # FIXME
+
+        loopy_knl = lp.make_kernel(
+                [
+                    "{[iglobal_center]: 0<=iglobal_center<nglobal_qbx_centers}",
+                    "{[icenter_tgt]: \
+                            icenter_tgt_start<=icenter_tgt<icenter_tgt_end}",
+                    "{[idim]: 0<=idim<dim}",
+                    ],
+                self.get_kernel_scaling_assignment() + sat_insns
+                + ["""
+                for iglobal_center
+                    <> src_icenter = global_qbx_centers[iglobal_center]
+
+                    <> icenter_tgt_start = center_to_targets_starts[src_icenter]
+                    <> icenter_tgt_end = center_to_targets_starts[src_icenter+1]
+
+                    <> center[idim] = qbx_centers[idim, src_icenter] {dup=idim}
+                    <> rscale = qbx_expansion_radii[src_icenter]
+                    <> normal[idim] = \
+                            nodes_of_qbx_balls_tangency[idim, src_icenter//2] - \
+                            qbx_centers[idim, src_icenter] {dup=idim}
+
+                    for icenter_tgt
+
+                        <> center_itgt = center_to_targets_lists[icenter_tgt]
+
+                        <> b[idim] = targets[idim, center_itgt] - center[idim]
+
+                        """] + ["""
+                        <> coeff{i} = qbmax_expansions[src_icenter, {i}]
+                        """.format(i=i) for i in range(ncoeffs)] + [
+
+                        ] + loopy_insns + ["""
+
+                        result[{i},center_itgt] = {sat} kernel_scaling \
+                                * result_{i}_p {{id_prefix=write_result}}
+                        """.format(i=i, sat=sat)
+                            for i in range(len(result_names))] + ["""
+                    end
+                end
+                """],
+                [
+                    lp.GlobalArg("result", None, shape="nresults, ntargets",
+                        dim_tags="sep,C"),
+                    lp.GlobalArg("qbx_centers", None, shape="dim, ncenters",
+                        dim_tags="sep,c"),
+                    lp.GlobalArg("nodes_of_qbx_balls_tangency", None,
+                        shape=(self.dim, "ncenters/2"), dim_tags="sep,C"),
+                    lp.GlobalArg("center_to_targets_starts,center_to_targets_lists",
+                        None, shape=None),
+                    lp.GlobalArg("qbmax_expansions", None,
+                        shape=("ncenters", ncoeffs)),
+                    lp.GlobalArg("targets", None, shape=(self.dim, "ntargets"),
+                        dim_tags="sep,C"),
+                    lp.ValueArg("ncenters,ntargets", np.int32),
+                    "..."
+                ] + [arg.loopy_arg for arg in self.expansion.get_args()],
+                name=self.name,
+                assumptions="nglobal_qbx_centers>=1",
+                silenced_warnings="write_race(write_result*)",
+                fixed_parameters=dict(dim=self.dim, nresults=len(result_names)),
+                lang_version=MOST_RECENT_LANGUAGE_VERSION)
+
+        loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
+        loopy_knl = self.expansion.prepare_loopy_kernel(loopy_knl)
+
+        return loopy_knl
+
+    @memoize_method
+    def get_optimized_kernel(self):
+        # FIXME
+        knl = self.get_kernel()
+        knl = lp.tag_inames(knl, dict(iglobal_center="g.0"))
+        return knl
+
+    def __call__(self, queue, **kwargs):
+        return self.get_cached_optimized_kernel()(queue, **kwargs)
+
+# }}}
+
 # vim: foldmethod=marker
-- 
GitLab


From b21c4d400cabdc3395dc073592d7cf2cb0fed2d4 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 30 Nov 2020 22:24:29 -0600
Subject: [PATCH 19/38] Fix residues of the name change

---
 examples/boundary-layer.py | 14 ++++++++++----
 pytential/qbx/fmmlib.py    |  4 ++--
 test/test_cost_model.py    |  4 ++--
 3 files changed, 14 insertions(+), 8 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index 9226f797..bbc7e093 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -23,12 +23,11 @@ from meshmode.discretization.connection import (
     make_refinement_connection, ChainedDiscretizationConnection)
 
 target_order = 16
-qbx_order = 3
+qbx_order = 5
 coarse_nelements = 20
 mode_nr = 3
-n_refine_cycles = 4
 
-k = 3 + 50j
+k = 10 + 100j
 
 
 class VolumeMultipoleLineLocalTaylorExpansionFactory(ExpansionFactoryBase):
@@ -50,11 +49,17 @@ def main(case="line", curve_fn=starfish, visualize=True):
 
     if case == "line":
         fmm_order = False  # cannot use FMM here
+        n_refine_cycles = 5
         expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
     elif case == "volume":
         # fmm_order = False
-        fmm_order = 3
+        fmm_order = qbx_order
         expn_factory = VolumeTaylorExpansionFactory()
+
+        if fmm_order:
+            n_refine_cycles = 10
+        else:
+            n_refine_cycles = 5
     else:
         raise ValueError
 
@@ -234,6 +239,7 @@ def main(case="line", curve_fn=starfish, visualize=True):
     from functools import partial
     inorm = partial(np.linalg.norm, ord=np.inf)
     last_diff = inorm(fs_ref[-1] - fs[-1]) / inorm(fs[-1])
+    print(f"2*pi/|k| = {2*np.pi / abs(k)}")
     print(f"Last diff = {last_diff}")
 
     # total length of the boundary curve
diff --git a/pytential/qbx/fmmlib.py b/pytential/qbx/fmmlib.py
index b169a53a..3e794996 100644
--- a/pytential/qbx/fmmlib.py
+++ b/pytential/qbx/fmmlib.py
@@ -452,12 +452,12 @@ class QBXFMMLibExpansionWrangler(FMMLibExpansionWrangler):
 
     @log_process(logger)
     @return_timing_data
-    def form_target_asymptotic_qbx_locals(self, src_weight_vecs):
+    def form_qbmax_locals(self, src_weight_vecs):
         return self.qbx_local_expansion_zeros()
 
     @log_process(logger)
     @return_timing_data
-    def eval_target_asymptotic_qbx_locals(self, qbmax_expansions):
+    def eval_qbmax_locals(self, qbmax_expansions):
         return self.full_output_zeros()
 
     @log_process(logger)
diff --git a/test/test_cost_model.py b/test/test_cost_model.py
index 0b2de25f..003c280b 100644
--- a/test/test_cost_model.py
+++ b/test/test_cost_model.py
@@ -656,7 +656,7 @@ class ConstantOneQBXExpansionWrangler(ConstantOneExpansionWrangler):
 
         return pot, self.timing_future(ops)
 
-    def form_target_asymptotic_qbx_locals(self, src_weight_vecs):
+    def form_qbmax_locals(self, src_weight_vecs):
         ta_local_exps = self.qbx_local_expansion_zeros()
         ops = 0
 
@@ -665,7 +665,7 @@ class ConstantOneQBXExpansionWrangler(ConstantOneExpansionWrangler):
 
         raise NotImplementedError
 
-    def eval_target_asymptotic_qbx_locals(self, taqbx_expansions):
+    def eval_qbmax_locals(self, taqbx_expansions):
         pot = self.full_output_zeros()
         ops = 0
 
-- 
GitLab


From 1ae0f13b00dccba3249d3bf5b564169534ad755b Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 7 Dec 2020 17:35:04 -0600
Subject: [PATCH 20/38] Refactor to make room for kernel derivatives

---
 examples/boundary-layer.py |  31 ++---
 pytential/qbx/__init__.py  | 272 +++++--------------------------------
 pytential/qbx/direct.py    |   2 +-
 pytential/qbx/geometry.py  |   9 +-
 4 files changed, 59 insertions(+), 255 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index bbc7e093..fa690c5f 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -13,7 +13,8 @@ if enable_mayavi:
 import numpy as np
 import pyopencl as cl
 from sumpy.expansion import ExpansionFactoryBase, VolumeTaylorExpansionFactory
-from sumpy.kernel import one_kernel_2d, LaplaceKernel, HelmholtzKernel  # noqa
+from sumpy.kernel import (
+    LaplaceKernel, HelmholtzKernel, AsymptoticallyInformedKernel)
 
 from pytential import bind, sym
 
@@ -52,8 +53,8 @@ def main(case="line", curve_fn=starfish, visualize=True):
         n_refine_cycles = 5
         expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
     elif case == "volume":
-        # fmm_order = False
-        fmm_order = qbx_order
+        fmm_order = False
+        # fmm_order = qbx_order
         expn_factory = VolumeTaylorExpansionFactory()
 
         if fmm_order:
@@ -109,12 +110,11 @@ def main(case="line", curve_fn=starfish, visualize=True):
         InterpolatoryQuadratureSimplexGroupFactory(target_order))
     previous_discr = base_density_discr
 
-    from pytential.qbx import QBXLayerPotentialAsymptotics
     import sympy as sp
     dist = sp.Symbol("dist")
     k_sym = sp.Symbol("k")
     expr = sp.exp(1j * k_sym * dist)
-    asmt = QBXLayerPotentialAsymptotics(2, kernel, expr=expr)
+    asymp_kernel = AsymptoticallyInformedKernel(kernel, expr)
 
     def op(**kwargs):
         kwargs.update(kernel_kwargs)
@@ -122,6 +122,10 @@ def main(case="line", curve_fn=starfish, visualize=True):
         # return sym.D(kernel, sym.var("sigma"), **kwargs)
         return sym.S(kernel, sym.var("sigma"), **kwargs)
 
+    def op_asymp(**kwargs):
+        kwargs.update(kernel_kwargs)
+        return sym.S(asymp_kernel, sym.var("sigma"), **kwargs)
+
     conns = []
     ns = []
     flds = []
@@ -141,23 +145,18 @@ def main(case="line", curve_fn=starfish, visualize=True):
                 InterpolatoryQuadratureSimplexGroupFactory(target_order)))
         ns.append(pre_density_discr.ndofs)
 
+        # by default, qbmax will be used whenever possible
+        # (have asymptotic information for the out kernels)
         qbx = QBXLayerPotentialSource(
             pre_density_discr, 4*target_order, qbx_order,
             fmm_order=fmm_order,
             target_association_tolerance=0.005,
-            _target_asymptotics=asmt,
             expansion_factory=expn_factory)
 
-        # If expansion_factory is not set, default expansion is H2DLocal which
-        # yields comparable results to Taylor.
-        qbx_ref = QBXLayerPotentialSource(
-            pre_density_discr, 4*target_order, qbx_order,
-            fmm_order=fmm_order,
-            target_association_tolerance=0.005,
-            expansion_factory=expn_factory)
+        # to disable qbmax explicitly
+        qbx_ref = qbx.copy(_use_qbmax=False)
 
         from pytential import GeometryCollection
-
         if case == "line":
             places = GeometryCollection({"qbx": qbx}, auto_where="qbx")
             places_ref = GeometryCollection({"qbx": qbx_ref}, auto_where="qbx")
@@ -187,7 +186,7 @@ def main(case="line", curve_fn=starfish, visualize=True):
 
         if case == "line":
             fld = bind(
-                places, op(source="qbx", qbx_forced_limit=-1))(
+                places, op_asymp(source="qbx", qbx_forced_limit=-1))(
                     actx, sigma=sigma, k=k_val)
             fld_ref = bind(
                 places_ref, op(source="qbx", qbx_forced_limit=-1))(
@@ -198,7 +197,7 @@ def main(case="line", curve_fn=starfish, visualize=True):
             flds_ref.append(fld_ref)
 
         elif case == "volume":
-            fld = bind(places, op(
+            fld = bind(places, op_asymp(
                 source="qbx", target="targets", qbx_forced_limit=None))(
                     actx, sigma=sigma, k=k_val)
             fld_ref = bind(places_ref, op(
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index cf4c4dcf..07bdefb0 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -39,8 +39,6 @@ logger = logging.getLogger(__name__)
 __doc__ = """
 .. autoclass:: QBXLayerPotentialSource
 
-.. autoclass:: QBXLayerPotentialAsymptotics
-
 .. autoclass:: QBXTargetAssociationFailedException
 """
 
@@ -87,7 +85,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             _from_sep_smaller_min_nsources_cumul=None,
             _tree_kind="adaptive",
             _use_target_specific_qbx=None,
-            _target_asymptotics=None,
+            _use_qbmax=None,
             geometry_data_inspector=None,
             cost_model=None,
             fmm_backend="sumpy",
@@ -112,10 +110,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         :arg cost_model: Either *None* or an object implementing the
              :class:`~pytential.qbx.cost.AbstractQBXCostModel` interface, used for
              gathering modeled costs if provided (experimental)
-        :arg _target_asymptotics: Either *None* or an object implementing the
-             :class:`~pytential.qbx.QBXLayerPotentialAsymptotics` interface, used for
-             enabling QBMAX. It stores the asymptotic information about layer
-             potential of the "main" kernel (the one used for FMM).
+        :arg _use_qbmax: Whether to use QBMAX. *None* means "use if possible"
         """
 
         # {{{ argument processing
@@ -215,7 +210,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 _from_sep_smaller_min_nsources_cumul
         self._tree_kind = _tree_kind
         self._use_target_specific_qbx = _use_target_specific_qbx
-        self._target_asymptotics = _target_asymptotics
+        self._use_qbmax = _use_qbmax
         self.geometry_data_inspector = geometry_data_inspector
 
         if cost_model is None:
@@ -245,7 +240,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             _from_sep_smaller_crit=None,
             _tree_kind=None,
             _use_target_specific_qbx=_not_provided,
-            _target_asymptotics=_not_provided,
+            _use_qbmax=_not_provided,
             geometry_data_inspector=None,
             cost_model=_not_provided,
             fmm_backend=None,
@@ -332,10 +327,10 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 _use_target_specific_qbx=(_use_target_specific_qbx
                     if _use_target_specific_qbx is not _not_provided
                     else self._use_target_specific_qbx),
-                _target_asymptotics=(
-                    self._target_asymptotics
-                    if _target_asymptotics is _not_provided
-                    else _target_asymptotics),
+                _use_qbmax=(
+                    self._use_qbmax
+                    if _use_qbmax is _not_provided
+                    else _use_qbmax),
                 geometry_data_inspector=(
                     geometry_data_inspector or self.geometry_data_inspector),
                 cost_model=(
@@ -543,6 +538,8 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         local_expn_class = \
                 self.expansion_factory.get_local_expansion_class(fmm_kernel)
 
+        import pudb; pu.db
+
         from functools import partial
         fmm_mpole_factory = partial(mpole_expn_class, fmm_kernel)
         fmm_local_factory = partial(local_expn_class, fmm_kernel)
@@ -552,7 +549,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             from pytential.qbx.fmm import \
                     QBXSumpyExpansionWranglerCodeContainer
 
-            if self._target_asymptotics:
+            if self._use_qbmax:
                 fmm_kernel_tascaled = \
                     self._target_asymptotics.get_rescaled_kernel(local_expn_class)
                 qbmax_local_factory = partial(local_expn_class, fmm_kernel_tascaled)
@@ -566,7 +563,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
 
         elif self.fmm_backend == "fmmlib":
 
-            if self._target_asymptotics:
+            if self._use_qbmax:
                 raise ValueError("QBMAX is not implemented in fmmlib")
 
             from pytential.qbx.fmmlib import \
@@ -716,13 +713,15 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             value_dtype = self.density_discr.real_dtype
 
         from sumpy.expansion.local import LineTaylorLocalExpansion
-        if self._target_asymptotics:
-            if len(kernels) > 1:
-                raise ValueError("direct evaluation with asymptotic rescaling "
-                                 "only supports one output kernel at a time")
-            else:
-                kernels = [self._target_asymptotics.get_rescaled_kernel(
-                    LineTaylorLocalExpansion)]
+        from sumpy.kernel import AsymptoticallyInformedKernel
+        if self._use_qbmax:
+            for knl in kernels:
+                assert isinstance(knl, AsymptoticallyInformedKernel)
+                knl.set_expansion_class(LineTaylorLocalExpansion)
+        elif self._use_qbmax is None:
+            for knl in kernels:
+                if isinstance(knl, AsymptoticallyInformedKernel):
+                    knl.set_expansion_class(LineTaylorLocalExpansion)
 
         from sumpy.qbx import LayerPotential
         return LayerPotential(
@@ -741,13 +740,15 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             value_dtype = self.density_discr.real_dtype
 
         from sumpy.expansion.local import VolumeTaylorLocalExpansion
-        if self._target_asymptotics:
-            if len(kernels) > 1:
-                raise ValueError("direct evaluation with asymptotic rescaling "
-                                 "only supports one output kernel at a time")
-            else:
-                kernels = [self._target_asymptotics.get_rescaled_kernel(
-                    VolumeTaylorLocalExpansion)]
+        from sumpy.kernel import AsymptoticallyInformedKernel
+        if self._use_qbmax:
+            for knl in kernels:
+                assert isinstance(knl, AsymptoticallyInformedKernel)
+                knl.set_expansion_class(VolumeTaylorLocalExpansion)
+        elif self._use_qbmax is None:
+            for knl in kernels:
+                if isinstance(knl, AsymptoticallyInformedKernel):
+                    knl.set_expansion_class(VolumeTaylorLocalExpansion)
 
         from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         return LayerPotentialOnTargetAndCenterSubset(
@@ -896,7 +897,11 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 for i, res_i in enumerate(output_for_each_kernel):
                     tgt_subset_kwargs[f"result_{i}"] = res_i
 
-                if self._target_asymptotics:
+                from sumpy.kernel import AsymptoticallyInformedKernel
+                if self._use_qbmax or (
+                    self._use_qbmax is None and any([
+                        isinstance(knl, AsymptoticallyInformedKernel)
+                        for knl in insn.kernels])):
                     qbmax_extra_kwargs = {
                         "nodes_of_qbx_balls_tangency": geo_data.flat_stage1_nodes()
                     }
@@ -931,217 +936,10 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
 # }}}
 
 
-# {{{ QBX layer potential asymptotics
-
-class QBXLayerPotentialAsymptotics:
-    """Asymptotic behavior of a layer potential near its source. The class
-    provides a symbolic description of the near-surface asymptotic behavior of
-    the layer potential and properly dispatch it to different expansion
-    classes.
-
-    The main use of this class is to make :class:
-    `sumpy.kernel.AsymptoticallyRescaledKernel` objects. The rescaled kernels
-    depend on expansion methods. This class tries to isolate mathematical
-    asymptotic expansions that depend solely on the kernel and domain geometry.
-
-    .. attribute :: dim
-
-       The dimension of the ambient space.
-
-    .. attribute :: kernel
-
-       The potential kernel. A :class:`~sumpy.kernel.Kernel` object.
-
-    .. attribute :: expr
-
-       The asymptotic expansions. A scalar expression that depends on distance
-       from the boundary (denoted by the symbol "dist"), satisfying the
-       normalizing condition:
-
-         expr(dist=0) = 1
-
-    .. attribute :: geometric_order
-
-       Order of geometric approximation when computing the distance to
-       boundary.
-    """
-
-    def __init__(self, dim, kernel, expr, geometric_order=1):
-        self.dim = dim
-        self.kernel = kernel
-        self.expr = expr
-        self.geometric_order = geometric_order
-
-    @memoize_method
-    def get_rescaled_kernel(self, expn_class):
-        """Return a :mod:`sumpy` kernel with the rescaled expression.
-        """
-        resd_expr = self._get_rescaled_kernel_expr(expn_class)
-        base_kernel = self.kernel
-        scaling = self._get_scaling_at_target(expn_class)
-
-        from pymbolic.interop.sympy import SympyToPymbolicMapper
-        resd_expr = SympyToPymbolicMapper()(resd_expr)
-        scaling = SympyToPymbolicMapper()(scaling)
-
-        from sumpy.kernel import AsymptoticallyRescaledKernel
-        return AsymptoticallyRescaledKernel(base_kernel, resd_expr, scaling)
-
-    @memoize_method
-    def _get_scaling_at_target(self, expn_class):
-        """Target-dependent scaling expression, used for scaling back the
-        potential after summing up the expansion.
-        """
-        full_scaling = self._get_scaling_for_expansion(expn_class)
-
-        from sumpy.expansion.local import (
-            LineTaylorLocalExpansion, VolumeTaylorLocalExpansionBase)
-        if issubclass(expn_class, LineTaylorLocalExpansion):
-            sym_map = {sym.sym.Symbol("tau"): 1}  # target is at tau=1
-        elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
-            sym_map = {}
-        else:
-            raise ValueError("unsupported expansion class")
-
-        return full_scaling.subs(sym_map)
-
-    @memoize_method
-    def _get_scaling_for_expansion(self, expn_class):
-        """Target-dependent scaling expression, including the virtual variables
-        like "tau" for taking expansions.
-        """
-        sym_map = self._get_symbol_map(expn_class)
-        expr_h = self._approximate_expr()
-        scaling = expr_h.subs(sym_map)
-        return scaling
-
-    @memoize_method
-    def _get_rescaled_kernel_expr(self, expn_class):
-        """Apply scaling to the kernel expression.
-        """
-        kernel_expr = self._get_kernel_expression_at_source(expn_class)
-        scaling = self._get_scaling_for_expansion(expn_class)
-        return kernel_expr / scaling
-
-    @memoize_method
-    def _approximate_expr(self):
-        """Transform the expression by approximating the distance with
-        geometric information known to the QBX routine.
-        """
-        normal, target, dist, rad = (
-            self._nvec, self._tvec, self._dist, self._radius)
-
-        if self.geometric_order == 1:
-            dist_approx = rad - normal.dot(target)
-        else:
-            # need curvature information for higher order approximations
-            raise NotImplementedError
-
-        return self.expr.subs(dist, dist_approx)
-
-    @memoize_method
-    def _get_symbol_map(self, expn_class):
-        """Get interpretation of ``nvec`` and ``tvec`` that depends on the
-        expansion class.
-        """
-        from sumpy.expansion.local import (
-            LineTaylorLocalExpansion, VolumeTaylorLocalExpansionBase)
-
-        bvec = sym.make_sym_vector("b", self.dim)
-
-        if issubclass(expn_class, LineTaylorLocalExpansion):
-            # in a line expansion, bvec is the normal, and the actual target is
-            # identified with tau.
-
-            bvec_norm = sym.sym.sqrt(bvec.dot(bvec))
-            sym_map = {
-                self._radius: bvec_norm
-            }
-
-            # self._nvec: bvec / bvec_norm
-            for lhs, rhs in zip(self._nvec, bvec):
-                sym_map[lhs] = rhs / bvec_norm
-
-            # self._tvec: sym.Symbol("tau") * bvec
-            for lhs, rhs in zip(self._tvec, bvec):
-                sym_map[lhs] = sym.sym.Symbol("tau") * rhs
-
-        elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
-            sym_map = {
-                # disk radius is used as rscale
-                self._radius: sym.sym.Symbol("rscale"),
-            }
-
-            # self._nvec: normal / norm(normal)
-            normal = sym.make_sym_vector("normal", self.dim)
-            normal_norm = sym.sym.sqrt(normal.dot(normal))
-            for lhs, rhs in zip(self._nvec, normal):
-                sym_map[lhs] = rhs / normal_norm
-
-            # self._tvec: bvec
-            for lhs, rhs in zip(self._tvec, bvec):
-                sym_map[lhs] = rhs
-
-        else:
-            raise ValueError("unsupported expansion class")
-
-        return sym_map
-
-    @memoize_method
-    def _get_kernel_expression_at_source(self, expn_class):
-        """Kernel expression used by ``coefficients_from_source``.
-        """
-        from sumpy.expansion.local import (
-            LineTaylorLocalExpansion, VolumeTaylorLocalExpansionBase)
-
-        avec = sym.make_sym_vector("a", self.dim)
-        bvec = sym.make_sym_vector("b", self.dim)
-
-        if issubclass(expn_class, LineTaylorLocalExpansion):
-            tau = sym.sym.Symbol("tau")
-            avec_line = avec + tau*bvec
-            return self.kernel.get_expression(avec_line)
-        elif issubclass(expn_class, VolumeTaylorLocalExpansionBase):
-            rad = avec + bvec
-            return self.kernel.postprocess_at_source(
-                self.kernel.get_expression(rad), avec)
-        else:
-            raise ValueError(
-                f"unsupported expansion class for QBMAX: {expn_class.__name__}")
-
-    @property
-    def _dist(self):
-        """The distance of the target point from the boundary.
-        """
-        return sym.sym.Symbol("dist")
-
-    @property
-    def _nvec(self):
-        """The unit normal vector obtained by normalizing the vector from the
-        QBX expansion center to the point of tangency.
-        """
-        return sym.make_sym_vector("nvec", self.dim)
-
-    @property
-    def _tvec(self):
-        """The vector from the QBX expansion center to the evaluation target
-        point.
-        """
-        return sym.make_sym_vector("tvec", self.dim)
-
-    @property
-    def _radius(self):
-        """Radius of the QBX disk, aka distance of the expansion center from
-        the boundary.
-        """
-        return sym.sym.Symbol("radius")
-
-# }}}
 
 
 __all__ = (
         "QBXLayerPotentialSource",
-        "QBXLayerPotentialAsymptotics",
         "QBXTargetAssociationFailedException",
         )
 
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 53fcd83b..4594a186 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -82,7 +82,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 knl = self.expansions[iknl]
 
             try:
-                sat_expr = knl.get_scaling_expression()
+                sat_expr = knl.get_scaling_expression(None)
             except AttributeError:
                 sat_expr = None
 
diff --git a/pytential/qbx/geometry.py b/pytential/qbx/geometry.py
index b19537b8..613e2674 100644
--- a/pytential/qbx/geometry.py
+++ b/pytential/qbx/geometry.py
@@ -566,7 +566,14 @@ class QBXFMMGeometryData(FMMLibRotationDataInterface):
         if lpot_source._expansions_in_tree_have_extent:
             target_radii = cl.array.zeros(queue, target_info.ntargets,
                     self.coord_dtype)
-            target_radii[:self.ncenters] = self.flat_expansion_radii()
+            if 0:
+                target_radii[:self.ncenters] = cl.array.maximum(
+                    self.flat_expansion_radii().with_queue(queue),
+                    cl.array.zeros(queue, (self.ncenters,), self.coord_dtype) + 0.06 * 2
+                ).with_queue(None)
+                # target_radii[:self.ncenters] *= 2.0
+            else:
+                target_radii[:self.ncenters] = self.flat_expansion_radii()
 
         refine_weights = cl.array.empty(queue, nparticles, dtype=np.int32)
 
-- 
GitLab


From efde32a27f2dbd4f372a770d64c3d7d36daaf94c Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 7 Dec 2020 21:08:43 -0600
Subject: [PATCH 21/38] More fixes

---
 examples/boundary-layer.py    | 13 +++++++------
 pytential/qbx/__init__.py     | 16 ++++++----------
 pytential/qbx/geometry.py     |  9 +--------
 pytential/qbx/interactions.py | 21 ++++++++++-----------
 4 files changed, 24 insertions(+), 35 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index fa690c5f..b736114a 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -53,12 +53,12 @@ def main(case="line", curve_fn=starfish, visualize=True):
         n_refine_cycles = 5
         expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
     elif case == "volume":
-        fmm_order = False
-        # fmm_order = qbx_order
+        # fmm_order = False
+        fmm_order = qbx_order
         expn_factory = VolumeTaylorExpansionFactory()
 
         if fmm_order:
-            n_refine_cycles = 10
+            n_refine_cycles = 7
         else:
             n_refine_cycles = 5
     else:
@@ -119,12 +119,13 @@ def main(case="line", curve_fn=starfish, visualize=True):
     def op(**kwargs):
         kwargs.update(kernel_kwargs)
         # op = sym.d_dx(sym.S(kernel, sym.var("sigma"), **kwargs))
-        # return sym.D(kernel, sym.var("sigma"), **kwargs)
-        return sym.S(kernel, sym.var("sigma"), **kwargs)
+        return sym.D(kernel, sym.var("sigma"), **kwargs)
+        # return sym.S(kernel, sym.var("sigma"), **kwargs)
 
     def op_asymp(**kwargs):
         kwargs.update(kernel_kwargs)
-        return sym.S(asymp_kernel, sym.var("sigma"), **kwargs)
+        return sym.D(asymp_kernel, sym.var("sigma"), **kwargs)
+        # return sym.S(asymp_kernel, sym.var("sigma"), **kwargs)
 
     conns = []
     ns = []
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 07bdefb0..5f9480a4 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -28,8 +28,6 @@ from pytools import memoize_method, memoize_in
 from pytential.qbx.target_assoc import QBXTargetAssociationFailedException
 from pytential.source import LayerPotentialSourceBase
 
-import sumpy.symbolic as sym
-
 import pyopencl as cl
 
 import logging
@@ -538,8 +536,6 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         local_expn_class = \
                 self.expansion_factory.get_local_expansion_class(fmm_kernel)
 
-        import pudb; pu.db
-
         from functools import partial
         fmm_mpole_factory = partial(mpole_expn_class, fmm_kernel)
         fmm_local_factory = partial(local_expn_class, fmm_kernel)
@@ -549,10 +545,12 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             from pytential.qbx.fmm import \
                     QBXSumpyExpansionWranglerCodeContainer
 
-            if self._use_qbmax:
-                fmm_kernel_tascaled = \
-                    self._target_asymptotics.get_rescaled_kernel(local_expn_class)
-                qbmax_local_factory = partial(local_expn_class, fmm_kernel_tascaled)
+            from sumpy.kernel import AsymptoticallyInformedKernel
+            if self._use_qbmax or (
+                self._use_qbmax is None
+                    and isinstance(fmm_kernel, AsymptoticallyInformedKernel)):
+                qbmax_local_factory = partial(local_expn_class, fmm_kernel)
+                fmm_kernel.set_expansion_class(local_expn_class)
             else:
                 qbmax_local_factory = None
 
@@ -936,8 +934,6 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
 # }}}
 
 
-
-
 __all__ = (
         "QBXLayerPotentialSource",
         "QBXTargetAssociationFailedException",
diff --git a/pytential/qbx/geometry.py b/pytential/qbx/geometry.py
index 613e2674..b19537b8 100644
--- a/pytential/qbx/geometry.py
+++ b/pytential/qbx/geometry.py
@@ -566,14 +566,7 @@ class QBXFMMGeometryData(FMMLibRotationDataInterface):
         if lpot_source._expansions_in_tree_have_extent:
             target_radii = cl.array.zeros(queue, target_info.ntargets,
                     self.coord_dtype)
-            if 0:
-                target_radii[:self.ncenters] = cl.array.maximum(
-                    self.flat_expansion_radii().with_queue(queue),
-                    cl.array.zeros(queue, (self.ncenters,), self.coord_dtype) + 0.06 * 2
-                ).with_queue(None)
-                # target_radii[:self.ncenters] *= 2.0
-            else:
-                target_radii[:self.ncenters] = self.flat_expansion_radii()
+            target_radii[:self.ncenters] = self.flat_expansion_radii()
 
         refine_weights = cl.array.empty(queue, nparticles, dtype=np.int32)
 
diff --git a/pytential/qbx/interactions.py b/pytential/qbx/interactions.py
index 6ddfc424..d0f1c2a7 100644
--- a/pytential/qbx/interactions.py
+++ b/pytential/qbx/interactions.py
@@ -228,7 +228,6 @@ class P2QBMAXLFromCSR(P2EBase):
 
     @memoize_method
     def get_optimized_kernel(self):
-        # FIXME
         knl = self.get_kernel()
         knl = lp.split_iname(knl, "itgt_center", 16, outer_tag="g.0")
         return knl
@@ -555,18 +554,19 @@ class QBMAXL2P(E2PBase):
         self._vector_names.add("normal")
         loopy_insns, result_names = self.get_loopy_insns_and_result_names()
 
-        # all output kernels share the same scaling at targets
-        sat_expr = self.expansion.kernel.get_scaling_expression()
-        sat = "sat * "
+        sat_exprs = [knl.get_scaling_expression(None, type(self.expansion))
+                     for knl in self.kernels]
+        sats = [f"sat{i} * " for i in range(len(result_names))]
+        sat_names = [f"sat{i}" for i in range(len(result_names))]
 
         from sumpy.codegen import to_loopy_insns
         sat_insns = to_loopy_insns(
-                [("sat", sat_expr)],
+                [(sn, se) for sn, se in zip(sat_names, sat_exprs)],
                 vector_names=self._vector_names,
-                pymbolic_expr_maps=[
-                    self.expansion.kernel.get_code_transformer()],
-                retain_names=["sat"],
-                complex_dtype=np.complex128)  # FIXME
+                pymbolic_expr_maps=[knl.get_code_transformer()
+                                    for knl in self.kernels],
+                retain_names=sat_names,
+                complex_dtype=np.complex128)
 
         loopy_knl = lp.make_kernel(
                 [
@@ -603,7 +603,7 @@ class QBMAXL2P(E2PBase):
 
                         result[{i},center_itgt] = {sat} kernel_scaling \
                                 * result_{i}_p {{id_prefix=write_result}}
-                        """.format(i=i, sat=sat)
+                        """.format(i=i, sat=sats[i])
                             for i in range(len(result_names))] + ["""
                     end
                 end
@@ -637,7 +637,6 @@ class QBMAXL2P(E2PBase):
 
     @memoize_method
     def get_optimized_kernel(self):
-        # FIXME
         knl = self.get_kernel()
         knl = lp.tag_inames(knl, dict(iglobal_center="g.0"))
         return knl
-- 
GitLab


From ba1338775828fb6d37705a24cf48f70661cf9ce7 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 7 Dec 2020 21:12:15 -0600
Subject: [PATCH 22/38] More fixes

---
 pytential/qbx/fmm.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index a81ad2ed..fa4afbb4 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -283,6 +283,8 @@ non_qbx_box_target_lists`),
         kwargs.update(self.box_source_list_kwargs())
 
         p2qbmaxl = self.code.p2qbmaxl(self.qbx_order)
+        print(p2qbmaxl.get_kernel())
+        1/0
 
         evt, (result,) = p2qbmaxl(
                 self.queue,
-- 
GitLab


From 792e14ab8092e089fd0f3cb0cef01e4ac652d596 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 7 Dec 2020 21:44:50 -0600
Subject: [PATCH 23/38] Remove debugging widget

---
 pytential/qbx/fmm.py | 2 --
 1 file changed, 2 deletions(-)

diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index fa4afbb4..a81ad2ed 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -283,8 +283,6 @@ non_qbx_box_target_lists`),
         kwargs.update(self.box_source_list_kwargs())
 
         p2qbmaxl = self.code.p2qbmaxl(self.qbx_order)
-        print(p2qbmaxl.get_kernel())
-        1/0
 
         evt, (result,) = p2qbmaxl(
                 self.queue,
-- 
GitLab


From 8a66070e5d1f339aa3c1a3ee5e19def03c989646 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 14 Dec 2020 14:24:12 -0600
Subject: [PATCH 24/38] Refactoring in preparation for target derivatives

---
 examples/boundary-layer.py | 39 +++++++++++++++++++++-----------------
 pytential/qbx/__init__.py  | 37 ++++++++++++++----------------------
 pytential/qbx/direct.py    |  5 ++++-
 3 files changed, 40 insertions(+), 41 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index b736114a..d15a34b0 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -1,9 +1,11 @@
 # Cases:
-# - "Line": use line Taylor expansion to compute on-surface.  Using LineTaylor
+# - "line": use line Taylor expansion to compute on-surface.  Using LineTaylor
 #   for local expansion (must force direct evaluation because cannot translate
 #   from VolumeTaylor to LineTaylor)
 #
-# - "Volume": use volume Taylor expansion to compute anywhere.
+# - "volume": use volume Taylor expansion to compute anywhere. FMM is used.
+#
+# - "volume-direct": like the volume case, but with direct evaluation.
 #
 
 enable_mayavi = 0
@@ -52,9 +54,11 @@ def main(case="line", curve_fn=starfish, visualize=True):
         fmm_order = False  # cannot use FMM here
         n_refine_cycles = 5
         expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
-    elif case == "volume":
-        # fmm_order = False
-        fmm_order = qbx_order
+    elif case[:6] == "volume":
+        if case[6:] == "-direct":
+            fmm_order = False
+        else:
+            fmm_order = qbx_order
         expn_factory = VolumeTaylorExpansionFactory()
 
         if fmm_order:
@@ -74,7 +78,7 @@ def main(case="line", curve_fn=starfish, visualize=True):
             target_order)
     refiner = RefinerWithoutAdjacency(base_mesh)
 
-    if case == "volume":
+    if case[:6] == "volume":
         from pytential.target import PointsTarget
         if 1:
             # in the volume
@@ -118,13 +122,14 @@ def main(case="line", curve_fn=starfish, visualize=True):
 
     def op(**kwargs):
         kwargs.update(kernel_kwargs)
-        # op = sym.d_dx(sym.S(kernel, sym.var("sigma"), **kwargs))
-        return sym.D(kernel, sym.var("sigma"), **kwargs)
+        return sym.d_dx(ambient_dim=2, operand=sym.S(kernel, sym.var("sigma"), **kwargs))
+        # return sym.D(kernel, sym.var("sigma"), **kwargs)
         # return sym.S(kernel, sym.var("sigma"), **kwargs)
 
     def op_asymp(**kwargs):
         kwargs.update(kernel_kwargs)
-        return sym.D(asymp_kernel, sym.var("sigma"), **kwargs)
+        return sym.d_dx(ambient_dim=2, operand=sym.S(asymp_kernel, sym.var("sigma"), **kwargs))
+        # return sym.D(asymp_kernel, sym.var("sigma"), **kwargs)
         # return sym.S(asymp_kernel, sym.var("sigma"), **kwargs)
 
     conns = []
@@ -161,7 +166,7 @@ def main(case="line", curve_fn=starfish, visualize=True):
         if case == "line":
             places = GeometryCollection({"qbx": qbx}, auto_where="qbx")
             places_ref = GeometryCollection({"qbx": qbx_ref}, auto_where="qbx")
-        elif case == "volume":
+        elif case[:6] == "volume":
             places = GeometryCollection({
                 "qbx": qbx, "targets": PointsTarget(targets_dev),
             }, auto_where="qbx")
@@ -186,22 +191,22 @@ def main(case="line", curve_fn=starfish, visualize=True):
             k_val = np.float64(k)
 
         if case == "line":
-            fld = bind(
-                places, op_asymp(source="qbx", qbx_forced_limit=-1))(
-                    actx, sigma=sigma, k=k_val)
             fld_ref = bind(
                 places_ref, op(source="qbx", qbx_forced_limit=-1))(
                     actx, sigma=sigma, k=k_val)
+            fld = bind(
+                places, op_asymp(source="qbx", qbx_forced_limit=-1))(
+                    actx, sigma=sigma, k=k_val)
 
             # DoFArray
             flds.append(fld)
             flds_ref.append(fld_ref)
 
-        elif case == "volume":
-            fld = bind(places, op_asymp(
+        elif case[:6] == "volume":
+            fld_ref = bind(places_ref, op(
                 source="qbx", target="targets", qbx_forced_limit=None))(
                     actx, sigma=sigma, k=k_val)
-            fld_ref = bind(places_ref, op(
+            fld = bind(places, op_asymp(
                 source="qbx", target="targets", qbx_forced_limit=None))(
                     actx, sigma=sigma, k=k_val)
 
@@ -230,7 +235,7 @@ def main(case="line", curve_fn=starfish, visualize=True):
                     flds[iexp])))
                 fs_ref.append(actx.to_numpy(flatten(
                     flds_ref[iexp])))
-    elif case == "volume":
+    elif case[:6] == "volume":
         fs = flds
         fs_ref = flds_ref
     else:
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 5f9480a4..28b5eeb5 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -546,11 +546,12 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                     QBXSumpyExpansionWranglerCodeContainer
 
             from sumpy.kernel import AsymptoticallyInformedKernel
+            # assuming fmm_kernel does not have target derivatives
             if self._use_qbmax or (
                 self._use_qbmax is None
                     and isinstance(fmm_kernel, AsymptoticallyInformedKernel)):
+                fmm_kernel = fmm_kernel.replace_expansion_class(local_expn_class)
                 qbmax_local_factory = partial(local_expn_class, fmm_kernel)
-                fmm_kernel.set_expansion_class(local_expn_class)
             else:
                 qbmax_local_factory = None
 
@@ -711,20 +712,14 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             value_dtype = self.density_discr.real_dtype
 
         from sumpy.expansion.local import LineTaylorLocalExpansion
-        from sumpy.kernel import AsymptoticallyInformedKernel
-        if self._use_qbmax:
-            for knl in kernels:
-                assert isinstance(knl, AsymptoticallyInformedKernel)
-                knl.set_expansion_class(LineTaylorLocalExpansion)
-        elif self._use_qbmax is None:
-            for knl in kernels:
-                if isinstance(knl, AsymptoticallyInformedKernel):
-                    knl.set_expansion_class(LineTaylorLocalExpansion)
+        from sumpy.kernel import AsymptoticallyInformedKernel, ExpaniosnClassReplacer
+        ecr = ExpaniosnClassReplacer(LineTaylorLocalExpansion)
+        kwe = [ecr(knl) for knl in kernels]
 
         from sumpy.qbx import LayerPotential
         return LayerPotential(
             self.cl_context,
-            [LineTaylorLocalExpansion(knl, self.qbx_order) for knl in kernels],
+            [LineTaylorLocalExpansion(knl, self.qbx_order) for knl in kwe],
             value_dtypes=value_dtype)
 
     @memoize_method
@@ -738,20 +733,14 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             value_dtype = self.density_discr.real_dtype
 
         from sumpy.expansion.local import VolumeTaylorLocalExpansion
-        from sumpy.kernel import AsymptoticallyInformedKernel
-        if self._use_qbmax:
-            for knl in kernels:
-                assert isinstance(knl, AsymptoticallyInformedKernel)
-                knl.set_expansion_class(VolumeTaylorLocalExpansion)
-        elif self._use_qbmax is None:
-            for knl in kernels:
-                if isinstance(knl, AsymptoticallyInformedKernel):
-                    knl.set_expansion_class(VolumeTaylorLocalExpansion)
+        from sumpy.kernel import AsymptoticallyInformedKernel, ExpaniosnClassReplacer
+        ecr = ExpaniosnClassReplacer(VolumeTaylorLocalExpansion)
+        kwe = [ecr(knl) for knl in kernels]
 
         from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         return LayerPotentialOnTargetAndCenterSubset(
             self.cl_context,
-            [VolumeTaylorLocalExpansion(knl, self.qbx_order) for knl in kernels],
+            [VolumeTaylorLocalExpansion(knl, self.qbx_order) for knl in kwe],
             value_dtypes=value_dtype)
 
     @memoize_method
@@ -895,10 +884,12 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 for i, res_i in enumerate(output_for_each_kernel):
                     tgt_subset_kwargs[f"result_{i}"] = res_i
 
-                from sumpy.kernel import AsymptoticallyInformedKernel
+                from sumpy.kernel import (AsymptoticallyInformedKernel,
+                                          TargetDerivativeRemover)
+                tdr = TargetDerivativeRemover()
                 if self._use_qbmax or (
                     self._use_qbmax is None and any([
-                        isinstance(knl, AsymptoticallyInformedKernel)
+                        isinstance(tdr(knl), AsymptoticallyInformedKernel)
                         for knl in insn.kernels])):
                     qbmax_extra_kwargs = {
                         "nodes_of_qbx_balls_tangency": geo_data.flat_stage1_nodes()
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 4594a186..c6462c98 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -81,8 +81,11 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 assert isinstance(self.expansions[iknl], Kernel)
                 knl = self.expansions[iknl]
 
+            from sumpy.kernel import TargetDerivativeRemover
+            tdr = TargetDerivativeRemover()
             try:
-                sat_expr = knl.get_scaling_expression(None)
+                raw_knl = tdr(knl)
+                sat_expr = raw_knl.get_scaling_expression(None)
             except AttributeError:
                 sat_expr = None
 
-- 
GitLab


From 858cf9a404c7f6b0f8813e6bbc2ce685c1e375cd Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 5 Jul 2021 15:27:03 -0500
Subject: [PATCH 25/38] QBMAX fixes

---
 pytential/qbx/__init__.py | 34 ++++++++++++++++++++++++----------
 pytential/qbx/direct.py   | 18 ++----------------
 2 files changed, 26 insertions(+), 26 deletions(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 1408a963..b23b8d8d 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -550,12 +550,22 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                     QBXSumpyExpansionWranglerCodeContainer
 
             from sumpy.kernel import AsymptoticallyInformedKernel
-            # assuming fmm_kernel does not have target derivatives
-            if self._use_qbmax or (
-                self._use_qbmax is None
-                    and isinstance(fmm_kernel, AsymptoticallyInformedKernel)):
-                fmm_kernel = fmm_kernel.replace_expansion_class(local_expn_class)
-                qbmax_local_factory = partial(local_expn_class, fmm_kernel)
+            if self._use_qbmax is None or self._use_qbmax:
+                source_kernels = [
+                    sk.replace_expansion_class(local_expn_class)
+                    if isinstance(sk, AsymptoticallyInformedKernel) else sk
+                    for sk in source_kernels]
+                target_kernels = [
+                    tk.replace_expansion_class(local_expn_class)
+                    if isinstance(tk, AsymptoticallyInformedKernel) else tk
+                    for tk in target_kernels]
+                if any(isinstance(tk, AsymptoticallyInformedKernel)
+                       for tk in target_kernels) or any(
+                           isinstance(sk, AsymptoticallyInformedKernel)
+                           for sk in source_kernels):
+                    qbmax_local_factory = partial(local_expn_class, base_kernel)
+                else:
+                    qbmax_local_factory = None
             else:
                 qbmax_local_factory = None
 
@@ -756,7 +766,12 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         from sumpy.expansion.local import VolumeTaylorLocalExpansion
         from sumpy.kernel import AsymptoticallyInformedKernel, ExpaniosnClassReplacer
         ecr = ExpaniosnClassReplacer(VolumeTaylorLocalExpansion)
-        kwe = [ecr(knl) for knl in kernels]
+        source_kernels = [ecr(knl)
+                          if isinstance(knl, AsymptoticallyInformedKernel) else knl
+                          for knl in source_kernels]
+        target_kernels = [ecr(knl)
+                          if isinstance(knl, AsymptoticallyInformedKernel) else knl
+                          for knl in target_kernels]
 
         from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         return LayerPotentialOnTargetAndCenterSubset(
@@ -954,10 +969,9 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             from sumpy.kernel import (AsymptoticallyInformedKernel,
                                           TargetDerivativeRemover)
             tdr = TargetDerivativeRemover()
-            if self._use_qbmax or (
-                self._use_qbmax is None and any([
+            if (self._use_qbmax is None or self._use_qbmax) and any([
                     isinstance(tdr(knl), AsymptoticallyInformedKernel)
-                    for knl in insn.kernels])):
+                    for knl in insn.target_kernels]):
                 qbmax_extra_kwargs = {
                     "nodes_of_qbx_balls_tangency": geo_data.flat_stage1_nodes()
                 }
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 475d32d6..011a4375 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -33,11 +33,6 @@ from pytential.version import PYTENTIAL_KERNEL_VERSION
 class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
     default_name = "qbx_tgt_ctr_subset"
 
-    def __init__(self, ctx, expansions, strength_usage=None,
-                 value_dtypes=None, name=None, device=None):
-        super().__init__(ctx, expansions, strength_usage,
-                         value_dtypes, name, device)
-
     def get_cache_key(self):
         return super().get_cache_key() + (PYTENTIAL_KERNEL_VERSION,)
 
@@ -72,16 +67,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
 
         sats = []
         sat_insns_data = []
-        for iknl in range(len(self.expansions)):
-
-            from sumpy.expansion import ExpansionBase
-            if isinstance(self.expansions[iknl], ExpansionBase):
-                knl = self.expansions[iknl].kernel
-            else:
-                from sumpy.kernel import Kernel
-                assert isinstance(self.expansions[iknl], Kernel)
-                knl = self.expansions[iknl]
-
+        for iknl, knl in enumerate(self.target_kernels):
             from sumpy.kernel import TargetDerivativeRemover
             tdr = TargetDerivativeRemover()
             try:
@@ -126,7 +112,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 sat_insns_data,
                 vector_names=self._vector_names,
                 pymbolic_expr_maps=[
-                    expn.kernel.get_code_transformer() for expn in self.expansions],
+                    expn.kernel.get_code_transformer() for expn in self.target_kernels],
                 retain_names=[datpair[0] for datpair in sat_insns_data],
                 complex_dtype=np.complex128)  # FIXME
 
-- 
GitLab


From 5b243dcef883ba159b141327b25d11e0fc5c533a Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 5 Jul 2021 19:03:25 -0500
Subject: [PATCH 26/38] QBMAX fixes, now direct evaluation works again

---
 pytential/qbx/__init__.py     | 15 +++++++++++++--
 pytential/qbx/direct.py       |  2 --
 pytential/qbx/fmm.py          |  4 ++--
 pytential/qbx/interactions.py | 14 ++++++++------
 4 files changed, 23 insertions(+), 12 deletions(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index b23b8d8d..3881c478 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -743,11 +743,22 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             value_dtype = self.density_discr.real_dtype
 
         base_kernel = single_valued(knl.get_base_kernel() for knl in source_kernels)
+        expansion=self.get_expansion_for_qbx_direct_eval(base_kernel, target_kernels)
+
+        from sumpy.kernel import AsymptoticallyInformedKernel
+        if self._use_qbmax is None or self._use_qbmax:
+            source_kernels = [
+                sk.replace_expansion_class(type(expansion))
+                if isinstance(sk, AsymptoticallyInformedKernel) else sk
+                for sk in source_kernels]
+            target_kernels = [
+                tk.replace_expansion_class(type(expansion))
+                if isinstance(tk, AsymptoticallyInformedKernel) else tk
+                for tk in target_kernels]
 
         from sumpy.qbx import LayerPotential
         return LayerPotential(self.cl_context,
-                    expansion=self.get_expansion_for_qbx_direct_eval(
-                        base_kernel, target_kernels),
+                    expansion=expansion,
                     target_kernels=target_kernels, source_kernels=source_kernels,
                     value_dtypes=value_dtype)
 
diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 011a4375..3ee33826 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -111,8 +111,6 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
             sat_insns = to_loopy_insns(
                 sat_insns_data,
                 vector_names=self._vector_names,
-                pymbolic_expr_maps=[
-                    expn.kernel.get_code_transformer() for expn in self.target_kernels],
                 retain_names=[datpair[0] for datpair in sat_insns_data],
                 complex_dtype=np.complex128)  # FIXME
 
diff --git a/pytential/qbx/fmm.py b/pytential/qbx/fmm.py
index 541bd940..a6c83b60 100644
--- a/pytential/qbx/fmm.py
+++ b/pytential/qbx/fmm.py
@@ -77,7 +77,7 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
     @memoize_method
     def p2qbmaxl(self, order):
         return P2QBMAXLFromCSR(self.cl_context,
-                self.qbmax_local_expansion(order))
+                self.qbmax_local_expansion(order), kernels=self.source_kernels)
 
     @memoize_method
     def m2qbxl(self, source_order, target_order):
@@ -101,7 +101,7 @@ class QBXSumpyExpansionWranglerCodeContainer(SumpyExpansionWranglerCodeContainer
     def qbmaxl2p(self, order):
         return QBMAXL2P(self.cl_context,
                 self.qbmax_local_expansion_factory(order),
-                self.out_kernels)
+                self.target_kernels)
 
     def get_wrangler(self, queue, geo_data, dtype,
             qbx_order, fmm_level_to_order,
diff --git a/pytential/qbx/interactions.py b/pytential/qbx/interactions.py
index 6de2da98..2a7c1faa 100644
--- a/pytential/qbx/interactions.py
+++ b/pytential/qbx/interactions.py
@@ -204,15 +204,14 @@ class P2QBMAXLFromCSR(P2EBase):
                         for isrc
                             <> a[idim] = center[idim] - sources[idim, isrc] \
                                     {dup=idim}
-                            """]
-                + self.get_loopy_instructions(isotropic_expansion=False) + ["""
+                            """] + [f"<> strength_{i} = strengths[{i}, isrc]" for
+                            i in set(self.strength_usage)] + self.get_loopy_instructions() + ["""
                         end
                     end
 
                     """] + [f"""
                     qbmax_expansions[tgt_icenter, {i}] = \
-                            simul_reduce(sum, (isrc_box, isrc), \
-                                         {self.get_result_expr(i)}) \
+                            simul_reduce(sum, (isrc_box, isrc), coeff{i}) \
                             {{id_prefix=write_expn}}
                     """ for i in range(ncoeffs)] + ["""
 
@@ -225,7 +224,8 @@ class P2QBMAXLFromCSR(P2EBase):
                     strength_count=self.strength_count),
                 lang_version=MOST_RECENT_LANGUAGE_VERSION)
 
-        loopy_knl = self.expansion.prepare_loopy_kernel(loopy_knl)
+        for knl in self.source_kernels:
+            loopy_knl = knl.prepare_loopy_kernel(loopy_knl)
         loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
 
         return loopy_knl
@@ -639,7 +639,8 @@ class QBMAXL2P(E2PBase):
                 lang_version=MOST_RECENT_LANGUAGE_VERSION)
 
         loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
-        loopy_knl = self.expansion.prepare_loopy_kernel(loopy_knl)
+        for knl in self.kernels:
+            loopy_knl = knl.prepare_loopy_kernel(loopy_knl)
 
         return loopy_knl
 
@@ -647,6 +648,7 @@ class QBMAXL2P(E2PBase):
     def get_optimized_kernel(self):
         knl = self.get_kernel()
         knl = lp.tag_inames(knl, dict(iglobal_center="g.0"))
+        knl = self._allow_redundant_execution_of_knl_scaling(knl)
         return knl
 
     def __call__(self, queue, **kwargs):
-- 
GitLab


From 87c8a2c4fa59b65f776d9a2d87bd1ddd93c4b68e Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 5 Jul 2021 19:23:45 -0500
Subject: [PATCH 27/38] QBMAX fixes, now FMM also works

---
 pytential/qbx/interactions.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/pytential/qbx/interactions.py b/pytential/qbx/interactions.py
index 2a7c1faa..6f975166 100644
--- a/pytential/qbx/interactions.py
+++ b/pytential/qbx/interactions.py
@@ -205,7 +205,8 @@ class P2QBMAXLFromCSR(P2EBase):
                             <> a[idim] = center[idim] - sources[idim, isrc] \
                                     {dup=idim}
                             """] + [f"<> strength_{i} = strengths[{i}, isrc]" for
-                            i in set(self.strength_usage)] + self.get_loopy_instructions() + ["""
+                            i in set(self.strength_usage)]
+                            + self.get_loopy_instructions(isotropic_expansion=False) + ["""
                         end
                     end
 
-- 
GitLab


From 12562fef2b8a998d8b85daa508bc1be7a5077b77 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 5 Jul 2021 23:42:53 -0500
Subject: [PATCH 28/38] Remove ccls-cache

---
 .../pytential@qbx@target_specific@impl.c      | 26381 ----------------
 .../pytential@qbx@target_specific@impl.c.blob |   Bin 288 -> 0 bytes
 .gitignore                                    |     1 +
 3 files changed, 1 insertion(+), 26381 deletions(-)
 delete mode 100644 .ccls-cache/@home@xywei@Projects@pytential/pytential@qbx@target_specific@impl.c
 delete mode 100644 .ccls-cache/@home@xywei@Projects@pytential/pytential@qbx@target_specific@impl.c.blob

diff --git a/.ccls-cache/@home@xywei@Projects@pytential/pytential@qbx@target_specific@impl.c b/.ccls-cache/@home@xywei@Projects@pytential/pytential@qbx@target_specific@impl.c
deleted file mode 100644
index 01a419ac..00000000
--- a/.ccls-cache/@home@xywei@Projects@pytential/pytential@qbx@target_specific@impl.c
+++ /dev/null
@@ -1,26381 +0,0 @@
-/* Generated by Cython 0.29.21 */
-
-/* BEGIN: Cython Metadata
-{
-    "distutils": {
-        "depends": [
-            "pytential/qbx/target_specific/helmholtz_utils.h",
-            "pytential/qbx/target_specific/impl.h"
-        ],
-        "extra_compile_args": [
-            "-Wall",
-            "-fopenmp",
-            "-Ofast"
-        ],
-        "extra_link_args": [
-            "-fopenmp"
-        ],
-        "include_dirs": [
-            "pytential/qbx/target_specific"
-        ],
-        "name": "pytential.qbx.target_specific.impl",
-        "sources": [
-            "pytential/qbx/target_specific/impl.pyx",
-            "pytential/qbx/target_specific/helmholtz_utils.c"
-        ]
-    },
-    "module_name": "pytential.qbx.target_specific.impl"
-}
-END: Cython Metadata */
-
-#define PY_SSIZE_T_CLEAN
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-#define CYTHON_ABI "0_29_21"
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-  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
-          PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
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-  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
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-#ifndef Py_TPFLAGS_CHECKTYPES
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-#ifndef Py_TPFLAGS_HAVE_FINALIZE
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-  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args,
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-  #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
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-#define __Pyx_PyFastCFunction_Check(func)\
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-#define __Pyx_PyFastCFunction_Check(func) 0
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-  #define PyObject_Realloc(p)  PyMem_Realloc(p)
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-  #define PyMem_RawFree(p)             PyMem_Free(p)
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-  #define __Pyx_PyCode_HasFreeVars(co)  PyCode_HasFreeVars(co)
-  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)
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-  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
-  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)
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-#elif PY_VERSION_HEX >= 0x03060000
-  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
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-typedef int Py_tss_t;
-static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) {
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-  Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t));
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-static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) {
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-static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) {
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-static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) {
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-  *key = Py_tss_NEEDS_INIT;
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-static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) {
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-static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) {
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-#define __Pyx_PyDict_NewPresized(n)  ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
-#else
-#define __Pyx_PyDict_NewPresized(n)  PyDict_New()
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-#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
-  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
-  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
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-  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
-  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
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-#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS
-#define __Pyx_PyDict_GetItemStr(dict, name)  _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash)
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-#define __Pyx_PyDict_GetItemStr(dict, name)  PyDict_GetItem(dict, name)
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-  #define CYTHON_PEP393_ENABLED 1
-  #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
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-  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_LENGTH(u)
-  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
-  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)
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-  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
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-  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, ch)
-  #if defined(PyUnicode_IS_READY) && defined(PyUnicode_GET_SIZE)
-  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
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-  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_LENGTH(u))
-  #endif
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-  #define PyUnicode_1BYTE_KIND  1
-  #define PyUnicode_2BYTE_KIND  2
-  #define PyUnicode_4BYTE_KIND  4
-  #define __Pyx_PyUnicode_READY(op)       (0)
-  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)
-  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
-  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)
-  #define __Pyx_PyUnicode_KIND(u)         (sizeof(Py_UNICODE))
-  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))
-  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
-  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  (((void)(k)), ((Py_UNICODE*)d)[i] = ch)
-  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_SIZE(u))
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-  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
-  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
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-  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
-  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
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-  #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
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-  #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
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-#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
-  #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
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-#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
-#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
-#if PY_MAJOR_VERSION >= 3
-  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
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-  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
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-  #define PyObject_ASCII(o)            PyObject_Repr(o)
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-#if PY_MAJOR_VERSION >= 3
-  #define PyBaseString_Type            PyUnicode_Type
-  #define PyStringObject               PyUnicodeObject
-  #define PyString_Type                PyUnicode_Type
-  #define PyString_Check               PyUnicode_Check
-  #define PyString_CheckExact          PyUnicode_CheckExact
-#ifndef PyObject_Unicode
-  #define PyObject_Unicode             PyObject_Str
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-#endif
-#if PY_MAJOR_VERSION >= 3
-  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
-  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
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-  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
-  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
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-  #define __Pyx_SET_REFCNT(obj, refcnt) Py_REFCNT(obj) = (refcnt)
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-  #define __Pyx_PySequence_SIZE(seq)  Py_SIZE(seq)
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-  #define __Pyx_PySequence_SIZE(seq)  PySequence_Size(seq)
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-  #define PyIntObject                  PyLongObject
-  #define PyInt_Type                   PyLong_Type
-  #define PyInt_Check(op)              PyLong_Check(op)
-  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
-  #define PyInt_FromString             PyLong_FromString
-  #define PyInt_FromUnicode            PyLong_FromUnicode
-  #define PyInt_FromLong               PyLong_FromLong
-  #define PyInt_FromSize_t             PyLong_FromSize_t
-  #define PyInt_FromSsize_t            PyLong_FromSsize_t
-  #define PyInt_AsLong                 PyLong_AsLong
-  #define PyInt_AS_LONG                PyLong_AS_LONG
-  #define PyInt_AsSsize_t              PyLong_AsSsize_t
-  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
-  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
-  #define PyNumber_Int                 PyNumber_Long
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-#if PY_MAJOR_VERSION >= 3
-  #define PyBoolObject                 PyLongObject
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-  #ifndef PyUnicode_InternFromString
-    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
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-  typedef long Py_hash_t;
-  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
-  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
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-  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
-  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
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-  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? ((void)(klass), PyMethod_New(func, self)) : __Pyx_NewRef(func))
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-  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
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-  #if PY_VERSION_HEX >= 0x030500B1
-    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
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-    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
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-  #define __Pyx_PyType_AsAsync(obj) NULL
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-#ifndef __Pyx_PyAsyncMethodsStruct
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-  #define _USE_MATH_DEFINES
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-#include <math.h>
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-#define __PYX_NAN() ((float) NAN)
-#else
-static CYTHON_INLINE float __PYX_NAN() {
-  float value;
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-#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
-#define __Pyx_truncl trunc
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-#define __Pyx_truncl truncl
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-#define __PYX_MARK_ERR_POS(f_index, lineno) \
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-  #else
-    #define __PYX_EXTERN_C extern
-  #endif
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-
-#define __PYX_HAVE__pytential__qbx__target_specific__impl
-#define __PYX_HAVE_API__pytential__qbx__target_specific__impl
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-#include <math.h>
-#include <string.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <omp.h>
-#include "complex.h"
-#include "helmholtz_utils.h"
-#include "impl.h"
-#include "pythread.h"
-#include "pystate.h"
-#ifdef _OPENMP
-#include <omp.h>
-#endif /* _OPENMP */
-
-#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
-#define CYTHON_WITHOUT_ASSERTIONS
-#endif
-
-typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
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-
-#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
-#define __PYX_DEFAULT_STRING_ENCODING_IS_UTF8 0
-#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT (PY_MAJOR_VERSION >= 3 && __PYX_DEFAULT_STRING_ENCODING_IS_UTF8)
-#define __PYX_DEFAULT_STRING_ENCODING ""
-#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
-#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
-#define __Pyx_uchar_cast(c) ((unsigned char)c)
-#define __Pyx_long_cast(x) ((long)x)
-#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
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-    (sizeof(type) > sizeof(Py_ssize_t) &&\
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-    (sizeof(type) == sizeof(Py_ssize_t) &&\
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-static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) {
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-#if defined (__cplusplus) && __cplusplus >= 201103L
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-    #define __Pyx_sst_abs(value) std::abs(value)
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-    #define __Pyx_sst_abs(value) abs(value)
-#elif SIZEOF_LONG >= SIZEOF_SIZE_T
-    #define __Pyx_sst_abs(value) labs(value)
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-    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
-#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
-    #define __Pyx_sst_abs(value) llabs(value)
-#elif defined (__GNUC__)
-    #define __Pyx_sst_abs(value) __builtin_llabs(value)
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-    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
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-static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
-static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
-#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
-#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
-#define __Pyx_PyBytes_FromString        PyBytes_FromString
-#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
-static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
-#if PY_MAJOR_VERSION < 3
-    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
-    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
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-    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
-    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
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-#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
-#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
-#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
-#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
-#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
-#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
-#define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))
-#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
-#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
-#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
-#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
-#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
-#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
-#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
-#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
-#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
-static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
-    const Py_UNICODE *u_end = u;
-    while (*u_end++) ;
-    return (size_t)(u_end - u - 1);
-}
-#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
-#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
-#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
-#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
-#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
-static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b);
-static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
-static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*);
-static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
-#define __Pyx_PySequence_Tuple(obj)\
-    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
-static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
-static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
-#if CYTHON_ASSUME_SAFE_MACROS
-#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
-#else
-#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
-#endif
-#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
-#if PY_MAJOR_VERSION >= 3
-#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
-#else
-#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
-#endif
-#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
-#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
-static int __Pyx_sys_getdefaultencoding_not_ascii;
-static int __Pyx_init_sys_getdefaultencoding_params(void) {
-    PyObject* sys;
-    PyObject* default_encoding = NULL;
-    PyObject* ascii_chars_u = NULL;
-    PyObject* ascii_chars_b = NULL;
-    const char* default_encoding_c;
-    sys = PyImport_ImportModule("sys");
-    if (!sys) goto bad;
-    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
-    Py_DECREF(sys);
-    if (!default_encoding) goto bad;
-    default_encoding_c = PyBytes_AsString(default_encoding);
-    if (!default_encoding_c) goto bad;
-    if (strcmp(default_encoding_c, "ascii") == 0) {
-        __Pyx_sys_getdefaultencoding_not_ascii = 0;
-    } else {
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-        int c;
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-        }
-        __Pyx_sys_getdefaultencoding_not_ascii = 1;
-        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
-        if (!ascii_chars_u) goto bad;
-        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
-        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
-            PyErr_Format(
-                PyExc_ValueError,
-                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
-                default_encoding_c);
-            goto bad;
-        }
-        Py_DECREF(ascii_chars_u);
-        Py_DECREF(ascii_chars_b);
-    }
-    Py_DECREF(default_encoding);
-    return 0;
-bad:
-    Py_XDECREF(default_encoding);
-    Py_XDECREF(ascii_chars_u);
-    Py_XDECREF(ascii_chars_b);
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-#endif
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-#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
-#else
-#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
-#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
-static char* __PYX_DEFAULT_STRING_ENCODING;
-static int __Pyx_init_sys_getdefaultencoding_params(void) {
-    PyObject* sys;
-    PyObject* default_encoding = NULL;
-    char* default_encoding_c;
-    sys = PyImport_ImportModule("sys");
-    if (!sys) goto bad;
-    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
-    Py_DECREF(sys);
-    if (!default_encoding) goto bad;
-    default_encoding_c = PyBytes_AsString(default_encoding);
-    if (!default_encoding_c) goto bad;
-    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1);
-    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
-    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
-    Py_DECREF(default_encoding);
-    return 0;
-bad:
-    Py_XDECREF(default_encoding);
-    return -1;
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-
-/* Test for GCC > 2.95 */
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-  #define unlikely(x) __builtin_expect(!!(x), 0)
-#else /* !__GNUC__ or GCC < 2.95 */
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-  #define unlikely(x) (x)
-#endif /* __GNUC__ */
-static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }
-
-static PyObject *__pyx_m = NULL;
-static PyObject *__pyx_d;
-static PyObject *__pyx_b;
-static PyObject *__pyx_cython_runtime = NULL;
-static PyObject *__pyx_empty_tuple;
-static PyObject *__pyx_empty_bytes;
-static PyObject *__pyx_empty_unicode;
-static int __pyx_lineno;
-static int __pyx_clineno = 0;
-static const char * __pyx_cfilenm= __FILE__;
-static const char *__pyx_filename;
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-/* Header.proto */
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-  #ifdef __cplusplus
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-  #undef _Complex_I
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-
-static const char *__pyx_f[] = {
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-typedef struct {
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-  char *data;
-  Py_ssize_t shape[8];
-  Py_ssize_t strides[8];
-  Py_ssize_t suboffsets[8];
-} __Pyx_memviewslice;
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-
-/* Atomics.proto */
-#include <pythread.h>
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-#define __pyx_atomic_int_type int
-#if CYTHON_ATOMICS && __GNUC__ >= 4 && (__GNUC_MINOR__ > 1 ||\
-                    (__GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL >= 2)) &&\
-                    !defined(__i386__)
-    #define __pyx_atomic_incr_aligned(value, lock) __sync_fetch_and_add(value, 1)
-    #define __pyx_atomic_decr_aligned(value, lock) __sync_fetch_and_sub(value, 1)
-    #ifdef __PYX_DEBUG_ATOMICS
-        #warning "Using GNU atomics"
-    #endif
-#elif CYTHON_ATOMICS && defined(_MSC_VER) && 0
-    #include <Windows.h>
-    #undef __pyx_atomic_int_type
-    #define __pyx_atomic_int_type LONG
-    #define __pyx_atomic_incr_aligned(value, lock) InterlockedIncrement(value)
-    #define __pyx_atomic_decr_aligned(value, lock) InterlockedDecrement(value)
-    #ifdef __PYX_DEBUG_ATOMICS
-        #pragma message ("Using MSVC atomics")
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-#elif CYTHON_ATOMICS && (defined(__ICC) || defined(__INTEL_COMPILER)) && 0
-    #define __pyx_atomic_incr_aligned(value, lock) _InterlockedIncrement(value)
-    #define __pyx_atomic_decr_aligned(value, lock) _InterlockedDecrement(value)
-    #ifdef __PYX_DEBUG_ATOMICS
-        #warning "Using Intel atomics"
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-    #undef CYTHON_ATOMICS
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-        #warning "Not using atomics"
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-#endif
-typedef volatile __pyx_atomic_int_type __pyx_atomic_int;
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-    #define __pyx_add_acquisition_count(memview)\
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-    #define __pyx_sub_acquisition_count(memview)\
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-#else
-    #define __pyx_add_acquisition_count(memview)\
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-    #define __pyx_sub_acquisition_count(memview)\
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-#define __Pyx_FastGilFuncInit()
-
-/* ForceInitThreads.proto */
-#ifndef __PYX_FORCE_INIT_THREADS
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-
-/* BufferFormatStructs.proto */
-#define IS_UNSIGNED(type) (((type) -1) > 0)
-struct __Pyx_StructField_;
-#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
-typedef struct {
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-
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-struct __pyx_vtabstruct__memoryviewslice {
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-static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
-#else
-#define __Pyx_PyCFunction_FastCall(func, args, nargs)  (assert(0), NULL)
-#endif
-
-/* PyFunctionFastCall.proto */
-#if CYTHON_FAST_PYCALL
-#define __Pyx_PyFunction_FastCall(func, args, nargs)\
-    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
-#if 1 || PY_VERSION_HEX < 0x030600B1
-static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs);
-#else
-#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
-#endif
-#define __Pyx_BUILD_ASSERT_EXPR(cond)\
-    (sizeof(char [1 - 2*!(cond)]) - 1)
-#ifndef Py_MEMBER_SIZE
-#define Py_MEMBER_SIZE(type, member) sizeof(((type *)0)->member)
-#endif
-  static size_t __pyx_pyframe_localsplus_offset = 0;
-  #include "frameobject.h"
-  #define __Pxy_PyFrame_Initialize_Offsets()\
-    ((void)__Pyx_BUILD_ASSERT_EXPR(sizeof(PyFrameObject) == offsetof(PyFrameObject, f_localsplus) + Py_MEMBER_SIZE(PyFrameObject, f_localsplus)),\
-     (void)(__pyx_pyframe_localsplus_offset = ((size_t)PyFrame_Type.tp_basicsize) - Py_MEMBER_SIZE(PyFrameObject, f_localsplus)))
-  #define __Pyx_PyFrame_GetLocalsplus(frame)\
-    (assert(__pyx_pyframe_localsplus_offset), (PyObject **)(((char *)(frame)) + __pyx_pyframe_localsplus_offset))
-#endif
-
-/* PyObjectCallMethO.proto */
-#if CYTHON_COMPILING_IN_CPYTHON
-static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
-#endif
-
-/* PyObjectCallOneArg.proto */
-static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);
-
-/* PyIntBinop.proto */
-#if !CYTHON_COMPILING_IN_PYPY
-static PyObject* __Pyx_PyInt_AddCObj(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
-#else
-#define __Pyx_PyInt_AddCObj(op1, op2, intval, inplace, zerodivision_check)\
-    (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
-#endif
-
-/* SetItemInt.proto */
-#define __Pyx_SetItemInt(o, i, v, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
-    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
-    __Pyx_SetItemInt_Fast(o, (Py_ssize_t)i, v, is_list, wraparound, boundscheck) :\
-    (is_list ? (PyErr_SetString(PyExc_IndexError, "list assignment index out of range"), -1) :\
-               __Pyx_SetItemInt_Generic(o, to_py_func(i), v)))
-static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v);
-static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v,
-                                               int is_list, int wraparound, int boundscheck);
-
-/* PyDictVersioning.proto */
-#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
-#define __PYX_DICT_VERSION_INIT  ((PY_UINT64_T) -1)
-#define __PYX_GET_DICT_VERSION(dict)  (((PyDictObject*)(dict))->ma_version_tag)
-#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\
-    (version_var) = __PYX_GET_DICT_VERSION(dict);\
-    (cache_var) = (value);
-#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\
-    static PY_UINT64_T __pyx_dict_version = 0;\
-    static PyObject *__pyx_dict_cached_value = NULL;\
-    if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\
-        (VAR) = __pyx_dict_cached_value;\
-    } else {\
-        (VAR) = __pyx_dict_cached_value = (LOOKUP);\
-        __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\
-    }\
-}
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj);
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj);
-static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version);
-#else
-#define __PYX_GET_DICT_VERSION(dict)  (0)
-#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)
-#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP)  (VAR) = (LOOKUP);
-#endif
-
-/* GetModuleGlobalName.proto */
-#if CYTHON_USE_DICT_VERSIONS
-#define __Pyx_GetModuleGlobalName(var, name)  {\
-    static PY_UINT64_T __pyx_dict_version = 0;\
-    static PyObject *__pyx_dict_cached_value = NULL;\
-    (var) = (likely(__pyx_dict_version == __PYX_GET_DICT_VERSION(__pyx_d))) ?\
-        (likely(__pyx_dict_cached_value) ? __Pyx_NewRef(__pyx_dict_cached_value) : __Pyx_GetBuiltinName(name)) :\
-        __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
-}
-#define __Pyx_GetModuleGlobalNameUncached(var, name)  {\
-    PY_UINT64_T __pyx_dict_version;\
-    PyObject *__pyx_dict_cached_value;\
-    (var) = __Pyx__GetModuleGlobalName(name, &__pyx_dict_version, &__pyx_dict_cached_value);\
-}
-static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value);
-#else
-#define __Pyx_GetModuleGlobalName(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
-#define __Pyx_GetModuleGlobalNameUncached(var, name)  (var) = __Pyx__GetModuleGlobalName(name)
-static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name);
-#endif
-
-/* SliceObject.proto */
-#define __Pyx_PyObject_DelSlice(obj, cstart, cstop, py_start, py_stop, py_slice, has_cstart, has_cstop, wraparound)\
-    __Pyx_PyObject_SetSlice(obj, (PyObject*)NULL, cstart, cstop, py_start, py_stop, py_slice, has_cstart, has_cstop, wraparound)
-static CYTHON_INLINE int __Pyx_PyObject_SetSlice(
-        PyObject* obj, PyObject* value, Py_ssize_t cstart, Py_ssize_t cstop,
-        PyObject** py_start, PyObject** py_stop, PyObject** py_slice,
-        int has_cstart, int has_cstop, int wraparound);
-
-/* MemviewSliceInit.proto */
-#define __Pyx_BUF_MAX_NDIMS %(BUF_MAX_NDIMS)d
-#define __Pyx_MEMVIEW_DIRECT   1
-#define __Pyx_MEMVIEW_PTR      2
-#define __Pyx_MEMVIEW_FULL     4
-#define __Pyx_MEMVIEW_CONTIG   8
-#define __Pyx_MEMVIEW_STRIDED  16
-#define __Pyx_MEMVIEW_FOLLOW   32
-#define __Pyx_IS_C_CONTIG 1
-#define __Pyx_IS_F_CONTIG 2
-static int __Pyx_init_memviewslice(
-                struct __pyx_memoryview_obj *memview,
-                int ndim,
-                __Pyx_memviewslice *memviewslice,
-                int memview_is_new_reference);
-static CYTHON_INLINE int __pyx_add_acquisition_count_locked(
-    __pyx_atomic_int *acquisition_count, PyThread_type_lock lock);
-static CYTHON_INLINE int __pyx_sub_acquisition_count_locked(
-    __pyx_atomic_int *acquisition_count, PyThread_type_lock lock);
-#define __pyx_get_slice_count_pointer(memview) (memview->acquisition_count_aligned_p)
-#define __pyx_get_slice_count(memview) (*__pyx_get_slice_count_pointer(memview))
-#define __PYX_INC_MEMVIEW(slice, have_gil) __Pyx_INC_MEMVIEW(slice, have_gil, __LINE__)
-#define __PYX_XDEC_MEMVIEW(slice, have_gil) __Pyx_XDEC_MEMVIEW(slice, have_gil, __LINE__)
-static CYTHON_INLINE void __Pyx_INC_MEMVIEW(__Pyx_memviewslice *, int, int);
-static CYTHON_INLINE void __Pyx_XDEC_MEMVIEW(__Pyx_memviewslice *, int, int);
-
-/* PyObjectCall2Args.proto */
-static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2);
-
-/* ArgTypeTest.proto */
-#define __Pyx_ArgTypeTest(obj, type, none_allowed, name, exact)\
-    ((likely((Py_TYPE(obj) == type) | (none_allowed && (obj == Py_None)))) ? 1 :\
-        __Pyx__ArgTypeTest(obj, type, name, exact))
-static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact);
-
-/* IncludeStringH.proto */
-#include <string.h>
-
-/* BytesEquals.proto */
-static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);
-
-/* UnicodeEquals.proto */
-static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);
-
-/* StrEquals.proto */
-#if PY_MAJOR_VERSION >= 3
-#define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals
-#else
-#define __Pyx_PyString_Equals __Pyx_PyBytes_Equals
-#endif
-
-/* UnaryNegOverflows.proto */
-#define UNARY_NEG_WOULD_OVERFLOW(x)\
-        (((x) < 0) & ((unsigned long)(x) == 0-(unsigned long)(x)))
-
-static CYTHON_UNUSED int __pyx_array_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
-static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *); /*proto*/
-/* GetAttr.proto */
-static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *, PyObject *);
-
-/* GetItemInt.proto */
-#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
-    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
-    __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\
-    (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\
-               __Pyx_GetItemInt_Generic(o, to_py_func(i))))
-#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
-    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
-    __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
-    (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
-static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
-                                                              int wraparound, int boundscheck);
-#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
-    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
-    __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
-    (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
-static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
-                                                              int wraparound, int boundscheck);
-static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
-static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
-                                                     int is_list, int wraparound, int boundscheck);
-
-/* ObjectGetItem.proto */
-#if CYTHON_USE_TYPE_SLOTS
-static CYTHON_INLINE PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key);
-#else
-#define __Pyx_PyObject_GetItem(obj, key)  PyObject_GetItem(obj, key)
-#endif
-
-/* decode_c_string_utf16.proto */
-static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16(const char *s, Py_ssize_t size, const char *errors) {
-    int byteorder = 0;
-    return PyUnicode_DecodeUTF16(s, size, errors, &byteorder);
-}
-static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16LE(const char *s, Py_ssize_t size, const char *errors) {
-    int byteorder = -1;
-    return PyUnicode_DecodeUTF16(s, size, errors, &byteorder);
-}
-static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16BE(const char *s, Py_ssize_t size, const char *errors) {
-    int byteorder = 1;
-    return PyUnicode_DecodeUTF16(s, size, errors, &byteorder);
-}
-
-/* decode_c_string.proto */
-static CYTHON_INLINE PyObject* __Pyx_decode_c_string(
-         const char* cstring, Py_ssize_t start, Py_ssize_t stop,
-         const char* encoding, const char* errors,
-         PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors));
-
-/* PyErrExceptionMatches.proto */
-#if CYTHON_FAST_THREAD_STATE
-#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
-static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
-#else
-#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
-#endif
-
-/* GetAttr3.proto */
-static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *, PyObject *, PyObject *);
-
-/* RaiseTooManyValuesToUnpack.proto */
-static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);
-
-/* RaiseNeedMoreValuesToUnpack.proto */
-static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);
-
-/* RaiseNoneIterError.proto */
-static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);
-
-/* ExtTypeTest.proto */
-static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);
-
-/* GetTopmostException.proto */
-#if CYTHON_USE_EXC_INFO_STACK
-static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate);
-#endif
-
-/* SaveResetException.proto */
-#if CYTHON_FAST_THREAD_STATE
-#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
-static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
-#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
-static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
-#else
-#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
-#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
-#endif
-
-/* GetException.proto */
-#if CYTHON_FAST_THREAD_STATE
-#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
-static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
-#else
-static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
-#endif
-
-/* SwapException.proto */
-#if CYTHON_FAST_THREAD_STATE
-#define __Pyx_ExceptionSwap(type, value, tb)  __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb)
-static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
-#else
-static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
-#endif
-
-/* Import.proto */
-static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);
-
-/* FastTypeChecks.proto */
-#if CYTHON_COMPILING_IN_CPYTHON
-#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
-static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
-static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
-static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
-#else
-#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
-#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
-#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
-#endif
-#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
-
-static CYTHON_UNUSED int __pyx_memoryview_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
-/* ListCompAppend.proto */
-#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
-static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
-    PyListObject* L = (PyListObject*) list;
-    Py_ssize_t len = Py_SIZE(list);
-    if (likely(L->allocated > len)) {
-        Py_INCREF(x);
-        PyList_SET_ITEM(list, len, x);
-        __Pyx_SET_SIZE(list, len + 1);
-        return 0;
-    }
-    return PyList_Append(list, x);
-}
-#else
-#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x)
-#endif
-
-/* PyIntBinop.proto */
-#if !CYTHON_COMPILING_IN_PYPY
-static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace, int zerodivision_check);
-#else
-#define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace, zerodivision_check)\
-    (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2))
-#endif
-
-/* ListExtend.proto */
-static CYTHON_INLINE int __Pyx_PyList_Extend(PyObject* L, PyObject* v) {
-#if CYTHON_COMPILING_IN_CPYTHON
-    PyObject* none = _PyList_Extend((PyListObject*)L, v);
-    if (unlikely(!none))
-        return -1;
-    Py_DECREF(none);
-    return 0;
-#else
-    return PyList_SetSlice(L, PY_SSIZE_T_MAX, PY_SSIZE_T_MAX, v);
-#endif
-}
-
-/* ListAppend.proto */
-#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
-static CYTHON_INLINE int __Pyx_PyList_Append(PyObject* list, PyObject* x) {
-    PyListObject* L = (PyListObject*) list;
-    Py_ssize_t len = Py_SIZE(list);
-    if (likely(L->allocated > len) & likely(len > (L->allocated >> 1))) {
-        Py_INCREF(x);
-        PyList_SET_ITEM(list, len, x);
-        __Pyx_SET_SIZE(list, len + 1);
-        return 0;
-    }
-    return PyList_Append(list, x);
-}
-#else
-#define __Pyx_PyList_Append(L,x) PyList_Append(L,x)
-#endif
-
-/* None.proto */
-static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname);
-
-/* ImportFrom.proto */
-static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);
-
-/* HasAttr.proto */
-static CYTHON_INLINE int __Pyx_HasAttr(PyObject *, PyObject *);
-
-/* PyObject_GenericGetAttrNoDict.proto */
-#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
-static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name);
-#else
-#define __Pyx_PyObject_GenericGetAttrNoDict PyObject_GenericGetAttr
-#endif
-
-/* PyObject_GenericGetAttr.proto */
-#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
-static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name);
-#else
-#define __Pyx_PyObject_GenericGetAttr PyObject_GenericGetAttr
-#endif
-
-/* SetVTable.proto */
-static int __Pyx_SetVtable(PyObject *dict, void *vtable);
-
-/* PyObjectGetAttrStrNoError.proto */
-static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name);
-
-/* SetupReduce.proto */
-static int __Pyx_setup_reduce(PyObject* type_obj);
-
-/* CLineInTraceback.proto */
-#ifdef CYTHON_CLINE_IN_TRACEBACK
-#define __Pyx_CLineForTraceback(tstate, c_line)  (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0)
-#else
-static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line);
-#endif
-
-/* CodeObjectCache.proto */
-typedef struct {
-    PyCodeObject* code_object;
-    int code_line;
-} __Pyx_CodeObjectCacheEntry;
-struct __Pyx_CodeObjectCache {
-    int count;
-    int max_count;
-    __Pyx_CodeObjectCacheEntry* entries;
-};
-static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
-static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
-static PyCodeObject *__pyx_find_code_object(int code_line);
-static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);
-
-/* AddTraceback.proto */
-static void __Pyx_AddTraceback(const char *funcname, int c_line,
-                               int py_line, const char *filename);
-
-/* RealImag.proto */
-#if CYTHON_CCOMPLEX
-  #ifdef __cplusplus
-    #define __Pyx_CREAL(z) ((z).real())
-    #define __Pyx_CIMAG(z) ((z).imag())
-  #else
-    #define __Pyx_CREAL(z) (__real__(z))
-    #define __Pyx_CIMAG(z) (__imag__(z))
-  #endif
-#else
-    #define __Pyx_CREAL(z) ((z).real)
-    #define __Pyx_CIMAG(z) ((z).imag)
-#endif
-#if defined(__cplusplus) && CYTHON_CCOMPLEX\
-        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
-    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
-    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
-#else
-    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
-    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
-#endif
-
-/* Arithmetic.proto */
-#if CYTHON_CCOMPLEX
-    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
-    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
-    #define __Pyx_c_diff_double(a, b) ((a)-(b))
-    #define __Pyx_c_prod_double(a, b) ((a)*(b))
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-    #define __Pyx_c_neg_double(a)     (-(a))
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-    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
-    #define __Pyx_c_conj_double(z)    (::std::conj(z))
-    #if 1
-        #define __Pyx_c_abs_double(z)     (::std::abs(z))
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-    #define __Pyx_c_is_zero_double(z) ((z)==0)
-    #define __Pyx_c_conj_double(z)    (conj(z))
-    #if 1
-        #define __Pyx_c_abs_double(z)     (cabs(z))
-        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
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- #endif
-#else
-    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
-    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
-    #if 1
-        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
-        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
-    #endif
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-    #define __Pyx_GetBuffer PyObject_GetBuffer
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-} __Pyx_Buf_DimInfo;
-typedef struct {
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-  Py_buffer pybuffer;
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-  char *data;
-  __Pyx_Buf_DimInfo diminfo[8];
-} __Pyx_LocalBuf_ND;
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-/* MemviewSliceIsContig.proto */
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-/* OverlappingSlices.proto */
-static int __pyx_slices_overlap(__Pyx_memviewslice *slice1,
-                                __Pyx_memviewslice *slice2,
-                                int ndim, size_t itemsize);
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-/* Capsule.proto */
-static CYTHON_INLINE PyObject *__pyx_capsule_create(void *p, const char *sig);
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-/* IsLittleEndian.proto */
-static CYTHON_INLINE int __Pyx_Is_Little_Endian(void);
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-/* BufferFormatCheck.proto */
-static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts);
-static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
-                              __Pyx_BufFmt_StackElem* stack,
-                              __Pyx_TypeInfo* type);
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-/* TypeInfoCompare.proto */
-static int __pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b);
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-/* MemviewSliceValidateAndInit.proto */
-static int __Pyx_ValidateAndInit_memviewslice(
-                int *axes_specs,
-                int c_or_f_flag,
-                int buf_flags,
-                int ndim,
-                __Pyx_TypeInfo *dtype,
-                __Pyx_BufFmt_StackElem stack[],
-                __Pyx_memviewslice *memviewslice,
-                PyObject *original_obj);
-
-/* ObjectToMemviewSlice.proto */
-static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds_double(PyObject *, int writable_flag);
-
-/* ObjectToMemviewSlice.proto */
-static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_int(PyObject *, int writable_flag);
-
-/* FromPy.proto */
-static __pyx_t_double_complex __Pyx_PyComplex_As___pyx_t_double_complex(PyObject*);
-
-/* ObjectToMemviewSlice.proto */
-static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds___pyx_t_double_complex(PyObject *, int writable_flag);
-
-/* ObjectToMemviewSlice.proto */
-static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(PyObject *, int writable_flag);
-
-/* CIntToPy.proto */
-static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);
-
-/* ToPy.proto */
-#define __pyx_PyComplex_FromComplex(z)\
-        PyComplex_FromDoubles((double)__Pyx_CREAL(z),\
-                              (double)__Pyx_CIMAG(z))
-
-/* MemviewDtypeToObject.proto */
-static CYTHON_INLINE PyObject *__pyx_memview_get___pyx_t_double_complex(const char *itemp);
-static CYTHON_INLINE int __pyx_memview_set___pyx_t_double_complex(const char *itemp, PyObject *obj);
-
-/* CIntToPy.proto */
-static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);
-
-/* MemviewSliceCopyTemplate.proto */
-static __Pyx_memviewslice
-__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs,
-                                 const char *mode, int ndim,
-                                 size_t sizeof_dtype, int contig_flag,
-                                 int dtype_is_object);
-
-/* CIntFromPy.proto */
-static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);
-
-/* CIntFromPy.proto */
-static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);
-
-/* CIntFromPy.proto */
-static CYTHON_INLINE char __Pyx_PyInt_As_char(PyObject *);
-
-/* CheckBinaryVersion.proto */
-static int __Pyx_check_binary_version(void);
-
-/* InitStrings.proto */
-static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);
-
-static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *__pyx_v_self); /* proto*/
-static char *__pyx_memoryview_get_item_pointer(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto*/
-static PyObject *__pyx_memoryview_is_slice(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj); /* proto*/
-static PyObject *__pyx_memoryview_setitem_slice_assignment(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_dst, PyObject *__pyx_v_src); /* proto*/
-static PyObject *__pyx_memoryview_setitem_slice_assign_scalar(struct __pyx_memoryview_obj *__pyx_v_self, struct __pyx_memoryview_obj *__pyx_v_dst, PyObject *__pyx_v_value); /* proto*/
-static PyObject *__pyx_memoryview_setitem_indexed(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto*/
-static PyObject *__pyx_memoryview_convert_item_to_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/
-static PyObject *__pyx_memoryview_assign_item_from_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/
-static PyObject *__pyx_memoryviewslice_convert_item_to_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/
-static PyObject *__pyx_memoryviewslice_assign_item_from_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/
-
-/* Module declarations from 'cython.view' */
-
-/* Module declarations from 'cython' */
-
-/* Module declarations from 'libc.math' */
-
-/* Module declarations from 'libc.string' */
-
-/* Module declarations from 'libc.stdio' */
-
-/* Module declarations from 'libc.stdlib' */
-
-/* Module declarations from 'openmp' */
-
-/* Module declarations from 'pytential.qbx.target_specific.impl' */
-static PyTypeObject *__pyx_array_type = 0;
-static PyTypeObject *__pyx_MemviewEnum_type = 0;
-static PyTypeObject *__pyx_memoryview_type = 0;
-static PyTypeObject *__pyx_memoryviewslice_type = 0;
-static PyObject *generic = 0;
-static PyObject *strided = 0;
-static PyObject *indirect = 0;
-static PyObject *contiguous = 0;
-static PyObject *indirect_contiguous = 0;
-static int __pyx_memoryview_thread_locks_used;
-static PyThread_type_lock __pyx_memoryview_thread_locks[8];
-static void __pyx_f_9pytential_3qbx_15target_specific_4impl_legvals(double, int, double *, double *); /*proto*/
-static double __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(double *, double *); /*proto*/
-static void __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_precompute(double *, double *, int, int, __pyx_t_double_complex, __pyx_t_double_complex *, __pyx_t_double_complex *, double *); /*proto*/
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_s(double *, double *, double *, __pyx_t_double_complex, int); /*proto*/
-static void __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_sp(__pyx_t_double_complex *, double *, double *, double *, __pyx_t_double_complex, int); /*proto*/
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_d(double *, double *, double *, double *, __pyx_t_double_complex, int); /*proto*/
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_s(double *, double *, double *, __pyx_t_double_complex, int, __pyx_t_double_complex, __pyx_t_double_complex *, double); /*proto*/
-static void __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_sp(__pyx_t_double_complex *, double *, double *, double *, __pyx_t_double_complex, int, __pyx_t_double_complex, __pyx_t_double_complex *, __pyx_t_double_complex *, double); /*proto*/
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_d(double *, double *, double *, double *, __pyx_t_double_complex, int, __pyx_t_double_complex, __pyx_t_double_complex *, double); /*proto*/
-static struct __pyx_array_obj *__pyx_array_new(PyObject *, Py_ssize_t, char *, char *, char *); /*proto*/
-static void *__pyx_align_pointer(void *, size_t); /*proto*/
-static PyObject *__pyx_memoryview_new(PyObject *, int, int, __Pyx_TypeInfo *); /*proto*/
-static CYTHON_INLINE int __pyx_memoryview_check(PyObject *); /*proto*/
-static PyObject *_unellipsify(PyObject *, int); /*proto*/
-static PyObject *assert_direct_dimensions(Py_ssize_t *, int); /*proto*/
-static struct __pyx_memoryview_obj *__pyx_memview_slice(struct __pyx_memoryview_obj *, PyObject *); /*proto*/
-static int __pyx_memoryview_slice_memviewslice(__Pyx_memviewslice *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int, int); /*proto*/
-static char *__pyx_pybuffer_index(Py_buffer *, char *, Py_ssize_t, Py_ssize_t); /*proto*/
-static int __pyx_memslice_transpose(__Pyx_memviewslice *); /*proto*/
-static PyObject *__pyx_memoryview_fromslice(__Pyx_memviewslice, int, PyObject *(*)(char *), int (*)(char *, PyObject *), int); /*proto*/
-static __Pyx_memviewslice *__pyx_memoryview_get_slice_from_memoryview(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/
-static void __pyx_memoryview_slice_copy(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/
-static PyObject *__pyx_memoryview_copy_object(struct __pyx_memoryview_obj *); /*proto*/
-static PyObject *__pyx_memoryview_copy_object_from_slice(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/
-static Py_ssize_t abs_py_ssize_t(Py_ssize_t); /*proto*/
-static char __pyx_get_best_slice_order(__Pyx_memviewslice *, int); /*proto*/
-static void _copy_strided_to_strided(char *, Py_ssize_t *, char *, Py_ssize_t *, Py_ssize_t *, Py_ssize_t *, int, size_t); /*proto*/
-static void copy_strided_to_strided(__Pyx_memviewslice *, __Pyx_memviewslice *, int, size_t); /*proto*/
-static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *, int); /*proto*/
-static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *, Py_ssize_t *, Py_ssize_t, int, char); /*proto*/
-static void *__pyx_memoryview_copy_data_to_temp(__Pyx_memviewslice *, __Pyx_memviewslice *, char, int); /*proto*/
-static int __pyx_memoryview_err_extents(int, Py_ssize_t, Py_ssize_t); /*proto*/
-static int __pyx_memoryview_err_dim(PyObject *, char *, int); /*proto*/
-static int __pyx_memoryview_err(PyObject *, char *); /*proto*/
-static int __pyx_memoryview_copy_contents(__Pyx_memviewslice, __Pyx_memviewslice, int, int, int); /*proto*/
-static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *, int, int); /*proto*/
-static void __pyx_memoryview_refcount_copying(__Pyx_memviewslice *, int, int, int); /*proto*/
-static void __pyx_memoryview_refcount_objects_in_slice_with_gil(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/
-static void __pyx_memoryview_refcount_objects_in_slice(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/
-static void __pyx_memoryview_slice_assign_scalar(__Pyx_memviewslice *, int, size_t, void *, int); /*proto*/
-static void __pyx_memoryview__slice_assign_scalar(char *, Py_ssize_t *, Py_ssize_t *, int, size_t, void *); /*proto*/
-static PyObject *__pyx_unpickle_Enum__set_state(struct __pyx_MemviewEnum_obj *, PyObject *); /*proto*/
-static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 };
-static __Pyx_TypeInfo __Pyx_TypeInfo_int = { "int", NULL, sizeof(int), { 0 }, 0, IS_UNSIGNED(int) ? 'U' : 'I', IS_UNSIGNED(int), 0 };
-static __Pyx_TypeInfo __Pyx_TypeInfo___pyx_t_double_complex = { "double complex", NULL, sizeof(__pyx_t_double_complex), { 0 }, 0, 'C', 0, 0 };
-#define __Pyx_MODULE_NAME "pytential.qbx.target_specific.impl"
-extern int __pyx_module_is_main_pytential__qbx__target_specific__impl;
-int __pyx_module_is_main_pytential__qbx__target_specific__impl = 0;
-
-/* Implementation of 'pytential.qbx.target_specific.impl' */
-static PyObject *__pyx_builtin_ValueError;
-static PyObject *__pyx_builtin_range;
-static PyObject *__pyx_builtin_any;
-static PyObject *__pyx_builtin_MemoryError;
-static PyObject *__pyx_builtin_enumerate;
-static PyObject *__pyx_builtin_TypeError;
-static PyObject *__pyx_builtin_Ellipsis;
-static PyObject *__pyx_builtin_id;
-static PyObject *__pyx_builtin_IndexError;
-static const char __pyx_k_O[] = "O";
-static const char __pyx_k_c[] = "c";
-static const char __pyx_k_i[] = "i";
-static const char __pyx_k_m[] = "m";
-static const char __pyx_k_z[] = "z";
-static const char __pyx_k_hs[] = "hs";
-static const char __pyx_k_id[] = "id";
-static const char __pyx_k_np[] = "np";
-static const char __pyx_k_any[] = "any";
-static const char __pyx_k_ctr[] = "ctr";
-static const char __pyx_k_fjs[] = "fjs";
-static const char __pyx_k_ier[] = "ier";
-static const char __pyx_k_new[] = "__new__";
-static const char __pyx_k_obj[] = "obj";
-static const char __pyx_k_pot[] = "pot";
-static const char __pyx_k_tgt[] = "tgt";
-static const char __pyx_k_tid[] = "tid";
-static const char __pyx_k_z_2[] = "z_";
-static const char __pyx_k_base[] = "base";
-static const char __pyx_k_dict[] = "__dict__";
-static const char __pyx_k_grad[] = "grad";
-static const char __pyx_k_hvec[] = "hvec";
-static const char __pyx_k_ictr[] = "ictr";
-static const char __pyx_k_isrc[] = "isrc";
-static const char __pyx_k_itgt[] = "itgt";
-static const char __pyx_k_main[] = "__main__";
-static const char __pyx_k_mode[] = "mode";
-static const char __pyx_k_name[] = "name";
-static const char __pyx_k_ndim[] = "ndim";
-static const char __pyx_k_ntop[] = "ntop";
-static const char __pyx_k_pack[] = "pack";
-static const char __pyx_k_size[] = "size";
-static const char __pyx_k_step[] = "step";
-static const char __pyx_k_stop[] = "stop";
-static const char __pyx_k_test[] = "__test__";
-static const char __pyx_k_ASCII[] = "ASCII";
-static const char __pyx_k_class[] = "__class__";
-static const char __pyx_k_dtype[] = "dtype";
-static const char __pyx_k_empty[] = "empty";
-static const char __pyx_k_error[] = "error";
-static const char __pyx_k_fjder[] = "fjder";
-static const char __pyx_k_flags[] = "flags";
-static const char __pyx_k_hders[] = "hders";
-static const char __pyx_k_ifder[] = "ifder";
-static const char __pyx_k_ifpot[] = "ifpot";
-static const char __pyx_k_jvals[] = "jvals";
-static const char __pyx_k_lwfjs[] = "lwfjs";
-static const char __pyx_k_numpy[] = "numpy";
-static const char __pyx_k_order[] = "order";
-static const char __pyx_k_range[] = "range";
-static const char __pyx_k_scale[] = "scale";
-static const char __pyx_k_shape[] = "shape";
-static const char __pyx_k_start[] = "start";
-static const char __pyx_k_zeros[] = "zeros";
-static const char __pyx_k_center[] = "center";
-static const char __pyx_k_charge[] = "charge";
-static const char __pyx_k_dipole[] = "dipole";
-static const char __pyx_k_dipstr[] = "dipstr";
-static const char __pyx_k_dipvec[] = "dipvec";
-static const char __pyx_k_encode[] = "encode";
-static const char __pyx_k_format[] = "format";
-static const char __pyx_k_ifgrad[] = "ifgrad";
-static const char __pyx_k_import[] = "__import__";
-static const char __pyx_k_iscale[] = "iscale";
-static const char __pyx_k_jscale[] = "jscale";
-static const char __pyx_k_name_2[] = "__name__";
-static const char __pyx_k_nterms[] = "nterms";
-static const char __pyx_k_pickle[] = "pickle";
-static const char __pyx_k_reduce[] = "__reduce__";
-static const char __pyx_k_result[] = "result";
-static const char __pyx_k_source[] = "source";
-static const char __pyx_k_struct[] = "struct";
-static const char __pyx_k_target[] = "target";
-static const char __pyx_k_unpack[] = "unpack";
-static const char __pyx_k_update[] = "update";
-static const char __pyx_k_centers[] = "centers";
-static const char __pyx_k_complex[] = "complex";
-static const char __pyx_k_fjstemp[] = "fjstemp";
-static const char __pyx_k_fortran[] = "fortran";
-static const char __pyx_k_hdervec[] = "hdervec";
-static const char __pyx_k_jderivs[] = "jderivs";
-static const char __pyx_k_memview[] = "memview";
-static const char __pyx_k_scale_2[] = "scale_";
-static const char __pyx_k_sources[] = "sources";
-static const char __pyx_k_targets[] = "targets";
-static const char __pyx_k_tgt_box[] = "tgt_box";
-static const char __pyx_k_Ellipsis[] = "Ellipsis";
-static const char __pyx_k_fjdertmp[] = "fjdertmp";
-static const char __pyx_k_getstate[] = "__getstate__";
-static const char __pyx_k_ifcharge[] = "ifcharge";
-static const char __pyx_k_ifdipole[] = "ifdipole";
-static const char __pyx_k_isrc_box[] = "isrc_box";
-static const char __pyx_k_isrc_end[] = "isrc_end";
-static const char __pyx_k_itemsize[] = "itemsize";
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-static const char __pyx_k_nterms_2[] = "nterms_";
-static const char __pyx_k_pyx_type[] = "__pyx_type";
-static const char __pyx_k_setstate[] = "__setstate__";
-static const char __pyx_k_src_ibox[] = "src_ibox";
-static const char __pyx_k_TypeError[] = "TypeError";
-static const char __pyx_k_enumerate[] = "enumerate";
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-static const char __pyx_k_laplace_s[] = "laplace_s";
-static const char __pyx_k_pyx_state[] = "__pyx_state";
-static const char __pyx_k_reduce_ex[] = "__reduce_ex__";
-static const char __pyx_k_IndexError[] = "IndexError";
-static const char __pyx_k_ValueError[] = "ValueError";
-static const char __pyx_k_isrc_start[] = "isrc_start";
-static const char __pyx_k_itgt_start[] = "itgt_start";
-static const char __pyx_k_laplace_sp[] = "laplace_sp";
-static const char __pyx_k_maxthreads[] = "maxthreads";
-static const char __pyx_k_pyx_result[] = "__pyx_result";
-static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
-static const char __pyx_k_MemoryError[] = "MemoryError";
-static const char __pyx_k_PickleError[] = "PickleError";
-static const char __pyx_k_helmholtz_d[] = "helmholtz_d";
-static const char __pyx_k_helmholtz_k[] = "helmholtz_k";
-static const char __pyx_k_helmholtz_s[] = "helmholtz_s";
-static const char __pyx_k_qbx_centers[] = "qbx_centers";
-static const char __pyx_k_result_grad[] = "result_grad";
-static const char __pyx_k_helmholtz_sp[] = "helmholtz_sp";
-static const char __pyx_k_isrc_box_end[] = "isrc_box_end";
-static const char __pyx_k_pyx_checksum[] = "__pyx_checksum";
-static const char __pyx_k_stringsource[] = "stringsource";
-static const char __pyx_k_pyx_getbuffer[] = "__pyx_getbuffer";
-static const char __pyx_k_reduce_cython[] = "__reduce_cython__";
-static const char __pyx_k_Missing_charge[] = "Missing charge";
-static const char __pyx_k_Missing_dipstr[] = "Missing dipstr";
-static const char __pyx_k_Missing_dipvec[] = "Missing dipvec";
-static const char __pyx_k_h3dall_wrapper[] = "h3dall_wrapper";
-static const char __pyx_k_isrc_box_start[] = "isrc_box_start";
-static const char __pyx_k_View_MemoryView[] = "View.MemoryView";
-static const char __pyx_k_allocate_buffer[] = "allocate_buffer";
-static const char __pyx_k_dtype_is_object[] = "dtype_is_object";
-static const char __pyx_k_jfuns3d_wrapper[] = "jfuns3d_wrapper";
-static const char __pyx_k_pyx_PickleError[] = "__pyx_PickleError";
-static const char __pyx_k_setstate_cython[] = "__setstate_cython__";
-static const char __pyx_k_source_box_lists[] = "source_box_lists";
-static const char __pyx_k_box_source_starts[] = "box_source_starts";
-static const char __pyx_k_pyx_unpickle_Enum[] = "__pyx_unpickle_Enum";
-static const char __pyx_k_source_box_starts[] = "source_box_starts";
-static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
-static const char __pyx_k_strided_and_direct[] = "<strided and direct>";
-static const char __pyx_k_strided_and_indirect[] = "<strided and indirect>";
-static const char __pyx_k_contiguous_and_direct[] = "<contiguous and direct>";
-static const char __pyx_k_MemoryView_of_r_object[] = "<MemoryView of %r object>";
-static const char __pyx_k_center_to_target_lists[] = "center_to_target_lists";
-static const char __pyx_k_MemoryView_of_r_at_0x_x[] = "<MemoryView of %r at 0x%x>";
-static const char __pyx_k_center_to_target_starts[] = "center_to_target_starts";
-static const char __pyx_k_contiguous_and_indirect[] = "<contiguous and indirect>";
-static const char __pyx_k_Cannot_index_with_type_s[] = "Cannot index with type '%s'";
-static const char __pyx_k_qbx_center_to_target_box[] = "qbx_center_to_target_box";
-static const char __pyx_k_Invalid_shape_in_axis_d_d[] = "Invalid shape in axis %d: %d.";
-static const char __pyx_k_nterms_should_be_positive[] = "nterms should be positive";
-static const char __pyx_k_box_source_counts_nonchild[] = "box_source_counts_nonchild";
-static const char __pyx_k_itemsize_0_for_cython_array[] = "itemsize <= 0 for cython.array";
-static const char __pyx_k_unable_to_allocate_array_data[] = "unable to allocate array data.";
-static const char __pyx_k_jfuns3d__returned_error_code_d[] = "jfuns3d_ returned error code %d";
-static const char __pyx_k_strided_and_direct_or_indirect[] = "<strided and direct or indirect>";
-static const char __pyx_k_eval_target_specific_qbx_locals[] = "eval_target_specific_qbx_locals";
-static const char __pyx_k_Buffer_view_does_not_expose_stri[] = "Buffer view does not expose strides";
-static const char __pyx_k_Can_only_create_a_buffer_that_is[] = "Can only create a buffer that is contiguous in memory.";
-static const char __pyx_k_Cannot_assign_to_read_only_memor[] = "Cannot assign to read-only memoryview";
-static const char __pyx_k_Cannot_create_writable_memory_vi[] = "Cannot create writable memory view from read-only memoryview";
-static const char __pyx_k_Copyright_C_2018_Matt_Wala_Permi[] = "Copyright (C) 2018 Matt Wala\n\nPermission is hereby granted, free of charge, to any person obtaining a copy\nof this software and associated documentation files (the \"Software\"), to deal\nin the Software without restriction, including without limitation the rights\nto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\ncopies of the Software, and to permit persons to whom the Software is\nfurnished to do so, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in\nall copies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\nTHE SOFTWARE.\n";
-static const char __pyx_k_Does_not_support_computing_gradi[] = "Does not support computing gradient of dipole sources";
-static const char __pyx_k_Empty_shape_tuple_for_cython_arr[] = "Empty shape tuple for cython.array";
-static const char __pyx_k_Incompatible_checksums_s_vs_0xb0[] = "Incompatible checksums (%s vs 0xb068931 = (name))";
-static const char __pyx_k_Indirect_dimensions_not_supporte[] = "Indirect dimensions not supported";
-static const char __pyx_k_Invalid_mode_expected_c_or_fortr[] = "Invalid mode, expected 'c' or 'fortran', got %s";
-static const char __pyx_k_Out_of_bounds_on_buffer_access_a[] = "Out of bounds on buffer access (axis %d)";
-static const char __pyx_k_Unable_to_convert_item_to_object[] = "Unable to convert item to object";
-static const char __pyx_k_got_differing_extents_in_dimensi[] = "got differing extents in dimension %d (got %d and %d)";
-static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__";
-static const char __pyx_k_pytential_qbx_target_specific_im[] = "pytential/qbx/target_specific/impl.pyx";
-static const char __pyx_k_unable_to_allocate_shape_and_str[] = "unable to allocate shape and strides.";
-static const char __pyx_k_pytential_qbx_target_specific_im_2[] = "pytential.qbx.target_specific.impl";
-static PyObject *__pyx_n_s_ASCII;
-static PyObject *__pyx_kp_s_Buffer_view_does_not_expose_stri;
-static PyObject *__pyx_kp_s_Can_only_create_a_buffer_that_is;
-static PyObject *__pyx_kp_s_Cannot_assign_to_read_only_memor;
-static PyObject *__pyx_kp_s_Cannot_create_writable_memory_vi;
-static PyObject *__pyx_kp_s_Cannot_index_with_type_s;
-static PyObject *__pyx_kp_u_Does_not_support_computing_gradi;
-static PyObject *__pyx_n_s_Ellipsis;
-static PyObject *__pyx_kp_s_Empty_shape_tuple_for_cython_arr;
-static PyObject *__pyx_kp_s_Incompatible_checksums_s_vs_0xb0;
-static PyObject *__pyx_n_s_IndexError;
-static PyObject *__pyx_kp_s_Indirect_dimensions_not_supporte;
-static PyObject *__pyx_kp_s_Invalid_mode_expected_c_or_fortr;
-static PyObject *__pyx_kp_s_Invalid_shape_in_axis_d_d;
-static PyObject *__pyx_n_s_MemoryError;
-static PyObject *__pyx_kp_s_MemoryView_of_r_at_0x_x;
-static PyObject *__pyx_kp_s_MemoryView_of_r_object;
-static PyObject *__pyx_kp_u_Missing_charge;
-static PyObject *__pyx_kp_u_Missing_dipstr;
-static PyObject *__pyx_kp_u_Missing_dipvec;
-static PyObject *__pyx_n_b_O;
-static PyObject *__pyx_kp_s_Out_of_bounds_on_buffer_access_a;
-static PyObject *__pyx_n_s_PickleError;
-static PyObject *__pyx_n_s_TypeError;
-static PyObject *__pyx_kp_s_Unable_to_convert_item_to_object;
-static PyObject *__pyx_n_s_ValueError;
-static PyObject *__pyx_n_s_View_MemoryView;
-static PyObject *__pyx_n_s_allocate_buffer;
-static PyObject *__pyx_n_s_any;
-static PyObject *__pyx_n_s_base;
-static PyObject *__pyx_n_s_box_source_counts_nonchild;
-static PyObject *__pyx_n_s_box_source_starts;
-static PyObject *__pyx_n_s_c;
-static PyObject *__pyx_n_u_c;
-static PyObject *__pyx_n_s_center;
-static PyObject *__pyx_n_s_center_to_target_lists;
-static PyObject *__pyx_n_s_center_to_target_starts;
-static PyObject *__pyx_n_s_centers;
-static PyObject *__pyx_n_s_charge;
-static PyObject *__pyx_n_s_class;
-static PyObject *__pyx_n_s_cline_in_traceback;
-static PyObject *__pyx_n_s_complex;
-static PyObject *__pyx_kp_s_contiguous_and_direct;
-static PyObject *__pyx_kp_s_contiguous_and_indirect;
-static PyObject *__pyx_n_s_ctr;
-static PyObject *__pyx_n_s_dict;
-static PyObject *__pyx_n_s_dipole;
-static PyObject *__pyx_n_s_dipstr;
-static PyObject *__pyx_n_s_dipvec;
-static PyObject *__pyx_n_s_dtype;
-static PyObject *__pyx_n_s_dtype_is_object;
-static PyObject *__pyx_n_s_empty;
-static PyObject *__pyx_n_s_encode;
-static PyObject *__pyx_n_s_enumerate;
-static PyObject *__pyx_n_s_error;
-static PyObject *__pyx_n_s_eval_target_specific_qbx_locals;
-static PyObject *__pyx_n_s_fjder;
-static PyObject *__pyx_n_s_fjdertmp;
-static PyObject *__pyx_n_s_fjs;
-static PyObject *__pyx_n_s_fjstemp;
-static PyObject *__pyx_n_s_flags;
-static PyObject *__pyx_n_s_format;
-static PyObject *__pyx_n_s_fortran;
-static PyObject *__pyx_n_u_fortran;
-static PyObject *__pyx_n_s_getstate;
-static PyObject *__pyx_kp_s_got_differing_extents_in_dimensi;
-static PyObject *__pyx_n_s_grad;
-static PyObject *__pyx_n_s_h3dall_wrapper;
-static PyObject *__pyx_n_s_hders;
-static PyObject *__pyx_n_s_hdervec;
-static PyObject *__pyx_n_s_helmholtz_d;
-static PyObject *__pyx_n_s_helmholtz_k;
-static PyObject *__pyx_n_s_helmholtz_s;
-static PyObject *__pyx_n_s_helmholtz_sp;
-static PyObject *__pyx_n_s_hs;
-static PyObject *__pyx_n_s_hvec;
-static PyObject *__pyx_n_s_i;
-static PyObject *__pyx_n_s_ictr;
-static PyObject *__pyx_n_s_id;
-static PyObject *__pyx_n_s_ier;
-static PyObject *__pyx_n_s_ifcharge;
-static PyObject *__pyx_n_s_ifder;
-static PyObject *__pyx_n_s_ifdipole;
-static PyObject *__pyx_n_s_ifgrad;
-static PyObject *__pyx_n_s_ifpot;
-static PyObject *__pyx_n_s_import;
-static PyObject *__pyx_n_s_iscale;
-static PyObject *__pyx_n_s_isrc;
-static PyObject *__pyx_n_s_isrc_box;
-static PyObject *__pyx_n_s_isrc_box_end;
-static PyObject *__pyx_n_s_isrc_box_start;
-static PyObject *__pyx_n_s_isrc_end;
-static PyObject *__pyx_n_s_isrc_start;
-static PyObject *__pyx_n_s_itemsize;
-static PyObject *__pyx_kp_s_itemsize_0_for_cython_array;
-static PyObject *__pyx_n_s_itgt;
-static PyObject *__pyx_n_s_itgt_end;
-static PyObject *__pyx_n_s_itgt_start;
-static PyObject *__pyx_n_s_jderivs;
-static PyObject *__pyx_kp_u_jfuns3d__returned_error_code_d;
-static PyObject *__pyx_n_s_jfuns3d_wrapper;
-static PyObject *__pyx_n_s_jscale;
-static PyObject *__pyx_n_s_jvals;
-static PyObject *__pyx_n_s_laplace_d;
-static PyObject *__pyx_n_s_laplace_s;
-static PyObject *__pyx_n_s_laplace_sp;
-static PyObject *__pyx_n_s_lwfjs;
-static PyObject *__pyx_n_s_m;
-static PyObject *__pyx_n_s_main;
-static PyObject *__pyx_n_s_maxthreads;
-static PyObject *__pyx_n_s_memview;
-static PyObject *__pyx_n_s_mode;
-static PyObject *__pyx_n_s_name;
-static PyObject *__pyx_n_s_name_2;
-static PyObject *__pyx_n_s_ndim;
-static PyObject *__pyx_n_s_new;
-static PyObject *__pyx_kp_s_no_default___reduce___due_to_non;
-static PyObject *__pyx_n_s_np;
-static PyObject *__pyx_n_s_nterms;
-static PyObject *__pyx_n_s_nterms_2;
-static PyObject *__pyx_kp_u_nterms_should_be_positive;
-static PyObject *__pyx_n_s_ntop;
-static PyObject *__pyx_n_s_numpy;
-static PyObject *__pyx_n_s_obj;
-static PyObject *__pyx_n_s_order;
-static PyObject *__pyx_n_s_pack;
-static PyObject *__pyx_n_s_pickle;
-static PyObject *__pyx_n_s_pot;
-static PyObject *__pyx_kp_s_pytential_qbx_target_specific_im;
-static PyObject *__pyx_n_s_pytential_qbx_target_specific_im_2;
-static PyObject *__pyx_n_s_pyx_PickleError;
-static PyObject *__pyx_n_s_pyx_checksum;
-static PyObject *__pyx_n_s_pyx_getbuffer;
-static PyObject *__pyx_n_s_pyx_result;
-static PyObject *__pyx_n_s_pyx_state;
-static PyObject *__pyx_n_s_pyx_type;
-static PyObject *__pyx_n_s_pyx_unpickle_Enum;
-static PyObject *__pyx_n_s_pyx_vtable;
-static PyObject *__pyx_n_s_qbx_center_to_target_box;
-static PyObject *__pyx_n_s_qbx_centers;
-static PyObject *__pyx_n_s_range;
-static PyObject *__pyx_n_s_reduce;
-static PyObject *__pyx_n_s_reduce_cython;
-static PyObject *__pyx_n_s_reduce_ex;
-static PyObject *__pyx_n_s_result;
-static PyObject *__pyx_n_s_result_grad;
-static PyObject *__pyx_n_s_scale;
-static PyObject *__pyx_n_s_scale_2;
-static PyObject *__pyx_n_s_setstate;
-static PyObject *__pyx_n_s_setstate_cython;
-static PyObject *__pyx_n_s_shape;
-static PyObject *__pyx_n_s_size;
-static PyObject *__pyx_n_s_source;
-static PyObject *__pyx_n_s_source_box_lists;
-static PyObject *__pyx_n_s_source_box_starts;
-static PyObject *__pyx_n_s_sources;
-static PyObject *__pyx_n_s_src_ibox;
-static PyObject *__pyx_n_s_start;
-static PyObject *__pyx_n_s_step;
-static PyObject *__pyx_n_s_stop;
-static PyObject *__pyx_kp_s_strided_and_direct;
-static PyObject *__pyx_kp_s_strided_and_direct_or_indirect;
-static PyObject *__pyx_kp_s_strided_and_indirect;
-static PyObject *__pyx_kp_s_stringsource;
-static PyObject *__pyx_n_s_struct;
-static PyObject *__pyx_n_s_target;
-static PyObject *__pyx_n_s_targets;
-static PyObject *__pyx_n_s_test;
-static PyObject *__pyx_n_s_tgt;
-static PyObject *__pyx_n_s_tgt_box;
-static PyObject *__pyx_n_s_tid;
-static PyObject *__pyx_kp_s_unable_to_allocate_array_data;
-static PyObject *__pyx_kp_s_unable_to_allocate_shape_and_str;
-static PyObject *__pyx_n_s_unpack;
-static PyObject *__pyx_n_s_update;
-static PyObject *__pyx_n_s_z;
-static PyObject *__pyx_n_s_z_2;
-static PyObject *__pyx_n_s_zeros;
-static PyObject *__pyx_pf_9pytential_3qbx_15target_specific_4impl_jfuns3d_wrapper(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_nterms, PyObject *__pyx_v_z, PyObject *__pyx_v_scale, PyObject *__pyx_v_fjs, PyObject *__pyx_v_fjder); /* proto */
-static PyObject *__pyx_pf_9pytential_3qbx_15target_specific_4impl_2h3dall_wrapper(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_nterms, PyObject *__pyx_v_z, PyObject *__pyx_v_scale, PyObject *__pyx_v_hs, PyObject *__pyx_v_hders); /* proto */
-static PyObject *__pyx_pf_9pytential_3qbx_15target_specific_4impl_4eval_target_specific_qbx_locals(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_ifpot, int __pyx_v_ifgrad, int __pyx_v_ifcharge, int __pyx_v_ifdipole, int __pyx_v_order, __Pyx_memviewslice __pyx_v_sources, __Pyx_memviewslice __pyx_v_targets, __Pyx_memviewslice __pyx_v_centers, __Pyx_memviewslice __pyx_v_qbx_centers, __Pyx_memviewslice __pyx_v_qbx_center_to_target_box, __Pyx_memviewslice __pyx_v_center_to_target_starts, __Pyx_memviewslice __pyx_v_center_to_target_lists, __Pyx_memviewslice __pyx_v_source_box_starts, __Pyx_memviewslice __pyx_v_source_box_lists, __Pyx_memviewslice __pyx_v_box_source_starts, __Pyx_memviewslice __pyx_v_box_source_counts_nonchild, __pyx_t_double_complex __pyx_v_helmholtz_k, __Pyx_memviewslice __pyx_v_charge, __Pyx_memviewslice __pyx_v_dipstr, __Pyx_memviewslice __pyx_v_dipvec, __Pyx_memviewslice __pyx_v_pot, __Pyx_memviewslice __pyx_v_grad); /* proto */
-static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array___cinit__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_shape, Py_ssize_t __pyx_v_itemsize, PyObject *__pyx_v_format, PyObject *__pyx_v_mode, int __pyx_v_allocate_buffer); /* proto */
-static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_2__getbuffer__(struct __pyx_array_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
-static void __pyx_array___pyx_pf_15View_dot_MemoryView_5array_4__dealloc__(struct __pyx_array_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_5array_7memview___get__(struct __pyx_array_obj *__pyx_v_self); /* proto */
-static Py_ssize_t __pyx_array___pyx_pf_15View_dot_MemoryView_5array_6__len__(struct __pyx_array_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_8__getattr__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_attr); /* proto */
-static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_10__getitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item); /* proto */
-static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_12__setitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item, PyObject *__pyx_v_value); /* proto */
-static PyObject *__pyx_pf___pyx_array___reduce_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf___pyx_array_2__setstate_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */
-static int __pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum___init__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v_name); /* proto */
-static PyObject *__pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum_2__repr__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf___pyx_MemviewEnum___reduce_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf___pyx_MemviewEnum_2__setstate_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* proto */
-static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview___cinit__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj, int __pyx_v_flags, int __pyx_v_dtype_is_object); /* proto */
-static void __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_2__dealloc__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_4__getitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto */
-static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_6__setitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto */
-static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_8__getbuffer__(struct __pyx_memoryview_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_1T___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4base___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_5shape___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_7strides___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_10suboffsets___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4ndim___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_8itemsize___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_6nbytes___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4size___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static Py_ssize_t __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_10__len__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_12__repr__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_14__str__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
-static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_16is_c_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
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- *     z = k * tc_d
- *     lwfjs = BUFSIZE             # <<<<<<<<<<<<<<
- *     # jfuns3d_ only supports order > 0 (goes out of bounds if order = 0)
- *     order = max(1, order)
- */
-  __pyx_v_lwfjs = BUFSIZE;
-
-  /* "pytential/qbx/target_specific/impl.pyx":209
- *     lwfjs = BUFSIZE
- *     # jfuns3d_ only supports order > 0 (goes out of bounds if order = 0)
- *     order = max(1, order)             # <<<<<<<<<<<<<<
- *     jfuns3d_(&ier, &order, &z, jscale, jvals, &ifder, jderivs, &lwfjs, iscale,
- *              &ntop)
- */
-  __pyx_t_2 = __pyx_v_order;
-  __pyx_t_3 = 1;
-  if (((__pyx_t_2 > __pyx_t_3) != 0)) {
-    __pyx_t_4 = __pyx_t_2;
-  } else {
-    __pyx_t_4 = __pyx_t_3;
-  }
-  __pyx_v_order = __pyx_t_4;
-
-  /* "pytential/qbx/target_specific/impl.pyx":210
- *     # jfuns3d_ only supports order > 0 (goes out of bounds if order = 0)
- *     order = max(1, order)
- *     jfuns3d_(&ier, &order, &z, jscale, jvals, &ifder, jderivs, &lwfjs, iscale,             # <<<<<<<<<<<<<<
- *              &ntop)
- *     if ier:
- */
-  (void)(jfuns3d_((&__pyx_v_ier), (&__pyx_v_order), (&__pyx_v_z), __pyx_v_jscale, __pyx_v_jvals, (&__pyx_v_ifder), __pyx_v_jderivs, (&__pyx_v_lwfjs), __pyx_v_iscale, (&__pyx_v_ntop)));
-
-  /* "pytential/qbx/target_specific/impl.pyx":212
- *     jfuns3d_(&ier, &order, &z, jscale, jvals, &ifder, jderivs, &lwfjs, iscale,
- *              &ntop)
- *     if ier:             # <<<<<<<<<<<<<<
- *         # This could in theory fail.
- *         fprintf(stderr, "array passed to jfuns3d_ was too small\n")
- */
-  __pyx_t_5 = (__pyx_v_ier != 0);
-  if (__pyx_t_5) {
-
-    /* "pytential/qbx/target_specific/impl.pyx":214
- *     if ier:
- *         # This could in theory fail.
- *         fprintf(stderr, "array passed to jfuns3d_ was too small\n")             # <<<<<<<<<<<<<<
- *         abort()
- * 
- */
-    (void)(fprintf(stderr, ((char const *)"array passed to jfuns3d_ was too small\n")));
-
-    /* "pytential/qbx/target_specific/impl.pyx":215
- *         # This could in theory fail.
- *         fprintf(stderr, "array passed to jfuns3d_ was too small\n")
- *         abort()             # <<<<<<<<<<<<<<
- * 
- * # }}}
- */
-    abort();
-
-    /* "pytential/qbx/target_specific/impl.pyx":212
- *     jfuns3d_(&ier, &order, &z, jscale, jvals, &ifder, jderivs, &lwfjs, iscale,
- *              &ntop)
- *     if ier:             # <<<<<<<<<<<<<<
- *         # This could in theory fail.
- *         fprintf(stderr, "array passed to jfuns3d_ was too small\n")
- */
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":184
- * 
- * 
- * cdef void ts_helmholtz_precompute(             # <<<<<<<<<<<<<<
- *         double[3] center,
- *         double[3] target,
- */
-
-  /* function exit code */
-}
-
-/* "pytential/qbx/target_specific/impl.pyx":222
- * # {{{ Laplace S
- * 
- * cdef double complex ts_laplace_s(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_s(double *__pyx_v_source, double *__pyx_v_center, double *__pyx_v_target, __pyx_t_double_complex __pyx_v_charge, int __pyx_v_order) {
-  double __pyx_v_j;
-  double __pyx_v_result;
-  double __pyx_v_r;
-  double __pyx_v_sc_d;
-  double __pyx_v_tc_d;
-  double __pyx_v_cos_angle;
-  double __pyx_v_pj;
-  double __pyx_v_pjm1;
-  double __pyx_v_pjm2;
-  CYTHON_UNUSED long __pyx_v__;
-  __pyx_t_double_complex __pyx_r;
-  int __pyx_t_1;
-  long __pyx_t_2;
-  long __pyx_t_3;
-  long __pyx_t_4;
-
-  /* "pytential/qbx/target_specific/impl.pyx":236
- *         double pj, pjm1, pjm2
- * 
- *     tc_d = dist(target, center)             # <<<<<<<<<<<<<<
- *     sc_d = dist(source, center)
- * 
- */
-  __pyx_v_tc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_target, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":237
- * 
- *     tc_d = dist(target, center)
- *     sc_d = dist(source, center)             # <<<<<<<<<<<<<<
- * 
- *     cos_angle = ((
- */
-  __pyx_v_sc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_source, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":243
- *             (target[1] - center[1]) * (source[1] - center[1]) +
- *             (target[2] - center[2]) * (source[2] - center[2]))
- *             / (tc_d * sc_d))             # <<<<<<<<<<<<<<
- * 
- *     if order == 0:
- */
-  __pyx_v_cos_angle = ((((((__pyx_v_target[0]) - (__pyx_v_center[0])) * ((__pyx_v_source[0]) - (__pyx_v_center[0]))) + (((__pyx_v_target[1]) - (__pyx_v_center[1])) * ((__pyx_v_source[1]) - (__pyx_v_center[1])))) + (((__pyx_v_target[2]) - (__pyx_v_center[2])) * ((__pyx_v_source[2]) - (__pyx_v_center[2])))) / (__pyx_v_tc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":245
- *             / (tc_d * sc_d))
- * 
- *     if order == 0:             # <<<<<<<<<<<<<<
- *         return charge / sc_d
- * 
- */
-  __pyx_t_1 = ((__pyx_v_order == 0) != 0);
-  if (__pyx_t_1) {
-
-    /* "pytential/qbx/target_specific/impl.pyx":246
- * 
- *     if order == 0:
- *         return charge / sc_d             # <<<<<<<<<<<<<<
- * 
- *     pjm2 = 1
- */
-    __pyx_r = __Pyx_c_quot_double(__pyx_v_charge, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0));
-    goto __pyx_L0;
-
-    /* "pytential/qbx/target_specific/impl.pyx":245
- *             / (tc_d * sc_d))
- * 
- *     if order == 0:             # <<<<<<<<<<<<<<
- *         return charge / sc_d
- * 
- */
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":248
- *         return charge / sc_d
- * 
- *     pjm2 = 1             # <<<<<<<<<<<<<<
- *     pjm1 = cos_angle
- * 
- */
-  __pyx_v_pjm2 = 1.0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":249
- * 
- *     pjm2 = 1
- *     pjm1 = cos_angle             # <<<<<<<<<<<<<<
- * 
- *     result = 1 / sc_d + (cos_angle * tc_d) / (sc_d * sc_d)
- */
-  __pyx_v_pjm1 = __pyx_v_cos_angle;
-
-  /* "pytential/qbx/target_specific/impl.pyx":251
- *     pjm1 = cos_angle
- * 
- *     result = 1 / sc_d + (cos_angle * tc_d) / (sc_d * sc_d)             # <<<<<<<<<<<<<<
- * 
- *     r = (tc_d * tc_d) / (sc_d * sc_d * sc_d)
- */
-  __pyx_v_result = ((1.0 / __pyx_v_sc_d) + ((__pyx_v_cos_angle * __pyx_v_tc_d) / (__pyx_v_sc_d * __pyx_v_sc_d)));
-
-  /* "pytential/qbx/target_specific/impl.pyx":253
- *     result = 1 / sc_d + (cos_angle * tc_d) / (sc_d * sc_d)
- * 
- *     r = (tc_d * tc_d) / (sc_d * sc_d * sc_d)             # <<<<<<<<<<<<<<
- * 
- *     # Invariant: j matches loop counter. Using a double-precision version of the
- */
-  __pyx_v_r = ((__pyx_v_tc_d * __pyx_v_tc_d) / ((__pyx_v_sc_d * __pyx_v_sc_d) * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":257
- *     # Invariant: j matches loop counter. Using a double-precision version of the
- *     # loop counter avoids an int-to-double conversion inside the loop.
- *     j = 2.             # <<<<<<<<<<<<<<
- * 
- *     for _ in range(2, order + 1):
- */
-  __pyx_v_j = 2.;
-
-  /* "pytential/qbx/target_specific/impl.pyx":259
- *     j = 2.
- * 
- *     for _ in range(2, order + 1):             # <<<<<<<<<<<<<<
- *         pj = ( (2.*j-1.)*cos_angle*pjm1-(j-1.)*pjm2 ) / j
- *         result += pj * r
- */
-  __pyx_t_2 = (__pyx_v_order + 1);
-  __pyx_t_3 = __pyx_t_2;
-  for (__pyx_t_4 = 2; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
-    __pyx_v__ = __pyx_t_4;
-
-    /* "pytential/qbx/target_specific/impl.pyx":260
- * 
- *     for _ in range(2, order + 1):
- *         pj = ( (2.*j-1.)*cos_angle*pjm1-(j-1.)*pjm2 ) / j             # <<<<<<<<<<<<<<
- *         result += pj * r
- * 
- */
-    __pyx_v_pj = ((((((2. * __pyx_v_j) - 1.) * __pyx_v_cos_angle) * __pyx_v_pjm1) - ((__pyx_v_j - 1.) * __pyx_v_pjm2)) / __pyx_v_j);
-
-    /* "pytential/qbx/target_specific/impl.pyx":261
- *     for _ in range(2, order + 1):
- *         pj = ( (2.*j-1.)*cos_angle*pjm1-(j-1.)*pjm2 ) / j
- *         result += pj * r             # <<<<<<<<<<<<<<
- * 
- *         r *= (tc_d / sc_d)
- */
-    __pyx_v_result = (__pyx_v_result + (__pyx_v_pj * __pyx_v_r));
-
-    /* "pytential/qbx/target_specific/impl.pyx":263
- *         result += pj * r
- * 
- *         r *= (tc_d / sc_d)             # <<<<<<<<<<<<<<
- *         j += 1
- *         pjm2 = pjm1
- */
-    __pyx_v_r = (__pyx_v_r * (__pyx_v_tc_d / __pyx_v_sc_d));
-
-    /* "pytential/qbx/target_specific/impl.pyx":264
- * 
- *         r *= (tc_d / sc_d)
- *         j += 1             # <<<<<<<<<<<<<<
- *         pjm2 = pjm1
- *         pjm1 = pj
- */
-    __pyx_v_j = (__pyx_v_j + 1.0);
-
-    /* "pytential/qbx/target_specific/impl.pyx":265
- *         r *= (tc_d / sc_d)
- *         j += 1
- *         pjm2 = pjm1             # <<<<<<<<<<<<<<
- *         pjm1 = pj
- * 
- */
-    __pyx_v_pjm2 = __pyx_v_pjm1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":266
- *         j += 1
- *         pjm2 = pjm1
- *         pjm1 = pj             # <<<<<<<<<<<<<<
- * 
- *     return charge * result
- */
-    __pyx_v_pjm1 = __pyx_v_pj;
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":268
- *         pjm1 = pj
- * 
- *     return charge * result             # <<<<<<<<<<<<<<
- * 
- * # }}}
- */
-  __pyx_r = __Pyx_c_prod_double(__pyx_v_charge, __pyx_t_double_complex_from_parts(__pyx_v_result, 0));
-  goto __pyx_L0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":222
- * # {{{ Laplace S
- * 
- * cdef double complex ts_laplace_s(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-  /* function exit code */
-  __pyx_L0:;
-  return __pyx_r;
-}
-
-/* "pytential/qbx/target_specific/impl.pyx":275
- * # {{{ Laplace grad(S)
- * 
- * cdef void ts_laplace_sp(             # <<<<<<<<<<<<<<
- *         double complex[3] grad,
- *         double[3] source,
- */
-
-static void __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_sp(__pyx_t_double_complex *__pyx_v_grad, double *__pyx_v_source, double *__pyx_v_center, double *__pyx_v_target, __pyx_t_double_complex __pyx_v_charge, int __pyx_v_order) {
-  double __pyx_v_grad_tmp[3];
-  double __pyx_v_sc_d;
-  double __pyx_v_tc_d;
-  double __pyx_v_cos_angle;
-  double __pyx_v_Rn;
-  double __pyx_v_lvals[BUFSIZE];
-  double __pyx_v_lderivs[BUFSIZE];
-  double __pyx_v_smc[3];
-  double __pyx_v_tmc[3];
-  int __pyx_v_n;
-  long __pyx_v_m;
-  long __pyx_t_1;
-  long __pyx_t_2;
-  int __pyx_t_3;
-  long __pyx_t_4;
-  long __pyx_t_5;
-
-  /* "pytential/qbx/target_specific/impl.pyx":292
- *         int n
- * 
- *     for m in range(3):             # <<<<<<<<<<<<<<
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- */
-  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
-    __pyx_v_m = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":293
- * 
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]             # <<<<<<<<<<<<<<
- *         tmc[m] = target[m] - center[m]
- *         grad_tmp[m] = 0
- */
-    (__pyx_v_smc[__pyx_v_m]) = ((__pyx_v_source[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":294
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]             # <<<<<<<<<<<<<<
- *         grad_tmp[m] = 0
- * 
- */
-    (__pyx_v_tmc[__pyx_v_m]) = ((__pyx_v_target[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":295
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- *         grad_tmp[m] = 0             # <<<<<<<<<<<<<<
- * 
- *     tc_d = dist(target, center)
- */
-    (__pyx_v_grad_tmp[__pyx_v_m]) = 0.0;
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":297
- *         grad_tmp[m] = 0
- * 
- *     tc_d = dist(target, center)             # <<<<<<<<<<<<<<
- *     sc_d = dist(source, center)
- * 
- */
-  __pyx_v_tc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_target, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":298
- * 
- *     tc_d = dist(target, center)
- *     sc_d = dist(source, center)             # <<<<<<<<<<<<<<
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)
- */
-  __pyx_v_sc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_source, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":300
- *     sc_d = dist(source, center)
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)             # <<<<<<<<<<<<<<
- *     legvals(cos_angle, order, lvals, lderivs)
- * 
- */
-  __pyx_v_cos_angle = (((((__pyx_v_tmc[0]) * (__pyx_v_smc[0])) + ((__pyx_v_tmc[1]) * (__pyx_v_smc[1]))) + ((__pyx_v_tmc[2]) * (__pyx_v_smc[2]))) / (__pyx_v_tc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":301
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)
- *     legvals(cos_angle, order, lvals, lderivs)             # <<<<<<<<<<<<<<
- * 
- *     # Invariant: Rn = tc_d ** (n - 1) / sc_d ** (n + 1)
- */
-  __pyx_f_9pytential_3qbx_15target_specific_4impl_legvals(__pyx_v_cos_angle, __pyx_v_order, __pyx_v_lvals, __pyx_v_lderivs);
-
-  /* "pytential/qbx/target_specific/impl.pyx":304
- * 
- *     # Invariant: Rn = tc_d ** (n - 1) / sc_d ** (n + 1)
- *     Rn = 1 / (sc_d * sc_d)             # <<<<<<<<<<<<<<
- * 
- *     for n in range(1, 1 + order):
- */
-  __pyx_v_Rn = (1.0 / (__pyx_v_sc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":306
- *     Rn = 1 / (sc_d * sc_d)
- * 
- *     for n in range(1, 1 + order):             # <<<<<<<<<<<<<<
- *         for m in range(3):
- *             grad_tmp[m] += Rn * (
- */
-  __pyx_t_1 = (1 + __pyx_v_order);
-  __pyx_t_2 = __pyx_t_1;
-  for (__pyx_t_3 = 1; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
-    __pyx_v_n = __pyx_t_3;
-
-    /* "pytential/qbx/target_specific/impl.pyx":307
- * 
- *     for n in range(1, 1 + order):
- *         for m in range(3):             # <<<<<<<<<<<<<<
- *             grad_tmp[m] += Rn * (
- *                 n * (tmc[m] / tc_d) * lvals[n]
- */
-    for (__pyx_t_4 = 0; __pyx_t_4 < 3; __pyx_t_4+=1) {
-      __pyx_v_m = __pyx_t_4;
-
-      /* "pytential/qbx/target_specific/impl.pyx":308
- *     for n in range(1, 1 + order):
- *         for m in range(3):
- *             grad_tmp[m] += Rn * (             # <<<<<<<<<<<<<<
- *                 n * (tmc[m] / tc_d) * lvals[n]
- *                 + (smc[m] / sc_d - cos_angle * tmc[m] / tc_d) * lderivs[n])
- */
-      __pyx_t_5 = __pyx_v_m;
-
-      /* "pytential/qbx/target_specific/impl.pyx":310
- *             grad_tmp[m] += Rn * (
- *                 n * (tmc[m] / tc_d) * lvals[n]
- *                 + (smc[m] / sc_d - cos_angle * tmc[m] / tc_d) * lderivs[n])             # <<<<<<<<<<<<<<
- *         Rn *= tc_d / sc_d
- * 
- */
-      (__pyx_v_grad_tmp[__pyx_t_5]) = ((__pyx_v_grad_tmp[__pyx_t_5]) + (__pyx_v_Rn * (((__pyx_v_n * ((__pyx_v_tmc[__pyx_v_m]) / __pyx_v_tc_d)) * (__pyx_v_lvals[__pyx_v_n])) + ((((__pyx_v_smc[__pyx_v_m]) / __pyx_v_sc_d) - ((__pyx_v_cos_angle * (__pyx_v_tmc[__pyx_v_m])) / __pyx_v_tc_d)) * (__pyx_v_lderivs[__pyx_v_n])))));
-    }
-
-    /* "pytential/qbx/target_specific/impl.pyx":311
- *                 n * (tmc[m] / tc_d) * lvals[n]
- *                 + (smc[m] / sc_d - cos_angle * tmc[m] / tc_d) * lderivs[n])
- *         Rn *= tc_d / sc_d             # <<<<<<<<<<<<<<
- * 
- *     for m in range(3):
- */
-    __pyx_v_Rn = (__pyx_v_Rn * (__pyx_v_tc_d / __pyx_v_sc_d));
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":313
- *         Rn *= tc_d / sc_d
- * 
- *     for m in range(3):             # <<<<<<<<<<<<<<
- *         grad[m] += charge * grad_tmp[m]
- * 
- */
-  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
-    __pyx_v_m = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":314
- * 
- *     for m in range(3):
- *         grad[m] += charge * grad_tmp[m]             # <<<<<<<<<<<<<<
- * 
- * # }}}
- */
-    __pyx_t_2 = __pyx_v_m;
-    (__pyx_v_grad[__pyx_t_2]) = __Pyx_c_sum_double((__pyx_v_grad[__pyx_t_2]), __Pyx_c_prod_double(__pyx_v_charge, __pyx_t_double_complex_from_parts((__pyx_v_grad_tmp[__pyx_v_m]), 0)));
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":275
- * # {{{ Laplace grad(S)
- * 
- * cdef void ts_laplace_sp(             # <<<<<<<<<<<<<<
- *         double complex[3] grad,
- *         double[3] source,
- */
-
-  /* function exit code */
-}
-
-/* "pytential/qbx/target_specific/impl.pyx":321
- * # {{{ Laplace D
- * 
- * cdef double complex ts_laplace_d(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_d(double *__pyx_v_source, double *__pyx_v_center, double *__pyx_v_target, double *__pyx_v_dipole, __pyx_t_double_complex __pyx_v_dipstr, int __pyx_v_order) {
-  int __pyx_v_n;
-  int __pyx_v_m;
-  double __pyx_v_sc_d;
-  double __pyx_v_tc_d;
-  double __pyx_v_cos_angle;
-  double __pyx_v_Rn;
-  double __pyx_v_lvals[BUFSIZE];
-  double __pyx_v_lderivs[BUFSIZE];
-  double __pyx_v_smc[3];
-  double __pyx_v_tmc[3];
-  double __pyx_v_grad[3];
-  __pyx_t_double_complex __pyx_r;
-  int __pyx_t_1;
-  long __pyx_t_2;
-  long __pyx_t_3;
-  int __pyx_t_4;
-  int __pyx_t_5;
-
-  /* "pytential/qbx/target_specific/impl.pyx":336
- *         double[3] smc, tmc, grad
- * 
- *     for m in range(3):             # <<<<<<<<<<<<<<
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- */
-  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
-    __pyx_v_m = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":337
- * 
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]             # <<<<<<<<<<<<<<
- *         tmc[m] = target[m] - center[m]
- *         grad[m] = 0
- */
-    (__pyx_v_smc[__pyx_v_m]) = ((__pyx_v_source[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":338
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]             # <<<<<<<<<<<<<<
- *         grad[m] = 0
- * 
- */
-    (__pyx_v_tmc[__pyx_v_m]) = ((__pyx_v_target[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":339
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- *         grad[m] = 0             # <<<<<<<<<<<<<<
- * 
- *     tc_d = dist(target, center)
- */
-    (__pyx_v_grad[__pyx_v_m]) = 0.0;
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":341
- *         grad[m] = 0
- * 
- *     tc_d = dist(target, center)             # <<<<<<<<<<<<<<
- *     sc_d = dist(source, center)
- * 
- */
-  __pyx_v_tc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_target, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":342
- * 
- *     tc_d = dist(target, center)
- *     sc_d = dist(source, center)             # <<<<<<<<<<<<<<
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)
- */
-  __pyx_v_sc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_source, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":344
- *     sc_d = dist(source, center)
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)             # <<<<<<<<<<<<<<
- *     legvals(cos_angle, order, lvals, lderivs)
- * 
- */
-  __pyx_v_cos_angle = (((((__pyx_v_tmc[0]) * (__pyx_v_smc[0])) + ((__pyx_v_tmc[1]) * (__pyx_v_smc[1]))) + ((__pyx_v_tmc[2]) * (__pyx_v_smc[2]))) / (__pyx_v_tc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":345
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)
- *     legvals(cos_angle, order, lvals, lderivs)             # <<<<<<<<<<<<<<
- * 
- *     # Invariant: Rn = (tc_d ** n / sc_d ** (n + 2))
- */
-  __pyx_f_9pytential_3qbx_15target_specific_4impl_legvals(__pyx_v_cos_angle, __pyx_v_order, __pyx_v_lvals, __pyx_v_lderivs);
-
-  /* "pytential/qbx/target_specific/impl.pyx":348
- * 
- *     # Invariant: Rn = (tc_d ** n / sc_d ** (n + 2))
- *     Rn = 1 / (sc_d * sc_d)             # <<<<<<<<<<<<<<
- * 
- *     for n in range(0, order + 1):
- */
-  __pyx_v_Rn = (1.0 / (__pyx_v_sc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":350
- *     Rn = 1 / (sc_d * sc_d)
- * 
- *     for n in range(0, order + 1):             # <<<<<<<<<<<<<<
- *         for m in range(3):
- *             grad[m] += Rn * (
- */
-  __pyx_t_2 = (__pyx_v_order + 1);
-  __pyx_t_3 = __pyx_t_2;
-  for (__pyx_t_1 = 0; __pyx_t_1 < __pyx_t_3; __pyx_t_1+=1) {
-    __pyx_v_n = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":351
- * 
- *     for n in range(0, order + 1):
- *         for m in range(3):             # <<<<<<<<<<<<<<
- *             grad[m] += Rn * (
- *                     -(n + 1) * (smc[m] / sc_d) * lvals[n]
- */
-    for (__pyx_t_4 = 0; __pyx_t_4 < 3; __pyx_t_4+=1) {
-      __pyx_v_m = __pyx_t_4;
-
-      /* "pytential/qbx/target_specific/impl.pyx":352
- *     for n in range(0, order + 1):
- *         for m in range(3):
- *             grad[m] += Rn * (             # <<<<<<<<<<<<<<
- *                     -(n + 1) * (smc[m] / sc_d) * lvals[n]
- *                     + (tmc[m] / tc_d - cos_angle * smc[m] / sc_d) * lderivs[n])
- */
-      __pyx_t_5 = __pyx_v_m;
-
-      /* "pytential/qbx/target_specific/impl.pyx":354
- *             grad[m] += Rn * (
- *                     -(n + 1) * (smc[m] / sc_d) * lvals[n]
- *                     + (tmc[m] / tc_d - cos_angle * smc[m] / sc_d) * lderivs[n])             # <<<<<<<<<<<<<<
- *         Rn *= (tc_d / sc_d)
- * 
- */
-      (__pyx_v_grad[__pyx_t_5]) = ((__pyx_v_grad[__pyx_t_5]) + (__pyx_v_Rn * ((((-(__pyx_v_n + 1)) * ((__pyx_v_smc[__pyx_v_m]) / __pyx_v_sc_d)) * (__pyx_v_lvals[__pyx_v_n])) + ((((__pyx_v_tmc[__pyx_v_m]) / __pyx_v_tc_d) - ((__pyx_v_cos_angle * (__pyx_v_smc[__pyx_v_m])) / __pyx_v_sc_d)) * (__pyx_v_lderivs[__pyx_v_n])))));
-    }
-
-    /* "pytential/qbx/target_specific/impl.pyx":355
- *                     -(n + 1) * (smc[m] / sc_d) * lvals[n]
- *                     + (tmc[m] / tc_d - cos_angle * smc[m] / sc_d) * lderivs[n])
- *         Rn *= (tc_d / sc_d)             # <<<<<<<<<<<<<<
- * 
- *     return dipstr * (
- */
-    __pyx_v_Rn = (__pyx_v_Rn * (__pyx_v_tc_d / __pyx_v_sc_d));
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":357
- *         Rn *= (tc_d / sc_d)
- * 
- *     return dipstr * (             # <<<<<<<<<<<<<<
- *             dipole[0] * grad[0] + dipole[1] * grad[1] + dipole[2] * grad[2])
- * 
- */
-  __pyx_r = __Pyx_c_prod_double(__pyx_v_dipstr, __pyx_t_double_complex_from_parts(((((__pyx_v_dipole[0]) * (__pyx_v_grad[0])) + ((__pyx_v_dipole[1]) * (__pyx_v_grad[1]))) + ((__pyx_v_dipole[2]) * (__pyx_v_grad[2]))), 0));
-  goto __pyx_L0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":321
- * # {{{ Laplace D
- * 
- * cdef double complex ts_laplace_d(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-  /* function exit code */
-  __pyx_L0:;
-  return __pyx_r;
-}
-
-/* "pytential/qbx/target_specific/impl.pyx":365
- * # {{{ Helmholtz S
- * 
- * cdef double complex ts_helmholtz_s(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_s(double *__pyx_v_source, double *__pyx_v_center, double *__pyx_v_target, __pyx_t_double_complex __pyx_v_charge, int __pyx_v_order, __pyx_t_double_complex __pyx_v_k, __pyx_t_double_complex *__pyx_v_jvals, double __pyx_v_jscale) {
-  int __pyx_v_n;
-  int __pyx_v_ifder;
-  double __pyx_v_sc_d;
-  double __pyx_v_tc_d;
-  double __pyx_v_cos_angle;
-  double __pyx_v_lvals[BUFSIZE];
-  __pyx_t_double_complex __pyx_v_hvals[BUFSIZE];
-  double __pyx_v_hscale;
-  double __pyx_v_unscale;
-  __pyx_t_double_complex __pyx_v_z;
-  __pyx_t_double_complex __pyx_v_result;
-  __pyx_t_double_complex __pyx_r;
-  double __pyx_t_1;
-  long __pyx_t_2;
-  long __pyx_t_3;
-  int __pyx_t_4;
-
-  /* "pytential/qbx/target_specific/impl.pyx":385
- *         double complex z, result
- * 
- *     tc_d = dist(target, center)             # <<<<<<<<<<<<<<
- *     sc_d = dist(source, center)
- * 
- */
-  __pyx_v_tc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_target, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":386
- * 
- *     tc_d = dist(target, center)
- *     sc_d = dist(source, center)             # <<<<<<<<<<<<<<
- * 
- *     cos_angle = ((
- */
-  __pyx_v_sc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_source, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":392
- *             (target[1] - center[1]) * (source[1] - center[1]) +
- *             (target[2] - center[2]) * (source[2] - center[2]))
- *             / (tc_d * sc_d))             # <<<<<<<<<<<<<<
- * 
- *     # Evaluate the Legendre terms.
- */
-  __pyx_v_cos_angle = ((((((__pyx_v_target[0]) - (__pyx_v_center[0])) * ((__pyx_v_source[0]) - (__pyx_v_center[0]))) + (((__pyx_v_target[1]) - (__pyx_v_center[1])) * ((__pyx_v_source[1]) - (__pyx_v_center[1])))) + (((__pyx_v_target[2]) - (__pyx_v_center[2])) * ((__pyx_v_source[2]) - (__pyx_v_center[2])))) / (__pyx_v_tc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":395
- * 
- *     # Evaluate the Legendre terms.
- *     legvals(cos_angle, order, lvals, NULL)             # <<<<<<<<<<<<<<
- * 
- *     # Scaling magic for Hankel terms.
- */
-  __pyx_f_9pytential_3qbx_15target_specific_4impl_legvals(__pyx_v_cos_angle, __pyx_v_order, __pyx_v_lvals, NULL);
-
-  /* "pytential/qbx/target_specific/impl.pyx":399
- *     # Scaling magic for Hankel terms.
- *     # These values are taken from the fmmlib documentation.
- *     hscale = cabs(k * sc_d) if (cabs(k * sc_d) < 1) else 1             # <<<<<<<<<<<<<<
- *     # unscale = (jscale / hscale) ** n
- *     # Multiply against unscale to remove the scaling.
- */
-  if (((cabs(__Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0))) < 1.0) != 0)) {
-    __pyx_t_1 = cabs(__Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0)));
-  } else {
-    __pyx_t_1 = 1.0;
-  }
-  __pyx_v_hscale = __pyx_t_1;
-
-  /* "pytential/qbx/target_specific/impl.pyx":402
- *     # unscale = (jscale / hscale) ** n
- *     # Multiply against unscale to remove the scaling.
- *     unscale = 1             # <<<<<<<<<<<<<<
- * 
- *     # Evaluate the spherical Hankel terms.
- */
-  __pyx_v_unscale = 1.0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":405
- * 
- *     # Evaluate the spherical Hankel terms.
- *     z = k * sc_d             # <<<<<<<<<<<<<<
- *     ifder = 0
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, NULL)
- */
-  __pyx_v_z = __Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0));
-
-  /* "pytential/qbx/target_specific/impl.pyx":406
- *     # Evaluate the spherical Hankel terms.
- *     z = k * sc_d
- *     ifder = 0             # <<<<<<<<<<<<<<
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, NULL)
- * 
- */
-  __pyx_v_ifder = 0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":407
- *     z = k * sc_d
- *     ifder = 0
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, NULL)             # <<<<<<<<<<<<<<
- * 
- *     result = 0
- */
-  (void)(h3dall_((&__pyx_v_order), (&__pyx_v_z), (&__pyx_v_hscale), __pyx_v_hvals, (&__pyx_v_ifder), NULL));
-
-  /* "pytential/qbx/target_specific/impl.pyx":409
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, NULL)
- * 
- *     result = 0             # <<<<<<<<<<<<<<
- * 
- *     for n in range(1 + order):
- */
-  __pyx_v_result = __pyx_t_double_complex_from_parts(0, 0);
-
-  /* "pytential/qbx/target_specific/impl.pyx":411
- *     result = 0
- * 
- *     for n in range(1 + order):             # <<<<<<<<<<<<<<
- *         result += (2 * n + 1) * unscale * (jvals[n] * hvals[n] * lvals[n])
- *         unscale *= jscale / hscale
- */
-  __pyx_t_2 = (1 + __pyx_v_order);
-  __pyx_t_3 = __pyx_t_2;
-  for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
-    __pyx_v_n = __pyx_t_4;
-
-    /* "pytential/qbx/target_specific/impl.pyx":412
- * 
- *     for n in range(1 + order):
- *         result += (2 * n + 1) * unscale * (jvals[n] * hvals[n] * lvals[n])             # <<<<<<<<<<<<<<
- *         unscale *= jscale / hscale
- * 
- */
-    __pyx_v_result = __Pyx_c_sum_double(__pyx_v_result, __Pyx_c_prod_double(__pyx_t_double_complex_from_parts((((2 * __pyx_v_n) + 1) * __pyx_v_unscale), 0), __Pyx_c_prod_double(__Pyx_c_prod_double((__pyx_v_jvals[__pyx_v_n]), (__pyx_v_hvals[__pyx_v_n])), __pyx_t_double_complex_from_parts((__pyx_v_lvals[__pyx_v_n]), 0))));
-
-    /* "pytential/qbx/target_specific/impl.pyx":413
- *     for n in range(1 + order):
- *         result += (2 * n + 1) * unscale * (jvals[n] * hvals[n] * lvals[n])
- *         unscale *= jscale / hscale             # <<<<<<<<<<<<<<
- * 
- *     return 1j * k * charge * result
- */
-    __pyx_v_unscale = (__pyx_v_unscale * (__pyx_v_jscale / __pyx_v_hscale));
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":415
- *         unscale *= jscale / hscale
- * 
- *     return 1j * k * charge * result             # <<<<<<<<<<<<<<
- * 
- * # }}}
- */
-  __pyx_r = __Pyx_c_prod_double(__Pyx_c_prod_double(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts(0, 1.0), __pyx_v_k), __pyx_v_charge), __pyx_v_result);
-  goto __pyx_L0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":365
- * # {{{ Helmholtz S
- * 
- * cdef double complex ts_helmholtz_s(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-  /* function exit code */
-  __pyx_L0:;
-  return __pyx_r;
-}
-
-/* "pytential/qbx/target_specific/impl.pyx":422
- * # {{{ Helmholtz grad(S)
- * 
- * cdef void ts_helmholtz_sp(             # <<<<<<<<<<<<<<
- *         double complex[3] grad,
- *         double[3] source,
- */
-
-static void __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_sp(__pyx_t_double_complex *__pyx_v_grad, double *__pyx_v_source, double *__pyx_v_center, double *__pyx_v_target, __pyx_t_double_complex __pyx_v_charge, int __pyx_v_order, __pyx_t_double_complex __pyx_v_k, __pyx_t_double_complex *__pyx_v_jvals, __pyx_t_double_complex *__pyx_v_jderivs, double __pyx_v_jscale) {
-  int __pyx_v_n;
-  int __pyx_v_m;
-  int __pyx_v_ifder;
-  double __pyx_v_sc_d;
-  double __pyx_v_tc_d;
-  double __pyx_v_cos_angle;
-  double __pyx_v_smc[3];
-  double __pyx_v_tmc[3];
-  __pyx_t_double_complex __pyx_v_grad_tmp[3];
-  double __pyx_v_lvals[BUFSIZE];
-  double __pyx_v_lderivs[BUFSIZE];
-  __pyx_t_double_complex __pyx_v_z;
-  __pyx_t_double_complex __pyx_v_hvals[BUFSIZE];
-  double __pyx_v_hscale;
-  double __pyx_v_unscale;
-  int __pyx_t_1;
-  double __pyx_t_2;
-  long __pyx_t_3;
-  long __pyx_t_4;
-  int __pyx_t_5;
-  int __pyx_t_6;
-
-  /* "pytential/qbx/target_specific/impl.pyx":447
- *         double hscale, unscale
- * 
- *     for m in range(3):             # <<<<<<<<<<<<<<
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- */
-  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
-    __pyx_v_m = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":448
- * 
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]             # <<<<<<<<<<<<<<
- *         tmc[m] = target[m] - center[m]
- *         grad_tmp[m] = 0
- */
-    (__pyx_v_smc[__pyx_v_m]) = ((__pyx_v_source[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":449
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]             # <<<<<<<<<<<<<<
- *         grad_tmp[m] = 0
- * 
- */
-    (__pyx_v_tmc[__pyx_v_m]) = ((__pyx_v_target[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":450
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- *         grad_tmp[m] = 0             # <<<<<<<<<<<<<<
- * 
- *     tc_d = dist(target, center)
- */
-    (__pyx_v_grad_tmp[__pyx_v_m]) = __pyx_t_double_complex_from_parts(0, 0);
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":452
- *         grad_tmp[m] = 0
- * 
- *     tc_d = dist(target, center)             # <<<<<<<<<<<<<<
- *     sc_d = dist(source, center)
- * 
- */
-  __pyx_v_tc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_target, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":453
- * 
- *     tc_d = dist(target, center)
- *     sc_d = dist(source, center)             # <<<<<<<<<<<<<<
- * 
- *     # Evaluate the Legendre terms.
- */
-  __pyx_v_sc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_source, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":456
- * 
- *     # Evaluate the Legendre terms.
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)             # <<<<<<<<<<<<<<
- *     legvals(cos_angle, order, lvals, lderivs)
- * 
- */
-  __pyx_v_cos_angle = (((((__pyx_v_tmc[0]) * (__pyx_v_smc[0])) + ((__pyx_v_tmc[1]) * (__pyx_v_smc[1]))) + ((__pyx_v_tmc[2]) * (__pyx_v_smc[2]))) / (__pyx_v_tc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":457
- *     # Evaluate the Legendre terms.
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)
- *     legvals(cos_angle, order, lvals, lderivs)             # <<<<<<<<<<<<<<
- * 
- *     # Scaling magic for Hankel terms.
- */
-  __pyx_f_9pytential_3qbx_15target_specific_4impl_legvals(__pyx_v_cos_angle, __pyx_v_order, __pyx_v_lvals, __pyx_v_lderivs);
-
-  /* "pytential/qbx/target_specific/impl.pyx":461
- *     # Scaling magic for Hankel terms.
- *     # These values are taken from the fmmlib documentation.
- *     hscale = cabs(k * sc_d) if (cabs(k * sc_d) < 1) else 1             # <<<<<<<<<<<<<<
- *     # unscale = (jscale / hscale) ** n
- *     # Multiply against unscale to remove the scaling.
- */
-  if (((cabs(__Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0))) < 1.0) != 0)) {
-    __pyx_t_2 = cabs(__Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0)));
-  } else {
-    __pyx_t_2 = 1.0;
-  }
-  __pyx_v_hscale = __pyx_t_2;
-
-  /* "pytential/qbx/target_specific/impl.pyx":464
- *     # unscale = (jscale / hscale) ** n
- *     # Multiply against unscale to remove the scaling.
- *     unscale = 1             # <<<<<<<<<<<<<<
- * 
- *     # Evaluate the spherical Hankel terms.
- */
-  __pyx_v_unscale = 1.0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":467
- * 
- *     # Evaluate the spherical Hankel terms.
- *     z = k * sc_d             # <<<<<<<<<<<<<<
- *     ifder = 0
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, NULL)
- */
-  __pyx_v_z = __Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0));
-
-  /* "pytential/qbx/target_specific/impl.pyx":468
- *     # Evaluate the spherical Hankel terms.
- *     z = k * sc_d
- *     ifder = 0             # <<<<<<<<<<<<<<
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, NULL)
- * 
- */
-  __pyx_v_ifder = 0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":469
- *     z = k * sc_d
- *     ifder = 0
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, NULL)             # <<<<<<<<<<<<<<
- * 
- *     #
- */
-  (void)(h3dall_((&__pyx_v_order), (&__pyx_v_z), (&__pyx_v_hscale), __pyx_v_hvals, (&__pyx_v_ifder), NULL));
-
-  /* "pytential/qbx/target_specific/impl.pyx":479
- *     #
- *     #
- *     for n in range(0, order + 1):             # <<<<<<<<<<<<<<
- *         for m in range(3):
- *             grad_tmp[m] += (2 * n + 1) * unscale * hvals[n] / tc_d * (
- */
-  __pyx_t_3 = (__pyx_v_order + 1);
-  __pyx_t_4 = __pyx_t_3;
-  for (__pyx_t_1 = 0; __pyx_t_1 < __pyx_t_4; __pyx_t_1+=1) {
-    __pyx_v_n = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":480
- *     #
- *     for n in range(0, order + 1):
- *         for m in range(3):             # <<<<<<<<<<<<<<
- *             grad_tmp[m] += (2 * n + 1) * unscale * hvals[n] / tc_d * (
- *                     k * jderivs[n] * lvals[n] * tmc[m]
- */
-    for (__pyx_t_5 = 0; __pyx_t_5 < 3; __pyx_t_5+=1) {
-      __pyx_v_m = __pyx_t_5;
-
-      /* "pytential/qbx/target_specific/impl.pyx":481
- *     for n in range(0, order + 1):
- *         for m in range(3):
- *             grad_tmp[m] += (2 * n + 1) * unscale * hvals[n] / tc_d * (             # <<<<<<<<<<<<<<
- *                     k * jderivs[n] * lvals[n] * tmc[m]
- *                     + (smc[m] / sc_d - cos_angle * tmc[m] / tc_d)
- */
-      __pyx_t_6 = __pyx_v_m;
-
-      /* "pytential/qbx/target_specific/impl.pyx":483
- *             grad_tmp[m] += (2 * n + 1) * unscale * hvals[n] / tc_d * (
- *                     k * jderivs[n] * lvals[n] * tmc[m]
- *                     + (smc[m] / sc_d - cos_angle * tmc[m] / tc_d)             # <<<<<<<<<<<<<<
- *                     * jvals[n] * lderivs[n])
- *         unscale *= jscale / hscale
- */
-      (__pyx_v_grad_tmp[__pyx_t_6]) = __Pyx_c_sum_double((__pyx_v_grad_tmp[__pyx_t_6]), __Pyx_c_prod_double(__Pyx_c_quot_double(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts((((2 * __pyx_v_n) + 1) * __pyx_v_unscale), 0), (__pyx_v_hvals[__pyx_v_n])), __pyx_t_double_complex_from_parts(__pyx_v_tc_d, 0)), __Pyx_c_sum_double(__Pyx_c_prod_double(__Pyx_c_prod_double(__Pyx_c_prod_double(__pyx_v_k, (__pyx_v_jderivs[__pyx_v_n])), __pyx_t_double_complex_from_parts((__pyx_v_lvals[__pyx_v_n]), 0)), __pyx_t_double_complex_from_parts((__pyx_v_tmc[__pyx_v_m]), 0)), __Pyx_c_prod_double(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts((((__pyx_v_smc[__pyx_v_m]) / __pyx_v_sc_d) - ((__pyx_v_cos_angle * (__pyx_v_tmc[__pyx_v_m])) / __pyx_v_tc_d)), 0), (__pyx_v_jvals[__pyx_v_n])), __pyx_t_double_complex_from_parts((__pyx_v_lderivs[__pyx_v_n]), 0)))));
-    }
-
-    /* "pytential/qbx/target_specific/impl.pyx":485
- *                     + (smc[m] / sc_d - cos_angle * tmc[m] / tc_d)
- *                     * jvals[n] * lderivs[n])
- *         unscale *= jscale / hscale             # <<<<<<<<<<<<<<
- * 
- *     for m in range(3):
- */
-    __pyx_v_unscale = (__pyx_v_unscale * (__pyx_v_jscale / __pyx_v_hscale));
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":487
- *         unscale *= jscale / hscale
- * 
- *     for m in range(3):             # <<<<<<<<<<<<<<
- *         grad[m] += 1j * k * charge * grad_tmp[m]
- * 
- */
-  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
-    __pyx_v_m = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":488
- * 
- *     for m in range(3):
- *         grad[m] += 1j * k * charge * grad_tmp[m]             # <<<<<<<<<<<<<<
- * 
- * # }}}
- */
-    __pyx_t_5 = __pyx_v_m;
-    (__pyx_v_grad[__pyx_t_5]) = __Pyx_c_sum_double((__pyx_v_grad[__pyx_t_5]), __Pyx_c_prod_double(__Pyx_c_prod_double(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts(0, 1.0), __pyx_v_k), __pyx_v_charge), (__pyx_v_grad_tmp[__pyx_v_m])));
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":422
- * # {{{ Helmholtz grad(S)
- * 
- * cdef void ts_helmholtz_sp(             # <<<<<<<<<<<<<<
- *         double complex[3] grad,
- *         double[3] source,
- */
-
-  /* function exit code */
-}
-
-/* "pytential/qbx/target_specific/impl.pyx":495
- * # {{{ Helmholtz D
- * 
- * cdef double complex ts_helmholtz_d(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-static __pyx_t_double_complex __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_d(double *__pyx_v_source, double *__pyx_v_center, double *__pyx_v_target, double *__pyx_v_dipole, __pyx_t_double_complex __pyx_v_dipstr, int __pyx_v_order, __pyx_t_double_complex __pyx_v_k, __pyx_t_double_complex *__pyx_v_jvals, double __pyx_v_jscale) {
-  int __pyx_v_n;
-  int __pyx_v_m;
-  int __pyx_v_ifder;
-  double __pyx_v_sc_d;
-  double __pyx_v_tc_d;
-  double __pyx_v_cos_angle;
-  double __pyx_v_smc[3];
-  double __pyx_v_tmc[3];
-  __pyx_t_double_complex __pyx_v_grad[3];
-  double __pyx_v_lvals[BUFSIZE];
-  double __pyx_v_lderivs[BUFSIZE];
-  __pyx_t_double_complex __pyx_v_z;
-  __pyx_t_double_complex __pyx_v_hvals[BUFSIZE];
-  __pyx_t_double_complex __pyx_v_hderivs[BUFSIZE];
-  double __pyx_v_hscale;
-  double __pyx_v_unscale;
-  __pyx_t_double_complex __pyx_r;
-  int __pyx_t_1;
-  double __pyx_t_2;
-  long __pyx_t_3;
-  long __pyx_t_4;
-  int __pyx_t_5;
-  int __pyx_t_6;
-
-  /* "pytential/qbx/target_specific/impl.pyx":519
- *         double hscale, unscale
- * 
- *     for m in range(3):             # <<<<<<<<<<<<<<
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- */
-  for (__pyx_t_1 = 0; __pyx_t_1 < 3; __pyx_t_1+=1) {
-    __pyx_v_m = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":520
- * 
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]             # <<<<<<<<<<<<<<
- *         tmc[m] = target[m] - center[m]
- *         grad[m] = 0
- */
-    (__pyx_v_smc[__pyx_v_m]) = ((__pyx_v_source[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":521
- *     for m in range(3):
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]             # <<<<<<<<<<<<<<
- *         grad[m] = 0
- * 
- */
-    (__pyx_v_tmc[__pyx_v_m]) = ((__pyx_v_target[__pyx_v_m]) - (__pyx_v_center[__pyx_v_m]));
-
-    /* "pytential/qbx/target_specific/impl.pyx":522
- *         smc[m] = source[m] - center[m]
- *         tmc[m] = target[m] - center[m]
- *         grad[m] = 0             # <<<<<<<<<<<<<<
- * 
- *     tc_d = dist(target, center)
- */
-    (__pyx_v_grad[__pyx_v_m]) = __pyx_t_double_complex_from_parts(0, 0);
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":524
- *         grad[m] = 0
- * 
- *     tc_d = dist(target, center)             # <<<<<<<<<<<<<<
- *     sc_d = dist(source, center)
- * 
- */
-  __pyx_v_tc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_target, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":525
- * 
- *     tc_d = dist(target, center)
- *     sc_d = dist(source, center)             # <<<<<<<<<<<<<<
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)
- */
-  __pyx_v_sc_d = __pyx_f_9pytential_3qbx_15target_specific_4impl_dist(__pyx_v_source, __pyx_v_center);
-
-  /* "pytential/qbx/target_specific/impl.pyx":527
- *     sc_d = dist(source, center)
- * 
- *     cos_angle = (tmc[0] * smc[0] + tmc[1] * smc[1] + tmc[2] * smc[2]) / (tc_d * sc_d)             # <<<<<<<<<<<<<<
- * 
- *     # Evaluate the Legendre terms.
- */
-  __pyx_v_cos_angle = (((((__pyx_v_tmc[0]) * (__pyx_v_smc[0])) + ((__pyx_v_tmc[1]) * (__pyx_v_smc[1]))) + ((__pyx_v_tmc[2]) * (__pyx_v_smc[2]))) / (__pyx_v_tc_d * __pyx_v_sc_d));
-
-  /* "pytential/qbx/target_specific/impl.pyx":530
- * 
- *     # Evaluate the Legendre terms.
- *     legvals(cos_angle, order, lvals, lderivs)             # <<<<<<<<<<<<<<
- * 
- *     # Scaling magic for Hankel terms.
- */
-  __pyx_f_9pytential_3qbx_15target_specific_4impl_legvals(__pyx_v_cos_angle, __pyx_v_order, __pyx_v_lvals, __pyx_v_lderivs);
-
-  /* "pytential/qbx/target_specific/impl.pyx":534
- *     # Scaling magic for Hankel terms.
- *     # These values are taken from the fmmlib documentation.
- *     hscale = cabs(k * sc_d) if (cabs(k * sc_d) < 1) else 1             # <<<<<<<<<<<<<<
- *     # unscale = (jscale / hscale) ** n
- *     # Multiply against unscale to remove the scaling.
- */
-  if (((cabs(__Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0))) < 1.0) != 0)) {
-    __pyx_t_2 = cabs(__Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0)));
-  } else {
-    __pyx_t_2 = 1.0;
-  }
-  __pyx_v_hscale = __pyx_t_2;
-
-  /* "pytential/qbx/target_specific/impl.pyx":537
- *     # unscale = (jscale / hscale) ** n
- *     # Multiply against unscale to remove the scaling.
- *     unscale = 1             # <<<<<<<<<<<<<<
- * 
- *     # Evaluate the spherical Hankel terms.
- */
-  __pyx_v_unscale = 1.0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":540
- * 
- *     # Evaluate the spherical Hankel terms.
- *     z = k * sc_d             # <<<<<<<<<<<<<<
- *     ifder = 1
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, hderivs)
- */
-  __pyx_v_z = __Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0));
-
-  /* "pytential/qbx/target_specific/impl.pyx":541
- *     # Evaluate the spherical Hankel terms.
- *     z = k * sc_d
- *     ifder = 1             # <<<<<<<<<<<<<<
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, hderivs)
- * 
- */
-  __pyx_v_ifder = 1;
-
-  /* "pytential/qbx/target_specific/impl.pyx":542
- *     z = k * sc_d
- *     ifder = 1
- *     h3dall_(&order, &z, &hscale, hvals, &ifder, hderivs)             # <<<<<<<<<<<<<<
- * 
- *     #
- */
-  (void)(h3dall_((&__pyx_v_order), (&__pyx_v_z), (&__pyx_v_hscale), __pyx_v_hvals, (&__pyx_v_ifder), __pyx_v_hderivs));
-
-  /* "pytential/qbx/target_specific/impl.pyx":552
- *     #
- *     #
- *     for n in range(0, order + 1):             # <<<<<<<<<<<<<<
- *         for m in range(3):
- *             grad[m] += (2 * n + 1) * unscale * jvals[n] / sc_d * (
- */
-  __pyx_t_3 = (__pyx_v_order + 1);
-  __pyx_t_4 = __pyx_t_3;
-  for (__pyx_t_1 = 0; __pyx_t_1 < __pyx_t_4; __pyx_t_1+=1) {
-    __pyx_v_n = __pyx_t_1;
-
-    /* "pytential/qbx/target_specific/impl.pyx":553
- *     #
- *     for n in range(0, order + 1):
- *         for m in range(3):             # <<<<<<<<<<<<<<
- *             grad[m] += (2 * n + 1) * unscale * jvals[n] / sc_d * (
- *                     k * smc[m] * hderivs[n] * lvals[n]
- */
-    for (__pyx_t_5 = 0; __pyx_t_5 < 3; __pyx_t_5+=1) {
-      __pyx_v_m = __pyx_t_5;
-
-      /* "pytential/qbx/target_specific/impl.pyx":554
- *     for n in range(0, order + 1):
- *         for m in range(3):
- *             grad[m] += (2 * n + 1) * unscale * jvals[n] / sc_d * (             # <<<<<<<<<<<<<<
- *                     k * smc[m] * hderivs[n] * lvals[n]
- *                     + (tmc[m] / tc_d - cos_angle * smc[m] / sc_d)
- */
-      __pyx_t_6 = __pyx_v_m;
-
-      /* "pytential/qbx/target_specific/impl.pyx":556
- *             grad[m] += (2 * n + 1) * unscale * jvals[n] / sc_d * (
- *                     k * smc[m] * hderivs[n] * lvals[n]
- *                     + (tmc[m] / tc_d - cos_angle * smc[m] / sc_d)             # <<<<<<<<<<<<<<
- *                     * hvals[n] * lderivs[n])
- *         unscale *= jscale / hscale
- */
-      (__pyx_v_grad[__pyx_t_6]) = __Pyx_c_sum_double((__pyx_v_grad[__pyx_t_6]), __Pyx_c_prod_double(__Pyx_c_quot_double(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts((((2 * __pyx_v_n) + 1) * __pyx_v_unscale), 0), (__pyx_v_jvals[__pyx_v_n])), __pyx_t_double_complex_from_parts(__pyx_v_sc_d, 0)), __Pyx_c_sum_double(__Pyx_c_prod_double(__Pyx_c_prod_double(__Pyx_c_prod_double(__pyx_v_k, __pyx_t_double_complex_from_parts((__pyx_v_smc[__pyx_v_m]), 0)), (__pyx_v_hderivs[__pyx_v_n])), __pyx_t_double_complex_from_parts((__pyx_v_lvals[__pyx_v_n]), 0)), __Pyx_c_prod_double(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts((((__pyx_v_tmc[__pyx_v_m]) / __pyx_v_tc_d) - ((__pyx_v_cos_angle * (__pyx_v_smc[__pyx_v_m])) / __pyx_v_sc_d)), 0), (__pyx_v_hvals[__pyx_v_n])), __pyx_t_double_complex_from_parts((__pyx_v_lderivs[__pyx_v_n]), 0)))));
-    }
-
-    /* "pytential/qbx/target_specific/impl.pyx":558
- *                     + (tmc[m] / tc_d - cos_angle * smc[m] / sc_d)
- *                     * hvals[n] * lderivs[n])
- *         unscale *= jscale / hscale             # <<<<<<<<<<<<<<
- * 
- *     return 1j * k * dipstr * (
- */
-    __pyx_v_unscale = (__pyx_v_unscale * (__pyx_v_jscale / __pyx_v_hscale));
-  }
-
-  /* "pytential/qbx/target_specific/impl.pyx":560
- *         unscale *= jscale / hscale
- * 
- *     return 1j * k * dipstr * (             # <<<<<<<<<<<<<<
- *             grad[0] * dipole[0] + grad[1] * dipole[1] + grad[2] * dipole[2])
- * 
- */
-  __pyx_r = __Pyx_c_prod_double(__Pyx_c_prod_double(__Pyx_c_prod_double(__pyx_t_double_complex_from_parts(0, 1.0), __pyx_v_k), __pyx_v_dipstr), __Pyx_c_sum_double(__Pyx_c_sum_double(__Pyx_c_prod_double((__pyx_v_grad[0]), __pyx_t_double_complex_from_parts((__pyx_v_dipole[0]), 0)), __Pyx_c_prod_double((__pyx_v_grad[1]), __pyx_t_double_complex_from_parts((__pyx_v_dipole[1]), 0))), __Pyx_c_prod_double((__pyx_v_grad[2]), __pyx_t_double_complex_from_parts((__pyx_v_dipole[2]), 0))));
-  goto __pyx_L0;
-
-  /* "pytential/qbx/target_specific/impl.pyx":495
- * # {{{ Helmholtz D
- * 
- * cdef double complex ts_helmholtz_d(             # <<<<<<<<<<<<<<
- *         double[3] source,
- *         double[3] center,
- */
-
-  /* function exit code */
-  __pyx_L0:;
-  return __pyx_r;
-}
-
-/* "pytential/qbx/target_specific/impl.pyx":566
- * 
- * 
- * def eval_target_specific_qbx_locals(             # <<<<<<<<<<<<<<
- *         int ifpot,
- *         int ifgrad,
- */
-
-/* Python wrapper */
-static PyObject *__pyx_pw_9pytential_3qbx_15target_specific_4impl_5eval_target_specific_qbx_locals(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
-static char __pyx_doc_9pytential_3qbx_15target_specific_4impl_4eval_target_specific_qbx_locals[] = "eval_target_specific_qbx_locals(int ifpot, int ifgrad, int ifcharge, int ifdipole, int order, double[:, :] sources, double[:, :] targets, double[:, :] centers, int[:] qbx_centers, int[:] qbx_center_to_target_box, int[:] center_to_target_starts, int[:] center_to_target_lists, int[:] source_box_starts, int[:] source_box_lists, int[:] box_source_starts, int[:] box_source_counts_nonchild, double complex helmholtz_k, double complex[:] charge, double complex[:] dipstr, double[:, :] dipvec, double complex[:] pot, double complex[:, :] grad)\nTSQBX entry point.\n\n    Arguments:\n        ifpot: Flag indicating whether to evaluate the potential\n        ifgrad: Flag indicating whether to evaluate the gradient of the potential\n        ifcharge: Flag indicating whether to include monopole sources\n        ifdipole: Flag indicating whether to include dipole sources\n        order: Expansion order\n        sources: Array of sources of shape (3, *nsrcs*)\n        targets: Array of targets of shape (3, *ntgts*)\n        centers: Array of centers of shape (3, *nctrs*)\n        qbx_centers: Array of subset of indices into *centers* which are QBX centers\n        qbx_center_to_target_box: Array mapping centers to target box numbers\n        center_to_target_starts: \"Start\" indices for center-to-target CSR list\n        center_to_target_lists: Center-to-target CSR list\n        source_box_starts: \"Start\" indices for target-box-to-source-box CSR list\n        source_box_lists: Target-box-to-source-box CSR list\n        box_source_starts: \"Start\" indices for sources for each box\n        box_source_counts_nonchild: Number of sources per box\n        helmholtz_k: Helmholtz parameter (Pass 0 for Laplace)\n        charge: (Complex) Source strengths, shape (*nsrcs*,), or *None*\n        dipstr: (Complex) Dipole source strengths, shape (*nsrcs*,) or *None*\n        dipvec: (Real) Dipole source orientations, shape (3, *nsrcs*), or *None*\n        pot: (Complex) Output potential, shape (""*ngts*,), or *None*\n        grad: (Complex) Output gradient, shape (3, *ntgts*), or *None*\n    ";
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-                              }
-
-                              /* "pytential/qbx/target_specific/impl.pyx":713
- *                     result_grad[tid, m] = 0
- * 
- *             if helmholtz_s or helmholtz_sp or helmholtz_d:             # <<<<<<<<<<<<<<
- *                 # Precompute source-invariant Helmholtz terms.
- *                 ts_helmholtz_precompute(
- */
-                              __pyx_t_1 = (__pyx_v_helmholtz_s != 0);
-                              if (!__pyx_t_1) {
-                              } else {
-                                __pyx_t_3 = __pyx_t_1;
-                                goto __pyx_L33_bool_binop_done;
-                              }
-                              __pyx_t_1 = (__pyx_v_helmholtz_sp != 0);
-                              if (!__pyx_t_1) {
-                              } else {
-                                __pyx_t_3 = __pyx_t_1;
-                                goto __pyx_L33_bool_binop_done;
-                              }
-                              __pyx_t_1 = (__pyx_v_helmholtz_d != 0);
-                              __pyx_t_3 = __pyx_t_1;
-                              __pyx_L33_bool_binop_done:;
-                              if (__pyx_t_3) {
-
-                                /* "pytential/qbx/target_specific/impl.pyx":716
- *                 # Precompute source-invariant Helmholtz terms.
- *                 ts_helmholtz_precompute(
- *                         &center[tid, 0], &target[tid, 0],             # <<<<<<<<<<<<<<
- *                         order, ifgrad, helmholtz_k, &jvals[tid, 0],
- *                         &jderivs[tid, 0], &jscale)
- */
-                                __pyx_t_18 = __pyx_v_tid;
-                                __pyx_t_16 = 0;
-                                __pyx_t_19 = __pyx_v_tid;
-                                __pyx_t_20 = 0;
-
-                                /* "pytential/qbx/target_specific/impl.pyx":717
- *                 ts_helmholtz_precompute(
- *                         &center[tid, 0], &target[tid, 0],
- *                         order, ifgrad, helmholtz_k, &jvals[tid, 0],             # <<<<<<<<<<<<<<
- *                         &jderivs[tid, 0], &jscale)
- * 
- */
-                                __pyx_t_24 = __pyx_v_tid;
-                                __pyx_t_25 = 0;
-
-                                /* "pytential/qbx/target_specific/impl.pyx":718
- *                         &center[tid, 0], &target[tid, 0],
- *                         order, ifgrad, helmholtz_k, &jvals[tid, 0],
- *                         &jderivs[tid, 0], &jscale)             # <<<<<<<<<<<<<<
- * 
- *             isrc_box_start = source_box_starts[tgt_box]
- */
-                                __pyx_t_26 = __pyx_v_tid;
-                                __pyx_t_27 = 0;
-
-                                /* "pytential/qbx/target_specific/impl.pyx":715
- *             if helmholtz_s or helmholtz_sp or helmholtz_d:
- *                 # Precompute source-invariant Helmholtz terms.
- *                 ts_helmholtz_precompute(             # <<<<<<<<<<<<<<
- *                         &center[tid, 0], &target[tid, 0],
- *                         order, ifgrad, helmholtz_k, &jvals[tid, 0],
- */
-                                __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_helmholtz_precompute((&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_center.data + __pyx_t_18 * __pyx_v_center.strides[0]) ) + __pyx_t_16 * __pyx_v_center.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_target.data + __pyx_t_19 * __pyx_v_target.strides[0]) ) + __pyx_t_20 * __pyx_v_target.strides[1]) )))), __pyx_v_order, __pyx_v_ifgrad, __pyx_v_helmholtz_k, (&(*((__pyx_t_double_complex *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_jvals.data + __pyx_t_24 * __pyx_v_jvals.strides[0]) ) + __pyx_t_25 * __pyx_v_jvals.strides[1]) )))), (&(*((__pyx_t_double_complex *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_jderivs.data + __pyx_t_26 * __pyx_v_jderivs.strides[0]) ) + __pyx_t_27 * __pyx_v_jderivs.strides[1]) )))), (&__pyx_v_jscale));
-
-                                /* "pytential/qbx/target_specific/impl.pyx":713
- *                     result_grad[tid, m] = 0
- * 
- *             if helmholtz_s or helmholtz_sp or helmholtz_d:             # <<<<<<<<<<<<<<
- *                 # Precompute source-invariant Helmholtz terms.
- *                 ts_helmholtz_precompute(
- */
-                              }
-
-                              /* "pytential/qbx/target_specific/impl.pyx":720
- *                         &jderivs[tid, 0], &jscale)
- * 
- *             isrc_box_start = source_box_starts[tgt_box]             # <<<<<<<<<<<<<<
- *             isrc_box_end = source_box_starts[tgt_box + 1]
- * 
- */
-                              __pyx_t_27 = __pyx_v_tgt_box;
-                              __pyx_v_isrc_box_start = (*((int *) ( /* dim=0 */ (__pyx_v_source_box_starts.data + __pyx_t_27 * __pyx_v_source_box_starts.strides[0]) )));
-
-                              /* "pytential/qbx/target_specific/impl.pyx":721
- * 
- *             isrc_box_start = source_box_starts[tgt_box]
- *             isrc_box_end = source_box_starts[tgt_box + 1]             # <<<<<<<<<<<<<<
- * 
- *             for isrc_box in range(isrc_box_start, isrc_box_end):
- */
-                              __pyx_t_27 = (__pyx_v_tgt_box + 1);
-                              __pyx_v_isrc_box_end = (*((int *) ( /* dim=0 */ (__pyx_v_source_box_starts.data + __pyx_t_27 * __pyx_v_source_box_starts.strides[0]) )));
-
-                              /* "pytential/qbx/target_specific/impl.pyx":723
- *             isrc_box_end = source_box_starts[tgt_box + 1]
- * 
- *             for isrc_box in range(isrc_box_start, isrc_box_end):             # <<<<<<<<<<<<<<
- *                 src_ibox = source_box_lists[isrc_box]
- *                 isrc_start = box_source_starts[src_ibox]
- */
-                              __pyx_t_23 = __pyx_v_isrc_box_end;
-                              __pyx_t_28 = __pyx_t_23;
-                              for (__pyx_t_29 = __pyx_v_isrc_box_start; __pyx_t_29 < __pyx_t_28; __pyx_t_29+=1) {
-                                __pyx_v_isrc_box = __pyx_t_29;
-
-                                /* "pytential/qbx/target_specific/impl.pyx":724
- * 
- *             for isrc_box in range(isrc_box_start, isrc_box_end):
- *                 src_ibox = source_box_lists[isrc_box]             # <<<<<<<<<<<<<<
- *                 isrc_start = box_source_starts[src_ibox]
- *                 isrc_end = isrc_start + box_source_counts_nonchild[src_ibox]
- */
-                                __pyx_t_27 = __pyx_v_isrc_box;
-                                __pyx_v_src_ibox = (*((int *) ( /* dim=0 */ (__pyx_v_source_box_lists.data + __pyx_t_27 * __pyx_v_source_box_lists.strides[0]) )));
-
-                                /* "pytential/qbx/target_specific/impl.pyx":725
- *             for isrc_box in range(isrc_box_start, isrc_box_end):
- *                 src_ibox = source_box_lists[isrc_box]
- *                 isrc_start = box_source_starts[src_ibox]             # <<<<<<<<<<<<<<
- *                 isrc_end = isrc_start + box_source_counts_nonchild[src_ibox]
- * 
- */
-                                __pyx_t_27 = __pyx_v_src_ibox;
-                                __pyx_v_isrc_start = (*((int *) ( /* dim=0 */ (__pyx_v_box_source_starts.data + __pyx_t_27 * __pyx_v_box_source_starts.strides[0]) )));
-
-                                /* "pytential/qbx/target_specific/impl.pyx":726
- *                 src_ibox = source_box_lists[isrc_box]
- *                 isrc_start = box_source_starts[src_ibox]
- *                 isrc_end = isrc_start + box_source_counts_nonchild[src_ibox]             # <<<<<<<<<<<<<<
- * 
- *                 for isrc in range(isrc_start, isrc_end):
- */
-                                __pyx_t_27 = __pyx_v_src_ibox;
-                                __pyx_v_isrc_end = (__pyx_v_isrc_start + (*((int *) ( /* dim=0 */ (__pyx_v_box_source_counts_nonchild.data + __pyx_t_27 * __pyx_v_box_source_counts_nonchild.strides[0]) ))));
-
-                                /* "pytential/qbx/target_specific/impl.pyx":728
- *                 isrc_end = isrc_start + box_source_counts_nonchild[src_ibox]
- * 
- *                 for isrc in range(isrc_start, isrc_end):             # <<<<<<<<<<<<<<
- * 
- *                     for m in range(3):
- */
-                                __pyx_t_30 = __pyx_v_isrc_end;
-                                __pyx_t_31 = __pyx_t_30;
-                                for (__pyx_t_32 = __pyx_v_isrc_start; __pyx_t_32 < __pyx_t_31; __pyx_t_32+=1) {
-                                  __pyx_v_isrc = __pyx_t_32;
-
-                                  /* "pytential/qbx/target_specific/impl.pyx":730
- *                 for isrc in range(isrc_start, isrc_end):
- * 
- *                     for m in range(3):             # <<<<<<<<<<<<<<
- *                         source[tid, m] = sources[m, isrc]
- *                         if ifdipole:
- */
-                                  for (__pyx_t_33 = 0; __pyx_t_33 < 3; __pyx_t_33+=1) {
-                                    __pyx_v_m = __pyx_t_33;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":731
- * 
- *                     for m in range(3):
- *                         source[tid, m] = sources[m, isrc]             # <<<<<<<<<<<<<<
- *                         if ifdipole:
- *                             dipole[tid, m] = dipvec[m, isrc]
- */
-                                    __pyx_t_27 = __pyx_v_m;
-                                    __pyx_t_26 = __pyx_v_isrc;
-                                    __pyx_t_25 = __pyx_v_tid;
-                                    __pyx_t_24 = __pyx_v_m;
-                                    *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_source.data + __pyx_t_25 * __pyx_v_source.strides[0]) ) + __pyx_t_24 * __pyx_v_source.strides[1]) )) = (*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_sources.data + __pyx_t_27 * __pyx_v_sources.strides[0]) ) + __pyx_t_26 * __pyx_v_sources.strides[1]) )));
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":732
- *                     for m in range(3):
- *                         source[tid, m] = sources[m, isrc]
- *                         if ifdipole:             # <<<<<<<<<<<<<<
- *                             dipole[tid, m] = dipvec[m, isrc]
- * 
- */
-                                    __pyx_t_3 = (__pyx_v_ifdipole != 0);
-                                    if (__pyx_t_3) {
-
-                                      /* "pytential/qbx/target_specific/impl.pyx":733
- *                         source[tid, m] = sources[m, isrc]
- *                         if ifdipole:
- *                             dipole[tid, m] = dipvec[m, isrc]             # <<<<<<<<<<<<<<
- * 
- *                     # NOTE: Don't use +=, since that makes Cython think we are
- */
-                                      __pyx_t_26 = __pyx_v_m;
-                                      __pyx_t_27 = __pyx_v_isrc;
-                                      __pyx_t_24 = __pyx_v_tid;
-                                      __pyx_t_25 = __pyx_v_m;
-                                      *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_dipole.data + __pyx_t_24 * __pyx_v_dipole.strides[0]) ) + __pyx_t_25 * __pyx_v_dipole.strides[1]) )) = (*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_dipvec.data + __pyx_t_26 * __pyx_v_dipvec.strides[0]) ) + __pyx_t_27 * __pyx_v_dipvec.strides[1]) )));
-
-                                      /* "pytential/qbx/target_specific/impl.pyx":732
- *                     for m in range(3):
- *                         source[tid, m] = sources[m, isrc]
- *                         if ifdipole:             # <<<<<<<<<<<<<<
- *                             dipole[tid, m] = dipvec[m, isrc]
- * 
- */
-                                    }
-                                  }
-
-                                  /* "pytential/qbx/target_specific/impl.pyx":740
- *                     # {{{ evaluate potentials
- * 
- *                     if laplace_s:             # <<<<<<<<<<<<<<
- *                         result = result + (
- *                                 ts_laplace_s(
- */
-                                  __pyx_t_3 = (__pyx_v_laplace_s != 0);
-                                  if (__pyx_t_3) {
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":743
- *                         result = result + (
- *                                 ts_laplace_s(
- *                                     &source[tid, 0], &center[tid, 0], &target[tid, 0],             # <<<<<<<<<<<<<<
- *                                     charge[isrc], order))
- * 
- */
-                                    __pyx_t_27 = __pyx_v_tid;
-                                    __pyx_t_26 = 0;
-                                    __pyx_t_25 = __pyx_v_tid;
-                                    __pyx_t_24 = 0;
-                                    __pyx_t_20 = __pyx_v_tid;
-                                    __pyx_t_19 = 0;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":744
- *                                 ts_laplace_s(
- *                                     &source[tid, 0], &center[tid, 0], &target[tid, 0],
- *                                     charge[isrc], order))             # <<<<<<<<<<<<<<
- * 
- *                     if laplace_sp:
- */
-                                    __pyx_t_16 = __pyx_v_isrc;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":741
- * 
- *                     if laplace_s:
- *                         result = result + (             # <<<<<<<<<<<<<<
- *                                 ts_laplace_s(
- *                                     &source[tid, 0], &center[tid, 0], &target[tid, 0],
- */
-                                    __pyx_v_result = __Pyx_c_sum_double(__pyx_v_result, __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_s((&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_source.data + __pyx_t_27 * __pyx_v_source.strides[0]) ) + __pyx_t_26 * __pyx_v_source.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_center.data + __pyx_t_25 * __pyx_v_center.strides[0]) ) + __pyx_t_24 * __pyx_v_center.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_target.data + __pyx_t_20 * __pyx_v_target.strides[0]) ) + __pyx_t_19 * __pyx_v_target.strides[1]) )))), (*((__pyx_t_double_complex *) ( /* dim=0 */ (__pyx_v_charge.data + __pyx_t_16 * __pyx_v_charge.strides[0]) ))), __pyx_v_order));
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":740
- *                     # {{{ evaluate potentials
- * 
- *                     if laplace_s:             # <<<<<<<<<<<<<<
- *                         result = result + (
- *                                 ts_laplace_s(
- */
-                                  }
-
-                                  /* "pytential/qbx/target_specific/impl.pyx":746
- *                                     charge[isrc], order))
- * 
- *                     if laplace_sp:             # <<<<<<<<<<<<<<
- *                         ts_laplace_sp(
- *                                 &result_grad[tid, 0],
- */
-                                  __pyx_t_3 = (__pyx_v_laplace_sp != 0);
-                                  if (__pyx_t_3) {
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":748
- *                     if laplace_sp:
- *                         ts_laplace_sp(
- *                                 &result_grad[tid, 0],             # <<<<<<<<<<<<<<
- *                                 &source[tid, 0], &center[tid, 0], &target[tid, 0],
- *                                 charge[isrc], order)
- */
-                                    __pyx_t_16 = __pyx_v_tid;
-                                    __pyx_t_19 = 0;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":749
- *                         ts_laplace_sp(
- *                                 &result_grad[tid, 0],
- *                                 &source[tid, 0], &center[tid, 0], &target[tid, 0],             # <<<<<<<<<<<<<<
- *                                 charge[isrc], order)
- * 
- */
-                                    __pyx_t_20 = __pyx_v_tid;
-                                    __pyx_t_24 = 0;
-                                    __pyx_t_25 = __pyx_v_tid;
-                                    __pyx_t_26 = 0;
-                                    __pyx_t_27 = __pyx_v_tid;
-                                    __pyx_t_18 = 0;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":750
- *                                 &result_grad[tid, 0],
- *                                 &source[tid, 0], &center[tid, 0], &target[tid, 0],
- *                                 charge[isrc], order)             # <<<<<<<<<<<<<<
- * 
- *                     if laplace_d:
- */
-                                    __pyx_t_34 = __pyx_v_isrc;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":747
- * 
- *                     if laplace_sp:
- *                         ts_laplace_sp(             # <<<<<<<<<<<<<<
- *                                 &result_grad[tid, 0],
- *                                 &source[tid, 0], &center[tid, 0], &target[tid, 0],
- */
-                                    __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_sp((&(*((__pyx_t_double_complex *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_result_grad.data + __pyx_t_16 * __pyx_v_result_grad.strides[0]) ) + __pyx_t_19 * __pyx_v_result_grad.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_source.data + __pyx_t_20 * __pyx_v_source.strides[0]) ) + __pyx_t_24 * __pyx_v_source.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_center.data + __pyx_t_25 * __pyx_v_center.strides[0]) ) + __pyx_t_26 * __pyx_v_center.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_target.data + __pyx_t_27 * __pyx_v_target.strides[0]) ) + __pyx_t_18 * __pyx_v_target.strides[1]) )))), (*((__pyx_t_double_complex *) ( /* dim=0 */ (__pyx_v_charge.data + __pyx_t_34 * __pyx_v_charge.strides[0]) ))), __pyx_v_order);
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":746
- *                                     charge[isrc], order))
- * 
- *                     if laplace_sp:             # <<<<<<<<<<<<<<
- *                         ts_laplace_sp(
- *                                 &result_grad[tid, 0],
- */
-                                  }
-
-                                  /* "pytential/qbx/target_specific/impl.pyx":752
- *                                 charge[isrc], order)
- * 
- *                     if laplace_d:             # <<<<<<<<<<<<<<
- *                         result = result + (
- *                                 ts_laplace_d(
- */
-                                  __pyx_t_3 = (__pyx_v_laplace_d != 0);
-                                  if (__pyx_t_3) {
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":755
- *                         result = result + (
- *                                 ts_laplace_d(
- *                                     &source[tid, 0], &center[tid, 0], &target[tid, 0],             # <<<<<<<<<<<<<<
- *                                     &dipole[tid, 0], dipstr[isrc], order))
- * 
- */
-                                    __pyx_t_34 = __pyx_v_tid;
-                                    __pyx_t_18 = 0;
-                                    __pyx_t_27 = __pyx_v_tid;
-                                    __pyx_t_26 = 0;
-                                    __pyx_t_25 = __pyx_v_tid;
-                                    __pyx_t_24 = 0;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":756
- *                                 ts_laplace_d(
- *                                     &source[tid, 0], &center[tid, 0], &target[tid, 0],
- *                                     &dipole[tid, 0], dipstr[isrc], order))             # <<<<<<<<<<<<<<
- * 
- *                     if helmholtz_s:
- */
-                                    __pyx_t_20 = __pyx_v_tid;
-                                    __pyx_t_19 = 0;
-                                    __pyx_t_16 = __pyx_v_isrc;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":753
- * 
- *                     if laplace_d:
- *                         result = result + (             # <<<<<<<<<<<<<<
- *                                 ts_laplace_d(
- *                                     &source[tid, 0], &center[tid, 0], &target[tid, 0],
- */
-                                    __pyx_v_result = __Pyx_c_sum_double(__pyx_v_result, __pyx_f_9pytential_3qbx_15target_specific_4impl_ts_laplace_d((&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_source.data + __pyx_t_34 * __pyx_v_source.strides[0]) ) + __pyx_t_18 * __pyx_v_source.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_center.data + __pyx_t_27 * __pyx_v_center.strides[0]) ) + __pyx_t_26 * __pyx_v_center.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_target.data + __pyx_t_25 * __pyx_v_target.strides[0]) ) + __pyx_t_24 * __pyx_v_target.strides[1]) )))), (&(*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_dipole.data + __pyx_t_20 * __pyx_v_dipole.strides[0]) ) + __pyx_t_19 * __pyx_v_dipole.strides[1]) )))), (*((__pyx_t_double_complex *) ( /* dim=0 */ (__pyx_v_dipstr.data + __pyx_t_16 * __pyx_v_dipstr.strides[0]) ))), __pyx_v_order));
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":752
- *                                 charge[isrc], order)
- * 
- *                     if laplace_d:             # <<<<<<<<<<<<<<
- *                         result = result + (
- *                                 ts_laplace_d(
- */
-                                  }
-
-                                  /* "pytential/qbx/target_specific/impl.pyx":758
- *                                     &dipole[tid, 0], dipstr[isrc], order))
- * 
- *                     if helmholtz_s:             # <<<<<<<<<<<<<<
- *                         result = result + (
- *                                 ts_helmholtz_s(&source[tid, 0], &center[tid, 0],
- */
-                                  __pyx_t_3 = (__pyx_v_helmholtz_s != 0);
-                                  if (__pyx_t_3) {
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":760
- *                     if helmholtz_s:
- *                         result = result + (
- *                                 ts_helmholtz_s(&source[tid, 0], &center[tid, 0],             # <<<<<<<<<<<<<<
- *                                     &target[tid, 0], charge[isrc], order, helmholtz_k,
- *                                     &jvals[tid, 0], jscale))
- */
-                                    __pyx_t_16 = __pyx_v_tid;
-                                    __pyx_t_19 = 0;
-                                    __pyx_t_20 = __pyx_v_tid;
-                                    __pyx_t_24 = 0;
-
-                                    /* "pytential/qbx/target_specific/impl.pyx":761
- *                         result = result + (
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- *                                     &target[tid, 0], charge[isrc], order, helmholtz_k,             # <<<<<<<<<<<<<<
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- * 
- */
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- */
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- */
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- */
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- * 
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-    __pyx_t_3 = 0;
-    goto __pyx_L0;
-  }
-
-  /* "View.MemoryView":710
- * 
- * @cname('__pyx_memview_slice')
- * cdef memoryview memview_slice(memoryview memview, object indices):             # <<<<<<<<<<<<<<
- *     cdef int new_ndim = 0, suboffset_dim = -1, dim
- *     cdef bint negative_step
- */
-
-  /* function exit code */
-  __pyx_L1_error:;
-  __Pyx_XDECREF(__pyx_t_3);
-  __Pyx_XDECREF(__pyx_t_9);
-  __Pyx_AddTraceback("View.MemoryView.memview_slice", __pyx_clineno, __pyx_lineno, __pyx_filename);
-  __pyx_r = 0;
-  __pyx_L0:;
-  __Pyx_XDECREF((PyObject *)__pyx_v_memviewsliceobj);
-  __Pyx_XDECREF(__pyx_v_index);
-  __Pyx_XGIVEREF((PyObject *)__pyx_r);
-  __Pyx_RefNannyFinishContext();
-  return __pyx_r;
-}
-
-/* "View.MemoryView":807
- * 
- * @cname('__pyx_memoryview_slice_memviewslice')
- * cdef int slice_memviewslice(             # <<<<<<<<<<<<<<
- *         __Pyx_memviewslice *dst,
- *         Py_ssize_t shape, Py_ssize_t stride, Py_ssize_t suboffset,
- */
-
-static int __pyx_memoryview_slice_memviewslice(__Pyx_memviewslice *__pyx_v_dst, Py_ssize_t __pyx_v_shape, Py_ssize_t __pyx_v_stride, Py_ssize_t __pyx_v_suboffset, int __pyx_v_dim, int __pyx_v_new_ndim, int *__pyx_v_suboffset_dim, Py_ssize_t __pyx_v_start, Py_ssize_t __pyx_v_stop, Py_ssize_t __pyx_v_step, int __pyx_v_have_start, int __pyx_v_have_stop, int __pyx_v_have_step, int __pyx_v_is_slice) {
-  Py_ssize_t __pyx_v_new_shape;
-  int __pyx_v_negative_step;
-  int __pyx_r;
-  int __pyx_t_1;
-  int __pyx_t_2;
-  int __pyx_t_3;
-  int __pyx_lineno = 0;
-  const char *__pyx_filename = NULL;
-  int __pyx_clineno = 0;
-
-  /* "View.MemoryView":827
- *     cdef bint negative_step
- * 
- *     if not is_slice:             # <<<<<<<<<<<<<<
- * 
- *         if start < 0:
- */
-  __pyx_t_1 = ((!(__pyx_v_is_slice != 0)) != 0);
-  if (__pyx_t_1) {
-
-    /* "View.MemoryView":829
- *     if not is_slice:
- * 
- *         if start < 0:             # <<<<<<<<<<<<<<
- *             start += shape
- *         if not 0 <= start < shape:
- */
-    __pyx_t_1 = ((__pyx_v_start < 0) != 0);
-    if (__pyx_t_1) {
-
-      /* "View.MemoryView":830
- * 
- *         if start < 0:
- *             start += shape             # <<<<<<<<<<<<<<
- *         if not 0 <= start < shape:
- *             _err_dim(IndexError, "Index out of bounds (axis %d)", dim)
- */
-      __pyx_v_start = (__pyx_v_start + __pyx_v_shape);
-
-      /* "View.MemoryView":829
- *     if not is_slice:
- * 
- *         if start < 0:             # <<<<<<<<<<<<<<
- *             start += shape
- *         if not 0 <= start < shape:
- */
-    }
-
-    /* "View.MemoryView":831
- *         if start < 0:
- *             start += shape
- *         if not 0 <= start < shape:             # <<<<<<<<<<<<<<
- *             _err_dim(IndexError, "Index out of bounds (axis %d)", dim)
- *     else:
- */
-    __pyx_t_1 = (0 <= __pyx_v_start);
-    if (__pyx_t_1) {
-      __pyx_t_1 = (__pyx_v_start < __pyx_v_shape);
-    }
-    __pyx_t_2 = ((!(__pyx_t_1 != 0)) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":832
- *             start += shape
- *         if not 0 <= start < shape:
- *             _err_dim(IndexError, "Index out of bounds (axis %d)", dim)             # <<<<<<<<<<<<<<
- *     else:
- * 
- */
-      __pyx_t_3 = __pyx_memoryview_err_dim(__pyx_builtin_IndexError, ((char *)"Index out of bounds (axis %d)"), __pyx_v_dim); if (unlikely(__pyx_t_3 == ((int)-1))) __PYX_ERR(1, 832, __pyx_L1_error)
-
-      /* "View.MemoryView":831
- *         if start < 0:
- *             start += shape
- *         if not 0 <= start < shape:             # <<<<<<<<<<<<<<
- *             _err_dim(IndexError, "Index out of bounds (axis %d)", dim)
- *     else:
- */
-    }
-
-    /* "View.MemoryView":827
- *     cdef bint negative_step
- * 
- *     if not is_slice:             # <<<<<<<<<<<<<<
- * 
- *         if start < 0:
- */
-    goto __pyx_L3;
-  }
-
-  /* "View.MemoryView":835
- *     else:
- * 
- *         negative_step = have_step != 0 and step < 0             # <<<<<<<<<<<<<<
- * 
- *         if have_step and step == 0:
- */
-  /*else*/ {
-    __pyx_t_1 = ((__pyx_v_have_step != 0) != 0);
-    if (__pyx_t_1) {
-    } else {
-      __pyx_t_2 = __pyx_t_1;
-      goto __pyx_L6_bool_binop_done;
-    }
-    __pyx_t_1 = ((__pyx_v_step < 0) != 0);
-    __pyx_t_2 = __pyx_t_1;
-    __pyx_L6_bool_binop_done:;
-    __pyx_v_negative_step = __pyx_t_2;
-
-    /* "View.MemoryView":837
- *         negative_step = have_step != 0 and step < 0
- * 
- *         if have_step and step == 0:             # <<<<<<<<<<<<<<
- *             _err_dim(ValueError, "Step may not be zero (axis %d)", dim)
- * 
- */
-    __pyx_t_1 = (__pyx_v_have_step != 0);
-    if (__pyx_t_1) {
-    } else {
-      __pyx_t_2 = __pyx_t_1;
-      goto __pyx_L9_bool_binop_done;
-    }
-    __pyx_t_1 = ((__pyx_v_step == 0) != 0);
-    __pyx_t_2 = __pyx_t_1;
-    __pyx_L9_bool_binop_done:;
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":838
- * 
- *         if have_step and step == 0:
- *             _err_dim(ValueError, "Step may not be zero (axis %d)", dim)             # <<<<<<<<<<<<<<
- * 
- * 
- */
-      __pyx_t_3 = __pyx_memoryview_err_dim(__pyx_builtin_ValueError, ((char *)"Step may not be zero (axis %d)"), __pyx_v_dim); if (unlikely(__pyx_t_3 == ((int)-1))) __PYX_ERR(1, 838, __pyx_L1_error)
-
-      /* "View.MemoryView":837
- *         negative_step = have_step != 0 and step < 0
- * 
- *         if have_step and step == 0:             # <<<<<<<<<<<<<<
- *             _err_dim(ValueError, "Step may not be zero (axis %d)", dim)
- * 
- */
-    }
-
-    /* "View.MemoryView":841
- * 
- * 
- *         if have_start:             # <<<<<<<<<<<<<<
- *             if start < 0:
- *                 start += shape
- */
-    __pyx_t_2 = (__pyx_v_have_start != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":842
- * 
- *         if have_start:
- *             if start < 0:             # <<<<<<<<<<<<<<
- *                 start += shape
- *                 if start < 0:
- */
-      __pyx_t_2 = ((__pyx_v_start < 0) != 0);
-      if (__pyx_t_2) {
-
-        /* "View.MemoryView":843
- *         if have_start:
- *             if start < 0:
- *                 start += shape             # <<<<<<<<<<<<<<
- *                 if start < 0:
- *                     start = 0
- */
-        __pyx_v_start = (__pyx_v_start + __pyx_v_shape);
-
-        /* "View.MemoryView":844
- *             if start < 0:
- *                 start += shape
- *                 if start < 0:             # <<<<<<<<<<<<<<
- *                     start = 0
- *             elif start >= shape:
- */
-        __pyx_t_2 = ((__pyx_v_start < 0) != 0);
-        if (__pyx_t_2) {
-
-          /* "View.MemoryView":845
- *                 start += shape
- *                 if start < 0:
- *                     start = 0             # <<<<<<<<<<<<<<
- *             elif start >= shape:
- *                 if negative_step:
- */
-          __pyx_v_start = 0;
-
-          /* "View.MemoryView":844
- *             if start < 0:
- *                 start += shape
- *                 if start < 0:             # <<<<<<<<<<<<<<
- *                     start = 0
- *             elif start >= shape:
- */
-        }
-
-        /* "View.MemoryView":842
- * 
- *         if have_start:
- *             if start < 0:             # <<<<<<<<<<<<<<
- *                 start += shape
- *                 if start < 0:
- */
-        goto __pyx_L12;
-      }
-
-      /* "View.MemoryView":846
- *                 if start < 0:
- *                     start = 0
- *             elif start >= shape:             # <<<<<<<<<<<<<<
- *                 if negative_step:
- *                     start = shape - 1
- */
-      __pyx_t_2 = ((__pyx_v_start >= __pyx_v_shape) != 0);
-      if (__pyx_t_2) {
-
-        /* "View.MemoryView":847
- *                     start = 0
- *             elif start >= shape:
- *                 if negative_step:             # <<<<<<<<<<<<<<
- *                     start = shape - 1
- *                 else:
- */
-        __pyx_t_2 = (__pyx_v_negative_step != 0);
-        if (__pyx_t_2) {
-
-          /* "View.MemoryView":848
- *             elif start >= shape:
- *                 if negative_step:
- *                     start = shape - 1             # <<<<<<<<<<<<<<
- *                 else:
- *                     start = shape
- */
-          __pyx_v_start = (__pyx_v_shape - 1);
-
-          /* "View.MemoryView":847
- *                     start = 0
- *             elif start >= shape:
- *                 if negative_step:             # <<<<<<<<<<<<<<
- *                     start = shape - 1
- *                 else:
- */
-          goto __pyx_L14;
-        }
-
-        /* "View.MemoryView":850
- *                     start = shape - 1
- *                 else:
- *                     start = shape             # <<<<<<<<<<<<<<
- *         else:
- *             if negative_step:
- */
-        /*else*/ {
-          __pyx_v_start = __pyx_v_shape;
-        }
-        __pyx_L14:;
-
-        /* "View.MemoryView":846
- *                 if start < 0:
- *                     start = 0
- *             elif start >= shape:             # <<<<<<<<<<<<<<
- *                 if negative_step:
- *                     start = shape - 1
- */
-      }
-      __pyx_L12:;
-
-      /* "View.MemoryView":841
- * 
- * 
- *         if have_start:             # <<<<<<<<<<<<<<
- *             if start < 0:
- *                 start += shape
- */
-      goto __pyx_L11;
-    }
-
-    /* "View.MemoryView":852
- *                     start = shape
- *         else:
- *             if negative_step:             # <<<<<<<<<<<<<<
- *                 start = shape - 1
- *             else:
- */
-    /*else*/ {
-      __pyx_t_2 = (__pyx_v_negative_step != 0);
-      if (__pyx_t_2) {
-
-        /* "View.MemoryView":853
- *         else:
- *             if negative_step:
- *                 start = shape - 1             # <<<<<<<<<<<<<<
- *             else:
- *                 start = 0
- */
-        __pyx_v_start = (__pyx_v_shape - 1);
-
-        /* "View.MemoryView":852
- *                     start = shape
- *         else:
- *             if negative_step:             # <<<<<<<<<<<<<<
- *                 start = shape - 1
- *             else:
- */
-        goto __pyx_L15;
-      }
-
-      /* "View.MemoryView":855
- *                 start = shape - 1
- *             else:
- *                 start = 0             # <<<<<<<<<<<<<<
- * 
- *         if have_stop:
- */
-      /*else*/ {
-        __pyx_v_start = 0;
-      }
-      __pyx_L15:;
-    }
-    __pyx_L11:;
-
-    /* "View.MemoryView":857
- *                 start = 0
- * 
- *         if have_stop:             # <<<<<<<<<<<<<<
- *             if stop < 0:
- *                 stop += shape
- */
-    __pyx_t_2 = (__pyx_v_have_stop != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":858
- * 
- *         if have_stop:
- *             if stop < 0:             # <<<<<<<<<<<<<<
- *                 stop += shape
- *                 if stop < 0:
- */
-      __pyx_t_2 = ((__pyx_v_stop < 0) != 0);
-      if (__pyx_t_2) {
-
-        /* "View.MemoryView":859
- *         if have_stop:
- *             if stop < 0:
- *                 stop += shape             # <<<<<<<<<<<<<<
- *                 if stop < 0:
- *                     stop = 0
- */
-        __pyx_v_stop = (__pyx_v_stop + __pyx_v_shape);
-
-        /* "View.MemoryView":860
- *             if stop < 0:
- *                 stop += shape
- *                 if stop < 0:             # <<<<<<<<<<<<<<
- *                     stop = 0
- *             elif stop > shape:
- */
-        __pyx_t_2 = ((__pyx_v_stop < 0) != 0);
-        if (__pyx_t_2) {
-
-          /* "View.MemoryView":861
- *                 stop += shape
- *                 if stop < 0:
- *                     stop = 0             # <<<<<<<<<<<<<<
- *             elif stop > shape:
- *                 stop = shape
- */
-          __pyx_v_stop = 0;
-
-          /* "View.MemoryView":860
- *             if stop < 0:
- *                 stop += shape
- *                 if stop < 0:             # <<<<<<<<<<<<<<
- *                     stop = 0
- *             elif stop > shape:
- */
-        }
-
-        /* "View.MemoryView":858
- * 
- *         if have_stop:
- *             if stop < 0:             # <<<<<<<<<<<<<<
- *                 stop += shape
- *                 if stop < 0:
- */
-        goto __pyx_L17;
-      }
-
-      /* "View.MemoryView":862
- *                 if stop < 0:
- *                     stop = 0
- *             elif stop > shape:             # <<<<<<<<<<<<<<
- *                 stop = shape
- *         else:
- */
-      __pyx_t_2 = ((__pyx_v_stop > __pyx_v_shape) != 0);
-      if (__pyx_t_2) {
-
-        /* "View.MemoryView":863
- *                     stop = 0
- *             elif stop > shape:
- *                 stop = shape             # <<<<<<<<<<<<<<
- *         else:
- *             if negative_step:
- */
-        __pyx_v_stop = __pyx_v_shape;
-
-        /* "View.MemoryView":862
- *                 if stop < 0:
- *                     stop = 0
- *             elif stop > shape:             # <<<<<<<<<<<<<<
- *                 stop = shape
- *         else:
- */
-      }
-      __pyx_L17:;
-
-      /* "View.MemoryView":857
- *                 start = 0
- * 
- *         if have_stop:             # <<<<<<<<<<<<<<
- *             if stop < 0:
- *                 stop += shape
- */
-      goto __pyx_L16;
-    }
-
-    /* "View.MemoryView":865
- *                 stop = shape
- *         else:
- *             if negative_step:             # <<<<<<<<<<<<<<
- *                 stop = -1
- *             else:
- */
-    /*else*/ {
-      __pyx_t_2 = (__pyx_v_negative_step != 0);
-      if (__pyx_t_2) {
-
-        /* "View.MemoryView":866
- *         else:
- *             if negative_step:
- *                 stop = -1             # <<<<<<<<<<<<<<
- *             else:
- *                 stop = shape
- */
-        __pyx_v_stop = -1L;
-
-        /* "View.MemoryView":865
- *                 stop = shape
- *         else:
- *             if negative_step:             # <<<<<<<<<<<<<<
- *                 stop = -1
- *             else:
- */
-        goto __pyx_L19;
-      }
-
-      /* "View.MemoryView":868
- *                 stop = -1
- *             else:
- *                 stop = shape             # <<<<<<<<<<<<<<
- * 
- *         if not have_step:
- */
-      /*else*/ {
-        __pyx_v_stop = __pyx_v_shape;
-      }
-      __pyx_L19:;
-    }
-    __pyx_L16:;
-
-    /* "View.MemoryView":870
- *                 stop = shape
- * 
- *         if not have_step:             # <<<<<<<<<<<<<<
- *             step = 1
- * 
- */
-    __pyx_t_2 = ((!(__pyx_v_have_step != 0)) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":871
- * 
- *         if not have_step:
- *             step = 1             # <<<<<<<<<<<<<<
- * 
- * 
- */
-      __pyx_v_step = 1;
-
-      /* "View.MemoryView":870
- *                 stop = shape
- * 
- *         if not have_step:             # <<<<<<<<<<<<<<
- *             step = 1
- * 
- */
-    }
-
-    /* "View.MemoryView":875
- * 
- *         with cython.cdivision(True):
- *             new_shape = (stop - start) // step             # <<<<<<<<<<<<<<
- * 
- *             if (stop - start) - step * new_shape:
- */
-    __pyx_v_new_shape = ((__pyx_v_stop - __pyx_v_start) / __pyx_v_step);
-
-    /* "View.MemoryView":877
- *             new_shape = (stop - start) // step
- * 
- *             if (stop - start) - step * new_shape:             # <<<<<<<<<<<<<<
- *                 new_shape += 1
- * 
- */
-    __pyx_t_2 = (((__pyx_v_stop - __pyx_v_start) - (__pyx_v_step * __pyx_v_new_shape)) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":878
- * 
- *             if (stop - start) - step * new_shape:
- *                 new_shape += 1             # <<<<<<<<<<<<<<
- * 
- *         if new_shape < 0:
- */
-      __pyx_v_new_shape = (__pyx_v_new_shape + 1);
-
-      /* "View.MemoryView":877
- *             new_shape = (stop - start) // step
- * 
- *             if (stop - start) - step * new_shape:             # <<<<<<<<<<<<<<
- *                 new_shape += 1
- * 
- */
-    }
-
-    /* "View.MemoryView":880
- *                 new_shape += 1
- * 
- *         if new_shape < 0:             # <<<<<<<<<<<<<<
- *             new_shape = 0
- * 
- */
-    __pyx_t_2 = ((__pyx_v_new_shape < 0) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":881
- * 
- *         if new_shape < 0:
- *             new_shape = 0             # <<<<<<<<<<<<<<
- * 
- * 
- */
-      __pyx_v_new_shape = 0;
-
-      /* "View.MemoryView":880
- *                 new_shape += 1
- * 
- *         if new_shape < 0:             # <<<<<<<<<<<<<<
- *             new_shape = 0
- * 
- */
-    }
-
-    /* "View.MemoryView":884
- * 
- * 
- *         dst.strides[new_ndim] = stride * step             # <<<<<<<<<<<<<<
- *         dst.shape[new_ndim] = new_shape
- *         dst.suboffsets[new_ndim] = suboffset
- */
-    (__pyx_v_dst->strides[__pyx_v_new_ndim]) = (__pyx_v_stride * __pyx_v_step);
-
-    /* "View.MemoryView":885
- * 
- *         dst.strides[new_ndim] = stride * step
- *         dst.shape[new_ndim] = new_shape             # <<<<<<<<<<<<<<
- *         dst.suboffsets[new_ndim] = suboffset
- * 
- */
-    (__pyx_v_dst->shape[__pyx_v_new_ndim]) = __pyx_v_new_shape;
-
-    /* "View.MemoryView":886
- *         dst.strides[new_ndim] = stride * step
- *         dst.shape[new_ndim] = new_shape
- *         dst.suboffsets[new_ndim] = suboffset             # <<<<<<<<<<<<<<
- * 
- * 
- */
-    (__pyx_v_dst->suboffsets[__pyx_v_new_ndim]) = __pyx_v_suboffset;
-  }
-  __pyx_L3:;
-
-  /* "View.MemoryView":889
- * 
- * 
- *     if suboffset_dim[0] < 0:             # <<<<<<<<<<<<<<
- *         dst.data += start * stride
- *     else:
- */
-  __pyx_t_2 = (((__pyx_v_suboffset_dim[0]) < 0) != 0);
-  if (__pyx_t_2) {
-
-    /* "View.MemoryView":890
- * 
- *     if suboffset_dim[0] < 0:
- *         dst.data += start * stride             # <<<<<<<<<<<<<<
- *     else:
- *         dst.suboffsets[suboffset_dim[0]] += start * stride
- */
-    __pyx_v_dst->data = (__pyx_v_dst->data + (__pyx_v_start * __pyx_v_stride));
-
-    /* "View.MemoryView":889
- * 
- * 
- *     if suboffset_dim[0] < 0:             # <<<<<<<<<<<<<<
- *         dst.data += start * stride
- *     else:
- */
-    goto __pyx_L23;
-  }
-
-  /* "View.MemoryView":892
- *         dst.data += start * stride
- *     else:
- *         dst.suboffsets[suboffset_dim[0]] += start * stride             # <<<<<<<<<<<<<<
- * 
- *     if suboffset >= 0:
- */
-  /*else*/ {
-    __pyx_t_3 = (__pyx_v_suboffset_dim[0]);
-    (__pyx_v_dst->suboffsets[__pyx_t_3]) = ((__pyx_v_dst->suboffsets[__pyx_t_3]) + (__pyx_v_start * __pyx_v_stride));
-  }
-  __pyx_L23:;
-
-  /* "View.MemoryView":894
- *         dst.suboffsets[suboffset_dim[0]] += start * stride
- * 
- *     if suboffset >= 0:             # <<<<<<<<<<<<<<
- *         if not is_slice:
- *             if new_ndim == 0:
- */
-  __pyx_t_2 = ((__pyx_v_suboffset >= 0) != 0);
-  if (__pyx_t_2) {
-
-    /* "View.MemoryView":895
- * 
- *     if suboffset >= 0:
- *         if not is_slice:             # <<<<<<<<<<<<<<
- *             if new_ndim == 0:
- *                 dst.data = (<char **> dst.data)[0] + suboffset
- */
-    __pyx_t_2 = ((!(__pyx_v_is_slice != 0)) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":896
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-    __pyx_t_3 = (__pyx_t_2 != 0);
-    __pyx_t_1 = __pyx_t_3;
-    __pyx_L5_bool_binop_done:;
-
-    /* "View.MemoryView":1153
- * 
- *     if ndim == 1:
- *        if (src_stride > 0 and dst_stride > 0 and             # <<<<<<<<<<<<<<
- *            <size_t> src_stride == itemsize == <size_t> dst_stride):
- *            memcpy(dst_data, src_data, itemsize * dst_extent)
- */
-    if (__pyx_t_1) {
-
-      /* "View.MemoryView":1155
- *        if (src_stride > 0 and dst_stride > 0 and
- *            <size_t> src_stride == itemsize == <size_t> dst_stride):
- *            memcpy(dst_data, src_data, itemsize * dst_extent)             # <<<<<<<<<<<<<<
- *        else:
- *            for i in range(dst_extent):
- */
-      (void)(memcpy(__pyx_v_dst_data, __pyx_v_src_data, (__pyx_v_itemsize * __pyx_v_dst_extent)));
-
-      /* "View.MemoryView":1153
- * 
- *     if ndim == 1:
- *        if (src_stride > 0 and dst_stride > 0 and             # <<<<<<<<<<<<<<
- *            <size_t> src_stride == itemsize == <size_t> dst_stride):
- *            memcpy(dst_data, src_data, itemsize * dst_extent)
- */
-      goto __pyx_L4;
-    }
-
-    /* "View.MemoryView":1157
- *            memcpy(dst_data, src_data, itemsize * dst_extent)
- *        else:
- *            for i in range(dst_extent):             # <<<<<<<<<<<<<<
- *                memcpy(dst_data, src_data, itemsize)
- *                src_data += src_stride
- */
-    /*else*/ {
-      __pyx_t_4 = __pyx_v_dst_extent;
-      __pyx_t_5 = __pyx_t_4;
-      for (__pyx_t_6 = 0; __pyx_t_6 < __pyx_t_5; __pyx_t_6+=1) {
-        __pyx_v_i = __pyx_t_6;
-
-        /* "View.MemoryView":1158
- *        else:
- *            for i in range(dst_extent):
- *                memcpy(dst_data, src_data, itemsize)             # <<<<<<<<<<<<<<
- *                src_data += src_stride
- *                dst_data += dst_stride
- */
-        (void)(memcpy(__pyx_v_dst_data, __pyx_v_src_data, __pyx_v_itemsize));
-
-        /* "View.MemoryView":1159
- *            for i in range(dst_extent):
- *                memcpy(dst_data, src_data, itemsize)
- *                src_data += src_stride             # <<<<<<<<<<<<<<
- *                dst_data += dst_stride
- *     else:
- */
-        __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride);
-
-        /* "View.MemoryView":1160
- *                memcpy(dst_data, src_data, itemsize)
- *                src_data += src_stride
- *                dst_data += dst_stride             # <<<<<<<<<<<<<<
- *     else:
- *         for i in range(dst_extent):
- */
-        __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride);
-      }
-    }
-    __pyx_L4:;
-
-    /* "View.MemoryView":1152
- *     cdef Py_ssize_t dst_stride = dst_strides[0]
- * 
- *     if ndim == 1:             # <<<<<<<<<<<<<<
- *        if (src_stride > 0 and dst_stride > 0 and
- *            <size_t> src_stride == itemsize == <size_t> dst_stride):
- */
-    goto __pyx_L3;
-  }
-
-  /* "View.MemoryView":1162
- *                dst_data += dst_stride
- *     else:
- *         for i in range(dst_extent):             # <<<<<<<<<<<<<<
- *             _copy_strided_to_strided(src_data, src_strides + 1,
- *                                      dst_data, dst_strides + 1,
- */
-  /*else*/ {
-    __pyx_t_4 = __pyx_v_dst_extent;
-    __pyx_t_5 = __pyx_t_4;
-    for (__pyx_t_6 = 0; __pyx_t_6 < __pyx_t_5; __pyx_t_6+=1) {
-      __pyx_v_i = __pyx_t_6;
-
-      /* "View.MemoryView":1163
- *     else:
- *         for i in range(dst_extent):
- *             _copy_strided_to_strided(src_data, src_strides + 1,             # <<<<<<<<<<<<<<
- *                                      dst_data, dst_strides + 1,
- *                                      src_shape + 1, dst_shape + 1,
- */
-      _copy_strided_to_strided(__pyx_v_src_data, (__pyx_v_src_strides + 1), __pyx_v_dst_data, (__pyx_v_dst_strides + 1), (__pyx_v_src_shape + 1), (__pyx_v_dst_shape + 1), (__pyx_v_ndim - 1), __pyx_v_itemsize);
-
-      /* "View.MemoryView":1167
- *                                      src_shape + 1, dst_shape + 1,
- *                                      ndim - 1, itemsize)
- *             src_data += src_stride             # <<<<<<<<<<<<<<
- *             dst_data += dst_stride
- * 
- */
-      __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride);
-
-      /* "View.MemoryView":1168
- *                                      ndim - 1, itemsize)
- *             src_data += src_stride
- *             dst_data += dst_stride             # <<<<<<<<<<<<<<
- * 
- * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,
- */
-      __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride);
-    }
-  }
-  __pyx_L3:;
-
-  /* "View.MemoryView":1140
- * 
- * @cython.cdivision(True)
- * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides,             # <<<<<<<<<<<<<<
- *                                    char *dst_data, Py_ssize_t *dst_strides,
- *                                    Py_ssize_t *src_shape, Py_ssize_t *dst_shape,
- */
-
-  /* function exit code */
-}
-
-/* "View.MemoryView":1170
- *             dst_data += dst_stride
- * 
- * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,             # <<<<<<<<<<<<<<
- *                                   __Pyx_memviewslice *dst,
- *                                   int ndim, size_t itemsize) nogil:
- */
-
-static void copy_strided_to_strided(__Pyx_memviewslice *__pyx_v_src, __Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize) {
-
-  /* "View.MemoryView":1173
- *                                   __Pyx_memviewslice *dst,
- *                                   int ndim, size_t itemsize) nogil:
- *     _copy_strided_to_strided(src.data, src.strides, dst.data, dst.strides,             # <<<<<<<<<<<<<<
- *                              src.shape, dst.shape, ndim, itemsize)
- * 
- */
-  _copy_strided_to_strided(__pyx_v_src->data, __pyx_v_src->strides, __pyx_v_dst->data, __pyx_v_dst->strides, __pyx_v_src->shape, __pyx_v_dst->shape, __pyx_v_ndim, __pyx_v_itemsize);
-
-  /* "View.MemoryView":1170
- *             dst_data += dst_stride
- * 
- * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,             # <<<<<<<<<<<<<<
- *                                   __Pyx_memviewslice *dst,
- *                                   int ndim, size_t itemsize) nogil:
- */
-
-  /* function exit code */
-}
-
-/* "View.MemoryView":1177
- * 
- * @cname('__pyx_memoryview_slice_get_size')
- * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) nogil:             # <<<<<<<<<<<<<<
- *     "Return the size of the memory occupied by the slice in number of bytes"
- *     cdef Py_ssize_t shape, size = src.memview.view.itemsize
- */
-
-static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *__pyx_v_src, int __pyx_v_ndim) {
-  Py_ssize_t __pyx_v_shape;
-  Py_ssize_t __pyx_v_size;
-  Py_ssize_t __pyx_r;
-  Py_ssize_t __pyx_t_1;
-  Py_ssize_t *__pyx_t_2;
-  Py_ssize_t *__pyx_t_3;
-  Py_ssize_t *__pyx_t_4;
-
-  /* "View.MemoryView":1179
- * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) nogil:
- *     "Return the size of the memory occupied by the slice in number of bytes"
- *     cdef Py_ssize_t shape, size = src.memview.view.itemsize             # <<<<<<<<<<<<<<
- * 
- *     for shape in src.shape[:ndim]:
- */
-  __pyx_t_1 = __pyx_v_src->memview->view.itemsize;
-  __pyx_v_size = __pyx_t_1;
-
-  /* "View.MemoryView":1181
- *     cdef Py_ssize_t shape, size = src.memview.view.itemsize
- * 
- *     for shape in src.shape[:ndim]:             # <<<<<<<<<<<<<<
- *         size *= shape
- * 
- */
-  __pyx_t_3 = (__pyx_v_src->shape + __pyx_v_ndim);
-  for (__pyx_t_4 = __pyx_v_src->shape; __pyx_t_4 < __pyx_t_3; __pyx_t_4++) {
-    __pyx_t_2 = __pyx_t_4;
-    __pyx_v_shape = (__pyx_t_2[0]);
-
-    /* "View.MemoryView":1182
- * 
- *     for shape in src.shape[:ndim]:
- *         size *= shape             # <<<<<<<<<<<<<<
- * 
- *     return size
- */
-    __pyx_v_size = (__pyx_v_size * __pyx_v_shape);
-  }
-
-  /* "View.MemoryView":1184
- *         size *= shape
- * 
- *     return size             # <<<<<<<<<<<<<<
- * 
- * @cname('__pyx_fill_contig_strides_array')
- */
-  __pyx_r = __pyx_v_size;
-  goto __pyx_L0;
-
-  /* "View.MemoryView":1177
- * 
- * @cname('__pyx_memoryview_slice_get_size')
- * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) nogil:             # <<<<<<<<<<<<<<
- *     "Return the size of the memory occupied by the slice in number of bytes"
- *     cdef Py_ssize_t shape, size = src.memview.view.itemsize
- */
-
-  /* function exit code */
-  __pyx_L0:;
-  return __pyx_r;
-}
-
-/* "View.MemoryView":1187
- * 
- * @cname('__pyx_fill_contig_strides_array')
- * cdef Py_ssize_t fill_contig_strides_array(             # <<<<<<<<<<<<<<
- *                 Py_ssize_t *shape, Py_ssize_t *strides, Py_ssize_t stride,
- *                 int ndim, char order) nogil:
- */
-
-static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, Py_ssize_t __pyx_v_stride, int __pyx_v_ndim, char __pyx_v_order) {
-  int __pyx_v_idx;
-  Py_ssize_t __pyx_r;
-  int __pyx_t_1;
-  int __pyx_t_2;
-  int __pyx_t_3;
-  int __pyx_t_4;
-
-  /* "View.MemoryView":1196
- *     cdef int idx
- * 
- *     if order == 'F':             # <<<<<<<<<<<<<<
- *         for idx in range(ndim):
- *             strides[idx] = stride
- */
-  __pyx_t_1 = ((__pyx_v_order == 'F') != 0);
-  if (__pyx_t_1) {
-
-    /* "View.MemoryView":1197
- * 
- *     if order == 'F':
- *         for idx in range(ndim):             # <<<<<<<<<<<<<<
- *             strides[idx] = stride
- *             stride *= shape[idx]
- */
-    __pyx_t_2 = __pyx_v_ndim;
-    __pyx_t_3 = __pyx_t_2;
-    for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
-      __pyx_v_idx = __pyx_t_4;
-
-      /* "View.MemoryView":1198
- *     if order == 'F':
- *         for idx in range(ndim):
- *             strides[idx] = stride             # <<<<<<<<<<<<<<
- *             stride *= shape[idx]
- *     else:
- */
-      (__pyx_v_strides[__pyx_v_idx]) = __pyx_v_stride;
-
-      /* "View.MemoryView":1199
- *         for idx in range(ndim):
- *             strides[idx] = stride
- *             stride *= shape[idx]             # <<<<<<<<<<<<<<
- *     else:
- *         for idx in range(ndim - 1, -1, -1):
- */
-      __pyx_v_stride = (__pyx_v_stride * (__pyx_v_shape[__pyx_v_idx]));
-    }
-
-    /* "View.MemoryView":1196
- *     cdef int idx
- * 
- *     if order == 'F':             # <<<<<<<<<<<<<<
- *         for idx in range(ndim):
- *             strides[idx] = stride
- */
-    goto __pyx_L3;
-  }
-
-  /* "View.MemoryView":1201
- *             stride *= shape[idx]
- *     else:
- *         for idx in range(ndim - 1, -1, -1):             # <<<<<<<<<<<<<<
- *             strides[idx] = stride
- *             stride *= shape[idx]
- */
-  /*else*/ {
-    for (__pyx_t_2 = (__pyx_v_ndim - 1); __pyx_t_2 > -1; __pyx_t_2-=1) {
-      __pyx_v_idx = __pyx_t_2;
-
-      /* "View.MemoryView":1202
- *     else:
- *         for idx in range(ndim - 1, -1, -1):
- *             strides[idx] = stride             # <<<<<<<<<<<<<<
- *             stride *= shape[idx]
- * 
- */
-      (__pyx_v_strides[__pyx_v_idx]) = __pyx_v_stride;
-
-      /* "View.MemoryView":1203
- *         for idx in range(ndim - 1, -1, -1):
- *             strides[idx] = stride
- *             stride *= shape[idx]             # <<<<<<<<<<<<<<
- * 
- *     return stride
- */
-      __pyx_v_stride = (__pyx_v_stride * (__pyx_v_shape[__pyx_v_idx]));
-    }
-  }
-  __pyx_L3:;
-
-  /* "View.MemoryView":1205
- *             stride *= shape[idx]
- * 
- *     return stride             # <<<<<<<<<<<<<<
- * 
- * @cname('__pyx_memoryview_copy_data_to_temp')
- */
-  __pyx_r = __pyx_v_stride;
-  goto __pyx_L0;
-
-  /* "View.MemoryView":1187
- * 
- * @cname('__pyx_fill_contig_strides_array')
- * cdef Py_ssize_t fill_contig_strides_array(             # <<<<<<<<<<<<<<
- *                 Py_ssize_t *shape, Py_ssize_t *strides, Py_ssize_t stride,
- *                 int ndim, char order) nogil:
- */
-
-  /* function exit code */
-  __pyx_L0:;
-  return __pyx_r;
-}
-
-/* "View.MemoryView":1208
- * 
- * @cname('__pyx_memoryview_copy_data_to_temp')
- * cdef void *copy_data_to_temp(__Pyx_memviewslice *src,             # <<<<<<<<<<<<<<
- *                              __Pyx_memviewslice *tmpslice,
- *                              char order,
- */
-
-static void *__pyx_memoryview_copy_data_to_temp(__Pyx_memviewslice *__pyx_v_src, __Pyx_memviewslice *__pyx_v_tmpslice, char __pyx_v_order, int __pyx_v_ndim) {
-  int __pyx_v_i;
-  void *__pyx_v_result;
-  size_t __pyx_v_itemsize;
-  size_t __pyx_v_size;
-  void *__pyx_r;
-  Py_ssize_t __pyx_t_1;
-  int __pyx_t_2;
-  int __pyx_t_3;
-  struct __pyx_memoryview_obj *__pyx_t_4;
-  int __pyx_t_5;
-  int __pyx_t_6;
-  int __pyx_lineno = 0;
-  const char *__pyx_filename = NULL;
-  int __pyx_clineno = 0;
-
-  /* "View.MemoryView":1219
- *     cdef void *result
- * 
- *     cdef size_t itemsize = src.memview.view.itemsize             # <<<<<<<<<<<<<<
- *     cdef size_t size = slice_get_size(src, ndim)
- * 
- */
-  __pyx_t_1 = __pyx_v_src->memview->view.itemsize;
-  __pyx_v_itemsize = __pyx_t_1;
-
-  /* "View.MemoryView":1220
- * 
- *     cdef size_t itemsize = src.memview.view.itemsize
- *     cdef size_t size = slice_get_size(src, ndim)             # <<<<<<<<<<<<<<
- * 
- *     result = malloc(size)
- */
-  __pyx_v_size = __pyx_memoryview_slice_get_size(__pyx_v_src, __pyx_v_ndim);
-
-  /* "View.MemoryView":1222
- *     cdef size_t size = slice_get_size(src, ndim)
- * 
- *     result = malloc(size)             # <<<<<<<<<<<<<<
- *     if not result:
- *         _err(MemoryError, NULL)
- */
-  __pyx_v_result = malloc(__pyx_v_size);
-
-  /* "View.MemoryView":1223
- * 
- *     result = malloc(size)
- *     if not result:             # <<<<<<<<<<<<<<
- *         _err(MemoryError, NULL)
- * 
- */
-  __pyx_t_2 = ((!(__pyx_v_result != 0)) != 0);
-  if (__pyx_t_2) {
-
-    /* "View.MemoryView":1224
- *     result = malloc(size)
- *     if not result:
- *         _err(MemoryError, NULL)             # <<<<<<<<<<<<<<
- * 
- * 
- */
-    __pyx_t_3 = __pyx_memoryview_err(__pyx_builtin_MemoryError, NULL); if (unlikely(__pyx_t_3 == ((int)-1))) __PYX_ERR(1, 1224, __pyx_L1_error)
-
-    /* "View.MemoryView":1223
- * 
- *     result = malloc(size)
- *     if not result:             # <<<<<<<<<<<<<<
- *         _err(MemoryError, NULL)
- * 
- */
-  }
-
-  /* "View.MemoryView":1227
- * 
- * 
- *     tmpslice.data = <char *> result             # <<<<<<<<<<<<<<
- *     tmpslice.memview = src.memview
- *     for i in range(ndim):
- */
-  __pyx_v_tmpslice->data = ((char *)__pyx_v_result);
-
-  /* "View.MemoryView":1228
- * 
- *     tmpslice.data = <char *> result
- *     tmpslice.memview = src.memview             # <<<<<<<<<<<<<<
- *     for i in range(ndim):
- *         tmpslice.shape[i] = src.shape[i]
- */
-  __pyx_t_4 = __pyx_v_src->memview;
-  __pyx_v_tmpslice->memview = __pyx_t_4;
-
-  /* "View.MemoryView":1229
- *     tmpslice.data = <char *> result
- *     tmpslice.memview = src.memview
- *     for i in range(ndim):             # <<<<<<<<<<<<<<
- *         tmpslice.shape[i] = src.shape[i]
- *         tmpslice.suboffsets[i] = -1
- */
-  __pyx_t_3 = __pyx_v_ndim;
-  __pyx_t_5 = __pyx_t_3;
-  for (__pyx_t_6 = 0; __pyx_t_6 < __pyx_t_5; __pyx_t_6+=1) {
-    __pyx_v_i = __pyx_t_6;
-
-    /* "View.MemoryView":1230
- *     tmpslice.memview = src.memview
- *     for i in range(ndim):
- *         tmpslice.shape[i] = src.shape[i]             # <<<<<<<<<<<<<<
- *         tmpslice.suboffsets[i] = -1
- * 
- */
-    (__pyx_v_tmpslice->shape[__pyx_v_i]) = (__pyx_v_src->shape[__pyx_v_i]);
-
-    /* "View.MemoryView":1231
- *     for i in range(ndim):
- *         tmpslice.shape[i] = src.shape[i]
- *         tmpslice.suboffsets[i] = -1             # <<<<<<<<<<<<<<
- * 
- *     fill_contig_strides_array(&tmpslice.shape[0], &tmpslice.strides[0], itemsize,
- */
-    (__pyx_v_tmpslice->suboffsets[__pyx_v_i]) = -1L;
-  }
-
-  /* "View.MemoryView":1233
- *         tmpslice.suboffsets[i] = -1
- * 
- *     fill_contig_strides_array(&tmpslice.shape[0], &tmpslice.strides[0], itemsize,             # <<<<<<<<<<<<<<
- *                               ndim, order)
- * 
- */
-  (void)(__pyx_fill_contig_strides_array((&(__pyx_v_tmpslice->shape[0])), (&(__pyx_v_tmpslice->strides[0])), __pyx_v_itemsize, __pyx_v_ndim, __pyx_v_order));
-
-  /* "View.MemoryView":1237
- * 
- * 
- *     for i in range(ndim):             # <<<<<<<<<<<<<<
- *         if tmpslice.shape[i] == 1:
- *             tmpslice.strides[i] = 0
- */
-  __pyx_t_3 = __pyx_v_ndim;
-  __pyx_t_5 = __pyx_t_3;
-  for (__pyx_t_6 = 0; __pyx_t_6 < __pyx_t_5; __pyx_t_6+=1) {
-    __pyx_v_i = __pyx_t_6;
-
-    /* "View.MemoryView":1238
- * 
- *     for i in range(ndim):
- *         if tmpslice.shape[i] == 1:             # <<<<<<<<<<<<<<
- *             tmpslice.strides[i] = 0
- * 
- */
-    __pyx_t_2 = (((__pyx_v_tmpslice->shape[__pyx_v_i]) == 1) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":1239
- *     for i in range(ndim):
- *         if tmpslice.shape[i] == 1:
- *             tmpslice.strides[i] = 0             # <<<<<<<<<<<<<<
- * 
- *     if slice_is_contig(src[0], order, ndim):
- */
-      (__pyx_v_tmpslice->strides[__pyx_v_i]) = 0;
-
-      /* "View.MemoryView":1238
- * 
- *     for i in range(ndim):
- *         if tmpslice.shape[i] == 1:             # <<<<<<<<<<<<<<
- *             tmpslice.strides[i] = 0
- * 
- */
-    }
-  }
-
-  /* "View.MemoryView":1241
- *             tmpslice.strides[i] = 0
- * 
- *     if slice_is_contig(src[0], order, ndim):             # <<<<<<<<<<<<<<
- *         memcpy(result, src.data, size)
- *     else:
- */
-  __pyx_t_2 = (__pyx_memviewslice_is_contig((__pyx_v_src[0]), __pyx_v_order, __pyx_v_ndim) != 0);
-  if (__pyx_t_2) {
-
-    /* "View.MemoryView":1242
- * 
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- *         memcpy(result, src.data, size)             # <<<<<<<<<<<<<<
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- *     cdef int ndim = max(src_ndim, dst_ndim)             # <<<<<<<<<<<<<<
- * 
- *     for i in range(ndim):
- */
-  __pyx_t_3 = __pyx_v_dst_ndim;
-  __pyx_t_4 = __pyx_v_src_ndim;
-  if (((__pyx_t_3 > __pyx_t_4) != 0)) {
-    __pyx_t_5 = __pyx_t_3;
-  } else {
-    __pyx_t_5 = __pyx_t_4;
-  }
-  __pyx_v_ndim = __pyx_t_5;
-
-  /* "View.MemoryView":1291
- *     cdef int ndim = max(src_ndim, dst_ndim)
- * 
- *     for i in range(ndim):             # <<<<<<<<<<<<<<
- *         if src.shape[i] != dst.shape[i]:
- *             if src.shape[i] == 1:
- */
-  __pyx_t_5 = __pyx_v_ndim;
-  __pyx_t_3 = __pyx_t_5;
-  for (__pyx_t_4 = 0; __pyx_t_4 < __pyx_t_3; __pyx_t_4+=1) {
-    __pyx_v_i = __pyx_t_4;
-
-    /* "View.MemoryView":1292
- * 
- *     for i in range(ndim):
- *         if src.shape[i] != dst.shape[i]:             # <<<<<<<<<<<<<<
- *             if src.shape[i] == 1:
- *                 broadcasting = True
- */
-    __pyx_t_2 = (((__pyx_v_src.shape[__pyx_v_i]) != (__pyx_v_dst.shape[__pyx_v_i])) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":1293
- *     for i in range(ndim):
- *         if src.shape[i] != dst.shape[i]:
- *             if src.shape[i] == 1:             # <<<<<<<<<<<<<<
- *                 broadcasting = True
- *                 src.strides[i] = 0
- */
-      __pyx_t_2 = (((__pyx_v_src.shape[__pyx_v_i]) == 1) != 0);
-      if (__pyx_t_2) {
-
-        /* "View.MemoryView":1294
- *         if src.shape[i] != dst.shape[i]:
- *             if src.shape[i] == 1:
- *                 broadcasting = True             # <<<<<<<<<<<<<<
- *                 src.strides[i] = 0
- *             else:
- */
-        __pyx_v_broadcasting = 1;
-
-        /* "View.MemoryView":1295
- *             if src.shape[i] == 1:
- *                 broadcasting = True
- *                 src.strides[i] = 0             # <<<<<<<<<<<<<<
- *             else:
- *                 _err_extents(i, dst.shape[i], src.shape[i])
- */
-        (__pyx_v_src.strides[__pyx_v_i]) = 0;
-
-        /* "View.MemoryView":1293
- *     for i in range(ndim):
- *         if src.shape[i] != dst.shape[i]:
- *             if src.shape[i] == 1:             # <<<<<<<<<<<<<<
- *                 broadcasting = True
- *                 src.strides[i] = 0
- */
-        goto __pyx_L7;
-      }
-
-      /* "View.MemoryView":1297
- *                 src.strides[i] = 0
- *             else:
- *                 _err_extents(i, dst.shape[i], src.shape[i])             # <<<<<<<<<<<<<<
- * 
- *         if src.suboffsets[i] >= 0:
- */
-      /*else*/ {
-        __pyx_t_6 = __pyx_memoryview_err_extents(__pyx_v_i, (__pyx_v_dst.shape[__pyx_v_i]), (__pyx_v_src.shape[__pyx_v_i])); if (unlikely(__pyx_t_6 == ((int)-1))) __PYX_ERR(1, 1297, __pyx_L1_error)
-      }
-      __pyx_L7:;
-
-      /* "View.MemoryView":1292
- * 
- *     for i in range(ndim):
- *         if src.shape[i] != dst.shape[i]:             # <<<<<<<<<<<<<<
- *             if src.shape[i] == 1:
- *                 broadcasting = True
- */
-    }
-
-    /* "View.MemoryView":1299
- *                 _err_extents(i, dst.shape[i], src.shape[i])
- * 
- *         if src.suboffsets[i] >= 0:             # <<<<<<<<<<<<<<
- *             _err_dim(ValueError, "Dimension %d is not direct", i)
- * 
- */
-    __pyx_t_2 = (((__pyx_v_src.suboffsets[__pyx_v_i]) >= 0) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":1300
- * 
- *         if src.suboffsets[i] >= 0:
- *             _err_dim(ValueError, "Dimension %d is not direct", i)             # <<<<<<<<<<<<<<
- * 
- *     if slices_overlap(&src, &dst, ndim, itemsize):
- */
-      __pyx_t_6 = __pyx_memoryview_err_dim(__pyx_builtin_ValueError, ((char *)"Dimension %d is not direct"), __pyx_v_i); if (unlikely(__pyx_t_6 == ((int)-1))) __PYX_ERR(1, 1300, __pyx_L1_error)
-
-      /* "View.MemoryView":1299
- *                 _err_extents(i, dst.shape[i], src.shape[i])
- * 
- *         if src.suboffsets[i] >= 0:             # <<<<<<<<<<<<<<
- *             _err_dim(ValueError, "Dimension %d is not direct", i)
- * 
- */
-    }
-  }
-
-  /* "View.MemoryView":1302
- *             _err_dim(ValueError, "Dimension %d is not direct", i)
- * 
- *     if slices_overlap(&src, &dst, ndim, itemsize):             # <<<<<<<<<<<<<<
- * 
- *         if not slice_is_contig(src, order, ndim):
- */
-  __pyx_t_2 = (__pyx_slices_overlap((&__pyx_v_src), (&__pyx_v_dst), __pyx_v_ndim, __pyx_v_itemsize) != 0);
-  if (__pyx_t_2) {
-
-    /* "View.MemoryView":1304
- *     if slices_overlap(&src, &dst, ndim, itemsize):
- * 
- *         if not slice_is_contig(src, order, ndim):             # <<<<<<<<<<<<<<
- *             order = get_best_order(&dst, ndim)
- * 
- */
-    __pyx_t_2 = ((!(__pyx_memviewslice_is_contig(__pyx_v_src, __pyx_v_order, __pyx_v_ndim) != 0)) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":1305
- * 
- *         if not slice_is_contig(src, order, ndim):
- *             order = get_best_order(&dst, ndim)             # <<<<<<<<<<<<<<
- * 
- *         tmpdata = copy_data_to_temp(&src, &tmp, order, ndim)
- */
-      __pyx_v_order = __pyx_get_best_slice_order((&__pyx_v_dst), __pyx_v_ndim);
-
-      /* "View.MemoryView":1304
- *     if slices_overlap(&src, &dst, ndim, itemsize):
- * 
- *         if not slice_is_contig(src, order, ndim):             # <<<<<<<<<<<<<<
- *             order = get_best_order(&dst, ndim)
- * 
- */
-    }
-
-    /* "View.MemoryView":1307
- *             order = get_best_order(&dst, ndim)
- * 
- *         tmpdata = copy_data_to_temp(&src, &tmp, order, ndim)             # <<<<<<<<<<<<<<
- *         src = tmp
- * 
- */
-    __pyx_t_7 = __pyx_memoryview_copy_data_to_temp((&__pyx_v_src), (&__pyx_v_tmp), __pyx_v_order, __pyx_v_ndim); if (unlikely(__pyx_t_7 == ((void *)NULL))) __PYX_ERR(1, 1307, __pyx_L1_error)
-    __pyx_v_tmpdata = __pyx_t_7;
-
-    /* "View.MemoryView":1308
- * 
- *         tmpdata = copy_data_to_temp(&src, &tmp, order, ndim)
- *         src = tmp             # <<<<<<<<<<<<<<
- * 
- *     if not broadcasting:
- */
-    __pyx_v_src = __pyx_v_tmp;
-
-    /* "View.MemoryView":1302
- *             _err_dim(ValueError, "Dimension %d is not direct", i)
- * 
- *     if slices_overlap(&src, &dst, ndim, itemsize):             # <<<<<<<<<<<<<<
- * 
- *         if not slice_is_contig(src, order, ndim):
- */
-  }
-
-  /* "View.MemoryView":1310
- *         src = tmp
- * 
- *     if not broadcasting:             # <<<<<<<<<<<<<<
- * 
- * 
- */
-  __pyx_t_2 = ((!(__pyx_v_broadcasting != 0)) != 0);
-  if (__pyx_t_2) {
-
-    /* "View.MemoryView":1313
- * 
- * 
- *         if slice_is_contig(src, 'C', ndim):             # <<<<<<<<<<<<<<
- *             direct_copy = slice_is_contig(dst, 'C', ndim)
- *         elif slice_is_contig(src, 'F', ndim):
- */
-    __pyx_t_2 = (__pyx_memviewslice_is_contig(__pyx_v_src, 'C', __pyx_v_ndim) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":1314
- * 
- *         if slice_is_contig(src, 'C', ndim):
- *             direct_copy = slice_is_contig(dst, 'C', ndim)             # <<<<<<<<<<<<<<
- *         elif slice_is_contig(src, 'F', ndim):
- *             direct_copy = slice_is_contig(dst, 'F', ndim)
- */
-      __pyx_v_direct_copy = __pyx_memviewslice_is_contig(__pyx_v_dst, 'C', __pyx_v_ndim);
-
-      /* "View.MemoryView":1313
- * 
- * 
- *         if slice_is_contig(src, 'C', ndim):             # <<<<<<<<<<<<<<
- *             direct_copy = slice_is_contig(dst, 'C', ndim)
- *         elif slice_is_contig(src, 'F', ndim):
- */
-      goto __pyx_L12;
-    }
-
-    /* "View.MemoryView":1315
- *         if slice_is_contig(src, 'C', ndim):
- *             direct_copy = slice_is_contig(dst, 'C', ndim)
- *         elif slice_is_contig(src, 'F', ndim):             # <<<<<<<<<<<<<<
- *             direct_copy = slice_is_contig(dst, 'F', ndim)
- * 
- */
-    __pyx_t_2 = (__pyx_memviewslice_is_contig(__pyx_v_src, 'F', __pyx_v_ndim) != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":1316
- *             direct_copy = slice_is_contig(dst, 'C', ndim)
- *         elif slice_is_contig(src, 'F', ndim):
- *             direct_copy = slice_is_contig(dst, 'F', ndim)             # <<<<<<<<<<<<<<
- * 
- *         if direct_copy:
- */
-      __pyx_v_direct_copy = __pyx_memviewslice_is_contig(__pyx_v_dst, 'F', __pyx_v_ndim);
-
-      /* "View.MemoryView":1315
- *         if slice_is_contig(src, 'C', ndim):
- *             direct_copy = slice_is_contig(dst, 'C', ndim)
- *         elif slice_is_contig(src, 'F', ndim):             # <<<<<<<<<<<<<<
- *             direct_copy = slice_is_contig(dst, 'F', ndim)
- * 
- */
-    }
-    __pyx_L12:;
-
-    /* "View.MemoryView":1318
- *             direct_copy = slice_is_contig(dst, 'F', ndim)
- * 
- *         if direct_copy:             # <<<<<<<<<<<<<<
- * 
- *             refcount_copying(&dst, dtype_is_object, ndim, False)
- */
-    __pyx_t_2 = (__pyx_v_direct_copy != 0);
-    if (__pyx_t_2) {
-
-      /* "View.MemoryView":1320
- *         if direct_copy:
- * 
- *             refcount_copying(&dst, dtype_is_object, ndim, False)             # <<<<<<<<<<<<<<
- *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))
- *             refcount_copying(&dst, dtype_is_object, ndim, True)
- */
-      __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 0);
-
-      /* "View.MemoryView":1321
- * 
- *             refcount_copying(&dst, dtype_is_object, ndim, False)
- *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))             # <<<<<<<<<<<<<<
- *             refcount_copying(&dst, dtype_is_object, ndim, True)
- *             free(tmpdata)
- */
-      (void)(memcpy(__pyx_v_dst.data, __pyx_v_src.data, __pyx_memoryview_slice_get_size((&__pyx_v_src), __pyx_v_ndim)));
-
-      /* "View.MemoryView":1322
- *             refcount_copying(&dst, dtype_is_object, ndim, False)
- *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))
- *             refcount_copying(&dst, dtype_is_object, ndim, True)             # <<<<<<<<<<<<<<
- *             free(tmpdata)
- *             return 0
- */
-      __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1);
-
-      /* "View.MemoryView":1323
- *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))
- *             refcount_copying(&dst, dtype_is_object, ndim, True)
- *             free(tmpdata)             # <<<<<<<<<<<<<<
- *             return 0
- * 
- */
-      free(__pyx_v_tmpdata);
-
-      /* "View.MemoryView":1324
- *             refcount_copying(&dst, dtype_is_object, ndim, True)
- *             free(tmpdata)
- *             return 0             # <<<<<<<<<<<<<<
- * 
- *     if order == 'F' == get_best_order(&dst, ndim):
- */
-      __pyx_r = 0;
-      goto __pyx_L0;
-
-      /* "View.MemoryView":1318
- *             direct_copy = slice_is_contig(dst, 'F', ndim)
- * 
- *         if direct_copy:             # <<<<<<<<<<<<<<
- * 
- *             refcount_copying(&dst, dtype_is_object, ndim, False)
- */
-    }
-
-    /* "View.MemoryView":1310
- *         src = tmp
- * 
- *     if not broadcasting:             # <<<<<<<<<<<<<<
- * 
- * 
- */
-  }
-
-  /* "View.MemoryView":1326
- *             return 0
- * 
- *     if order == 'F' == get_best_order(&dst, ndim):             # <<<<<<<<<<<<<<
- * 
- * 
- */
-  __pyx_t_2 = (__pyx_v_order == 'F');
-  if (__pyx_t_2) {
-    __pyx_t_2 = ('F' == __pyx_get_best_slice_order((&__pyx_v_dst), __pyx_v_ndim));
-  }
-  __pyx_t_8 = (__pyx_t_2 != 0);
-  if (__pyx_t_8) {
-
-    /* "View.MemoryView":1329
- * 
- * 
- *         transpose_memslice(&src)             # <<<<<<<<<<<<<<
- *         transpose_memslice(&dst)
- * 
- */
-    __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_src)); if (unlikely(__pyx_t_5 == ((int)0))) __PYX_ERR(1, 1329, __pyx_L1_error)
-
-    /* "View.MemoryView":1330
- * 
- *         transpose_memslice(&src)
- *         transpose_memslice(&dst)             # <<<<<<<<<<<<<<
- * 
- *     refcount_copying(&dst, dtype_is_object, ndim, False)
- */
-    __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_dst)); if (unlikely(__pyx_t_5 == ((int)0))) __PYX_ERR(1, 1330, __pyx_L1_error)
-
-    /* "View.MemoryView":1326
- *             return 0
- * 
- *     if order == 'F' == get_best_order(&dst, ndim):             # <<<<<<<<<<<<<<
- * 
- * 
- */
-  }
-
-  /* "View.MemoryView":1332
- *         transpose_memslice(&dst)
- * 
- *     refcount_copying(&dst, dtype_is_object, ndim, False)             # <<<<<<<<<<<<<<
- *     copy_strided_to_strided(&src, &dst, ndim, itemsize)
- *     refcount_copying(&dst, dtype_is_object, ndim, True)
- */
-  __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 0);
-
-  /* "View.MemoryView":1333
- * 
- *     refcount_copying(&dst, dtype_is_object, ndim, False)
- *     copy_strided_to_strided(&src, &dst, ndim, itemsize)             # <<<<<<<<<<<<<<
- *     refcount_copying(&dst, dtype_is_object, ndim, True)
- * 
- */
-  copy_strided_to_strided((&__pyx_v_src), (&__pyx_v_dst), __pyx_v_ndim, __pyx_v_itemsize);
-
-  /* "View.MemoryView":1334
- *     refcount_copying(&dst, dtype_is_object, ndim, False)
- *     copy_strided_to_strided(&src, &dst, ndim, itemsize)
- *     refcount_copying(&dst, dtype_is_object, ndim, True)             # <<<<<<<<<<<<<<
- * 
- *     free(tmpdata)
- */
-  __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1);
-
-  /* "View.MemoryView":1336
- *     refcount_copying(&dst, dtype_is_object, ndim, True)
- * 
- *     free(tmpdata)             # <<<<<<<<<<<<<<
- *     return 0
- * 
- */
-  free(__pyx_v_tmpdata);
-
-  /* "View.MemoryView":1337
- * 
- *     free(tmpdata)
- *     return 0             # <<<<<<<<<<<<<<
- * 
- * @cname('__pyx_memoryview_broadcast_leading')
- */
-  __pyx_r = 0;
-  goto __pyx_L0;
-
-  /* "View.MemoryView":1268
- * 
- * @cname('__pyx_memoryview_copy_contents')
- * cdef int memoryview_copy_contents(__Pyx_memviewslice src,             # <<<<<<<<<<<<<<
- *                                   __Pyx_memviewslice dst,
- *                                   int src_ndim, int dst_ndim,
- */
-
-  /* function exit code */
-  __pyx_L1_error:;
-  {
-    #ifdef WITH_THREAD
-    PyGILState_STATE __pyx_gilstate_save = __Pyx_PyGILState_Ensure();
-    #endif
-    __Pyx_AddTraceback("View.MemoryView.memoryview_copy_contents", __pyx_clineno, __pyx_lineno, __pyx_filename);
-    #ifdef WITH_THREAD
-    __Pyx_PyGILState_Release(__pyx_gilstate_save);
-    #endif
-  }
-  __pyx_r = -1;
-  __pyx_L0:;
-  return __pyx_r;
-}
-
-/* "View.MemoryView":1340
- * 
- * @cname('__pyx_memoryview_broadcast_leading')
- * cdef void broadcast_leading(__Pyx_memviewslice *mslice,             # <<<<<<<<<<<<<<
- *                             int ndim,
- *                             int ndim_other) nogil:
- */
-
-static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *__pyx_v_mslice, int __pyx_v_ndim, int __pyx_v_ndim_other) {
-  int __pyx_v_i;
-  int __pyx_v_offset;
-  int __pyx_t_1;
-  int __pyx_t_2;
-  int __pyx_t_3;
-
-  /* "View.MemoryView":1344
- *                             int ndim_other) nogil:
- *     cdef int i
- *     cdef int offset = ndim_other - ndim             # <<<<<<<<<<<<<<
- * 
- *     for i in range(ndim - 1, -1, -1):
- */
-  __pyx_v_offset = (__pyx_v_ndim_other - __pyx_v_ndim);
-
-  /* "View.MemoryView":1346
- *     cdef int offset = ndim_other - ndim
- * 
- *     for i in range(ndim - 1, -1, -1):             # <<<<<<<<<<<<<<
- *         mslice.shape[i + offset] = mslice.shape[i]
- *         mslice.strides[i + offset] = mslice.strides[i]
- */
-  for (__pyx_t_1 = (__pyx_v_ndim - 1); __pyx_t_1 > -1; __pyx_t_1-=1) {
-    __pyx_v_i = __pyx_t_1;
-
-    /* "View.MemoryView":1347
- * 
- *     for i in range(ndim - 1, -1, -1):
- *         mslice.shape[i + offset] = mslice.shape[i]             # <<<<<<<<<<<<<<
- *         mslice.strides[i + offset] = mslice.strides[i]
- *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]
- */
-    (__pyx_v_mslice->shape[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->shape[__pyx_v_i]);
-
-    /* "View.MemoryView":1348
- *     for i in range(ndim - 1, -1, -1):
- *         mslice.shape[i + offset] = mslice.shape[i]
- *         mslice.strides[i + offset] = mslice.strides[i]             # <<<<<<<<<<<<<<
- *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]
- * 
- */
-    (__pyx_v_mslice->strides[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->strides[__pyx_v_i]);
-
-    /* "View.MemoryView":1349
- *         mslice.shape[i + offset] = mslice.shape[i]
- *         mslice.strides[i + offset] = mslice.strides[i]
- *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]             # <<<<<<<<<<<<<<
- * 
- *     for i in range(offset):
- */
-    (__pyx_v_mslice->suboffsets[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_mslice->suboffsets[__pyx_v_i]);
-  }
-
-  /* "View.MemoryView":1351
- *         mslice.suboffsets[i + offset] = mslice.suboffsets[i]
- * 
- *     for i in range(offset):             # <<<<<<<<<<<<<<
- *         mslice.shape[i] = 1
- *         mslice.strides[i] = mslice.strides[0]
- */
-  __pyx_t_1 = __pyx_v_offset;
-  __pyx_t_2 = __pyx_t_1;
-  for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
-    __pyx_v_i = __pyx_t_3;
-
-    /* "View.MemoryView":1352
- * 
- *     for i in range(offset):
- *         mslice.shape[i] = 1             # <<<<<<<<<<<<<<
- *         mslice.strides[i] = mslice.strides[0]
- *         mslice.suboffsets[i] = -1
- */
-    (__pyx_v_mslice->shape[__pyx_v_i]) = 1;
-
-    /* "View.MemoryView":1353
- *     for i in range(offset):
- *         mslice.shape[i] = 1
- *         mslice.strides[i] = mslice.strides[0]             # <<<<<<<<<<<<<<
- *         mslice.suboffsets[i] = -1
- * 
- */
-    (__pyx_v_mslice->strides[__pyx_v_i]) = (__pyx_v_mslice->strides[0]);
-
-    /* "View.MemoryView":1354
- *         mslice.shape[i] = 1
- *         mslice.strides[i] = mslice.strides[0]
- *         mslice.suboffsets[i] = -1             # <<<<<<<<<<<<<<
- * 
- * 
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-  0, /*sq_concat*/
-  0, /*sq_repeat*/
-  __pyx_sq_item_array, /*sq_item*/
-  0, /*sq_slice*/
-  0, /*sq_ass_item*/
-  0, /*sq_ass_slice*/
-  0, /*sq_contains*/
-  0, /*sq_inplace_concat*/
-  0, /*sq_inplace_repeat*/
-};
-
-static PyMappingMethods __pyx_tp_as_mapping_array = {
-  __pyx_array___len__, /*mp_length*/
-  __pyx_array___getitem__, /*mp_subscript*/
-  __pyx_mp_ass_subscript_array, /*mp_ass_subscript*/
-};
-
-static PyBufferProcs __pyx_tp_as_buffer_array = {
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getreadbuffer*/
-  #endif
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getwritebuffer*/
-  #endif
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getsegcount*/
-  #endif
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getcharbuffer*/
-  #endif
-  __pyx_array_getbuffer, /*bf_getbuffer*/
-  0, /*bf_releasebuffer*/
-};
-
-static PyTypeObject __pyx_type___pyx_array = {
-  PyVarObject_HEAD_INIT(0, 0)
-  "pytential.qbx.target_specific.impl.array", /*tp_name*/
-  sizeof(struct __pyx_array_obj), /*tp_basicsize*/
-  0, /*tp_itemsize*/
-  __pyx_tp_dealloc_array, /*tp_dealloc*/
-  #if PY_VERSION_HEX < 0x030800b4
-  0, /*tp_print*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b4
-  0, /*tp_vectorcall_offset*/
-  #endif
-  0, /*tp_getattr*/
-  0, /*tp_setattr*/
-  #if PY_MAJOR_VERSION < 3
-  0, /*tp_compare*/
-  #endif
-  #if PY_MAJOR_VERSION >= 3
-  0, /*tp_as_async*/
-  #endif
-  0, /*tp_repr*/
-  0, /*tp_as_number*/
-  &__pyx_tp_as_sequence_array, /*tp_as_sequence*/
-  &__pyx_tp_as_mapping_array, /*tp_as_mapping*/
-  0, /*tp_hash*/
-  0, /*tp_call*/
-  0, /*tp_str*/
-  __pyx_tp_getattro_array, /*tp_getattro*/
-  0, /*tp_setattro*/
-  &__pyx_tp_as_buffer_array, /*tp_as_buffer*/
-  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE, /*tp_flags*/
-  0, /*tp_doc*/
-  0, /*tp_traverse*/
-  0, /*tp_clear*/
-  0, /*tp_richcompare*/
-  0, /*tp_weaklistoffset*/
-  0, /*tp_iter*/
-  0, /*tp_iternext*/
-  __pyx_methods_array, /*tp_methods*/
-  0, /*tp_members*/
-  __pyx_getsets_array, /*tp_getset*/
-  0, /*tp_base*/
-  0, /*tp_dict*/
-  0, /*tp_descr_get*/
-  0, /*tp_descr_set*/
-  0, /*tp_dictoffset*/
-  0, /*tp_init*/
-  0, /*tp_alloc*/
-  __pyx_tp_new_array, /*tp_new*/
-  0, /*tp_free*/
-  0, /*tp_is_gc*/
-  0, /*tp_bases*/
-  0, /*tp_mro*/
-  0, /*tp_cache*/
-  0, /*tp_subclasses*/
-  0, /*tp_weaklist*/
-  0, /*tp_del*/
-  0, /*tp_version_tag*/
-  #if PY_VERSION_HEX >= 0x030400a1
-  0, /*tp_finalize*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b1
-  0, /*tp_vectorcall*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
-  0, /*tp_print*/
-  #endif
-};
-
-static PyObject *__pyx_tp_new_Enum(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
-  struct __pyx_MemviewEnum_obj *p;
-  PyObject *o;
-  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
-    o = (*t->tp_alloc)(t, 0);
-  } else {
-    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
-  }
-  if (unlikely(!o)) return 0;
-  p = ((struct __pyx_MemviewEnum_obj *)o);
-  p->name = Py_None; Py_INCREF(Py_None);
-  return o;
-}
-
-static void __pyx_tp_dealloc_Enum(PyObject *o) {
-  struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o;
-  #if CYTHON_USE_TP_FINALIZE
-  if (unlikely(PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE) && Py_TYPE(o)->tp_finalize) && !_PyGC_FINALIZED(o)) {
-    if (PyObject_CallFinalizerFromDealloc(o)) return;
-  }
-  #endif
-  PyObject_GC_UnTrack(o);
-  Py_CLEAR(p->name);
-  (*Py_TYPE(o)->tp_free)(o);
-}
-
-static int __pyx_tp_traverse_Enum(PyObject *o, visitproc v, void *a) {
-  int e;
-  struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o;
-  if (p->name) {
-    e = (*v)(p->name, a); if (e) return e;
-  }
-  return 0;
-}
-
-static int __pyx_tp_clear_Enum(PyObject *o) {
-  PyObject* tmp;
-  struct __pyx_MemviewEnum_obj *p = (struct __pyx_MemviewEnum_obj *)o;
-  tmp = ((PyObject*)p->name);
-  p->name = Py_None; Py_INCREF(Py_None);
-  Py_XDECREF(tmp);
-  return 0;
-}
-
-static PyMethodDef __pyx_methods_Enum[] = {
-  {"__reduce_cython__", (PyCFunction)__pyx_pw___pyx_MemviewEnum_1__reduce_cython__, METH_NOARGS, 0},
-  {"__setstate_cython__", (PyCFunction)__pyx_pw___pyx_MemviewEnum_3__setstate_cython__, METH_O, 0},
-  {0, 0, 0, 0}
-};
-
-static PyTypeObject __pyx_type___pyx_MemviewEnum = {
-  PyVarObject_HEAD_INIT(0, 0)
-  "pytential.qbx.target_specific.impl.Enum", /*tp_name*/
-  sizeof(struct __pyx_MemviewEnum_obj), /*tp_basicsize*/
-  0, /*tp_itemsize*/
-  __pyx_tp_dealloc_Enum, /*tp_dealloc*/
-  #if PY_VERSION_HEX < 0x030800b4
-  0, /*tp_print*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b4
-  0, /*tp_vectorcall_offset*/
-  #endif
-  0, /*tp_getattr*/
-  0, /*tp_setattr*/
-  #if PY_MAJOR_VERSION < 3
-  0, /*tp_compare*/
-  #endif
-  #if PY_MAJOR_VERSION >= 3
-  0, /*tp_as_async*/
-  #endif
-  __pyx_MemviewEnum___repr__, /*tp_repr*/
-  0, /*tp_as_number*/
-  0, /*tp_as_sequence*/
-  0, /*tp_as_mapping*/
-  0, /*tp_hash*/
-  0, /*tp_call*/
-  0, /*tp_str*/
-  0, /*tp_getattro*/
-  0, /*tp_setattro*/
-  0, /*tp_as_buffer*/
-  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
-  0, /*tp_doc*/
-  __pyx_tp_traverse_Enum, /*tp_traverse*/
-  __pyx_tp_clear_Enum, /*tp_clear*/
-  0, /*tp_richcompare*/
-  0, /*tp_weaklistoffset*/
-  0, /*tp_iter*/
-  0, /*tp_iternext*/
-  __pyx_methods_Enum, /*tp_methods*/
-  0, /*tp_members*/
-  0, /*tp_getset*/
-  0, /*tp_base*/
-  0, /*tp_dict*/
-  0, /*tp_descr_get*/
-  0, /*tp_descr_set*/
-  0, /*tp_dictoffset*/
-  __pyx_MemviewEnum___init__, /*tp_init*/
-  0, /*tp_alloc*/
-  __pyx_tp_new_Enum, /*tp_new*/
-  0, /*tp_free*/
-  0, /*tp_is_gc*/
-  0, /*tp_bases*/
-  0, /*tp_mro*/
-  0, /*tp_cache*/
-  0, /*tp_subclasses*/
-  0, /*tp_weaklist*/
-  0, /*tp_del*/
-  0, /*tp_version_tag*/
-  #if PY_VERSION_HEX >= 0x030400a1
-  0, /*tp_finalize*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b1
-  0, /*tp_vectorcall*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
-  0, /*tp_print*/
-  #endif
-};
-static struct __pyx_vtabstruct_memoryview __pyx_vtable_memoryview;
-
-static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k) {
-  struct __pyx_memoryview_obj *p;
-  PyObject *o;
-  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
-    o = (*t->tp_alloc)(t, 0);
-  } else {
-    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
-  }
-  if (unlikely(!o)) return 0;
-  p = ((struct __pyx_memoryview_obj *)o);
-  p->__pyx_vtab = __pyx_vtabptr_memoryview;
-  p->obj = Py_None; Py_INCREF(Py_None);
-  p->_size = Py_None; Py_INCREF(Py_None);
-  p->_array_interface = Py_None; Py_INCREF(Py_None);
-  p->view.obj = NULL;
-  if (unlikely(__pyx_memoryview___cinit__(o, a, k) < 0)) goto bad;
-  return o;
-  bad:
-  Py_DECREF(o); o = 0;
-  return NULL;
-}
-
-static void __pyx_tp_dealloc_memoryview(PyObject *o) {
-  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
-  #if CYTHON_USE_TP_FINALIZE
-  if (unlikely(PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE) && Py_TYPE(o)->tp_finalize) && !_PyGC_FINALIZED(o)) {
-    if (PyObject_CallFinalizerFromDealloc(o)) return;
-  }
-  #endif
-  PyObject_GC_UnTrack(o);
-  {
-    PyObject *etype, *eval, *etb;
-    PyErr_Fetch(&etype, &eval, &etb);
-    __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1);
-    __pyx_memoryview___dealloc__(o);
-    __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1);
-    PyErr_Restore(etype, eval, etb);
-  }
-  Py_CLEAR(p->obj);
-  Py_CLEAR(p->_size);
-  Py_CLEAR(p->_array_interface);
-  (*Py_TYPE(o)->tp_free)(o);
-}
-
-static int __pyx_tp_traverse_memoryview(PyObject *o, visitproc v, void *a) {
-  int e;
-  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
-  if (p->obj) {
-    e = (*v)(p->obj, a); if (e) return e;
-  }
-  if (p->_size) {
-    e = (*v)(p->_size, a); if (e) return e;
-  }
-  if (p->_array_interface) {
-    e = (*v)(p->_array_interface, a); if (e) return e;
-  }
-  if (p->view.obj) {
-    e = (*v)(p->view.obj, a); if (e) return e;
-  }
-  return 0;
-}
-
-static int __pyx_tp_clear_memoryview(PyObject *o) {
-  PyObject* tmp;
-  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
-  tmp = ((PyObject*)p->obj);
-  p->obj = Py_None; Py_INCREF(Py_None);
-  Py_XDECREF(tmp);
-  tmp = ((PyObject*)p->_size);
-  p->_size = Py_None; Py_INCREF(Py_None);
-  Py_XDECREF(tmp);
-  tmp = ((PyObject*)p->_array_interface);
-  p->_array_interface = Py_None; Py_INCREF(Py_None);
-  Py_XDECREF(tmp);
-  Py_CLEAR(p->view.obj);
-  return 0;
-}
-static PyObject *__pyx_sq_item_memoryview(PyObject *o, Py_ssize_t i) {
-  PyObject *r;
-  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
-  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
-  Py_DECREF(x);
-  return r;
-}
-
-static int __pyx_mp_ass_subscript_memoryview(PyObject *o, PyObject *i, PyObject *v) {
-  if (v) {
-    return __pyx_memoryview___setitem__(o, i, v);
-  }
-  else {
-    PyErr_Format(PyExc_NotImplementedError,
-      "Subscript deletion not supported by %.200s", Py_TYPE(o)->tp_name);
-    return -1;
-  }
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_T(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_1T_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_base(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_4base_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_shape(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_5shape_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_strides(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_7strides_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_suboffsets(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_10suboffsets_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_ndim(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_4ndim_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_itemsize(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_8itemsize_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_nbytes(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_6nbytes_1__get__(o);
-}
-
-static PyObject *__pyx_getprop___pyx_memoryview_size(PyObject *o, CYTHON_UNUSED void *x) {
-  return __pyx_pw_15View_dot_MemoryView_10memoryview_4size_1__get__(o);
-}
-
-static PyMethodDef __pyx_methods_memoryview[] = {
-  {"is_c_contig", (PyCFunction)__pyx_memoryview_is_c_contig, METH_NOARGS, 0},
-  {"is_f_contig", (PyCFunction)__pyx_memoryview_is_f_contig, METH_NOARGS, 0},
-  {"copy", (PyCFunction)__pyx_memoryview_copy, METH_NOARGS, 0},
-  {"copy_fortran", (PyCFunction)__pyx_memoryview_copy_fortran, METH_NOARGS, 0},
-  {"__reduce_cython__", (PyCFunction)__pyx_pw___pyx_memoryview_1__reduce_cython__, METH_NOARGS, 0},
-  {"__setstate_cython__", (PyCFunction)__pyx_pw___pyx_memoryview_3__setstate_cython__, METH_O, 0},
-  {0, 0, 0, 0}
-};
-
-static struct PyGetSetDef __pyx_getsets_memoryview[] = {
-  {(char *)"T", __pyx_getprop___pyx_memoryview_T, 0, (char *)0, 0},
-  {(char *)"base", __pyx_getprop___pyx_memoryview_base, 0, (char *)0, 0},
-  {(char *)"shape", __pyx_getprop___pyx_memoryview_shape, 0, (char *)0, 0},
-  {(char *)"strides", __pyx_getprop___pyx_memoryview_strides, 0, (char *)0, 0},
-  {(char *)"suboffsets", __pyx_getprop___pyx_memoryview_suboffsets, 0, (char *)0, 0},
-  {(char *)"ndim", __pyx_getprop___pyx_memoryview_ndim, 0, (char *)0, 0},
-  {(char *)"itemsize", __pyx_getprop___pyx_memoryview_itemsize, 0, (char *)0, 0},
-  {(char *)"nbytes", __pyx_getprop___pyx_memoryview_nbytes, 0, (char *)0, 0},
-  {(char *)"size", __pyx_getprop___pyx_memoryview_size, 0, (char *)0, 0},
-  {0, 0, 0, 0, 0}
-};
-
-static PySequenceMethods __pyx_tp_as_sequence_memoryview = {
-  __pyx_memoryview___len__, /*sq_length*/
-  0, /*sq_concat*/
-  0, /*sq_repeat*/
-  __pyx_sq_item_memoryview, /*sq_item*/
-  0, /*sq_slice*/
-  0, /*sq_ass_item*/
-  0, /*sq_ass_slice*/
-  0, /*sq_contains*/
-  0, /*sq_inplace_concat*/
-  0, /*sq_inplace_repeat*/
-};
-
-static PyMappingMethods __pyx_tp_as_mapping_memoryview = {
-  __pyx_memoryview___len__, /*mp_length*/
-  __pyx_memoryview___getitem__, /*mp_subscript*/
-  __pyx_mp_ass_subscript_memoryview, /*mp_ass_subscript*/
-};
-
-static PyBufferProcs __pyx_tp_as_buffer_memoryview = {
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getreadbuffer*/
-  #endif
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getwritebuffer*/
-  #endif
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getsegcount*/
-  #endif
-  #if PY_MAJOR_VERSION < 3
-  0, /*bf_getcharbuffer*/
-  #endif
-  __pyx_memoryview_getbuffer, /*bf_getbuffer*/
-  0, /*bf_releasebuffer*/
-};
-
-static PyTypeObject __pyx_type___pyx_memoryview = {
-  PyVarObject_HEAD_INIT(0, 0)
-  "pytential.qbx.target_specific.impl.memoryview", /*tp_name*/
-  sizeof(struct __pyx_memoryview_obj), /*tp_basicsize*/
-  0, /*tp_itemsize*/
-  __pyx_tp_dealloc_memoryview, /*tp_dealloc*/
-  #if PY_VERSION_HEX < 0x030800b4
-  0, /*tp_print*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b4
-  0, /*tp_vectorcall_offset*/
-  #endif
-  0, /*tp_getattr*/
-  0, /*tp_setattr*/
-  #if PY_MAJOR_VERSION < 3
-  0, /*tp_compare*/
-  #endif
-  #if PY_MAJOR_VERSION >= 3
-  0, /*tp_as_async*/
-  #endif
-  __pyx_memoryview___repr__, /*tp_repr*/
-  0, /*tp_as_number*/
-  &__pyx_tp_as_sequence_memoryview, /*tp_as_sequence*/
-  &__pyx_tp_as_mapping_memoryview, /*tp_as_mapping*/
-  0, /*tp_hash*/
-  0, /*tp_call*/
-  __pyx_memoryview___str__, /*tp_str*/
-  0, /*tp_getattro*/
-  0, /*tp_setattro*/
-  &__pyx_tp_as_buffer_memoryview, /*tp_as_buffer*/
-  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
-  0, /*tp_doc*/
-  __pyx_tp_traverse_memoryview, /*tp_traverse*/
-  __pyx_tp_clear_memoryview, /*tp_clear*/
-  0, /*tp_richcompare*/
-  0, /*tp_weaklistoffset*/
-  0, /*tp_iter*/
-  0, /*tp_iternext*/
-  __pyx_methods_memoryview, /*tp_methods*/
-  0, /*tp_members*/
-  __pyx_getsets_memoryview, /*tp_getset*/
-  0, /*tp_base*/
-  0, /*tp_dict*/
-  0, /*tp_descr_get*/
-  0, /*tp_descr_set*/
-  0, /*tp_dictoffset*/
-  0, /*tp_init*/
-  0, /*tp_alloc*/
-  __pyx_tp_new_memoryview, /*tp_new*/
-  0, /*tp_free*/
-  0, /*tp_is_gc*/
-  0, /*tp_bases*/
-  0, /*tp_mro*/
-  0, /*tp_cache*/
-  0, /*tp_subclasses*/
-  0, /*tp_weaklist*/
-  0, /*tp_del*/
-  0, /*tp_version_tag*/
-  #if PY_VERSION_HEX >= 0x030400a1
-  0, /*tp_finalize*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b1
-  0, /*tp_vectorcall*/
-  #endif
-  #if PY_VERSION_HEX >= 0x030800b4 && PY_VERSION_HEX < 0x03090000
-  0, /*tp_print*/
-  #endif
-};
-static struct __pyx_vtabstruct__memoryviewslice __pyx_vtable__memoryviewslice;
-
-static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k) {
-  struct __pyx_memoryviewslice_obj *p;
-  PyObject *o = __pyx_tp_new_memoryview(t, a, k);
-  if (unlikely(!o)) return 0;
-  p = ((struct __pyx_memoryviewslice_obj *)o);
-  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_memoryview*)__pyx_vtabptr__memoryviewslice;
-  p->from_object = Py_None; Py_INCREF(Py_None);
-  p->from_slice.memview = NULL;
-  return o;
-}
-
-static void __pyx_tp_dealloc__memoryviewslice(PyObject *o) {
-  struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o;
-  #if CYTHON_USE_TP_FINALIZE
-  if (unlikely(PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE) && Py_TYPE(o)->tp_finalize) && !_PyGC_FINALIZED(o)) {
-    if (PyObject_CallFinalizerFromDealloc(o)) return;
-  }
-  #endif
-  PyObject_GC_UnTrack(o);
-  {
-    PyObject *etype, *eval, *etb;
-    PyErr_Fetch(&etype, &eval, &etb);
-    __Pyx_SET_REFCNT(o, Py_REFCNT(o) + 1);
-    __pyx_memoryviewslice___dealloc__(o);
-    __Pyx_SET_REFCNT(o, Py_REFCNT(o) - 1);
-    PyErr_Restore(etype, eval, etb);
-  }
-  Py_CLEAR(p->from_object);
-  PyObject_GC_Track(o);
-  __pyx_tp_dealloc_memoryview(o);
-}
-
-static int __pyx_tp_traverse__memoryviewslice(PyObject *o, visitproc v, void *a) {
-  int e;
-  struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o;
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-#if CYTHON_USE_TYPE_SLOTS
-static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
-    PyTypeObject* tp = Py_TYPE(obj);
-    if (likely(tp->tp_getattro))
-        return tp->tp_getattro(obj, attr_name);
-#if PY_MAJOR_VERSION < 3
-    if (likely(tp->tp_getattr))
-        return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
-#endif
-    return PyObject_GetAttr(obj, attr_name);
-}
-#endif
-
-/* GetBuiltinName */
-static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
-    PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
-    if (unlikely(!result)) {
-        PyErr_Format(PyExc_NameError,
-#if PY_MAJOR_VERSION >= 3
-            "name '%U' is not defined", name);
-#else
-            "name '%.200s' is not defined", PyString_AS_STRING(name));
-#endif
-    }
-    return result;
-}
-
-/* RaiseArgTupleInvalid */
-static void __Pyx_RaiseArgtupleInvalid(
-    const char* func_name,
-    int exact,
-    Py_ssize_t num_min,
-    Py_ssize_t num_max,
-    Py_ssize_t num_found)
-{
-    Py_ssize_t num_expected;
-    const char *more_or_less;
-    if (num_found < num_min) {
-        num_expected = num_min;
-        more_or_less = "at least";
-    } else {
-        num_expected = num_max;
-        more_or_less = "at most";
-    }
-    if (exact) {
-        more_or_less = "exactly";
-    }
-    PyErr_Format(PyExc_TypeError,
-                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
-                 func_name, more_or_less, num_expected,
-                 (num_expected == 1) ? "" : "s", num_found);
-}
-
-/* RaiseDoubleKeywords */
-static void __Pyx_RaiseDoubleKeywordsError(
-    const char* func_name,
-    PyObject* kw_name)
-{
-    PyErr_Format(PyExc_TypeError,
-        #if PY_MAJOR_VERSION >= 3
-        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
-        #else
-        "%s() got multiple values for keyword argument '%s'", func_name,
-        PyString_AsString(kw_name));
-        #endif
-}
-
-/* ParseKeywords */
-static int __Pyx_ParseOptionalKeywords(
-    PyObject *kwds,
-    PyObject **argnames[],
-    PyObject *kwds2,
-    PyObject *values[],
-    Py_ssize_t num_pos_args,
-    const char* function_name)
-{
-    PyObject *key = 0, *value = 0;
-    Py_ssize_t pos = 0;
-    PyObject*** name;
-    PyObject*** first_kw_arg = argnames + num_pos_args;
-    while (PyDict_Next(kwds, &pos, &key, &value)) {
-        name = first_kw_arg;
-        while (*name && (**name != key)) name++;
-        if (*name) {
-            values[name-argnames] = value;
-            continue;
-        }
-        name = first_kw_arg;
-        #if PY_MAJOR_VERSION < 3
-        if (likely(PyString_Check(key))) {
-            while (*name) {
-                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
-                        && _PyString_Eq(**name, key)) {
-                    values[name-argnames] = value;
-                    break;
-                }
-                name++;
-            }
-            if (*name) continue;
-            else {
-                PyObject*** argname = argnames;
-                while (argname != first_kw_arg) {
-                    if ((**argname == key) || (
-                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
-                             && _PyString_Eq(**argname, key))) {
-                        goto arg_passed_twice;
-                    }
-                    argname++;
-                }
-            }
-        } else
-        #endif
-        if (likely(PyUnicode_Check(key))) {
-            while (*name) {
-                int cmp = (**name == key) ? 0 :
-                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
-                    (__Pyx_PyUnicode_GET_LENGTH(**name) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
-                #endif
-                    PyUnicode_Compare(**name, key);
-                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
-                if (cmp == 0) {
-                    values[name-argnames] = value;
-                    break;
-                }
-                name++;
-            }
-            if (*name) continue;
-            else {
-                PyObject*** argname = argnames;
-                while (argname != first_kw_arg) {
-                    int cmp = (**argname == key) ? 0 :
-                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
-                        (__Pyx_PyUnicode_GET_LENGTH(**argname) != __Pyx_PyUnicode_GET_LENGTH(key)) ? 1 :
-                    #endif
-                        PyUnicode_Compare(**argname, key);
-                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
-                    if (cmp == 0) goto arg_passed_twice;
-                    argname++;
-                }
-            }
-        } else
-            goto invalid_keyword_type;
-        if (kwds2) {
-            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
-        } else {
-            goto invalid_keyword;
-        }
-    }
-    return 0;
-arg_passed_twice:
-    __Pyx_RaiseDoubleKeywordsError(function_name, key);
-    goto bad;
-invalid_keyword_type:
-    PyErr_Format(PyExc_TypeError,
-        "%.200s() keywords must be strings", function_name);
-    goto bad;
-invalid_keyword:
-    PyErr_Format(PyExc_TypeError,
-    #if PY_MAJOR_VERSION < 3
-        "%.200s() got an unexpected keyword argument '%.200s'",
-        function_name, PyString_AsString(key));
-    #else
-        "%s() got an unexpected keyword argument '%U'",
-        function_name, key);
-    #endif
-bad:
-    return -1;
-}
-
-/* PyObjectCall */
-#if CYTHON_COMPILING_IN_CPYTHON
-static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
-    PyObject *result;
-    ternaryfunc call = func->ob_type->tp_call;
-    if (unlikely(!call))
-        return PyObject_Call(func, arg, kw);
-    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
-        return NULL;
-    result = (*call)(func, arg, kw);
-    Py_LeaveRecursiveCall();
-    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
-        PyErr_SetString(
-            PyExc_SystemError,
-            "NULL result without error in PyObject_Call");
-    }
-    return result;
-}
-#endif
-
-/* PyErrFetchRestore */
-#if CYTHON_FAST_THREAD_STATE
-static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
-    PyObject *tmp_type, *tmp_value, *tmp_tb;
-    tmp_type = tstate->curexc_type;
-    tmp_value = tstate->curexc_value;
-    tmp_tb = tstate->curexc_traceback;
-    tstate->curexc_type = type;
-    tstate->curexc_value = value;
-    tstate->curexc_traceback = tb;
-    Py_XDECREF(tmp_type);
-    Py_XDECREF(tmp_value);
-    Py_XDECREF(tmp_tb);
-}
-static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
-    *type = tstate->curexc_type;
-    *value = tstate->curexc_value;
-    *tb = tstate->curexc_traceback;
-    tstate->curexc_type = 0;
-    tstate->curexc_value = 0;
-    tstate->curexc_traceback = 0;
-}
-#endif
-
-/* RaiseException */
-#if PY_MAJOR_VERSION < 3
-static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
-                        CYTHON_UNUSED PyObject *cause) {
-    __Pyx_PyThreadState_declare
-    Py_XINCREF(type);
-    if (!value || value == Py_None)
-        value = NULL;
-    else
-        Py_INCREF(value);
-    if (!tb || tb == Py_None)
-        tb = NULL;
-    else {
-        Py_INCREF(tb);
-        if (!PyTraceBack_Check(tb)) {
-            PyErr_SetString(PyExc_TypeError,
-                "raise: arg 3 must be a traceback or None");
-            goto raise_error;
-        }
-    }
-    if (PyType_Check(type)) {
-#if CYTHON_COMPILING_IN_PYPY
-        if (!value) {
-            Py_INCREF(Py_None);
-            value = Py_None;
-        }
-#endif
-        PyErr_NormalizeException(&type, &value, &tb);
-    } else {
-        if (value) {
-            PyErr_SetString(PyExc_TypeError,
-                "instance exception may not have a separate value");
-            goto raise_error;
-        }
-        value = type;
-        type = (PyObject*) Py_TYPE(type);
-        Py_INCREF(type);
-        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
-            PyErr_SetString(PyExc_TypeError,
-                "raise: exception class must be a subclass of BaseException");
-            goto raise_error;
-        }
-    }
-    __Pyx_PyThreadState_assign
-    __Pyx_ErrRestore(type, value, tb);
-    return;
-raise_error:
-    Py_XDECREF(value);
-    Py_XDECREF(type);
-    Py_XDECREF(tb);
-    return;
-}
-#else
-static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
-    PyObject* owned_instance = NULL;
-    if (tb == Py_None) {
-        tb = 0;
-    } else if (tb && !PyTraceBack_Check(tb)) {
-        PyErr_SetString(PyExc_TypeError,
-            "raise: arg 3 must be a traceback or None");
-        goto bad;
-    }
-    if (value == Py_None)
-        value = 0;
-    if (PyExceptionInstance_Check(type)) {
-        if (value) {
-            PyErr_SetString(PyExc_TypeError,
-                "instance exception may not have a separate value");
-            goto bad;
-        }
-        value = type;
-        type = (PyObject*) Py_TYPE(value);
-    } else if (PyExceptionClass_Check(type)) {
-        PyObject *instance_class = NULL;
-        if (value && PyExceptionInstance_Check(value)) {
-            instance_class = (PyObject*) Py_TYPE(value);
-            if (instance_class != type) {
-                int is_subclass = PyObject_IsSubclass(instance_class, type);
-                if (!is_subclass) {
-                    instance_class = NULL;
-                } else if (unlikely(is_subclass == -1)) {
-                    goto bad;
-                } else {
-                    type = instance_class;
-                }
-            }
-        }
-        if (!instance_class) {
-            PyObject *args;
-            if (!value)
-                args = PyTuple_New(0);
-            else if (PyTuple_Check(value)) {
-                Py_INCREF(value);
-                args = value;
-            } else
-                args = PyTuple_Pack(1, value);
-            if (!args)
-                goto bad;
-            owned_instance = PyObject_Call(type, args, NULL);
-            Py_DECREF(args);
-            if (!owned_instance)
-                goto bad;
-            value = owned_instance;
-            if (!PyExceptionInstance_Check(value)) {
-                PyErr_Format(PyExc_TypeError,
-                             "calling %R should have returned an instance of "
-                             "BaseException, not %R",
-                             type, Py_TYPE(value));
-                goto bad;
-            }
-        }
-    } else {
-        PyErr_SetString(PyExc_TypeError,
-            "raise: exception class must be a subclass of BaseException");
-        goto bad;
-    }
-    if (cause) {
-        PyObject *fixed_cause;
-        if (cause == Py_None) {
-            fixed_cause = NULL;
-        } else if (PyExceptionClass_Check(cause)) {
-            fixed_cause = PyObject_CallObject(cause, NULL);
-            if (fixed_cause == NULL)
-                goto bad;
-        } else if (PyExceptionInstance_Check(cause)) {
-            fixed_cause = cause;
-            Py_INCREF(fixed_cause);
-        } else {
-            PyErr_SetString(PyExc_TypeError,
-                            "exception causes must derive from "
-                            "BaseException");
-            goto bad;
-        }
-        PyException_SetCause(value, fixed_cause);
-    }
-    PyErr_SetObject(type, value);
-    if (tb) {
-#if CYTHON_COMPILING_IN_PYPY
-        PyObject *tmp_type, *tmp_value, *tmp_tb;
-        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
-        Py_INCREF(tb);
-        PyErr_Restore(tmp_type, tmp_value, tb);
-        Py_XDECREF(tmp_tb);
-#else
-        PyThreadState *tstate = __Pyx_PyThreadState_Current;
-        PyObject* tmp_tb = tstate->curexc_traceback;
-        if (tb != tmp_tb) {
-            Py_INCREF(tb);
-            tstate->curexc_traceback = tb;
-            Py_XDECREF(tmp_tb);
-        }
-#endif
-    }
-bad:
-    Py_XDECREF(owned_instance);
-    return;
-}
-#endif
-
-/* PyCFunctionFastCall */
-#if CYTHON_FAST_PYCCALL
-static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
-    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
-    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
-    PyObject *self = PyCFunction_GET_SELF(func);
-    int flags = PyCFunction_GET_FLAGS(func);
-    assert(PyCFunction_Check(func));
-    assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS)));
-    assert(nargs >= 0);
-    assert(nargs == 0 || args != NULL);
-    /* _PyCFunction_FastCallDict() must not be called with an exception set,
-       because it may clear it (directly or indirectly) and so the
-       caller loses its exception */
-    assert(!PyErr_Occurred());
-    if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
-        return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL);
-    } else {
-        return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs);
-    }
-}
-#endif
-
-/* PyFunctionFastCall */
-#if CYTHON_FAST_PYCALL
-static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
-                                               PyObject *globals) {
-    PyFrameObject *f;
-    PyThreadState *tstate = __Pyx_PyThreadState_Current;
-    PyObject **fastlocals;
-    Py_ssize_t i;
-    PyObject *result;
-    assert(globals != NULL);
-    /* XXX Perhaps we should create a specialized
-       PyFrame_New() that doesn't take locals, but does
-       take builtins without sanity checking them.
-       */
-    assert(tstate != NULL);
-    f = PyFrame_New(tstate, co, globals, NULL);
-    if (f == NULL) {
-        return NULL;
-    }
-    fastlocals = __Pyx_PyFrame_GetLocalsplus(f);
-    for (i = 0; i < na; i++) {
-        Py_INCREF(*args);
-        fastlocals[i] = *args++;
-    }
-    result = PyEval_EvalFrameEx(f,0);
-    ++tstate->recursion_depth;
-    Py_DECREF(f);
-    --tstate->recursion_depth;
-    return result;
-}
-#if 1 || PY_VERSION_HEX < 0x030600B1
-static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, Py_ssize_t nargs, PyObject *kwargs) {
-    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
-    PyObject *globals = PyFunction_GET_GLOBALS(func);
-    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
-    PyObject *closure;
-#if PY_MAJOR_VERSION >= 3
-    PyObject *kwdefs;
-#endif
-    PyObject *kwtuple, **k;
-    PyObject **d;
-    Py_ssize_t nd;
-    Py_ssize_t nk;
-    PyObject *result;
-    assert(kwargs == NULL || PyDict_Check(kwargs));
-    nk = kwargs ? PyDict_Size(kwargs) : 0;
-    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
-        return NULL;
-    }
-    if (
-#if PY_MAJOR_VERSION >= 3
-            co->co_kwonlyargcount == 0 &&
-#endif
-            likely(kwargs == NULL || nk == 0) &&
-            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
-        if (argdefs == NULL && co->co_argcount == nargs) {
-            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
-            goto done;
-        }
-        else if (nargs == 0 && argdefs != NULL
-                 && co->co_argcount == Py_SIZE(argdefs)) {
-            /* function called with no arguments, but all parameters have
-               a default value: use default values as arguments .*/
-            args = &PyTuple_GET_ITEM(argdefs, 0);
-            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
-            goto done;
-        }
-    }
-    if (kwargs != NULL) {
-        Py_ssize_t pos, i;
-        kwtuple = PyTuple_New(2 * nk);
-        if (kwtuple == NULL) {
-            result = NULL;
-            goto done;
-        }
-        k = &PyTuple_GET_ITEM(kwtuple, 0);
-        pos = i = 0;
-        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
-            Py_INCREF(k[i]);
-            Py_INCREF(k[i+1]);
-            i += 2;
-        }
-        nk = i / 2;
-    }
-    else {
-        kwtuple = NULL;
-        k = NULL;
-    }
-    closure = PyFunction_GET_CLOSURE(func);
-#if PY_MAJOR_VERSION >= 3
-    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
-#endif
-    if (argdefs != NULL) {
-        d = &PyTuple_GET_ITEM(argdefs, 0);
-        nd = Py_SIZE(argdefs);
-    }
-    else {
-        d = NULL;
-        nd = 0;
-    }
-#if PY_MAJOR_VERSION >= 3
-    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
-                               args, (int)nargs,
-                               k, (int)nk,
-                               d, (int)nd, kwdefs, closure);
-#else
-    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
-                               args, (int)nargs,
-                               k, (int)nk,
-                               d, (int)nd, closure);
-#endif
-    Py_XDECREF(kwtuple);
-done:
-    Py_LeaveRecursiveCall();
-    return result;
-}
-#endif
-#endif
-
-/* PyObjectCallMethO */
-#if CYTHON_COMPILING_IN_CPYTHON
-static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
-    PyObject *self, *result;
-    PyCFunction cfunc;
-    cfunc = PyCFunction_GET_FUNCTION(func);
-    self = PyCFunction_GET_SELF(func);
-    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
-        return NULL;
-    result = cfunc(self, arg);
-    Py_LeaveRecursiveCall();
-    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
-        PyErr_SetString(
-            PyExc_SystemError,
-            "NULL result without error in PyObject_Call");
-    }
-    return result;
-}
-#endif
-
-/* PyObjectCallOneArg */
-#if CYTHON_COMPILING_IN_CPYTHON
-static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
-    PyObject *result;
-    PyObject *args = PyTuple_New(1);
-    if (unlikely(!args)) return NULL;
-    Py_INCREF(arg);
-    PyTuple_SET_ITEM(args, 0, arg);
-    result = __Pyx_PyObject_Call(func, args, NULL);
-    Py_DECREF(args);
-    return result;
-}
-static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
-#if CYTHON_FAST_PYCALL
-    if (PyFunction_Check(func)) {
-        return __Pyx_PyFunction_FastCall(func, &arg, 1);
-    }
-#endif
-    if (likely(PyCFunction_Check(func))) {
-        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
-            return __Pyx_PyObject_CallMethO(func, arg);
-#if CYTHON_FAST_PYCCALL
-        } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
-            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
-#endif
-        }
-    }
-    return __Pyx__PyObject_CallOneArg(func, arg);
-}
-#else
-static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
-    PyObject *result;
-    PyObject *args = PyTuple_Pack(1, arg);
-    if (unlikely(!args)) return NULL;
-    result = __Pyx_PyObject_Call(func, args, NULL);
-    Py_DECREF(args);
-    return result;
-}
-#endif
-
-/* PyIntBinop */
-#if !CYTHON_COMPILING_IN_PYPY
-static PyObject* __Pyx_PyInt_AddCObj(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
-    (void)inplace;
-    (void)zerodivision_check;
-    #if PY_MAJOR_VERSION < 3
-    if (likely(PyInt_CheckExact(op2))) {
-        const long a = intval;
-        long x;
-        long b = PyInt_AS_LONG(op2);
-            x = (long)((unsigned long)a + b);
-            if (likely((x^a) >= 0 || (x^b) >= 0))
-                return PyInt_FromLong(x);
-            return PyLong_Type.tp_as_number->nb_add(op1, op2);
-    }
-    #endif
-    #if CYTHON_USE_PYLONG_INTERNALS
-    if (likely(PyLong_CheckExact(op2))) {
-        const long a = intval;
-        long b, x;
-#ifdef HAVE_LONG_LONG
-        const PY_LONG_LONG lla = intval;
-        PY_LONG_LONG llb, llx;
-#endif
-        const digit* digits = ((PyLongObject*)op2)->ob_digit;
-        const Py_ssize_t size = Py_SIZE(op2);
-        if (likely(__Pyx_sst_abs(size) <= 1)) {
-            b = likely(size) ? digits[0] : 0;
-            if (size == -1) b = -b;
-        } else {
-            switch (size) {
-                case -2:
-                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
-                        b = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
-                        llb = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case 2:
-                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
-                        b = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
-                        llb = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case -3:
-                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
-                        b = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
-                        llb = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case 3:
-                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
-                        b = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
-                        llb = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case -4:
-                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
-                        b = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
-                        llb = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case 4:
-                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
-                        b = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
-                        llb = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
-            }
-        }
-                x = a + b;
-            return PyLong_FromLong(x);
-#ifdef HAVE_LONG_LONG
-        long_long:
-                llx = lla + llb;
-            return PyLong_FromLongLong(llx);
-#endif
-        
-        
-    }
-    #endif
-    if (PyFloat_CheckExact(op2)) {
-        const long a = intval;
-        double b = PyFloat_AS_DOUBLE(op2);
-            double result;
-            PyFPE_START_PROTECT("add", return NULL)
-            result = ((double)a) + (double)b;
-            PyFPE_END_PROTECT(result)
-            return PyFloat_FromDouble(result);
-    }
-    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
-}
-#endif
-
-/* SetItemInt */
-static int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
-    int r;
-    if (!j) return -1;
-    r = PyObject_SetItem(o, j, v);
-    Py_DECREF(j);
-    return r;
-}
-static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int is_list,
-                                               CYTHON_NCP_UNUSED int wraparound, CYTHON_NCP_UNUSED int boundscheck) {
-#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
-    if (is_list || PyList_CheckExact(o)) {
-        Py_ssize_t n = (!wraparound) ? i : ((likely(i >= 0)) ? i : i + PyList_GET_SIZE(o));
-        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o)))) {
-            PyObject* old = PyList_GET_ITEM(o, n);
-            Py_INCREF(v);
-            PyList_SET_ITEM(o, n, v);
-            Py_DECREF(old);
-            return 1;
-        }
-    } else {
-        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
-        if (likely(m && m->sq_ass_item)) {
-            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
-                Py_ssize_t l = m->sq_length(o);
-                if (likely(l >= 0)) {
-                    i += l;
-                } else {
-                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
-                        return -1;
-                    PyErr_Clear();
-                }
-            }
-            return m->sq_ass_item(o, i, v);
-        }
-    }
-#else
-#if CYTHON_COMPILING_IN_PYPY
-    if (is_list || (PySequence_Check(o) && !PyDict_Check(o)))
-#else
-    if (is_list || PySequence_Check(o))
-#endif
-    {
-        return PySequence_SetItem(o, i, v);
-    }
-#endif
-    return __Pyx_SetItemInt_Generic(o, PyInt_FromSsize_t(i), v);
-}
-
-/* PyDictVersioning */
-#if CYTHON_USE_DICT_VERSIONS && CYTHON_USE_TYPE_SLOTS
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_tp_dict_version(PyObject *obj) {
-    PyObject *dict = Py_TYPE(obj)->tp_dict;
-    return likely(dict) ? __PYX_GET_DICT_VERSION(dict) : 0;
-}
-static CYTHON_INLINE PY_UINT64_T __Pyx_get_object_dict_version(PyObject *obj) {
-    PyObject **dictptr = NULL;
-    Py_ssize_t offset = Py_TYPE(obj)->tp_dictoffset;
-    if (offset) {
-#if CYTHON_COMPILING_IN_CPYTHON
-        dictptr = (likely(offset > 0)) ? (PyObject **) ((char *)obj + offset) : _PyObject_GetDictPtr(obj);
-#else
-        dictptr = _PyObject_GetDictPtr(obj);
-#endif
-    }
-    return (dictptr && *dictptr) ? __PYX_GET_DICT_VERSION(*dictptr) : 0;
-}
-static CYTHON_INLINE int __Pyx_object_dict_version_matches(PyObject* obj, PY_UINT64_T tp_dict_version, PY_UINT64_T obj_dict_version) {
-    PyObject *dict = Py_TYPE(obj)->tp_dict;
-    if (unlikely(!dict) || unlikely(tp_dict_version != __PYX_GET_DICT_VERSION(dict)))
-        return 0;
-    return obj_dict_version == __Pyx_get_object_dict_version(obj);
-}
-#endif
-
-/* GetModuleGlobalName */
-#if CYTHON_USE_DICT_VERSIONS
-static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value)
-#else
-static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name)
-#endif
-{
-    PyObject *result;
-#if !CYTHON_AVOID_BORROWED_REFS
-#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1
-    result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash);
-    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
-    if (likely(result)) {
-        return __Pyx_NewRef(result);
-    } else if (unlikely(PyErr_Occurred())) {
-        return NULL;
-    }
-#else
-    result = PyDict_GetItem(__pyx_d, name);
-    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
-    if (likely(result)) {
-        return __Pyx_NewRef(result);
-    }
-#endif
-#else
-    result = PyObject_GetItem(__pyx_d, name);
-    __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version)
-    if (likely(result)) {
-        return __Pyx_NewRef(result);
-    }
-    PyErr_Clear();
-#endif
-    return __Pyx_GetBuiltinName(name);
-}
-
-/* SliceObject */
-static CYTHON_INLINE int __Pyx_PyObject_SetSlice(PyObject* obj, PyObject* value,
-        Py_ssize_t cstart, Py_ssize_t cstop,
-        PyObject** _py_start, PyObject** _py_stop, PyObject** _py_slice,
-        int has_cstart, int has_cstop, CYTHON_UNUSED int wraparound) {
-#if CYTHON_USE_TYPE_SLOTS
-    PyMappingMethods* mp;
-#if PY_MAJOR_VERSION < 3
-    PySequenceMethods* ms = Py_TYPE(obj)->tp_as_sequence;
-    if (likely(ms && ms->sq_ass_slice)) {
-        if (!has_cstart) {
-            if (_py_start && (*_py_start != Py_None)) {
-                cstart = __Pyx_PyIndex_AsSsize_t(*_py_start);
-                if ((cstart == (Py_ssize_t)-1) && PyErr_Occurred()) goto bad;
-            } else
-                cstart = 0;
-        }
-        if (!has_cstop) {
-            if (_py_stop && (*_py_stop != Py_None)) {
-                cstop = __Pyx_PyIndex_AsSsize_t(*_py_stop);
-                if ((cstop == (Py_ssize_t)-1) && PyErr_Occurred()) goto bad;
-            } else
-                cstop = PY_SSIZE_T_MAX;
-        }
-        if (wraparound && unlikely((cstart < 0) | (cstop < 0)) && likely(ms->sq_length)) {
-            Py_ssize_t l = ms->sq_length(obj);
-            if (likely(l >= 0)) {
-                if (cstop < 0) {
-                    cstop += l;
-                    if (cstop < 0) cstop = 0;
-                }
-                if (cstart < 0) {
-                    cstart += l;
-                    if (cstart < 0) cstart = 0;
-                }
-            } else {
-                if (!PyErr_ExceptionMatches(PyExc_OverflowError))
-                    goto bad;
-                PyErr_Clear();
-            }
-        }
-        return ms->sq_ass_slice(obj, cstart, cstop, value);
-    }
-#endif
-    mp = Py_TYPE(obj)->tp_as_mapping;
-    if (likely(mp && mp->mp_ass_subscript))
-#endif
-    {
-        int result;
-        PyObject *py_slice, *py_start, *py_stop;
-        if (_py_slice) {
-            py_slice = *_py_slice;
-        } else {
-            PyObject* owned_start = NULL;
-            PyObject* owned_stop = NULL;
-            if (_py_start) {
-                py_start = *_py_start;
-            } else {
-                if (has_cstart) {
-                    owned_start = py_start = PyInt_FromSsize_t(cstart);
-                    if (unlikely(!py_start)) goto bad;
-                } else
-                    py_start = Py_None;
-            }
-            if (_py_stop) {
-                py_stop = *_py_stop;
-            } else {
-                if (has_cstop) {
-                    owned_stop = py_stop = PyInt_FromSsize_t(cstop);
-                    if (unlikely(!py_stop)) {
-                        Py_XDECREF(owned_start);
-                        goto bad;
-                    }
-                } else
-                    py_stop = Py_None;
-            }
-            py_slice = PySlice_New(py_start, py_stop, Py_None);
-            Py_XDECREF(owned_start);
-            Py_XDECREF(owned_stop);
-            if (unlikely(!py_slice)) goto bad;
-        }
-#if CYTHON_USE_TYPE_SLOTS
-        result = mp->mp_ass_subscript(obj, py_slice, value);
-#else
-        result = value ? PyObject_SetItem(obj, py_slice, value) : PyObject_DelItem(obj, py_slice);
-#endif
-        if (!_py_slice) {
-            Py_DECREF(py_slice);
-        }
-        return result;
-    }
-    PyErr_Format(PyExc_TypeError,
-        "'%.200s' object does not support slice %.10s",
-        Py_TYPE(obj)->tp_name, value ? "assignment" : "deletion");
-bad:
-    return -1;
-}
-
-/* MemviewSliceInit */
-static int
-__Pyx_init_memviewslice(struct __pyx_memoryview_obj *memview,
-                        int ndim,
-                        __Pyx_memviewslice *memviewslice,
-                        int memview_is_new_reference)
-{
-    __Pyx_RefNannyDeclarations
-    int i, retval=-1;
-    Py_buffer *buf = &memview->view;
-    __Pyx_RefNannySetupContext("init_memviewslice", 0);
-    if (unlikely(memviewslice->memview || memviewslice->data)) {
-        PyErr_SetString(PyExc_ValueError,
-            "memviewslice is already initialized!");
-        goto fail;
-    }
-    if (buf->strides) {
-        for (i = 0; i < ndim; i++) {
-            memviewslice->strides[i] = buf->strides[i];
-        }
-    } else {
-        Py_ssize_t stride = buf->itemsize;
-        for (i = ndim - 1; i >= 0; i--) {
-            memviewslice->strides[i] = stride;
-            stride *= buf->shape[i];
-        }
-    }
-    for (i = 0; i < ndim; i++) {
-        memviewslice->shape[i]   = buf->shape[i];
-        if (buf->suboffsets) {
-            memviewslice->suboffsets[i] = buf->suboffsets[i];
-        } else {
-            memviewslice->suboffsets[i] = -1;
-        }
-    }
-    memviewslice->memview = memview;
-    memviewslice->data = (char *)buf->buf;
-    if (__pyx_add_acquisition_count(memview) == 0 && !memview_is_new_reference) {
-        Py_INCREF(memview);
-    }
-    retval = 0;
-    goto no_fail;
-fail:
-    memviewslice->memview = 0;
-    memviewslice->data = 0;
-    retval = -1;
-no_fail:
-    __Pyx_RefNannyFinishContext();
-    return retval;
-}
-#ifndef Py_NO_RETURN
-#define Py_NO_RETURN
-#endif
-static void __pyx_fatalerror(const char *fmt, ...) Py_NO_RETURN {
-    va_list vargs;
-    char msg[200];
-#ifdef HAVE_STDARG_PROTOTYPES
-    va_start(vargs, fmt);
-#else
-    va_start(vargs);
-#endif
-    vsnprintf(msg, 200, fmt, vargs);
-    va_end(vargs);
-    Py_FatalError(msg);
-}
-static CYTHON_INLINE int
-__pyx_add_acquisition_count_locked(__pyx_atomic_int *acquisition_count,
-                                   PyThread_type_lock lock)
-{
-    int result;
-    PyThread_acquire_lock(lock, 1);
-    result = (*acquisition_count)++;
-    PyThread_release_lock(lock);
-    return result;
-}
-static CYTHON_INLINE int
-__pyx_sub_acquisition_count_locked(__pyx_atomic_int *acquisition_count,
-                                   PyThread_type_lock lock)
-{
-    int result;
-    PyThread_acquire_lock(lock, 1);
-    result = (*acquisition_count)--;
-    PyThread_release_lock(lock);
-    return result;
-}
-static CYTHON_INLINE void
-__Pyx_INC_MEMVIEW(__Pyx_memviewslice *memslice, int have_gil, int lineno)
-{
-    int first_time;
-    struct __pyx_memoryview_obj *memview = memslice->memview;
-    if (unlikely(!memview || (PyObject *) memview == Py_None))
-        return;
-    if (unlikely(__pyx_get_slice_count(memview) < 0))
-        __pyx_fatalerror("Acquisition count is %d (line %d)",
-                         __pyx_get_slice_count(memview), lineno);
-    first_time = __pyx_add_acquisition_count(memview) == 0;
-    if (unlikely(first_time)) {
-        if (have_gil) {
-            Py_INCREF((PyObject *) memview);
-        } else {
-            PyGILState_STATE _gilstate = PyGILState_Ensure();
-            Py_INCREF((PyObject *) memview);
-            PyGILState_Release(_gilstate);
-        }
-    }
-}
-static CYTHON_INLINE void __Pyx_XDEC_MEMVIEW(__Pyx_memviewslice *memslice,
-                                             int have_gil, int lineno) {
-    int last_time;
-    struct __pyx_memoryview_obj *memview = memslice->memview;
-    if (unlikely(!memview || (PyObject *) memview == Py_None)) {
-        memslice->memview = NULL;
-        return;
-    }
-    if (unlikely(__pyx_get_slice_count(memview) <= 0))
-        __pyx_fatalerror("Acquisition count is %d (line %d)",
-                         __pyx_get_slice_count(memview), lineno);
-    last_time = __pyx_sub_acquisition_count(memview) == 1;
-    memslice->data = NULL;
-    if (unlikely(last_time)) {
-        if (have_gil) {
-            Py_CLEAR(memslice->memview);
-        } else {
-            PyGILState_STATE _gilstate = PyGILState_Ensure();
-            Py_CLEAR(memslice->memview);
-            PyGILState_Release(_gilstate);
-        }
-    } else {
-        memslice->memview = NULL;
-    }
-}
-
-/* PyObjectCall2Args */
-static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) {
-    PyObject *args, *result = NULL;
-    #if CYTHON_FAST_PYCALL
-    if (PyFunction_Check(function)) {
-        PyObject *args[2] = {arg1, arg2};
-        return __Pyx_PyFunction_FastCall(function, args, 2);
-    }
-    #endif
-    #if CYTHON_FAST_PYCCALL
-    if (__Pyx_PyFastCFunction_Check(function)) {
-        PyObject *args[2] = {arg1, arg2};
-        return __Pyx_PyCFunction_FastCall(function, args, 2);
-    }
-    #endif
-    args = PyTuple_New(2);
-    if (unlikely(!args)) goto done;
-    Py_INCREF(arg1);
-    PyTuple_SET_ITEM(args, 0, arg1);
-    Py_INCREF(arg2);
-    PyTuple_SET_ITEM(args, 1, arg2);
-    Py_INCREF(function);
-    result = __Pyx_PyObject_Call(function, args, NULL);
-    Py_DECREF(args);
-    Py_DECREF(function);
-done:
-    return result;
-}
-
-/* ArgTypeTest */
-static int __Pyx__ArgTypeTest(PyObject *obj, PyTypeObject *type, const char *name, int exact)
-{
-    if (unlikely(!type)) {
-        PyErr_SetString(PyExc_SystemError, "Missing type object");
-        return 0;
-    }
-    else if (exact) {
-        #if PY_MAJOR_VERSION == 2
-        if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
-        #endif
-    }
-    else {
-        if (likely(__Pyx_TypeCheck(obj, type))) return 1;
-    }
-    PyErr_Format(PyExc_TypeError,
-        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
-        name, type->tp_name, Py_TYPE(obj)->tp_name);
-    return 0;
-}
-
-/* BytesEquals */
-static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
-#if CYTHON_COMPILING_IN_PYPY
-    return PyObject_RichCompareBool(s1, s2, equals);
-#else
-    if (s1 == s2) {
-        return (equals == Py_EQ);
-    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
-        const char *ps1, *ps2;
-        Py_ssize_t length = PyBytes_GET_SIZE(s1);
-        if (length != PyBytes_GET_SIZE(s2))
-            return (equals == Py_NE);
-        ps1 = PyBytes_AS_STRING(s1);
-        ps2 = PyBytes_AS_STRING(s2);
-        if (ps1[0] != ps2[0]) {
-            return (equals == Py_NE);
-        } else if (length == 1) {
-            return (equals == Py_EQ);
-        } else {
-            int result;
-#if CYTHON_USE_UNICODE_INTERNALS
-            Py_hash_t hash1, hash2;
-            hash1 = ((PyBytesObject*)s1)->ob_shash;
-            hash2 = ((PyBytesObject*)s2)->ob_shash;
-            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
-                return (equals == Py_NE);
-            }
-#endif
-            result = memcmp(ps1, ps2, (size_t)length);
-            return (equals == Py_EQ) ? (result == 0) : (result != 0);
-        }
-    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
-        return (equals == Py_NE);
-    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
-        return (equals == Py_NE);
-    } else {
-        int result;
-        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
-        if (!py_result)
-            return -1;
-        result = __Pyx_PyObject_IsTrue(py_result);
-        Py_DECREF(py_result);
-        return result;
-    }
-#endif
-}
-
-/* UnicodeEquals */
-static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
-#if CYTHON_COMPILING_IN_PYPY
-    return PyObject_RichCompareBool(s1, s2, equals);
-#else
-#if PY_MAJOR_VERSION < 3
-    PyObject* owned_ref = NULL;
-#endif
-    int s1_is_unicode, s2_is_unicode;
-    if (s1 == s2) {
-        goto return_eq;
-    }
-    s1_is_unicode = PyUnicode_CheckExact(s1);
-    s2_is_unicode = PyUnicode_CheckExact(s2);
-#if PY_MAJOR_VERSION < 3
-    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
-        owned_ref = PyUnicode_FromObject(s2);
-        if (unlikely(!owned_ref))
-            return -1;
-        s2 = owned_ref;
-        s2_is_unicode = 1;
-    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
-        owned_ref = PyUnicode_FromObject(s1);
-        if (unlikely(!owned_ref))
-            return -1;
-        s1 = owned_ref;
-        s1_is_unicode = 1;
-    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
-        return __Pyx_PyBytes_Equals(s1, s2, equals);
-    }
-#endif
-    if (s1_is_unicode & s2_is_unicode) {
-        Py_ssize_t length;
-        int kind;
-        void *data1, *data2;
-        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
-            return -1;
-        length = __Pyx_PyUnicode_GET_LENGTH(s1);
-        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
-            goto return_ne;
-        }
-#if CYTHON_USE_UNICODE_INTERNALS
-        {
-            Py_hash_t hash1, hash2;
-        #if CYTHON_PEP393_ENABLED
-            hash1 = ((PyASCIIObject*)s1)->hash;
-            hash2 = ((PyASCIIObject*)s2)->hash;
-        #else
-            hash1 = ((PyUnicodeObject*)s1)->hash;
-            hash2 = ((PyUnicodeObject*)s2)->hash;
-        #endif
-            if (hash1 != hash2 && hash1 != -1 && hash2 != -1) {
-                goto return_ne;
-            }
-        }
-#endif
-        kind = __Pyx_PyUnicode_KIND(s1);
-        if (kind != __Pyx_PyUnicode_KIND(s2)) {
-            goto return_ne;
-        }
-        data1 = __Pyx_PyUnicode_DATA(s1);
-        data2 = __Pyx_PyUnicode_DATA(s2);
-        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
-            goto return_ne;
-        } else if (length == 1) {
-            goto return_eq;
-        } else {
-            int result = memcmp(data1, data2, (size_t)(length * kind));
-            #if PY_MAJOR_VERSION < 3
-            Py_XDECREF(owned_ref);
-            #endif
-            return (equals == Py_EQ) ? (result == 0) : (result != 0);
-        }
-    } else if ((s1 == Py_None) & s2_is_unicode) {
-        goto return_ne;
-    } else if ((s2 == Py_None) & s1_is_unicode) {
-        goto return_ne;
-    } else {
-        int result;
-        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
-        #if PY_MAJOR_VERSION < 3
-        Py_XDECREF(owned_ref);
-        #endif
-        if (!py_result)
-            return -1;
-        result = __Pyx_PyObject_IsTrue(py_result);
-        Py_DECREF(py_result);
-        return result;
-    }
-return_eq:
-    #if PY_MAJOR_VERSION < 3
-    Py_XDECREF(owned_ref);
-    #endif
-    return (equals == Py_EQ);
-return_ne:
-    #if PY_MAJOR_VERSION < 3
-    Py_XDECREF(owned_ref);
-    #endif
-    return (equals == Py_NE);
-#endif
-}
-
-/* GetAttr */
-static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) {
-#if CYTHON_USE_TYPE_SLOTS
-#if PY_MAJOR_VERSION >= 3
-    if (likely(PyUnicode_Check(n)))
-#else
-    if (likely(PyString_Check(n)))
-#endif
-        return __Pyx_PyObject_GetAttrStr(o, n);
-#endif
-    return PyObject_GetAttr(o, n);
-}
-
-/* GetItemInt */
-static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
-    PyObject *r;
-    if (!j) return NULL;
-    r = PyObject_GetItem(o, j);
-    Py_DECREF(j);
-    return r;
-}
-static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
-                                                              CYTHON_NCP_UNUSED int wraparound,
-                                                              CYTHON_NCP_UNUSED int boundscheck) {
-#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
-    Py_ssize_t wrapped_i = i;
-    if (wraparound & unlikely(i < 0)) {
-        wrapped_i += PyList_GET_SIZE(o);
-    }
-    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) {
-        PyObject *r = PyList_GET_ITEM(o, wrapped_i);
-        Py_INCREF(r);
-        return r;
-    }
-    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
-#else
-    return PySequence_GetItem(o, i);
-#endif
-}
-static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
-                                                              CYTHON_NCP_UNUSED int wraparound,
-                                                              CYTHON_NCP_UNUSED int boundscheck) {
-#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
-    Py_ssize_t wrapped_i = i;
-    if (wraparound & unlikely(i < 0)) {
-        wrapped_i += PyTuple_GET_SIZE(o);
-    }
-    if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) {
-        PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);
-        Py_INCREF(r);
-        return r;
-    }
-    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
-#else
-    return PySequence_GetItem(o, i);
-#endif
-}
-static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
-                                                     CYTHON_NCP_UNUSED int wraparound,
-                                                     CYTHON_NCP_UNUSED int boundscheck) {
-#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
-    if (is_list || PyList_CheckExact(o)) {
-        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
-        if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) {
-            PyObject *r = PyList_GET_ITEM(o, n);
-            Py_INCREF(r);
-            return r;
-        }
-    }
-    else if (PyTuple_CheckExact(o)) {
-        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
-        if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) {
-            PyObject *r = PyTuple_GET_ITEM(o, n);
-            Py_INCREF(r);
-            return r;
-        }
-    } else {
-        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
-        if (likely(m && m->sq_item)) {
-            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
-                Py_ssize_t l = m->sq_length(o);
-                if (likely(l >= 0)) {
-                    i += l;
-                } else {
-                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
-                        return NULL;
-                    PyErr_Clear();
-                }
-            }
-            return m->sq_item(o, i);
-        }
-    }
-#else
-    if (is_list || PySequence_Check(o)) {
-        return PySequence_GetItem(o, i);
-    }
-#endif
-    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
-}
-
-/* ObjectGetItem */
-#if CYTHON_USE_TYPE_SLOTS
-static PyObject *__Pyx_PyObject_GetIndex(PyObject *obj, PyObject* index) {
-    PyObject *runerr;
-    Py_ssize_t key_value;
-    PySequenceMethods *m = Py_TYPE(obj)->tp_as_sequence;
-    if (unlikely(!(m && m->sq_item))) {
-        PyErr_Format(PyExc_TypeError, "'%.200s' object is not subscriptable", Py_TYPE(obj)->tp_name);
-        return NULL;
-    }
-    key_value = __Pyx_PyIndex_AsSsize_t(index);
-    if (likely(key_value != -1 || !(runerr = PyErr_Occurred()))) {
-        return __Pyx_GetItemInt_Fast(obj, key_value, 0, 1, 1);
-    }
-    if (PyErr_GivenExceptionMatches(runerr, PyExc_OverflowError)) {
-        PyErr_Clear();
-        PyErr_Format(PyExc_IndexError, "cannot fit '%.200s' into an index-sized integer", Py_TYPE(index)->tp_name);
-    }
-    return NULL;
-}
-static PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key) {
-    PyMappingMethods *m = Py_TYPE(obj)->tp_as_mapping;
-    if (likely(m && m->mp_subscript)) {
-        return m->mp_subscript(obj, key);
-    }
-    return __Pyx_PyObject_GetIndex(obj, key);
-}
-#endif
-
-/* decode_c_string */
-static CYTHON_INLINE PyObject* __Pyx_decode_c_string(
-         const char* cstring, Py_ssize_t start, Py_ssize_t stop,
-         const char* encoding, const char* errors,
-         PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors)) {
-    Py_ssize_t length;
-    if (unlikely((start < 0) | (stop < 0))) {
-        size_t slen = strlen(cstring);
-        if (unlikely(slen > (size_t) PY_SSIZE_T_MAX)) {
-            PyErr_SetString(PyExc_OverflowError,
-                            "c-string too long to convert to Python");
-            return NULL;
-        }
-        length = (Py_ssize_t) slen;
-        if (start < 0) {
-            start += length;
-            if (start < 0)
-                start = 0;
-        }
-        if (stop < 0)
-            stop += length;
-    }
-    if (unlikely(stop <= start))
-        return __Pyx_NewRef(__pyx_empty_unicode);
-    length = stop - start;
-    cstring += start;
-    if (decode_func) {
-        return decode_func(cstring, length, errors);
-    } else {
-        return PyUnicode_Decode(cstring, length, encoding, errors);
-    }
-}
-
-/* PyErrExceptionMatches */
-#if CYTHON_FAST_THREAD_STATE
-static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
-    Py_ssize_t i, n;
-    n = PyTuple_GET_SIZE(tuple);
-#if PY_MAJOR_VERSION >= 3
-    for (i=0; i<n; i++) {
-        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
-    }
-#endif
-    for (i=0; i<n; i++) {
-        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
-    }
-    return 0;
-}
-static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
-    PyObject *exc_type = tstate->curexc_type;
-    if (exc_type == err) return 1;
-    if (unlikely(!exc_type)) return 0;
-    if (unlikely(PyTuple_Check(err)))
-        return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
-    return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
-}
-#endif
-
-/* GetAttr3 */
-static PyObject *__Pyx_GetAttr3Default(PyObject *d) {
-    __Pyx_PyThreadState_declare
-    __Pyx_PyThreadState_assign
-    if (unlikely(!__Pyx_PyErr_ExceptionMatches(PyExc_AttributeError)))
-        return NULL;
-    __Pyx_PyErr_Clear();
-    Py_INCREF(d);
-    return d;
-}
-static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *o, PyObject *n, PyObject *d) {
-    PyObject *r = __Pyx_GetAttr(o, n);
-    return (likely(r)) ? r : __Pyx_GetAttr3Default(d);
-}
-
-/* RaiseTooManyValuesToUnpack */
-static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
-    PyErr_Format(PyExc_ValueError,
-                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
-}
-
-/* RaiseNeedMoreValuesToUnpack */
-static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
-    PyErr_Format(PyExc_ValueError,
-                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
-                 index, (index == 1) ? "" : "s");
-}
-
-/* RaiseNoneIterError */
-static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
-    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
-}
-
-/* ExtTypeTest */
-static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
-    if (unlikely(!type)) {
-        PyErr_SetString(PyExc_SystemError, "Missing type object");
-        return 0;
-    }
-    if (likely(__Pyx_TypeCheck(obj, type)))
-        return 1;
-    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
-                 Py_TYPE(obj)->tp_name, type->tp_name);
-    return 0;
-}
-
-/* GetTopmostException */
-#if CYTHON_USE_EXC_INFO_STACK
-static _PyErr_StackItem *
-__Pyx_PyErr_GetTopmostException(PyThreadState *tstate)
-{
-    _PyErr_StackItem *exc_info = tstate->exc_info;
-    while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) &&
-           exc_info->previous_item != NULL)
-    {
-        exc_info = exc_info->previous_item;
-    }
-    return exc_info;
-}
-#endif
-
-/* SaveResetException */
-#if CYTHON_FAST_THREAD_STATE
-static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
-    #if CYTHON_USE_EXC_INFO_STACK
-    _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate);
-    *type = exc_info->exc_type;
-    *value = exc_info->exc_value;
-    *tb = exc_info->exc_traceback;
-    #else
-    *type = tstate->exc_type;
-    *value = tstate->exc_value;
-    *tb = tstate->exc_traceback;
-    #endif
-    Py_XINCREF(*type);
-    Py_XINCREF(*value);
-    Py_XINCREF(*tb);
-}
-static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
-    PyObject *tmp_type, *tmp_value, *tmp_tb;
-    #if CYTHON_USE_EXC_INFO_STACK
-    _PyErr_StackItem *exc_info = tstate->exc_info;
-    tmp_type = exc_info->exc_type;
-    tmp_value = exc_info->exc_value;
-    tmp_tb = exc_info->exc_traceback;
-    exc_info->exc_type = type;
-    exc_info->exc_value = value;
-    exc_info->exc_traceback = tb;
-    #else
-    tmp_type = tstate->exc_type;
-    tmp_value = tstate->exc_value;
-    tmp_tb = tstate->exc_traceback;
-    tstate->exc_type = type;
-    tstate->exc_value = value;
-    tstate->exc_traceback = tb;
-    #endif
-    Py_XDECREF(tmp_type);
-    Py_XDECREF(tmp_value);
-    Py_XDECREF(tmp_tb);
-}
-#endif
-
-/* GetException */
-#if CYTHON_FAST_THREAD_STATE
-static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb)
-#else
-static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb)
-#endif
-{
-    PyObject *local_type, *local_value, *local_tb;
-#if CYTHON_FAST_THREAD_STATE
-    PyObject *tmp_type, *tmp_value, *tmp_tb;
-    local_type = tstate->curexc_type;
-    local_value = tstate->curexc_value;
-    local_tb = tstate->curexc_traceback;
-    tstate->curexc_type = 0;
-    tstate->curexc_value = 0;
-    tstate->curexc_traceback = 0;
-#else
-    PyErr_Fetch(&local_type, &local_value, &local_tb);
-#endif
-    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
-#if CYTHON_FAST_THREAD_STATE
-    if (unlikely(tstate->curexc_type))
-#else
-    if (unlikely(PyErr_Occurred()))
-#endif
-        goto bad;
-    #if PY_MAJOR_VERSION >= 3
-    if (local_tb) {
-        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
-            goto bad;
-    }
-    #endif
-    Py_XINCREF(local_tb);
-    Py_XINCREF(local_type);
-    Py_XINCREF(local_value);
-    *type = local_type;
-    *value = local_value;
-    *tb = local_tb;
-#if CYTHON_FAST_THREAD_STATE
-    #if CYTHON_USE_EXC_INFO_STACK
-    {
-        _PyErr_StackItem *exc_info = tstate->exc_info;
-        tmp_type = exc_info->exc_type;
-        tmp_value = exc_info->exc_value;
-        tmp_tb = exc_info->exc_traceback;
-        exc_info->exc_type = local_type;
-        exc_info->exc_value = local_value;
-        exc_info->exc_traceback = local_tb;
-    }
-    #else
-    tmp_type = tstate->exc_type;
-    tmp_value = tstate->exc_value;
-    tmp_tb = tstate->exc_traceback;
-    tstate->exc_type = local_type;
-    tstate->exc_value = local_value;
-    tstate->exc_traceback = local_tb;
-    #endif
-    Py_XDECREF(tmp_type);
-    Py_XDECREF(tmp_value);
-    Py_XDECREF(tmp_tb);
-#else
-    PyErr_SetExcInfo(local_type, local_value, local_tb);
-#endif
-    return 0;
-bad:
-    *type = 0;
-    *value = 0;
-    *tb = 0;
-    Py_XDECREF(local_type);
-    Py_XDECREF(local_value);
-    Py_XDECREF(local_tb);
-    return -1;
-}
-
-/* SwapException */
-#if CYTHON_FAST_THREAD_STATE
-static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
-    PyObject *tmp_type, *tmp_value, *tmp_tb;
-    #if CYTHON_USE_EXC_INFO_STACK
-    _PyErr_StackItem *exc_info = tstate->exc_info;
-    tmp_type = exc_info->exc_type;
-    tmp_value = exc_info->exc_value;
-    tmp_tb = exc_info->exc_traceback;
-    exc_info->exc_type = *type;
-    exc_info->exc_value = *value;
-    exc_info->exc_traceback = *tb;
-    #else
-    tmp_type = tstate->exc_type;
-    tmp_value = tstate->exc_value;
-    tmp_tb = tstate->exc_traceback;
-    tstate->exc_type = *type;
-    tstate->exc_value = *value;
-    tstate->exc_traceback = *tb;
-    #endif
-    *type = tmp_type;
-    *value = tmp_value;
-    *tb = tmp_tb;
-}
-#else
-static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
-    PyObject *tmp_type, *tmp_value, *tmp_tb;
-    PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
-    PyErr_SetExcInfo(*type, *value, *tb);
-    *type = tmp_type;
-    *value = tmp_value;
-    *tb = tmp_tb;
-}
-#endif
-
-/* Import */
-static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
-    PyObject *empty_list = 0;
-    PyObject *module = 0;
-    PyObject *global_dict = 0;
-    PyObject *empty_dict = 0;
-    PyObject *list;
-    #if PY_MAJOR_VERSION < 3
-    PyObject *py_import;
-    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
-    if (!py_import)
-        goto bad;
-    #endif
-    if (from_list)
-        list = from_list;
-    else {
-        empty_list = PyList_New(0);
-        if (!empty_list)
-            goto bad;
-        list = empty_list;
-    }
-    global_dict = PyModule_GetDict(__pyx_m);
-    if (!global_dict)
-        goto bad;
-    empty_dict = PyDict_New();
-    if (!empty_dict)
-        goto bad;
-    {
-        #if PY_MAJOR_VERSION >= 3
-        if (level == -1) {
-            if ((1) && (strchr(__Pyx_MODULE_NAME, '.'))) {
-                module = PyImport_ImportModuleLevelObject(
-                    name, global_dict, empty_dict, list, 1);
-                if (!module) {
-                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
-                        goto bad;
-                    PyErr_Clear();
-                }
-            }
-            level = 0;
-        }
-        #endif
-        if (!module) {
-            #if PY_MAJOR_VERSION < 3
-            PyObject *py_level = PyInt_FromLong(level);
-            if (!py_level)
-                goto bad;
-            module = PyObject_CallFunctionObjArgs(py_import,
-                name, global_dict, empty_dict, list, py_level, (PyObject *)NULL);
-            Py_DECREF(py_level);
-            #else
-            module = PyImport_ImportModuleLevelObject(
-                name, global_dict, empty_dict, list, level);
-            #endif
-        }
-    }
-bad:
-    #if PY_MAJOR_VERSION < 3
-    Py_XDECREF(py_import);
-    #endif
-    Py_XDECREF(empty_list);
-    Py_XDECREF(empty_dict);
-    return module;
-}
-
-/* FastTypeChecks */
-#if CYTHON_COMPILING_IN_CPYTHON
-static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
-    while (a) {
-        a = a->tp_base;
-        if (a == b)
-            return 1;
-    }
-    return b == &PyBaseObject_Type;
-}
-static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
-    PyObject *mro;
-    if (a == b) return 1;
-    mro = a->tp_mro;
-    if (likely(mro)) {
-        Py_ssize_t i, n;
-        n = PyTuple_GET_SIZE(mro);
-        for (i = 0; i < n; i++) {
-            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
-                return 1;
-        }
-        return 0;
-    }
-    return __Pyx_InBases(a, b);
-}
-#if PY_MAJOR_VERSION == 2
-static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
-    PyObject *exception, *value, *tb;
-    int res;
-    __Pyx_PyThreadState_declare
-    __Pyx_PyThreadState_assign
-    __Pyx_ErrFetch(&exception, &value, &tb);
-    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
-    if (unlikely(res == -1)) {
-        PyErr_WriteUnraisable(err);
-        res = 0;
-    }
-    if (!res) {
-        res = PyObject_IsSubclass(err, exc_type2);
-        if (unlikely(res == -1)) {
-            PyErr_WriteUnraisable(err);
-            res = 0;
-        }
-    }
-    __Pyx_ErrRestore(exception, value, tb);
-    return res;
-}
-#else
-static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
-    int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
-    if (!res) {
-        res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
-    }
-    return res;
-}
-#endif
-static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
-    Py_ssize_t i, n;
-    assert(PyExceptionClass_Check(exc_type));
-    n = PyTuple_GET_SIZE(tuple);
-#if PY_MAJOR_VERSION >= 3
-    for (i=0; i<n; i++) {
-        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
-    }
-#endif
-    for (i=0; i<n; i++) {
-        PyObject *t = PyTuple_GET_ITEM(tuple, i);
-        #if PY_MAJOR_VERSION < 3
-        if (likely(exc_type == t)) return 1;
-        #endif
-        if (likely(PyExceptionClass_Check(t))) {
-            if (__Pyx_inner_PyErr_GivenExceptionMatches2(exc_type, NULL, t)) return 1;
-        } else {
-        }
-    }
-    return 0;
-}
-static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
-    if (likely(err == exc_type)) return 1;
-    if (likely(PyExceptionClass_Check(err))) {
-        if (likely(PyExceptionClass_Check(exc_type))) {
-            return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
-        } else if (likely(PyTuple_Check(exc_type))) {
-            return __Pyx_PyErr_GivenExceptionMatchesTuple(err, exc_type);
-        } else {
-        }
-    }
-    return PyErr_GivenExceptionMatches(err, exc_type);
-}
-static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
-    assert(PyExceptionClass_Check(exc_type1));
-    assert(PyExceptionClass_Check(exc_type2));
-    if (likely(err == exc_type1 || err == exc_type2)) return 1;
-    if (likely(PyExceptionClass_Check(err))) {
-        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
-    }
-    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
-}
-#endif
-
-/* PyIntBinop */
-#if !CYTHON_COMPILING_IN_PYPY
-static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, int inplace, int zerodivision_check) {
-    (void)inplace;
-    (void)zerodivision_check;
-    #if PY_MAJOR_VERSION < 3
-    if (likely(PyInt_CheckExact(op1))) {
-        const long b = intval;
-        long x;
-        long a = PyInt_AS_LONG(op1);
-            x = (long)((unsigned long)a + b);
-            if (likely((x^a) >= 0 || (x^b) >= 0))
-                return PyInt_FromLong(x);
-            return PyLong_Type.tp_as_number->nb_add(op1, op2);
-    }
-    #endif
-    #if CYTHON_USE_PYLONG_INTERNALS
-    if (likely(PyLong_CheckExact(op1))) {
-        const long b = intval;
-        long a, x;
-#ifdef HAVE_LONG_LONG
-        const PY_LONG_LONG llb = intval;
-        PY_LONG_LONG lla, llx;
-#endif
-        const digit* digits = ((PyLongObject*)op1)->ob_digit;
-        const Py_ssize_t size = Py_SIZE(op1);
-        if (likely(__Pyx_sst_abs(size) <= 1)) {
-            a = likely(size) ? digits[0] : 0;
-            if (size == -1) a = -a;
-        } else {
-            switch (size) {
-                case -2:
-                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
-                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
-                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case 2:
-                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
-                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
-                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case -3:
-                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
-                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
-                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case 3:
-                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
-                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
-                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case -4:
-                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
-                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
-                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                case 4:
-                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
-                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
-                        break;
-#ifdef HAVE_LONG_LONG
-                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
-                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
-                        goto long_long;
-#endif
-                    }
-                    CYTHON_FALLTHROUGH;
-                default: return PyLong_Type.tp_as_number->nb_add(op1, op2);
-            }
-        }
-                x = a + b;
-            return PyLong_FromLong(x);
-#ifdef HAVE_LONG_LONG
-        long_long:
-                llx = lla + llb;
-            return PyLong_FromLongLong(llx);
-#endif
-        
-        
-    }
-    #endif
-    if (PyFloat_CheckExact(op1)) {
-        const long b = intval;
-        double a = PyFloat_AS_DOUBLE(op1);
-            double result;
-            PyFPE_START_PROTECT("add", return NULL)
-            result = ((double)a) + (double)b;
-            PyFPE_END_PROTECT(result)
-            return PyFloat_FromDouble(result);
-    }
-    return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2);
-}
-#endif
-
-/* None */
-static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname) {
-    PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname);
-}
-
-/* ImportFrom */
-static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
-    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
-    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
-        PyErr_Format(PyExc_ImportError,
-        #if PY_MAJOR_VERSION < 3
-            "cannot import name %.230s", PyString_AS_STRING(name));
-        #else
-            "cannot import name %S", name);
-        #endif
-    }
-    return value;
-}
-
-/* HasAttr */
-static CYTHON_INLINE int __Pyx_HasAttr(PyObject *o, PyObject *n) {
-    PyObject *r;
-    if (unlikely(!__Pyx_PyBaseString_Check(n))) {
-        PyErr_SetString(PyExc_TypeError,
-                        "hasattr(): attribute name must be string");
-        return -1;
-    }
-    r = __Pyx_GetAttr(o, n);
-    if (unlikely(!r)) {
-        PyErr_Clear();
-        return 0;
-    } else {
-        Py_DECREF(r);
-        return 1;
-    }
-}
-
-/* PyObject_GenericGetAttrNoDict */
-#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
-static PyObject *__Pyx_RaiseGenericGetAttributeError(PyTypeObject *tp, PyObject *attr_name) {
-    PyErr_Format(PyExc_AttributeError,
-#if PY_MAJOR_VERSION >= 3
-                 "'%.50s' object has no attribute '%U'",
-                 tp->tp_name, attr_name);
-#else
-                 "'%.50s' object has no attribute '%.400s'",
-                 tp->tp_name, PyString_AS_STRING(attr_name));
-#endif
-    return NULL;
-}
-static CYTHON_INLINE PyObject* __Pyx_PyObject_GenericGetAttrNoDict(PyObject* obj, PyObject* attr_name) {
-    PyObject *descr;
-    PyTypeObject *tp = Py_TYPE(obj);
-    if (unlikely(!PyString_Check(attr_name))) {
-        return PyObject_GenericGetAttr(obj, attr_name);
-    }
-    assert(!tp->tp_dictoffset);
-    descr = _PyType_Lookup(tp, attr_name);
-    if (unlikely(!descr)) {
-        return __Pyx_RaiseGenericGetAttributeError(tp, attr_name);
-    }
-    Py_INCREF(descr);
-    #if PY_MAJOR_VERSION < 3
-    if (likely(PyType_HasFeature(Py_TYPE(descr), Py_TPFLAGS_HAVE_CLASS)))
-    #endif
-    {
-        descrgetfunc f = Py_TYPE(descr)->tp_descr_get;
-        if (unlikely(f)) {
-            PyObject *res = f(descr, obj, (PyObject *)tp);
-            Py_DECREF(descr);
-            return res;
-        }
-    }
-    return descr;
-}
-#endif
-
-/* PyObject_GenericGetAttr */
-#if CYTHON_USE_TYPE_SLOTS && CYTHON_USE_PYTYPE_LOOKUP && PY_VERSION_HEX < 0x03070000
-static PyObject* __Pyx_PyObject_GenericGetAttr(PyObject* obj, PyObject* attr_name) {
-    if (unlikely(Py_TYPE(obj)->tp_dictoffset)) {
-        return PyObject_GenericGetAttr(obj, attr_name);
-    }
-    return __Pyx_PyObject_GenericGetAttrNoDict(obj, attr_name);
-}
-#endif
-
-/* SetVTable */
-static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
-#if PY_VERSION_HEX >= 0x02070000
-    PyObject *ob = PyCapsule_New(vtable, 0, 0);
-#else
-    PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
-#endif
-    if (!ob)
-        goto bad;
-    if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
-        goto bad;
-    Py_DECREF(ob);
-    return 0;
-bad:
-    Py_XDECREF(ob);
-    return -1;
-}
-
-/* PyObjectGetAttrStrNoError */
-static void __Pyx_PyObject_GetAttrStr_ClearAttributeError(void) {
-    __Pyx_PyThreadState_declare
-    __Pyx_PyThreadState_assign
-    if (likely(__Pyx_PyErr_ExceptionMatches(PyExc_AttributeError)))
-        __Pyx_PyErr_Clear();
-}
-static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStrNoError(PyObject* obj, PyObject* attr_name) {
-    PyObject *result;
-#if CYTHON_COMPILING_IN_CPYTHON && CYTHON_USE_TYPE_SLOTS && PY_VERSION_HEX >= 0x030700B1
-    PyTypeObject* tp = Py_TYPE(obj);
-    if (likely(tp->tp_getattro == PyObject_GenericGetAttr)) {
-        return _PyObject_GenericGetAttrWithDict(obj, attr_name, NULL, 1);
-    }
-#endif
-    result = __Pyx_PyObject_GetAttrStr(obj, attr_name);
-    if (unlikely(!result)) {
-        __Pyx_PyObject_GetAttrStr_ClearAttributeError();
-    }
-    return result;
-}
-
-/* SetupReduce */
-static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) {
-  int ret;
-  PyObject *name_attr;
-  name_attr = __Pyx_PyObject_GetAttrStr(meth, __pyx_n_s_name_2);
-  if (likely(name_attr)) {
-      ret = PyObject_RichCompareBool(name_attr, name, Py_EQ);
-  } else {
-      ret = -1;
-  }
-  if (unlikely(ret < 0)) {
-      PyErr_Clear();
-      ret = 0;
-  }
-  Py_XDECREF(name_attr);
-  return ret;
-}
-static int __Pyx_setup_reduce(PyObject* type_obj) {
-    int ret = 0;
-    PyObject *object_reduce = NULL;
-    PyObject *object_reduce_ex = NULL;
-    PyObject *reduce = NULL;
-    PyObject *reduce_ex = NULL;
-    PyObject *reduce_cython = NULL;
-    PyObject *setstate = NULL;
-    PyObject *setstate_cython = NULL;
-#if CYTHON_USE_PYTYPE_LOOKUP
-    if (_PyType_Lookup((PyTypeObject*)type_obj, __pyx_n_s_getstate)) goto __PYX_GOOD;
-#else
-    if (PyObject_HasAttr(type_obj, __pyx_n_s_getstate)) goto __PYX_GOOD;
-#endif
-#if CYTHON_USE_PYTYPE_LOOKUP
-    object_reduce_ex = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD;
-#else
-    object_reduce_ex = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce_ex); if (!object_reduce_ex) goto __PYX_BAD;
-#endif
-    reduce_ex = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce_ex); if (unlikely(!reduce_ex)) goto __PYX_BAD;
-    if (reduce_ex == object_reduce_ex) {
-#if CYTHON_USE_PYTYPE_LOOKUP
-        object_reduce = _PyType_Lookup(&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto __PYX_BAD;
-#else
-        object_reduce = __Pyx_PyObject_GetAttrStr((PyObject*)&PyBaseObject_Type, __pyx_n_s_reduce); if (!object_reduce) goto __PYX_BAD;
-#endif
-        reduce = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_reduce); if (unlikely(!reduce)) goto __PYX_BAD;
-        if (reduce == object_reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) {
-            reduce_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_reduce_cython);
-            if (likely(reduce_cython)) {
-                ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce, reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
-                ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_reduce_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
-            } else if (reduce == object_reduce || PyErr_Occurred()) {
-                goto __PYX_BAD;
-            }
-            setstate = __Pyx_PyObject_GetAttrStr(type_obj, __pyx_n_s_setstate);
-            if (!setstate) PyErr_Clear();
-            if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) {
-                setstate_cython = __Pyx_PyObject_GetAttrStrNoError(type_obj, __pyx_n_s_setstate_cython);
-                if (likely(setstate_cython)) {
-                    ret = PyDict_SetItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate, setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
-                    ret = PyDict_DelItem(((PyTypeObject*)type_obj)->tp_dict, __pyx_n_s_setstate_cython); if (unlikely(ret < 0)) goto __PYX_BAD;
-                } else if (!setstate || PyErr_Occurred()) {
-                    goto __PYX_BAD;
-                }
-            }
-            PyType_Modified((PyTypeObject*)type_obj);
-        }
-    }
-    goto __PYX_GOOD;
-__PYX_BAD:
-    if (!PyErr_Occurred())
-        PyErr_Format(PyExc_RuntimeError, "Unable to initialize pickling for %s", ((PyTypeObject*)type_obj)->tp_name);
-    ret = -1;
-__PYX_GOOD:
-#if !CYTHON_USE_PYTYPE_LOOKUP
-    Py_XDECREF(object_reduce);
-    Py_XDECREF(object_reduce_ex);
-#endif
-    Py_XDECREF(reduce);
-    Py_XDECREF(reduce_ex);
-    Py_XDECREF(reduce_cython);
-    Py_XDECREF(setstate);
-    Py_XDECREF(setstate_cython);
-    return ret;
-}
-
-/* CLineInTraceback */
-#ifndef CYTHON_CLINE_IN_TRACEBACK
-static int __Pyx_CLineForTraceback(CYTHON_NCP_UNUSED PyThreadState *tstate, int c_line) {
-    PyObject *use_cline;
-    PyObject *ptype, *pvalue, *ptraceback;
-#if CYTHON_COMPILING_IN_CPYTHON
-    PyObject **cython_runtime_dict;
-#endif
-    if (unlikely(!__pyx_cython_runtime)) {
-        return c_line;
-    }
-    __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback);
-#if CYTHON_COMPILING_IN_CPYTHON
-    cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
-    if (likely(cython_runtime_dict)) {
-        __PYX_PY_DICT_LOOKUP_IF_MODIFIED(
-            use_cline, *cython_runtime_dict,
-            __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback))
-    } else
-#endif
-    {
-      PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
-      if (use_cline_obj) {
-        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
-        Py_DECREF(use_cline_obj);
-      } else {
-        PyErr_Clear();
-        use_cline = NULL;
-      }
-    }
-    if (!use_cline) {
-        c_line = 0;
-        PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
-    }
-    else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) {
-        c_line = 0;
-    }
-    __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback);
-    return c_line;
-}
-#endif
-
-/* CodeObjectCache */
-static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
-    int start = 0, mid = 0, end = count - 1;
-    if (end >= 0 && code_line > entries[end].code_line) {
-        return count;
-    }
-    while (start < end) {
-        mid = start + (end - start) / 2;
-        if (code_line < entries[mid].code_line) {
-            end = mid;
-        } else if (code_line > entries[mid].code_line) {
-             start = mid + 1;
-        } else {
-            return mid;
-        }
-    }
-    if (code_line <= entries[mid].code_line) {
-        return mid;
-    } else {
-        return mid + 1;
-    }
-}
-static PyCodeObject *__pyx_find_code_object(int code_line) {
-    PyCodeObject* code_object;
-    int pos;
-    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
-        return NULL;
-    }
-    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
-    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
-        return NULL;
-    }
-    code_object = __pyx_code_cache.entries[pos].code_object;
-    Py_INCREF(code_object);
-    return code_object;
-}
-static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
-    int pos, i;
-    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
-    if (unlikely(!code_line)) {
-        return;
-    }
-    if (unlikely(!entries)) {
-        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
-        if (likely(entries)) {
-            __pyx_code_cache.entries = entries;
-            __pyx_code_cache.max_count = 64;
-            __pyx_code_cache.count = 1;
-            entries[0].code_line = code_line;
-            entries[0].code_object = code_object;
-            Py_INCREF(code_object);
-        }
-        return;
-    }
-    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
-    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
-        PyCodeObject* tmp = entries[pos].code_object;
-        entries[pos].code_object = code_object;
-        Py_DECREF(tmp);
-        return;
-    }
-    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
-        int new_max = __pyx_code_cache.max_count + 64;
-        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
-            __pyx_code_cache.entries, ((size_t)new_max) * sizeof(__Pyx_CodeObjectCacheEntry));
-        if (unlikely(!entries)) {
-            return;
-        }
-        __pyx_code_cache.entries = entries;
-        __pyx_code_cache.max_count = new_max;
-    }
-    for (i=__pyx_code_cache.count; i>pos; i--) {
-        entries[i] = entries[i-1];
-    }
-    entries[pos].code_line = code_line;
-    entries[pos].code_object = code_object;
-    __pyx_code_cache.count++;
-    Py_INCREF(code_object);
-}
-
-/* AddTraceback */
-#include "compile.h"
-#include "frameobject.h"
-#include "traceback.h"
-static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
-            const char *funcname, int c_line,
-            int py_line, const char *filename) {
-    PyCodeObject *py_code = 0;
-    PyObject *py_srcfile = 0;
-    PyObject *py_funcname = 0;
-    #if PY_MAJOR_VERSION < 3
-    py_srcfile = PyString_FromString(filename);
-    #else
-    py_srcfile = PyUnicode_FromString(filename);
-    #endif
-    if (!py_srcfile) goto bad;
-    if (c_line) {
-        #if PY_MAJOR_VERSION < 3
-        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
-        #else
-        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
-        #endif
-    }
-    else {
-        #if PY_MAJOR_VERSION < 3
-        py_funcname = PyString_FromString(funcname);
-        #else
-        py_funcname = PyUnicode_FromString(funcname);
-        #endif
-    }
-    if (!py_funcname) goto bad;
-    py_code = __Pyx_PyCode_New(
-        0,
-        0,
-        0,
-        0,
-        0,
-        __pyx_empty_bytes, /*PyObject *code,*/
-        __pyx_empty_tuple, /*PyObject *consts,*/
-        __pyx_empty_tuple, /*PyObject *names,*/
-        __pyx_empty_tuple, /*PyObject *varnames,*/
-        __pyx_empty_tuple, /*PyObject *freevars,*/
-        __pyx_empty_tuple, /*PyObject *cellvars,*/
-        py_srcfile,   /*PyObject *filename,*/
-        py_funcname,  /*PyObject *name,*/
-        py_line,
-        __pyx_empty_bytes  /*PyObject *lnotab*/
-    );
-    Py_DECREF(py_srcfile);
-    Py_DECREF(py_funcname);
-    return py_code;
-bad:
-    Py_XDECREF(py_srcfile);
-    Py_XDECREF(py_funcname);
-    return NULL;
-}
-static void __Pyx_AddTraceback(const char *funcname, int c_line,
-                               int py_line, const char *filename) {
-    PyCodeObject *py_code = 0;
-    PyFrameObject *py_frame = 0;
-    PyThreadState *tstate = __Pyx_PyThreadState_Current;
-    if (c_line) {
-        c_line = __Pyx_CLineForTraceback(tstate, c_line);
-    }
-    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
-    if (!py_code) {
-        py_code = __Pyx_CreateCodeObjectForTraceback(
-            funcname, c_line, py_line, filename);
-        if (!py_code) goto bad;
-        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
-    }
-    py_frame = PyFrame_New(
-        tstate,            /*PyThreadState *tstate,*/
-        py_code,           /*PyCodeObject *code,*/
-        __pyx_d,    /*PyObject *globals,*/
-        0                  /*PyObject *locals*/
-    );
-    if (!py_frame) goto bad;
-    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
-    PyTraceBack_Here(py_frame);
-bad:
-    Py_XDECREF(py_code);
-    Py_XDECREF(py_frame);
-}
-
-/* Declarations */
-#if CYTHON_CCOMPLEX
-  #ifdef __cplusplus
-    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
-      return ::std::complex< double >(x, y);
-    }
-  #else
-    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
-      return x + y*(__pyx_t_double_complex)_Complex_I;
-    }
-  #endif
-#else
-    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
-      __pyx_t_double_complex z;
-      z.real = x;
-      z.imag = y;
-      return z;
-    }
-#endif
-
-/* Arithmetic */
-#if CYTHON_CCOMPLEX
-#else
-    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
-       return (a.real == b.real) && (a.imag == b.imag);
-    }
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
-        __pyx_t_double_complex z;
-        z.real = a.real + b.real;
-        z.imag = a.imag + b.imag;
-        return z;
-    }
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
-        __pyx_t_double_complex z;
-        z.real = a.real - b.real;
-        z.imag = a.imag - b.imag;
-        return z;
-    }
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
-        __pyx_t_double_complex z;
-        z.real = a.real * b.real - a.imag * b.imag;
-        z.imag = a.real * b.imag + a.imag * b.real;
-        return z;
-    }
-    #if 1
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
-        if (b.imag == 0) {
-            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
-        } else if (fabs(b.real) >= fabs(b.imag)) {
-            if (b.real == 0 && b.imag == 0) {
-                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
-            } else {
-                double r = b.imag / b.real;
-                double s = (double)(1.0) / (b.real + b.imag * r);
-                return __pyx_t_double_complex_from_parts(
-                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
-            }
-        } else {
-            double r = b.real / b.imag;
-            double s = (double)(1.0) / (b.imag + b.real * r);
-            return __pyx_t_double_complex_from_parts(
-                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
-        }
-    }
-    #else
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
-        if (b.imag == 0) {
-            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
-        } else {
-            double denom = b.real * b.real + b.imag * b.imag;
-            return __pyx_t_double_complex_from_parts(
-                (a.real * b.real + a.imag * b.imag) / denom,
-                (a.imag * b.real - a.real * b.imag) / denom);
-        }
-    }
-    #endif
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {
-        __pyx_t_double_complex z;
-        z.real = -a.real;
-        z.imag = -a.imag;
-        return z;
-    }
-    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {
-       return (a.real == 0) && (a.imag == 0);
-    }
-    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {
-        __pyx_t_double_complex z;
-        z.real =  a.real;
-        z.imag = -a.imag;
-        return z;
-    }
-    #if 1
-        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {
-          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
-            return sqrt(z.real*z.real + z.imag*z.imag);
-          #else
-            return hypot(z.real, z.imag);
-          #endif
-        }
-        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
-            __pyx_t_double_complex z;
-            double r, lnr, theta, z_r, z_theta;
-            if (b.imag == 0 && b.real == (int)b.real) {
-                if (b.real < 0) {
-                    double denom = a.real * a.real + a.imag * a.imag;
-                    a.real = a.real / denom;
-                    a.imag = -a.imag / denom;
-                    b.real = -b.real;
-                }
-                switch ((int)b.real) {
-                    case 0:
-                        z.real = 1;
-                        z.imag = 0;
-                        return z;
-                    case 1:
-                        return a;
-                    case 2:
-                        return __Pyx_c_prod_double(a, a);
-                    case 3:
-                        z = __Pyx_c_prod_double(a, a);
-                        return __Pyx_c_prod_double(z, a);
-                    case 4:
-                        z = __Pyx_c_prod_double(a, a);
-                        return __Pyx_c_prod_double(z, z);
-                }
-            }
-            if (a.imag == 0) {
-                if (a.real == 0) {
-                    return a;
-                } else if (b.imag == 0) {
-                    z.real = pow(a.real, b.real);
-                    z.imag = 0;
-                    return z;
-                } else if (a.real > 0) {
-                    r = a.real;
-                    theta = 0;
-                } else {
-                    r = -a.real;
-                    theta = atan2(0.0, -1.0);
-                }
-            } else {
-                r = __Pyx_c_abs_double(a);
-                theta = atan2(a.imag, a.real);
-            }
-            lnr = log(r);
-            z_r = exp(lnr * b.real - theta * b.imag);
-            z_theta = theta * b.real + lnr * b.imag;
-            z.real = z_r * cos(z_theta);
-            z.imag = z_r * sin(z_theta);
-            return z;
-        }
-    #endif
-#endif
-
-#if PY_MAJOR_VERSION < 3
-static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
-    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
-        if (__Pyx_TypeCheck(obj, __pyx_array_type)) return __pyx_array_getbuffer(obj, view, flags);
-        if (__Pyx_TypeCheck(obj, __pyx_memoryview_type)) return __pyx_memoryview_getbuffer(obj, view, flags);
-    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
-    return -1;
-}
-static void __Pyx_ReleaseBuffer(Py_buffer *view) {
-    PyObject *obj = view->obj;
-    if (!obj) return;
-    if (PyObject_CheckBuffer(obj)) {
-        PyBuffer_Release(view);
-        return;
-    }
-    if ((0)) {}
-    view->obj = NULL;
-    Py_DECREF(obj);
-}
-#endif
-
-
-/* MemviewSliceIsContig */
-static int
-__pyx_memviewslice_is_contig(const __Pyx_memviewslice mvs, char order, int ndim)
-{
-    int i, index, step, start;
-    Py_ssize_t itemsize = mvs.memview->view.itemsize;
-    if (order == 'F') {
-        step = 1;
-        start = 0;
-    } else {
-        step = -1;
-        start = ndim - 1;
-    }
-    for (i = 0; i < ndim; i++) {
-        index = start + step * i;
-        if (mvs.suboffsets[index] >= 0 || mvs.strides[index] != itemsize)
-            return 0;
-        itemsize *= mvs.shape[index];
-    }
-    return 1;
-}
-
-/* OverlappingSlices */
-static void
-__pyx_get_array_memory_extents(__Pyx_memviewslice *slice,
-                               void **out_start, void **out_end,
-                               int ndim, size_t itemsize)
-{
-    char *start, *end;
-    int i;
-    start = end = slice->data;
-    for (i = 0; i < ndim; i++) {
-        Py_ssize_t stride = slice->strides[i];
-        Py_ssize_t extent = slice->shape[i];
-        if (extent == 0) {
-            *out_start = *out_end = start;
-            return;
-        } else {
-            if (stride > 0)
-                end += stride * (extent - 1);
-            else
-                start += stride * (extent - 1);
-        }
-    }
-    *out_start = start;
-    *out_end = end + itemsize;
-}
-static int
-__pyx_slices_overlap(__Pyx_memviewslice *slice1,
-                     __Pyx_memviewslice *slice2,
-                     int ndim, size_t itemsize)
-{
-    void *start1, *end1, *start2, *end2;
-    __pyx_get_array_memory_extents(slice1, &start1, &end1, ndim, itemsize);
-    __pyx_get_array_memory_extents(slice2, &start2, &end2, ndim, itemsize);
-    return (start1 < end2) && (start2 < end1);
-}
-
-/* Capsule */
-static CYTHON_INLINE PyObject *
-__pyx_capsule_create(void *p, CYTHON_UNUSED const char *sig)
-{
-    PyObject *cobj;
-#if PY_VERSION_HEX >= 0x02070000
-    cobj = PyCapsule_New(p, sig, NULL);
-#else
-    cobj = PyCObject_FromVoidPtr(p, NULL);
-#endif
-    return cobj;
-}
-
-/* CIntFromPyVerify */
-#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
-    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
-#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
-    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
-#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
-    {\
-        func_type value = func_value;\
-        if (sizeof(target_type) < sizeof(func_type)) {\
-            if (unlikely(value != (func_type) (target_type) value)) {\
-                func_type zero = 0;\
-                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
-                    return (target_type) -1;\
-                if (is_unsigned && unlikely(value < zero))\
-                    goto raise_neg_overflow;\
-                else\
-                    goto raise_overflow;\
-            }\
-        }\
-        return (target_type) value;\
-    }
-
-/* IsLittleEndian */
-static CYTHON_INLINE int __Pyx_Is_Little_Endian(void)
-{
-  union {
-    uint32_t u32;
-    uint8_t u8[4];
-  } S;
-  S.u32 = 0x01020304;
-  return S.u8[0] == 4;
-}
-
-/* BufferFormatCheck */
-static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
-                              __Pyx_BufFmt_StackElem* stack,
-                              __Pyx_TypeInfo* type) {
-  stack[0].field = &ctx->root;
-  stack[0].parent_offset = 0;
-  ctx->root.type = type;
-  ctx->root.name = "buffer dtype";
-  ctx->root.offset = 0;
-  ctx->head = stack;
-  ctx->head->field = &ctx->root;
-  ctx->fmt_offset = 0;
-  ctx->head->parent_offset = 0;
-  ctx->new_packmode = '@';
-  ctx->enc_packmode = '@';
-  ctx->new_count = 1;
-  ctx->enc_count = 0;
-  ctx->enc_type = 0;
-  ctx->is_complex = 0;
-  ctx->is_valid_array = 0;
-  ctx->struct_alignment = 0;
-  while (type->typegroup == 'S') {
-    ++ctx->head;
-    ctx->head->field = type->fields;
-    ctx->head->parent_offset = 0;
-    type = type->fields->type;
-  }
-}
-static int __Pyx_BufFmt_ParseNumber(const char** ts) {
-    int count;
-    const char* t = *ts;
-    if (*t < '0' || *t > '9') {
-      return -1;
-    } else {
-        count = *t++ - '0';
-        while (*t >= '0' && *t <= '9') {
-            count *= 10;
-            count += *t++ - '0';
-        }
-    }
-    *ts = t;
-    return count;
-}
-static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
-    int number = __Pyx_BufFmt_ParseNumber(ts);
-    if (number == -1)
-        PyErr_Format(PyExc_ValueError,\
-                     "Does not understand character buffer dtype format string ('%c')", **ts);
-    return number;
-}
-static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
-  PyErr_Format(PyExc_ValueError,
-               "Unexpected format string character: '%c'", ch);
-}
-static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
-  switch (ch) {
-    case '?': return "'bool'";
-    case 'c': return "'char'";
-    case 'b': return "'signed char'";
-    case 'B': return "'unsigned char'";
-    case 'h': return "'short'";
-    case 'H': return "'unsigned short'";
-    case 'i': return "'int'";
-    case 'I': return "'unsigned int'";
-    case 'l': return "'long'";
-    case 'L': return "'unsigned long'";
-    case 'q': return "'long long'";
-    case 'Q': return "'unsigned long long'";
-    case 'f': return (is_complex ? "'complex float'" : "'float'");
-    case 'd': return (is_complex ? "'complex double'" : "'double'");
-    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
-    case 'T': return "a struct";
-    case 'O': return "Python object";
-    case 'P': return "a pointer";
-    case 's': case 'p': return "a string";
-    case 0: return "end";
-    default: return "unparseable format string";
-  }
-}
-static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
-  switch (ch) {
-    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
-    case 'h': case 'H': return 2;
-    case 'i': case 'I': case 'l': case 'L': return 4;
-    case 'q': case 'Q': return 8;
-    case 'f': return (is_complex ? 8 : 4);
-    case 'd': return (is_complex ? 16 : 8);
-    case 'g': {
-      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
-      return 0;
-    }
-    case 'O': case 'P': return sizeof(void*);
-    default:
-      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
-      return 0;
-    }
-}
-static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
-  switch (ch) {
-    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
-    case 'h': case 'H': return sizeof(short);
-    case 'i': case 'I': return sizeof(int);
-    case 'l': case 'L': return sizeof(long);
-    #ifdef HAVE_LONG_LONG
-    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
-    #endif
-    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
-    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
-    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
-    case 'O': case 'P': return sizeof(void*);
-    default: {
-      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
-      return 0;
-    }
-  }
-}
-typedef struct { char c; short x; } __Pyx_st_short;
-typedef struct { char c; int x; } __Pyx_st_int;
-typedef struct { char c; long x; } __Pyx_st_long;
-typedef struct { char c; float x; } __Pyx_st_float;
-typedef struct { char c; double x; } __Pyx_st_double;
-typedef struct { char c; long double x; } __Pyx_st_longdouble;
-typedef struct { char c; void *x; } __Pyx_st_void_p;
-#ifdef HAVE_LONG_LONG
-typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
-#endif
-static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
-  switch (ch) {
-    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
-    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
-    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
-    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
-#ifdef HAVE_LONG_LONG
-    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
-#endif
-    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
-    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
-    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
-    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
-    default:
-      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
-      return 0;
-    }
-}
-/* These are for computing the padding at the end of the struct to align
-   on the first member of the struct. This will probably the same as above,
-   but we don't have any guarantees.
- */
-typedef struct { short x; char c; } __Pyx_pad_short;
-typedef struct { int x; char c; } __Pyx_pad_int;
-typedef struct { long x; char c; } __Pyx_pad_long;
-typedef struct { float x; char c; } __Pyx_pad_float;
-typedef struct { double x; char c; } __Pyx_pad_double;
-typedef struct { long double x; char c; } __Pyx_pad_longdouble;
-typedef struct { void *x; char c; } __Pyx_pad_void_p;
-#ifdef HAVE_LONG_LONG
-typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
-#endif
-static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
-  switch (ch) {
-    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
-    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
-    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
-    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
-#ifdef HAVE_LONG_LONG
-    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
-#endif
-    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
-    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
-    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
-    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
-    default:
-      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
-      return 0;
-    }
-}
-static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
-  switch (ch) {
-    case 'c':
-        return 'H';
-    case 'b': case 'h': case 'i':
-    case 'l': case 'q': case 's': case 'p':
-        return 'I';
-    case '?': case 'B': case 'H': case 'I': case 'L': case 'Q':
-        return 'U';
-    case 'f': case 'd': case 'g':
-        return (is_complex ? 'C' : 'R');
-    case 'O':
-        return 'O';
-    case 'P':
-        return 'P';
-    default: {
-      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
-      return 0;
-    }
-  }
-}
-static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
-  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
-    const char* expected;
-    const char* quote;
-    if (ctx->head == NULL) {
-      expected = "end";
-      quote = "";
-    } else {
-      expected = ctx->head->field->type->name;
-      quote = "'";
-    }
-    PyErr_Format(PyExc_ValueError,
-                 "Buffer dtype mismatch, expected %s%s%s but got %s",
-                 quote, expected, quote,
-                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
-  } else {
-    __Pyx_StructField* field = ctx->head->field;
-    __Pyx_StructField* parent = (ctx->head - 1)->field;
-    PyErr_Format(PyExc_ValueError,
-                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
-                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
-                 parent->type->name, field->name);
-  }
-}
-static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
-  char group;
-  size_t size, offset, arraysize = 1;
-  if (ctx->enc_type == 0) return 0;
-  if (ctx->head->field->type->arraysize[0]) {
-    int i, ndim = 0;
-    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
-        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
-        ndim = 1;
-        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
-            PyErr_Format(PyExc_ValueError,
-                         "Expected a dimension of size %zu, got %zu",
-                         ctx->head->field->type->arraysize[0], ctx->enc_count);
-            return -1;
-        }
-    }
-    if (!ctx->is_valid_array) {
-      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
-                   ctx->head->field->type->ndim, ndim);
-      return -1;
-    }
-    for (i = 0; i < ctx->head->field->type->ndim; i++) {
-      arraysize *= ctx->head->field->type->arraysize[i];
-    }
-    ctx->is_valid_array = 0;
-    ctx->enc_count = 1;
-  }
-  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
-  do {
-    __Pyx_StructField* field = ctx->head->field;
-    __Pyx_TypeInfo* type = field->type;
-    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
-      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
-    } else {
-      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
-    }
-    if (ctx->enc_packmode == '@') {
-      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
-      size_t align_mod_offset;
-      if (align_at == 0) return -1;
-      align_mod_offset = ctx->fmt_offset % align_at;
-      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
-      if (ctx->struct_alignment == 0)
-          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
-                                                                 ctx->is_complex);
-    }
-    if (type->size != size || type->typegroup != group) {
-      if (type->typegroup == 'C' && type->fields != NULL) {
-        size_t parent_offset = ctx->head->parent_offset + field->offset;
-        ++ctx->head;
-        ctx->head->field = type->fields;
-        ctx->head->parent_offset = parent_offset;
-        continue;
-      }
-      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
-      } else {
-          __Pyx_BufFmt_RaiseExpected(ctx);
-          return -1;
-      }
-    }
-    offset = ctx->head->parent_offset + field->offset;
-    if (ctx->fmt_offset != offset) {
-      PyErr_Format(PyExc_ValueError,
-                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
-                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
-      return -1;
-    }
-    ctx->fmt_offset += size;
-    if (arraysize)
-      ctx->fmt_offset += (arraysize - 1) * size;
-    --ctx->enc_count;
-    while (1) {
-      if (field == &ctx->root) {
-        ctx->head = NULL;
-        if (ctx->enc_count != 0) {
-          __Pyx_BufFmt_RaiseExpected(ctx);
-          return -1;
-        }
-        break;
-      }
-      ctx->head->field = ++field;
-      if (field->type == NULL) {
-        --ctx->head;
-        field = ctx->head->field;
-        continue;
-      } else if (field->type->typegroup == 'S') {
-        size_t parent_offset = ctx->head->parent_offset + field->offset;
-        if (field->type->fields->type == NULL) continue;
-        field = field->type->fields;
-        ++ctx->head;
-        ctx->head->field = field;
-        ctx->head->parent_offset = parent_offset;
-        break;
-      } else {
-        break;
-      }
-    }
-  } while (ctx->enc_count);
-  ctx->enc_type = 0;
-  ctx->is_complex = 0;
-  return 0;
-}
-static PyObject *
-__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
-{
-    const char *ts = *tsp;
-    int i = 0, number, ndim;
-    ++ts;
-    if (ctx->new_count != 1) {
-        PyErr_SetString(PyExc_ValueError,
-                        "Cannot handle repeated arrays in format string");
-        return NULL;
-    }
-    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
-    ndim = ctx->head->field->type->ndim;
-    while (*ts && *ts != ')') {
-        switch (*ts) {
-            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
-            default:  break;
-        }
-        number = __Pyx_BufFmt_ExpectNumber(&ts);
-        if (number == -1) return NULL;
-        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
-            return PyErr_Format(PyExc_ValueError,
-                        "Expected a dimension of size %zu, got %d",
-                        ctx->head->field->type->arraysize[i], number);
-        if (*ts != ',' && *ts != ')')
-            return PyErr_Format(PyExc_ValueError,
-                                "Expected a comma in format string, got '%c'", *ts);
-        if (*ts == ',') ts++;
-        i++;
-    }
-    if (i != ndim)
-        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
-                            ctx->head->field->type->ndim, i);
-    if (!*ts) {
-        PyErr_SetString(PyExc_ValueError,
-                        "Unexpected end of format string, expected ')'");
-        return NULL;
-    }
-    ctx->is_valid_array = 1;
-    ctx->new_count = 1;
-    *tsp = ++ts;
-    return Py_None;
-}
-static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
-  int got_Z = 0;
-  while (1) {
-    switch(*ts) {
-      case 0:
-        if (ctx->enc_type != 0 && ctx->head == NULL) {
-          __Pyx_BufFmt_RaiseExpected(ctx);
-          return NULL;
-        }
-        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
-        if (ctx->head != NULL) {
-          __Pyx_BufFmt_RaiseExpected(ctx);
-          return NULL;
-        }
-        return ts;
-      case ' ':
-      case '\r':
-      case '\n':
-        ++ts;
-        break;
-      case '<':
-        if (!__Pyx_Is_Little_Endian()) {
-          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
-          return NULL;
-        }
-        ctx->new_packmode = '=';
-        ++ts;
-        break;
-      case '>':
-      case '!':
-        if (__Pyx_Is_Little_Endian()) {
-          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
-          return NULL;
-        }
-        ctx->new_packmode = '=';
-        ++ts;
-        break;
-      case '=':
-      case '@':
-      case '^':
-        ctx->new_packmode = *ts++;
-        break;
-      case 'T':
-        {
-          const char* ts_after_sub;
-          size_t i, struct_count = ctx->new_count;
-          size_t struct_alignment = ctx->struct_alignment;
-          ctx->new_count = 1;
-          ++ts;
-          if (*ts != '{') {
-            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
-            return NULL;
-          }
-          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
-          ctx->enc_type = 0;
-          ctx->enc_count = 0;
-          ctx->struct_alignment = 0;
-          ++ts;
-          ts_after_sub = ts;
-          for (i = 0; i != struct_count; ++i) {
-            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
-            if (!ts_after_sub) return NULL;
-          }
-          ts = ts_after_sub;
-          if (struct_alignment) ctx->struct_alignment = struct_alignment;
-        }
-        break;
-      case '}':
-        {
-          size_t alignment = ctx->struct_alignment;
-          ++ts;
-          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
-          ctx->enc_type = 0;
-          if (alignment && ctx->fmt_offset % alignment) {
-            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
-          }
-        }
-        return ts;
-      case 'x':
-        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
-        ctx->fmt_offset += ctx->new_count;
-        ctx->new_count = 1;
-        ctx->enc_count = 0;
-        ctx->enc_type = 0;
-        ctx->enc_packmode = ctx->new_packmode;
-        ++ts;
-        break;
-      case 'Z':
-        got_Z = 1;
-        ++ts;
-        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
-          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
-          return NULL;
-        }
-        CYTHON_FALLTHROUGH;
-      case '?': case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
-      case 'l': case 'L': case 'q': case 'Q':
-      case 'f': case 'd': case 'g':
-      case 'O': case 'p':
-        if ((ctx->enc_type == *ts) && (got_Z == ctx->is_complex) &&
-            (ctx->enc_packmode == ctx->new_packmode) && (!ctx->is_valid_array)) {
-          ctx->enc_count += ctx->new_count;
-          ctx->new_count = 1;
-          got_Z = 0;
-          ++ts;
-          break;
-        }
-        CYTHON_FALLTHROUGH;
-      case 's':
-        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
-        ctx->enc_count = ctx->new_count;
-        ctx->enc_packmode = ctx->new_packmode;
-        ctx->enc_type = *ts;
-        ctx->is_complex = got_Z;
-        ++ts;
-        ctx->new_count = 1;
-        got_Z = 0;
-        break;
-      case ':':
-        ++ts;
-        while(*ts != ':') ++ts;
-        ++ts;
-        break;
-      case '(':
-        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
-        break;
-      default:
-        {
-          int number = __Pyx_BufFmt_ExpectNumber(&ts);
-          if (number == -1) return NULL;
-          ctx->new_count = (size_t)number;
-        }
-    }
-  }
-}
-
-/* TypeInfoCompare */
-  static int
-__pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b)
-{
-    int i;
-    if (!a || !b)
-        return 0;
-    if (a == b)
-        return 1;
-    if (a->size != b->size || a->typegroup != b->typegroup ||
-            a->is_unsigned != b->is_unsigned || a->ndim != b->ndim) {
-        if (a->typegroup == 'H' || b->typegroup == 'H') {
-            return a->size == b->size;
-        } else {
-            return 0;
-        }
-    }
-    if (a->ndim) {
-        for (i = 0; i < a->ndim; i++)
-            if (a->arraysize[i] != b->arraysize[i])
-                return 0;
-    }
-    if (a->typegroup == 'S') {
-        if (a->flags != b->flags)
-            return 0;
-        if (a->fields || b->fields) {
-            if (!(a->fields && b->fields))
-                return 0;
-            for (i = 0; a->fields[i].type && b->fields[i].type; i++) {
-                __Pyx_StructField *field_a = a->fields + i;
-                __Pyx_StructField *field_b = b->fields + i;
-                if (field_a->offset != field_b->offset ||
-                    !__pyx_typeinfo_cmp(field_a->type, field_b->type))
-                    return 0;
-            }
-            return !a->fields[i].type && !b->fields[i].type;
-        }
-    }
-    return 1;
-}
-
-/* MemviewSliceValidateAndInit */
-  static int
-__pyx_check_strides(Py_buffer *buf, int dim, int ndim, int spec)
-{
-    if (buf->shape[dim] <= 1)
-        return 1;
-    if (buf->strides) {
-        if (spec & __Pyx_MEMVIEW_CONTIG) {
-            if (spec & (__Pyx_MEMVIEW_PTR|__Pyx_MEMVIEW_FULL)) {
-                if (unlikely(buf->strides[dim] != sizeof(void *))) {
-                    PyErr_Format(PyExc_ValueError,
-                                 "Buffer is not indirectly contiguous "
-                                 "in dimension %d.", dim);
-                    goto fail;
-                }
-            } else if (unlikely(buf->strides[dim] != buf->itemsize)) {
-                PyErr_SetString(PyExc_ValueError,
-                                "Buffer and memoryview are not contiguous "
-                                "in the same dimension.");
-                goto fail;
-            }
-        }
-        if (spec & __Pyx_MEMVIEW_FOLLOW) {
-            Py_ssize_t stride = buf->strides[dim];
-            if (stride < 0)
-                stride = -stride;
-            if (unlikely(stride < buf->itemsize)) {
-                PyErr_SetString(PyExc_ValueError,
-                                "Buffer and memoryview are not contiguous "
-                                "in the same dimension.");
-                goto fail;
-            }
-        }
-    } else {
-        if (unlikely(spec & __Pyx_MEMVIEW_CONTIG && dim != ndim - 1)) {
-            PyErr_Format(PyExc_ValueError,
-                         "C-contiguous buffer is not contiguous in "
-                         "dimension %d", dim);
-            goto fail;
-        } else if (unlikely(spec & (__Pyx_MEMVIEW_PTR))) {
-            PyErr_Format(PyExc_ValueError,
-                         "C-contiguous buffer is not indirect in "
-                         "dimension %d", dim);
-            goto fail;
-        } else if (unlikely(buf->suboffsets)) {
-            PyErr_SetString(PyExc_ValueError,
-                            "Buffer exposes suboffsets but no strides");
-            goto fail;
-        }
-    }
-    return 1;
-fail:
-    return 0;
-}
-static int
-__pyx_check_suboffsets(Py_buffer *buf, int dim, CYTHON_UNUSED int ndim, int spec)
-{
-    if (spec & __Pyx_MEMVIEW_DIRECT) {
-        if (unlikely(buf->suboffsets && buf->suboffsets[dim] >= 0)) {
-            PyErr_Format(PyExc_ValueError,
-                         "Buffer not compatible with direct access "
-                         "in dimension %d.", dim);
-            goto fail;
-        }
-    }
-    if (spec & __Pyx_MEMVIEW_PTR) {
-        if (unlikely(!buf->suboffsets || (buf->suboffsets[dim] < 0))) {
-            PyErr_Format(PyExc_ValueError,
-                         "Buffer is not indirectly accessible "
-                         "in dimension %d.", dim);
-            goto fail;
-        }
-    }
-    return 1;
-fail:
-    return 0;
-}
-static int
-__pyx_verify_contig(Py_buffer *buf, int ndim, int c_or_f_flag)
-{
-    int i;
-    if (c_or_f_flag & __Pyx_IS_F_CONTIG) {
-        Py_ssize_t stride = 1;
-        for (i = 0; i < ndim; i++) {
-            if (unlikely(stride * buf->itemsize != buf->strides[i]  &&  buf->shape[i] > 1)) {
-                PyErr_SetString(PyExc_ValueError,
-                    "Buffer not fortran contiguous.");
-                goto fail;
-            }
-            stride = stride * buf->shape[i];
-        }
-    } else if (c_or_f_flag & __Pyx_IS_C_CONTIG) {
-        Py_ssize_t stride = 1;
-        for (i = ndim - 1; i >- 1; i--) {
-            if (unlikely(stride * buf->itemsize != buf->strides[i]  &&  buf->shape[i] > 1)) {
-                PyErr_SetString(PyExc_ValueError,
-                    "Buffer not C contiguous.");
-                goto fail;
-            }
-            stride = stride * buf->shape[i];
-        }
-    }
-    return 1;
-fail:
-    return 0;
-}
-static int __Pyx_ValidateAndInit_memviewslice(
-                int *axes_specs,
-                int c_or_f_flag,
-                int buf_flags,
-                int ndim,
-                __Pyx_TypeInfo *dtype,
-                __Pyx_BufFmt_StackElem stack[],
-                __Pyx_memviewslice *memviewslice,
-                PyObject *original_obj)
-{
-    struct __pyx_memoryview_obj *memview, *new_memview;
-    __Pyx_RefNannyDeclarations
-    Py_buffer *buf;
-    int i, spec = 0, retval = -1;
-    __Pyx_BufFmt_Context ctx;
-    int from_memoryview = __pyx_memoryview_check(original_obj);
-    __Pyx_RefNannySetupContext("ValidateAndInit_memviewslice", 0);
-    if (from_memoryview && __pyx_typeinfo_cmp(dtype, ((struct __pyx_memoryview_obj *)
-                                                            original_obj)->typeinfo)) {
-        memview = (struct __pyx_memoryview_obj *) original_obj;
-        new_memview = NULL;
-    } else {
-        memview = (struct __pyx_memoryview_obj *) __pyx_memoryview_new(
-                                            original_obj, buf_flags, 0, dtype);
-        new_memview = memview;
-        if (unlikely(!memview))
-            goto fail;
-    }
-    buf = &memview->view;
-    if (unlikely(buf->ndim != ndim)) {
-        PyErr_Format(PyExc_ValueError,
-                "Buffer has wrong number of dimensions (expected %d, got %d)",
-                ndim, buf->ndim);
-        goto fail;
-    }
-    if (new_memview) {
-        __Pyx_BufFmt_Init(&ctx, stack, dtype);
-        if (unlikely(!__Pyx_BufFmt_CheckString(&ctx, buf->format))) goto fail;
-    }
-    if (unlikely((unsigned) buf->itemsize != dtype->size)) {
-        PyErr_Format(PyExc_ValueError,
-                     "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "u byte%s) "
-                     "does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "u byte%s)",
-                     buf->itemsize,
-                     (buf->itemsize > 1) ? "s" : "",
-                     dtype->name,
-                     dtype->size,
-                     (dtype->size > 1) ? "s" : "");
-        goto fail;
-    }
-    if (buf->len > 0) {
-        for (i = 0; i < ndim; i++) {
-            spec = axes_specs[i];
-            if (unlikely(!__pyx_check_strides(buf, i, ndim, spec)))
-                goto fail;
-            if (unlikely(!__pyx_check_suboffsets(buf, i, ndim, spec)))
-                goto fail;
-        }
-        if (unlikely(buf->strides && !__pyx_verify_contig(buf, ndim, c_or_f_flag)))
-            goto fail;
-    }
-    if (unlikely(__Pyx_init_memviewslice(memview, ndim, memviewslice,
-                                         new_memview != NULL) == -1)) {
-        goto fail;
-    }
-    retval = 0;
-    goto no_fail;
-fail:
-    Py_XDECREF(new_memview);
-    retval = -1;
-no_fail:
-    __Pyx_RefNannyFinishContext();
-    return retval;
-}
-
-/* ObjectToMemviewSlice */
-  static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds_double(PyObject *obj, int writable_flag) {
-    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
-    __Pyx_BufFmt_StackElem stack[1];
-    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED), (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) };
-    int retcode;
-    if (obj == Py_None) {
-        result.memview = (struct __pyx_memoryview_obj *) Py_None;
-        return result;
-    }
-    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0,
-                                                 PyBUF_RECORDS_RO | writable_flag, 2,
-                                                 &__Pyx_TypeInfo_double, stack,
-                                                 &result, obj);
-    if (unlikely(retcode == -1))
-        goto __pyx_fail;
-    return result;
-__pyx_fail:
-    result.memview = NULL;
-    result.data = NULL;
-    return result;
-}
-
-/* ObjectToMemviewSlice */
-  static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_int(PyObject *obj, int writable_flag) {
-    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
-    __Pyx_BufFmt_StackElem stack[1];
-    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) };
-    int retcode;
-    if (obj == Py_None) {
-        result.memview = (struct __pyx_memoryview_obj *) Py_None;
-        return result;
-    }
-    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0,
-                                                 PyBUF_RECORDS_RO | writable_flag, 1,
-                                                 &__Pyx_TypeInfo_int, stack,
-                                                 &result, obj);
-    if (unlikely(retcode == -1))
-        goto __pyx_fail;
-    return result;
-__pyx_fail:
-    result.memview = NULL;
-    result.data = NULL;
-    return result;
-}
-
-/* FromPy */
-  static __pyx_t_double_complex __Pyx_PyComplex_As___pyx_t_double_complex(PyObject* o) {
-    Py_complex cval;
-#if !CYTHON_COMPILING_IN_PYPY
-    if (PyComplex_CheckExact(o))
-        cval = ((PyComplexObject *)o)->cval;
-    else
-#endif
-        cval = PyComplex_AsCComplex(o);
-    return __pyx_t_double_complex_from_parts(
-               (double)cval.real,
-               (double)cval.imag);
-}
-
-/* ObjectToMemviewSlice */
-  static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds___pyx_t_double_complex(PyObject *obj, int writable_flag) {
-    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
-    __Pyx_BufFmt_StackElem stack[1];
-    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) };
-    int retcode;
-    if (obj == Py_None) {
-        result.memview = (struct __pyx_memoryview_obj *) Py_None;
-        return result;
-    }
-    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0,
-                                                 PyBUF_RECORDS_RO | writable_flag, 1,
-                                                 &__Pyx_TypeInfo___pyx_t_double_complex, stack,
-                                                 &result, obj);
-    if (unlikely(retcode == -1))
-        goto __pyx_fail;
-    return result;
-__pyx_fail:
-    result.memview = NULL;
-    result.data = NULL;
-    return result;
-}
-
-/* ObjectToMemviewSlice */
-  static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds___pyx_t_double_complex(PyObject *obj, int writable_flag) {
-    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
-    __Pyx_BufFmt_StackElem stack[1];
-    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED), (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) };
-    int retcode;
-    if (obj == Py_None) {
-        result.memview = (struct __pyx_memoryview_obj *) Py_None;
-        return result;
-    }
-    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0,
-                                                 PyBUF_RECORDS_RO | writable_flag, 2,
-                                                 &__Pyx_TypeInfo___pyx_t_double_complex, stack,
-                                                 &result, obj);
-    if (unlikely(retcode == -1))
-        goto __pyx_fail;
-    return result;
-__pyx_fail:
-    result.memview = NULL;
-    result.data = NULL;
-    return result;
-}
-
-/* CIntToPy */
-  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
-    const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
-    const int is_unsigned = neg_one > const_zero;
-    if (is_unsigned) {
-        if (sizeof(int) < sizeof(long)) {
-            return PyInt_FromLong((long) value);
-        } else if (sizeof(int) <= sizeof(unsigned long)) {
-            return PyLong_FromUnsignedLong((unsigned long) value);
-#ifdef HAVE_LONG_LONG
-        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
-            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
-#endif
-        }
-    } else {
-        if (sizeof(int) <= sizeof(long)) {
-            return PyInt_FromLong((long) value);
-#ifdef HAVE_LONG_LONG
-        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
-            return PyLong_FromLongLong((PY_LONG_LONG) value);
-#endif
-        }
-    }
-    {
-        int one = 1; int little = (int)*(unsigned char *)&one;
-        unsigned char *bytes = (unsigned char *)&value;
-        return _PyLong_FromByteArray(bytes, sizeof(int),
-                                     little, !is_unsigned);
-    }
-}
-
-/* MemviewDtypeToObject */
-  static CYTHON_INLINE PyObject *__pyx_memview_get___pyx_t_double_complex(const char *itemp) {
-    return (PyObject *) __pyx_PyComplex_FromComplex(*(__pyx_t_double_complex *) itemp);
-}
-static CYTHON_INLINE int __pyx_memview_set___pyx_t_double_complex(const char *itemp, PyObject *obj) {
-    __pyx_t_double_complex value = __Pyx_PyComplex_As___pyx_t_double_complex(obj);
-    if (PyErr_Occurred())
-        return 0;
-    *(__pyx_t_double_complex *) itemp = value;
-    return 1;
-}
-
-/* CIntToPy */
-  static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
-    const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
-    const int is_unsigned = neg_one > const_zero;
-    if (is_unsigned) {
-        if (sizeof(long) < sizeof(long)) {
-            return PyInt_FromLong((long) value);
-        } else if (sizeof(long) <= sizeof(unsigned long)) {
-            return PyLong_FromUnsignedLong((unsigned long) value);
-#ifdef HAVE_LONG_LONG
-        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
-            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
-#endif
-        }
-    } else {
-        if (sizeof(long) <= sizeof(long)) {
-            return PyInt_FromLong((long) value);
-#ifdef HAVE_LONG_LONG
-        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
-            return PyLong_FromLongLong((PY_LONG_LONG) value);
-#endif
-        }
-    }
-    {
-        int one = 1; int little = (int)*(unsigned char *)&one;
-        unsigned char *bytes = (unsigned char *)&value;
-        return _PyLong_FromByteArray(bytes, sizeof(long),
-                                     little, !is_unsigned);
-    }
-}
-
-/* MemviewSliceCopyTemplate */
-  static __Pyx_memviewslice
-__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs,
-                                 const char *mode, int ndim,
-                                 size_t sizeof_dtype, int contig_flag,
-                                 int dtype_is_object)
-{
-    __Pyx_RefNannyDeclarations
-    int i;
-    __Pyx_memviewslice new_mvs = { 0, 0, { 0 }, { 0 }, { 0 } };
-    struct __pyx_memoryview_obj *from_memview = from_mvs->memview;
-    Py_buffer *buf = &from_memview->view;
-    PyObject *shape_tuple = NULL;
-    PyObject *temp_int = NULL;
-    struct __pyx_array_obj *array_obj = NULL;
-    struct __pyx_memoryview_obj *memview_obj = NULL;
-    __Pyx_RefNannySetupContext("__pyx_memoryview_copy_new_contig", 0);
-    for (i = 0; i < ndim; i++) {
-        if (unlikely(from_mvs->suboffsets[i] >= 0)) {
-            PyErr_Format(PyExc_ValueError, "Cannot copy memoryview slice with "
-                                           "indirect dimensions (axis %d)", i);
-            goto fail;
-        }
-    }
-    shape_tuple = PyTuple_New(ndim);
-    if (unlikely(!shape_tuple)) {
-        goto fail;
-    }
-    __Pyx_GOTREF(shape_tuple);
-    for(i = 0; i < ndim; i++) {
-        temp_int = PyInt_FromSsize_t(from_mvs->shape[i]);
-        if(unlikely(!temp_int)) {
-            goto fail;
-        } else {
-            PyTuple_SET_ITEM(shape_tuple, i, temp_int);
-            temp_int = NULL;
-        }
-    }
-    array_obj = __pyx_array_new(shape_tuple, sizeof_dtype, buf->format, (char *) mode, NULL);
-    if (unlikely(!array_obj)) {
-        goto fail;
-    }
-    __Pyx_GOTREF(array_obj);
-    memview_obj = (struct __pyx_memoryview_obj *) __pyx_memoryview_new(
-                                    (PyObject *) array_obj, contig_flag,
-                                    dtype_is_object,
-                                    from_mvs->memview->typeinfo);
-    if (unlikely(!memview_obj))
-        goto fail;
-    if (unlikely(__Pyx_init_memviewslice(memview_obj, ndim, &new_mvs, 1) < 0))
-        goto fail;
-    if (unlikely(__pyx_memoryview_copy_contents(*from_mvs, new_mvs, ndim, ndim,
-                                                dtype_is_object) < 0))
-        goto fail;
-    goto no_fail;
-fail:
-    __Pyx_XDECREF(new_mvs.memview);
-    new_mvs.memview = NULL;
-    new_mvs.data = NULL;
-no_fail:
-    __Pyx_XDECREF(shape_tuple);
-    __Pyx_XDECREF(temp_int);
-    __Pyx_XDECREF(array_obj);
-    __Pyx_RefNannyFinishContext();
-    return new_mvs;
-}
-
-/* CIntFromPy */
-  static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
-    const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0;
-    const int is_unsigned = neg_one > const_zero;
-#if PY_MAJOR_VERSION < 3
-    if (likely(PyInt_Check(x))) {
-        if (sizeof(int) < sizeof(long)) {
-            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
-        } else {
-            long val = PyInt_AS_LONG(x);
-            if (is_unsigned && unlikely(val < 0)) {
-                goto raise_neg_overflow;
-            }
-            return (int) val;
-        }
-    } else
-#endif
-    if (likely(PyLong_Check(x))) {
-        if (is_unsigned) {
-#if CYTHON_USE_PYLONG_INTERNALS
-            const digit* digits = ((PyLongObject*)x)->ob_digit;
-            switch (Py_SIZE(x)) {
-                case  0: return (int) 0;
-                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
-                case 2:
-                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
-                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
-                        }
-                    }
-                    break;
-                case 3:
-                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
-                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
-                        }
-                    }
-                    break;
-                case 4:
-                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
-                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
-                        }
-                    }
-                    break;
-            }
-#endif
-#if CYTHON_COMPILING_IN_CPYTHON
-            if (unlikely(Py_SIZE(x) < 0)) {
-                goto raise_neg_overflow;
-            }
-#else
-            {
-                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
-                if (unlikely(result < 0))
-                    return (int) -1;
-                if (unlikely(result == 1))
-                    goto raise_neg_overflow;
-            }
-#endif
-            if (sizeof(int) <= sizeof(unsigned long)) {
-                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
-#ifdef HAVE_LONG_LONG
-            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
-                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
-#endif
-            }
-        } else {
-#if CYTHON_USE_PYLONG_INTERNALS
-            const digit* digits = ((PyLongObject*)x)->ob_digit;
-            switch (Py_SIZE(x)) {
-                case  0: return (int) 0;
-                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
-                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
-                case -2:
-                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
-                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
-                        }
-                    }
-                    break;
-                case 2:
-                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
-                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
-                        }
-                    }
-                    break;
-                case -3:
-                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
-                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
-                        }
-                    }
-                    break;
-                case 3:
-                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
-                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
-                        }
-                    }
-                    break;
-                case -4:
-                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
-                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
-                        }
-                    }
-                    break;
-                case 4:
-                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
-                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
-                        }
-                    }
-                    break;
-            }
-#endif
-            if (sizeof(int) <= sizeof(long)) {
-                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
-#ifdef HAVE_LONG_LONG
-            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
-                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
-#endif
-            }
-        }
-        {
-#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
-            PyErr_SetString(PyExc_RuntimeError,
-                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
-#else
-            int val;
-            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
- #if PY_MAJOR_VERSION < 3
-            if (likely(v) && !PyLong_Check(v)) {
-                PyObject *tmp = v;
-                v = PyNumber_Long(tmp);
-                Py_DECREF(tmp);
-            }
- #endif
-            if (likely(v)) {
-                int one = 1; int is_little = (int)*(unsigned char *)&one;
-                unsigned char *bytes = (unsigned char *)&val;
-                int ret = _PyLong_AsByteArray((PyLongObject *)v,
-                                              bytes, sizeof(val),
-                                              is_little, !is_unsigned);
-                Py_DECREF(v);
-                if (likely(!ret))
-                    return val;
-            }
-#endif
-            return (int) -1;
-        }
-    } else {
-        int val;
-        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
-        if (!tmp) return (int) -1;
-        val = __Pyx_PyInt_As_int(tmp);
-        Py_DECREF(tmp);
-        return val;
-    }
-raise_overflow:
-    PyErr_SetString(PyExc_OverflowError,
-        "value too large to convert to int");
-    return (int) -1;
-raise_neg_overflow:
-    PyErr_SetString(PyExc_OverflowError,
-        "can't convert negative value to int");
-    return (int) -1;
-}
-
-/* CIntFromPy */
-  static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
-    const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0;
-    const int is_unsigned = neg_one > const_zero;
-#if PY_MAJOR_VERSION < 3
-    if (likely(PyInt_Check(x))) {
-        if (sizeof(long) < sizeof(long)) {
-            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
-        } else {
-            long val = PyInt_AS_LONG(x);
-            if (is_unsigned && unlikely(val < 0)) {
-                goto raise_neg_overflow;
-            }
-            return (long) val;
-        }
-    } else
-#endif
-    if (likely(PyLong_Check(x))) {
-        if (is_unsigned) {
-#if CYTHON_USE_PYLONG_INTERNALS
-            const digit* digits = ((PyLongObject*)x)->ob_digit;
-            switch (Py_SIZE(x)) {
-                case  0: return (long) 0;
-                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
-                case 2:
-                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
-                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
-                        }
-                    }
-                    break;
-                case 3:
-                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
-                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
-                        }
-                    }
-                    break;
-                case 4:
-                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
-                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
-                        }
-                    }
-                    break;
-            }
-#endif
-#if CYTHON_COMPILING_IN_CPYTHON
-            if (unlikely(Py_SIZE(x) < 0)) {
-                goto raise_neg_overflow;
-            }
-#else
-            {
-                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
-                if (unlikely(result < 0))
-                    return (long) -1;
-                if (unlikely(result == 1))
-                    goto raise_neg_overflow;
-            }
-#endif
-            if (sizeof(long) <= sizeof(unsigned long)) {
-                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
-#ifdef HAVE_LONG_LONG
-            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
-                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
-#endif
-            }
-        } else {
-#if CYTHON_USE_PYLONG_INTERNALS
-            const digit* digits = ((PyLongObject*)x)->ob_digit;
-            switch (Py_SIZE(x)) {
-                case  0: return (long) 0;
-                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
-                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
-                case -2:
-                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
-                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
-                        }
-                    }
-                    break;
-                case 2:
-                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
-                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
-                        }
-                    }
-                    break;
-                case -3:
-                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
-                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
-                        }
-                    }
-                    break;
-                case 3:
-                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
-                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
-                        }
-                    }
-                    break;
-                case -4:
-                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
-                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
-                        }
-                    }
-                    break;
-                case 4:
-                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
-                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
-                        }
-                    }
-                    break;
-            }
-#endif
-            if (sizeof(long) <= sizeof(long)) {
-                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
-#ifdef HAVE_LONG_LONG
-            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
-                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
-#endif
-            }
-        }
-        {
-#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
-            PyErr_SetString(PyExc_RuntimeError,
-                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
-#else
-            long val;
-            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
- #if PY_MAJOR_VERSION < 3
-            if (likely(v) && !PyLong_Check(v)) {
-                PyObject *tmp = v;
-                v = PyNumber_Long(tmp);
-                Py_DECREF(tmp);
-            }
- #endif
-            if (likely(v)) {
-                int one = 1; int is_little = (int)*(unsigned char *)&one;
-                unsigned char *bytes = (unsigned char *)&val;
-                int ret = _PyLong_AsByteArray((PyLongObject *)v,
-                                              bytes, sizeof(val),
-                                              is_little, !is_unsigned);
-                Py_DECREF(v);
-                if (likely(!ret))
-                    return val;
-            }
-#endif
-            return (long) -1;
-        }
-    } else {
-        long val;
-        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
-        if (!tmp) return (long) -1;
-        val = __Pyx_PyInt_As_long(tmp);
-        Py_DECREF(tmp);
-        return val;
-    }
-raise_overflow:
-    PyErr_SetString(PyExc_OverflowError,
-        "value too large to convert to long");
-    return (long) -1;
-raise_neg_overflow:
-    PyErr_SetString(PyExc_OverflowError,
-        "can't convert negative value to long");
-    return (long) -1;
-}
-
-/* CIntFromPy */
-  static CYTHON_INLINE char __Pyx_PyInt_As_char(PyObject *x) {
-    const char neg_one = (char) ((char) 0 - (char) 1), const_zero = (char) 0;
-    const int is_unsigned = neg_one > const_zero;
-#if PY_MAJOR_VERSION < 3
-    if (likely(PyInt_Check(x))) {
-        if (sizeof(char) < sizeof(long)) {
-            __PYX_VERIFY_RETURN_INT(char, long, PyInt_AS_LONG(x))
-        } else {
-            long val = PyInt_AS_LONG(x);
-            if (is_unsigned && unlikely(val < 0)) {
-                goto raise_neg_overflow;
-            }
-            return (char) val;
-        }
-    } else
-#endif
-    if (likely(PyLong_Check(x))) {
-        if (is_unsigned) {
-#if CYTHON_USE_PYLONG_INTERNALS
-            const digit* digits = ((PyLongObject*)x)->ob_digit;
-            switch (Py_SIZE(x)) {
-                case  0: return (char) 0;
-                case  1: __PYX_VERIFY_RETURN_INT(char, digit, digits[0])
-                case 2:
-                    if (8 * sizeof(char) > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) >= 2 * PyLong_SHIFT) {
-                            return (char) (((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0]));
-                        }
-                    }
-                    break;
-                case 3:
-                    if (8 * sizeof(char) > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) >= 3 * PyLong_SHIFT) {
-                            return (char) (((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]));
-                        }
-                    }
-                    break;
-                case 4:
-                    if (8 * sizeof(char) > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) >= 4 * PyLong_SHIFT) {
-                            return (char) (((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]));
-                        }
-                    }
-                    break;
-            }
-#endif
-#if CYTHON_COMPILING_IN_CPYTHON
-            if (unlikely(Py_SIZE(x) < 0)) {
-                goto raise_neg_overflow;
-            }
-#else
-            {
-                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
-                if (unlikely(result < 0))
-                    return (char) -1;
-                if (unlikely(result == 1))
-                    goto raise_neg_overflow;
-            }
-#endif
-            if (sizeof(char) <= sizeof(unsigned long)) {
-                __PYX_VERIFY_RETURN_INT_EXC(char, unsigned long, PyLong_AsUnsignedLong(x))
-#ifdef HAVE_LONG_LONG
-            } else if (sizeof(char) <= sizeof(unsigned PY_LONG_LONG)) {
-                __PYX_VERIFY_RETURN_INT_EXC(char, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
-#endif
-            }
-        } else {
-#if CYTHON_USE_PYLONG_INTERNALS
-            const digit* digits = ((PyLongObject*)x)->ob_digit;
-            switch (Py_SIZE(x)) {
-                case  0: return (char) 0;
-                case -1: __PYX_VERIFY_RETURN_INT(char, sdigit, (sdigit) (-(sdigit)digits[0]))
-                case  1: __PYX_VERIFY_RETURN_INT(char,  digit, +digits[0])
-                case -2:
-                    if (8 * sizeof(char) - 1 > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) - 1 > 2 * PyLong_SHIFT) {
-                            return (char) (((char)-1)*(((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
-                        }
-                    }
-                    break;
-                case 2:
-                    if (8 * sizeof(char) > 1 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) - 1 > 2 * PyLong_SHIFT) {
-                            return (char) ((((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
-                        }
-                    }
-                    break;
-                case -3:
-                    if (8 * sizeof(char) - 1 > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) - 1 > 3 * PyLong_SHIFT) {
-                            return (char) (((char)-1)*(((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
-                        }
-                    }
-                    break;
-                case 3:
-                    if (8 * sizeof(char) > 2 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) - 1 > 3 * PyLong_SHIFT) {
-                            return (char) ((((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
-                        }
-                    }
-                    break;
-                case -4:
-                    if (8 * sizeof(char) - 1 > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) - 1 > 4 * PyLong_SHIFT) {
-                            return (char) (((char)-1)*(((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
-                        }
-                    }
-                    break;
-                case 4:
-                    if (8 * sizeof(char) > 3 * PyLong_SHIFT) {
-                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
-                            __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
-                        } else if (8 * sizeof(char) - 1 > 4 * PyLong_SHIFT) {
-                            return (char) ((((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])));
-                        }
-                    }
-                    break;
-            }
-#endif
-            if (sizeof(char) <= sizeof(long)) {
-                __PYX_VERIFY_RETURN_INT_EXC(char, long, PyLong_AsLong(x))
-#ifdef HAVE_LONG_LONG
-            } else if (sizeof(char) <= sizeof(PY_LONG_LONG)) {
-                __PYX_VERIFY_RETURN_INT_EXC(char, PY_LONG_LONG, PyLong_AsLongLong(x))
-#endif
-            }
-        }
-        {
-#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
-            PyErr_SetString(PyExc_RuntimeError,
-                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
-#else
-            char val;
-            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
- #if PY_MAJOR_VERSION < 3
-            if (likely(v) && !PyLong_Check(v)) {
-                PyObject *tmp = v;
-                v = PyNumber_Long(tmp);
-                Py_DECREF(tmp);
-            }
- #endif
-            if (likely(v)) {
-                int one = 1; int is_little = (int)*(unsigned char *)&one;
-                unsigned char *bytes = (unsigned char *)&val;
-                int ret = _PyLong_AsByteArray((PyLongObject *)v,
-                                              bytes, sizeof(val),
-                                              is_little, !is_unsigned);
-                Py_DECREF(v);
-                if (likely(!ret))
-                    return val;
-            }
-#endif
-            return (char) -1;
-        }
-    } else {
-        char val;
-        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
-        if (!tmp) return (char) -1;
-        val = __Pyx_PyInt_As_char(tmp);
-        Py_DECREF(tmp);
-        return val;
-    }
-raise_overflow:
-    PyErr_SetString(PyExc_OverflowError,
-        "value too large to convert to char");
-    return (char) -1;
-raise_neg_overflow:
-    PyErr_SetString(PyExc_OverflowError,
-        "can't convert negative value to char");
-    return (char) -1;
-}
-
-/* CheckBinaryVersion */
-  static int __Pyx_check_binary_version(void) {
-    char ctversion[4], rtversion[4];
-    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
-    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
-    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
-        char message[200];
-        PyOS_snprintf(message, sizeof(message),
-                      "compiletime version %s of module '%.100s' "
-                      "does not match runtime version %s",
-                      ctversion, __Pyx_MODULE_NAME, rtversion);
-        return PyErr_WarnEx(NULL, message, 1);
-    }
-    return 0;
-}
-
-/* InitStrings */
-  static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
-    while (t->p) {
-        #if PY_MAJOR_VERSION < 3
-        if (t->is_unicode) {
-            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
-        } else if (t->intern) {
-            *t->p = PyString_InternFromString(t->s);
-        } else {
-            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
-        }
-        #else
-        if (t->is_unicode | t->is_str) {
-            if (t->intern) {
-                *t->p = PyUnicode_InternFromString(t->s);
-            } else if (t->encoding) {
-                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
-            } else {
-                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
-            }
-        } else {
-            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
-        }
-        #endif
-        if (!*t->p)
-            return -1;
-        if (PyObject_Hash(*t->p) == -1)
-            return -1;
-        ++t;
-    }
-    return 0;
-}
-
-static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
-    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
-}
-static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
-    Py_ssize_t ignore;
-    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
-}
-#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
-#if !CYTHON_PEP393_ENABLED
-static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
-    char* defenc_c;
-    PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
-    if (!defenc) return NULL;
-    defenc_c = PyBytes_AS_STRING(defenc);
-#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
-    {
-        char* end = defenc_c + PyBytes_GET_SIZE(defenc);
-        char* c;
-        for (c = defenc_c; c < end; c++) {
-            if ((unsigned char) (*c) >= 128) {
-                PyUnicode_AsASCIIString(o);
-                return NULL;
-            }
-        }
-    }
-#endif
-    *length = PyBytes_GET_SIZE(defenc);
-    return defenc_c;
-}
-#else
-static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
-    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
-#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
-    if (likely(PyUnicode_IS_ASCII(o))) {
-        *length = PyUnicode_GET_LENGTH(o);
-        return PyUnicode_AsUTF8(o);
-    } else {
-        PyUnicode_AsASCIIString(o);
-        return NULL;
-    }
-#else
-    return PyUnicode_AsUTF8AndSize(o, length);
-#endif
-}
-#endif
-#endif
-static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
-#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
-    if (
-#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
-            __Pyx_sys_getdefaultencoding_not_ascii &&
-#endif
-            PyUnicode_Check(o)) {
-        return __Pyx_PyUnicode_AsStringAndSize(o, length);
-    } else
-#endif
-#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
-    if (PyByteArray_Check(o)) {
-        *length = PyByteArray_GET_SIZE(o);
-        return PyByteArray_AS_STRING(o);
-    } else
-#endif
-    {
-        char* result;
-        int r = PyBytes_AsStringAndSize(o, &result, length);
-        if (unlikely(r < 0)) {
-            return NULL;
-        } else {
-            return result;
-        }
-    }
-}
-static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
-   int is_true = x == Py_True;
-   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
-   else return PyObject_IsTrue(x);
-}
-static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) {
-    int retval;
-    if (unlikely(!x)) return -1;
-    retval = __Pyx_PyObject_IsTrue(x);
-    Py_DECREF(x);
-    return retval;
-}
-static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
-#if PY_MAJOR_VERSION >= 3
-    if (PyLong_Check(result)) {
-        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
-                "__int__ returned non-int (type %.200s).  "
-                "The ability to return an instance of a strict subclass of int "
-                "is deprecated, and may be removed in a future version of Python.",
-                Py_TYPE(result)->tp_name)) {
-            Py_DECREF(result);
-            return NULL;
-        }
-        return result;
-    }
-#endif
-    PyErr_Format(PyExc_TypeError,
-                 "__%.4s__ returned non-%.4s (type %.200s)",
-                 type_name, type_name, Py_TYPE(result)->tp_name);
-    Py_DECREF(result);
-    return NULL;
-}
-static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
-#if CYTHON_USE_TYPE_SLOTS
-  PyNumberMethods *m;
-#endif
-  const char *name = NULL;
-  PyObject *res = NULL;
-#if PY_MAJOR_VERSION < 3
-  if (likely(PyInt_Check(x) || PyLong_Check(x)))
-#else
-  if (likely(PyLong_Check(x)))
-#endif
-    return __Pyx_NewRef(x);
-#if CYTHON_USE_TYPE_SLOTS
-  m = Py_TYPE(x)->tp_as_number;
-  #if PY_MAJOR_VERSION < 3
-  if (m && m->nb_int) {
-    name = "int";
-    res = m->nb_int(x);
-  }
-  else if (m && m->nb_long) {
-    name = "long";
-    res = m->nb_long(x);
-  }
-  #else
-  if (likely(m && m->nb_int)) {
-    name = "int";
-    res = m->nb_int(x);
-  }
-  #endif
-#else
-  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
-    res = PyNumber_Int(x);
-  }
-#endif
-  if (likely(res)) {
-#if PY_MAJOR_VERSION < 3
-    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
-#else
-    if (unlikely(!PyLong_CheckExact(res))) {
-#endif
-        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
-    }
-  }
-  else if (!PyErr_Occurred()) {
-    PyErr_SetString(PyExc_TypeError,
-                    "an integer is required");
-  }
-  return res;
-}
-static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
-  Py_ssize_t ival;
-  PyObject *x;
-#if PY_MAJOR_VERSION < 3
-  if (likely(PyInt_CheckExact(b))) {
-    if (sizeof(Py_ssize_t) >= sizeof(long))
-        return PyInt_AS_LONG(b);
-    else
-        return PyInt_AsSsize_t(b);
-  }
-#endif
-  if (likely(PyLong_CheckExact(b))) {
-    #if CYTHON_USE_PYLONG_INTERNALS
-    const digit* digits = ((PyLongObject*)b)->ob_digit;
-    const Py_ssize_t size = Py_SIZE(b);
-    if (likely(__Pyx_sst_abs(size) <= 1)) {
-        ival = likely(size) ? digits[0] : 0;
-        if (size == -1) ival = -ival;
-        return ival;
-    } else {
-      switch (size) {
-         case 2:
-           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
-             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
-           }
-           break;
-         case -2:
-           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
-             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
-           }
-           break;
-         case 3:
-           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
-             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
-           }
-           break;
-         case -3:
-           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
-             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
-           }
-           break;
-         case 4:
-           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
-             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
-           }
-           break;
-         case -4:
-           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
-             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
-           }
-           break;
-      }
-    }
-    #endif
-    return PyLong_AsSsize_t(b);
-  }
-  x = PyNumber_Index(b);
-  if (!x) return -1;
-  ival = PyInt_AsSsize_t(x);
-  Py_DECREF(x);
-  return ival;
-}
-static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) {
-  return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False);
-}
-static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
-    return PyInt_FromSize_t(ival);
-}
-
-
-#endif /* Py_PYTHON_H */
diff --git a/.ccls-cache/@home@xywei@Projects@pytential/pytential@qbx@target_specific@impl.c.blob b/.ccls-cache/@home@xywei@Projects@pytential/pytential@qbx@target_specific@impl.c.blob
deleted file mode 100644
index 138b77c88a8a6ae12e44d73e2baf4e32759a7baa..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

literal 288
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zMkR*7Jn05N#(#mNN$N+PyC()j#s>#`M!Cj^#5?=AI{E=sDJZ9;re)@(DqzYn$_dCB
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diff --git a/.gitignore b/.gitignore
index b450b3b7..0e5b9fc6 100644
--- a/.gitignore
+++ b/.gitignore
@@ -31,3 +31,4 @@ pytential/_git_rev.py
 
 *.so
 pytential/qbx/target_specific/impl.c
+.ccls-cache/
-- 
GitLab


From bb72821b12a6b7ce65d2ff87ad42e604ad93a92a Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Mon, 5 Jul 2021 23:44:55 -0500
Subject: [PATCH 29/38] Remove mem-use.log

---
 .gitignore       |  1 +
 test/mem-use.log | 80 ------------------------------------------------
 2 files changed, 1 insertion(+), 80 deletions(-)
 delete mode 100644 test/mem-use.log

diff --git a/.gitignore b/.gitignore
index 0e5b9fc6..e3905bbf 100644
--- a/.gitignore
+++ b/.gitignore
@@ -32,3 +32,4 @@ pytential/_git_rev.py
 *.so
 pytential/qbx/target_specific/impl.c
 .ccls-cache/
+mem-use.log
diff --git a/test/mem-use.log b/test/mem-use.log
deleted file mode 100644
index 30738a26..00000000
--- a/test/mem-use.log
+++ /dev/null
@@ -1,80 +0,0 @@
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-- 
GitLab


From c8be8b1c58e7b844ad3b1a5ec4e2f477c3620eb9 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Tue, 6 Jul 2021 09:12:21 -0500
Subject: [PATCH 30/38] Flake8 fixes

---
 examples/boundary-layer.py    | 6 ++++--
 pytential/qbx/__init__.py     | 4 ++--
 pytential/qbx/interactions.py | 2 +-
 3 files changed, 7 insertions(+), 5 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index d15a34b0..58d57151 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -122,13 +122,15 @@ def main(case="line", curve_fn=starfish, visualize=True):
 
     def op(**kwargs):
         kwargs.update(kernel_kwargs)
-        return sym.d_dx(ambient_dim=2, operand=sym.S(kernel, sym.var("sigma"), **kwargs))
+        return sym.d_dx(
+            ambient_dim=2, operand=sym.S(kernel, sym.var("sigma"), **kwargs))
         # return sym.D(kernel, sym.var("sigma"), **kwargs)
         # return sym.S(kernel, sym.var("sigma"), **kwargs)
 
     def op_asymp(**kwargs):
         kwargs.update(kernel_kwargs)
-        return sym.d_dx(ambient_dim=2, operand=sym.S(asymp_kernel, sym.var("sigma"), **kwargs))
+        return sym.d_dx(
+            ambient_dim=2, operand=sym.S(asymp_kernel, sym.var("sigma"), **kwargs))
         # return sym.D(asymp_kernel, sym.var("sigma"), **kwargs)
         # return sym.S(asymp_kernel, sym.var("sigma"), **kwargs)
 
diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 3881c478..69440f60 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -743,7 +743,8 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             value_dtype = self.density_discr.real_dtype
 
         base_kernel = single_valued(knl.get_base_kernel() for knl in source_kernels)
-        expansion=self.get_expansion_for_qbx_direct_eval(base_kernel, target_kernels)
+        expansion = self.get_expansion_for_qbx_direct_eval(
+            base_kernel, target_kernels)
 
         from sumpy.kernel import AsymptoticallyInformedKernel
         if self._use_qbmax is None or self._use_qbmax:
@@ -773,7 +774,6 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
 
         base_kernel = single_valued(knl.get_base_kernel() for knl in source_kernels)
 
-        from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         from sumpy.expansion.local import VolumeTaylorLocalExpansion
         from sumpy.kernel import AsymptoticallyInformedKernel, ExpaniosnClassReplacer
         ecr = ExpaniosnClassReplacer(VolumeTaylorLocalExpansion)
diff --git a/pytential/qbx/interactions.py b/pytential/qbx/interactions.py
index 6f975166..99f8e73a 100644
--- a/pytential/qbx/interactions.py
+++ b/pytential/qbx/interactions.py
@@ -206,7 +206,7 @@ class P2QBMAXLFromCSR(P2EBase):
                                     {dup=idim}
                             """] + [f"<> strength_{i} = strengths[{i}, isrc]" for
                             i in set(self.strength_usage)]
-                            + self.get_loopy_instructions(isotropic_expansion=False) + ["""
+                + self.get_loopy_instructions(isotropic_expansion=False) + ["""
                         end
                     end
 
-- 
GitLab


From 98b15ac8e736536c011cacd5c24f4495220433f3 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Fri, 9 Jul 2021 09:32:58 -0500
Subject: [PATCH 31/38] Use ExpansionClassReplacer

---
 pytential/qbx/__init__.py | 35 +++++++++++------------------------
 1 file changed, 11 insertions(+), 24 deletions(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 69440f60..4d201cba 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -549,16 +549,12 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
             from pytential.qbx.fmm import \
                     QBXSumpyExpansionWranglerCodeContainer
 
-            from sumpy.kernel import AsymptoticallyInformedKernel
             if self._use_qbmax is None or self._use_qbmax:
-                source_kernels = [
-                    sk.replace_expansion_class(local_expn_class)
-                    if isinstance(sk, AsymptoticallyInformedKernel) else sk
-                    for sk in source_kernels]
-                target_kernels = [
-                    tk.replace_expansion_class(local_expn_class)
-                    if isinstance(tk, AsymptoticallyInformedKernel) else tk
-                    for tk in target_kernels]
+                from sumpy.kernel import (AsymptoticallyInformedKernel,
+                                          ExpaniosnClassReplacer)
+                ecr = ExpaniosnClassReplacer(local_expn_class)
+                source_kernels = tuple(ecr(sk) for sk in source_kernels)
+                target_kernels = tuple(ecr(tk) for tk in target_kernels)
                 if any(isinstance(tk, AsymptoticallyInformedKernel)
                        for tk in target_kernels) or any(
                            isinstance(sk, AsymptoticallyInformedKernel)
@@ -746,16 +742,11 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         expansion = self.get_expansion_for_qbx_direct_eval(
             base_kernel, target_kernels)
 
-        from sumpy.kernel import AsymptoticallyInformedKernel
         if self._use_qbmax is None or self._use_qbmax:
-            source_kernels = [
-                sk.replace_expansion_class(type(expansion))
-                if isinstance(sk, AsymptoticallyInformedKernel) else sk
-                for sk in source_kernels]
-            target_kernels = [
-                tk.replace_expansion_class(type(expansion))
-                if isinstance(tk, AsymptoticallyInformedKernel) else tk
-                for tk in target_kernels]
+            from sumpy.kernel import ExpaniosnClassReplacer
+            ecr = ExpaniosnClassReplacer(type(expansion))
+            source_kernels = tuple(ecr(sk) for sk in source_kernels)
+            target_kernels = tuple(ecr(tk) for tk in target_kernels)
 
         from sumpy.qbx import LayerPotential
         return LayerPotential(self.cl_context,
@@ -777,12 +768,8 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         from sumpy.expansion.local import VolumeTaylorLocalExpansion
         from sumpy.kernel import AsymptoticallyInformedKernel, ExpaniosnClassReplacer
         ecr = ExpaniosnClassReplacer(VolumeTaylorLocalExpansion)
-        source_kernels = [ecr(knl)
-                          if isinstance(knl, AsymptoticallyInformedKernel) else knl
-                          for knl in source_kernels]
-        target_kernels = [ecr(knl)
-                          if isinstance(knl, AsymptoticallyInformedKernel) else knl
-                          for knl in target_kernels]
+        source_kernels = tuple(ecr(knl) for knl in source_kernels)
+        target_kernels = tuple(ecr(knl) for knl in target_kernels)
 
         from pytential.qbx.direct import LayerPotentialOnTargetAndCenterSubset
         return LayerPotentialOnTargetAndCenterSubset(
-- 
GitLab


From a4276340caed184d24e02eec2429d2daeb050d3c Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Fri, 9 Jul 2021 14:49:10 -0500
Subject: [PATCH 32/38] Fix D with volume-direct

---
 pytential/qbx/direct.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/pytential/qbx/direct.py b/pytential/qbx/direct.py
index 3ee33826..f60b6979 100644
--- a/pytential/qbx/direct.py
+++ b/pytential/qbx/direct.py
@@ -65,6 +65,7 @@ class LayerPotentialOnTargetAndCenterSubset(LayerPotentialBase):
                 shape="ntargets_total", order="C")
             for i in range(len(self.target_kernels))])
 
+        # scaling at target for qbmax
         sats = []
         sat_insns_data = []
         for iknl, knl in enumerate(self.target_kernels):
-- 
GitLab


From 06f426f365542ba54f7dca13000040116a3d914d Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Fri, 9 Jul 2021 15:02:39 -0500
Subject: [PATCH 33/38] Fix D with volume expansion and FMM

---
 pytential/qbx/interactions.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/pytential/qbx/interactions.py b/pytential/qbx/interactions.py
index 99f8e73a..6e82487f 100644
--- a/pytential/qbx/interactions.py
+++ b/pytential/qbx/interactions.py
@@ -172,7 +172,9 @@ class P2QBMAXLFromCSR(P2EBase):
                     lp.ValueArg("ncenters", np.int32),
                     lp.ValueArg("nsources", np.int32),
                     "..."
-                ] + gather_loopy_source_arguments([self.expansion]))
+                ] + gather_loopy_source_arguments(
+                        self.source_kernels + (self.expansion,))
+        )
 
         loopy_knl = lp.make_kernel(
                 [
-- 
GitLab


From 1949a663f518c6e3955f9a37007ad150e5a1646e Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Fri, 9 Jul 2021 18:43:29 -0500
Subject: [PATCH 34/38] Flake8 fixes

---
 pytential/qbx/__init__.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 4d201cba..6aee74c0 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -766,7 +766,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         base_kernel = single_valued(knl.get_base_kernel() for knl in source_kernels)
 
         from sumpy.expansion.local import VolumeTaylorLocalExpansion
-        from sumpy.kernel import AsymptoticallyInformedKernel, ExpaniosnClassReplacer
+        from sumpy.kernel import ExpaniosnClassReplacer
         ecr = ExpaniosnClassReplacer(VolumeTaylorLocalExpansion)
         source_kernels = tuple(ecr(knl) for knl in source_kernels)
         target_kernels = tuple(ecr(knl) for knl in target_kernels)
-- 
GitLab


From 9fcb41c85c8fc5e982893218da9d3615009e9766 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Fri, 9 Jul 2021 22:23:21 -0500
Subject: [PATCH 35/38] Add qbmax tests: single layer, double layer, with or
 w/t fmm

---
 test/test_layer_pot.py | 38 ++++++++++++++++++++++++++++++++------
 1 file changed, 32 insertions(+), 6 deletions(-)

diff --git a/test/test_layer_pot.py b/test/test_layer_pot.py
index f9ce9c83..9854f5a3 100644
--- a/test/test_layer_pot.py
+++ b/test/test_layer_pot.py
@@ -77,7 +77,8 @@ def test_geometry(actx_factory):
 # {{{ test off-surface eval
 
 @pytest.mark.parametrize("use_fmm", [True, False])
-def test_off_surface_eval(actx_factory, use_fmm, visualize=False):
+@pytest.mark.parametrize("use_qbmax", [True, False])
+def test_off_surface_eval(actx_factory, use_fmm, use_qbmax, visualize=False):
     logging.basicConfig(level=logging.INFO)
 
     actx = actx_factory()
@@ -120,7 +121,15 @@ def test_off_surface_eval(actx_factory, use_fmm, visualize=False):
     density_discr = places.get_discretization(places.auto_source.geometry)
 
     from sumpy.kernel import LaplaceKernel
-    op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=-2)
+    if use_qbmax:
+        from sumpy.kernel import AsymptoticallyInformedKernel
+        import sympy as sp
+        # no, this scaling doesn't do anything but test the machinary
+        knl = AsymptoticallyInformedKernel(
+            LaplaceKernel(2), sp.exp(-sp.Symbol("dist")))
+    else:
+        knl = LaplaceKernel(2)
+    op = sym.D(knl, sym.var("sigma"), qbx_forced_limit=-2)
 
     sigma = density_discr.zeros(actx) + 1
     fld_in_vol = bind(places, op)(actx, sigma=sigma)
@@ -143,7 +152,8 @@ def test_off_surface_eval(actx_factory, use_fmm, visualize=False):
 
 # {{{ test off-surface eval vs direct
 
-def test_off_surface_eval_vs_direct(actx_factory,  do_plot=False):
+@pytest.mark.parametrize("use_qbmax", [True, False])
+def test_off_surface_eval_vs_direct(actx_factory, use_qbmax, do_plot=False):
     logging.basicConfig(level=logging.INFO)
 
     actx = actx_factory()
@@ -183,6 +193,14 @@ def test_off_surface_eval_vs_direct(actx_factory,  do_plot=False):
     from pytential.target import PointsTarget
     ptarget = PointsTarget(actx.freeze(actx.from_numpy(fplot.points)))
     from sumpy.kernel import LaplaceKernel
+    if use_qbmax:
+        from sumpy.kernel import AsymptoticallyInformedKernel
+        import sympy as sp
+        # no, this scaling doesn't do anything but test the machinary
+        knl = AsymptoticallyInformedKernel(
+            LaplaceKernel(2), sp.exp(-sp.Symbol("dist")))
+    else:
+        knl = LaplaceKernel(2)
 
     places = GeometryCollection({
         "direct_qbx": direct_qbx,
@@ -193,7 +211,7 @@ def test_off_surface_eval_vs_direct(actx_factory,  do_plot=False):
     fmm_density_discr = places.get_discretization("fmm_qbx")
 
     from pytential.qbx import QBXTargetAssociationFailedException
-    op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None)
+    op = sym.D(knl, sym.var("sigma"), qbx_forced_limit=None)
     try:
         direct_sigma = direct_density_discr.zeros(actx) + 1
         direct_fld_in_vol = bind(places, op,
@@ -229,7 +247,8 @@ def test_off_surface_eval_vs_direct(actx_factory,  do_plot=False):
 
 # {{{
 
-def test_single_plus_double_with_single_fmm(actx_factory,  do_plot=False):
+@pytest.mark.parametrize("use_qbmax", [True, False])
+def test_single_plus_double_with_single_fmm(actx_factory, use_qbmax, do_plot=False):
     logging.basicConfig(level=logging.INFO)
 
     actx = actx_factory()
@@ -269,6 +288,14 @@ def test_single_plus_double_with_single_fmm(actx_factory,  do_plot=False):
     from pytential.target import PointsTarget
     ptarget = PointsTarget(actx.freeze(actx.from_numpy(fplot.points)))
     from sumpy.kernel import LaplaceKernel
+    if use_qbmax:
+        from sumpy.kernel import AsymptoticallyInformedKernel
+        import sympy as sp
+        # no, this scaling doesn't do anything but test the machinary
+        knl = AsymptoticallyInformedKernel(
+            LaplaceKernel(2), sp.exp(-sp.Symbol("dist")))
+    else:
+        knl = LaplaceKernel(2)
 
     places = GeometryCollection({
         "direct_qbx": direct_qbx,
@@ -278,7 +305,6 @@ def test_single_plus_double_with_single_fmm(actx_factory,  do_plot=False):
     direct_density_discr = places.get_discretization("direct_qbx")
     fmm_density_discr = places.get_discretization("fmm_qbx")
 
-    knl = LaplaceKernel(2)
     from pytential.qbx import QBXTargetAssociationFailedException
     op_d = sym.D(knl, sym.var("sigma"), qbx_forced_limit=None)
     op_s = sym.S(knl, sym.var("sigma"), qbx_forced_limit=None)
-- 
GitLab


From 255404b8f7aceb73d3d12607f341f617bf33be7c Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Sat, 10 Jul 2021 12:53:56 -0500
Subject: [PATCH 36/38] Fix scaling expression getter

---
 pytential/qbx/__init__.py     | 4 ++--
 pytential/qbx/interactions.py | 8 +++++---
 2 files changed, 7 insertions(+), 5 deletions(-)

diff --git a/pytential/qbx/__init__.py b/pytential/qbx/__init__.py
index 6aee74c0..0ff61fe1 100644
--- a/pytential/qbx/__init__.py
+++ b/pytential/qbx/__init__.py
@@ -752,7 +752,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
         return LayerPotential(self.cl_context,
                     expansion=expansion,
                     target_kernels=target_kernels, source_kernels=source_kernels,
-                    value_dtypes=value_dtype)
+                    value_dtypes=value_dtype, _use_qbmax=self._use_qbmax)
 
     @memoize_method
     def get_lpot_applier_on_tgt_subset(self, target_kernels, source_kernels):
@@ -776,7 +776,7 @@ class QBXLayerPotentialSource(LayerPotentialSourceBase):
                 self.cl_context,
                 expansion=VolumeTaylorLocalExpansion(base_kernel, self.qbx_order),
                 target_kernels=target_kernels, source_kernels=source_kernels,
-                value_dtypes=value_dtype)
+                value_dtypes=value_dtype, _use_qbmax=self._use_qbmax)
 
     @memoize_method
     def get_qbx_target_numberer(self, dtype):
diff --git a/pytential/qbx/interactions.py b/pytential/qbx/interactions.py
index 6e82487f..afedc65d 100644
--- a/pytential/qbx/interactions.py
+++ b/pytential/qbx/interactions.py
@@ -563,10 +563,12 @@ class QBMAXL2P(E2PBase):
         ncoeffs = len(self.expansion)
 
         self._vector_names.add("normal")
-        loopy_insns, result_names = self.get_loopy_insns_and_result_names()
+        loopy_insns, result_names = self.get_loopy_insns_and_result_names(
+            use_qbmax=True)
 
-        sat_exprs = [knl.get_scaling_expression(None, type(self.expansion))
-                     for knl in self.kernels]
+        from sumpy.kernel import AsymptoticScalingGetter
+        asg = AsymptoticScalingGetter()
+        sat_exprs = [asg(knl) for knl in self.kernels]
         sats = [f"sat{i} * " for i in range(len(result_names))]
         sat_names = [f"sat{i}" for i in range(len(result_names))]
 
-- 
GitLab


From c176f3ff5a427c13bbe1483a328e978fcbf9b96c Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Sat, 10 Jul 2021 13:09:46 -0500
Subject: [PATCH 37/38] Update qbmax example

---
 examples/boundary-layer.py | 115 +++++++++++++++++++++++++++----------
 1 file changed, 84 insertions(+), 31 deletions(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index 58d57151..96fb0a72 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -28,9 +28,9 @@ from meshmode.discretization.connection import (
 target_order = 16
 qbx_order = 5
 coarse_nelements = 20
-mode_nr = 3
+mode_nr = 23  # frequency of the source density as a cos mode
 
-k = 10 + 100j
+k = 100 + 100j
 
 
 class VolumeMultipoleLineLocalTaylorExpansionFactory(ExpansionFactoryBase):
@@ -50,9 +50,23 @@ def main(case="line", curve_fn=starfish, visualize=True):
     import logging
     logging.basicConfig(level=logging.WARN)  # INFO for more progress info
 
+    if curve_fn is not None:
+        dim = 2
+    else:
+        dim = 3
+
+    # case for expansion type, subcase for operator type
+    if isinstance(case, tuple):
+        case, subcase = case
+    else:
+        subcase = "S"
+
+    print(f"Running case {case}:{subcase}, dim={dim}")
+
     if case == "line":
         fmm_order = False  # cannot use FMM here
-        n_refine_cycles = 5
+        if dim == 2:
+            n_refine_cycles = 5
         expn_factory = VolumeMultipoleLineLocalTaylorExpansionFactory()
     elif case[:6] == "volume":
         if case[6:] == "-direct":
@@ -62,20 +76,25 @@ def main(case="line", curve_fn=starfish, visualize=True):
         expn_factory = VolumeTaylorExpansionFactory()
 
         if fmm_order:
-            n_refine_cycles = 7
+            if dim == 2:
+                n_refine_cycles = 7
         else:
-            n_refine_cycles = 5
+            if dim == 2:
+                n_refine_cycles = 5
     else:
         raise ValueError
 
     cl_ctx = cl.create_some_context()
     queue = cl.CommandQueue(cl_ctx)
 
-    from meshmode.mesh.generation import make_curve_mesh
-    base_mesh = make_curve_mesh(
-            curve_fn,
-            np.linspace(0, 1, coarse_nelements+1),
-            target_order)
+    if dim == 2:
+        from meshmode.mesh.generation import make_curve_mesh
+        base_mesh = make_curve_mesh(
+                curve_fn,
+                np.linspace(0, 1, coarse_nelements+1),
+                target_order)
+    elif dim == 3:
+        pass
     refiner = RefinerWithoutAdjacency(base_mesh)
 
     if case[:6] == "volume":
@@ -83,22 +102,23 @@ def main(case="line", curve_fn=starfish, visualize=True):
         if 1:
             # in the volume
             from sumpy.visualization import FieldPlotter
-            fplot = FieldPlotter(np.zeros(2), extent=2, npoints=100)
+            fplot = FieldPlotter(np.zeros(dim), extent=2, npoints=100)
             targets_dev = cl.array.to_device(queue, fplot.points)
         else:
             # near surface
+            assert dim == 2
             target_mesh = make_curve_mesh(curve_fn, np.linspace(0, 1, 83), 1)
             targets_dev = cl.array.to_device(
                 queue, np.ascontiguousarray(target_mesh.vertices))
 
     if k:
         if k.imag:
-            kernel = HelmholtzKernel(2, allow_evanescent=True)
+            kernel = HelmholtzKernel(dim, allow_evanescent=True)
         else:
-            kernel = HelmholtzKernel(2, allow_evanescent=False)
+            kernel = HelmholtzKernel(dim, allow_evanescent=False)
         kernel_kwargs = {"k": sym.var("k")}
     else:
-        kernel = LaplaceKernel(2)
+        kernel = LaplaceKernel(dim)
         kernel_kwargs = {}
 
     from pytential.qbx import QBXLayerPotentialSource
@@ -122,17 +142,35 @@ def main(case="line", curve_fn=starfish, visualize=True):
 
     def op(**kwargs):
         kwargs.update(kernel_kwargs)
-        return sym.d_dx(
-            ambient_dim=2, operand=sym.S(kernel, sym.var("sigma"), **kwargs))
-        # return sym.D(kernel, sym.var("sigma"), **kwargs)
-        # return sym.S(kernel, sym.var("sigma"), **kwargs)
+        if subcase == "S":
+            return sym.S(kernel, sym.var("sigma"), **kwargs)
+        elif subcase == "D":
+            return sym.D(kernel, sym.var("sigma"), **kwargs)
+        elif subcase == "dS":
+            return sym.d_dx(
+                ambient_dim=dim, operand=sym.S(kernel, sym.var("sigma"), **kwargs))
+        elif subcase == "dD":
+            return sym.d_dx(
+                ambient_dim=dim, operand=sym.D(kernel, sym.var("sigma"), **kwargs))
+        else:
+            raise ValueError(f"unrecognized operator type: {subcase}")
 
     def op_asymp(**kwargs):
         kwargs.update(kernel_kwargs)
-        return sym.d_dx(
-            ambient_dim=2, operand=sym.S(asymp_kernel, sym.var("sigma"), **kwargs))
-        # return sym.D(asymp_kernel, sym.var("sigma"), **kwargs)
-        # return sym.S(asymp_kernel, sym.var("sigma"), **kwargs)
+        if subcase == "S":
+            return sym.S(asymp_kernel, sym.var("sigma"), **kwargs)
+        elif subcase == "D":
+            return sym.D(asymp_kernel, sym.var("sigma"), **kwargs)
+        elif subcase == "dS":
+            return sym.d_dx(
+                ambient_dim=dim, operand=sym.S(
+                    asymp_kernel, sym.var("sigma"), **kwargs))
+        elif subcase == "dD":
+            return sym.d_dx(
+                ambient_dim=dim, operand=sym.D(
+                    asymp_kernel, sym.var("sigma"), **kwargs))
+        else:
+            raise ValueError(f"unrecognized operator type: {subcase}")
 
     conns = []
     ns = []
@@ -186,6 +224,9 @@ def main(case="line", curve_fn=starfish, visualize=True):
         nodes = thaw(actx, density_discr.nodes())
         angle = actx.np.arctan2(nodes[1], nodes[0])
         sigma = actx.np.cos(mode_nr*angle)
+        if dim == 3:
+            angle2 = actx.np.arctan2(nodes[2], nodes[0])
+            sigma *= actx.np.cos(mode_nr*angle2)
 
         if isinstance(kernel, HelmholtzKernel):
             k_val = np.complex128(k)
@@ -193,9 +234,10 @@ def main(case="line", curve_fn=starfish, visualize=True):
             k_val = np.float64(k)
 
         if case == "line":
-            fld_ref = bind(
-                places_ref, op(source="qbx", qbx_forced_limit=-1))(
-                    actx, sigma=sigma, k=k_val)
+            if 1:
+                fld_ref = bind(
+                    places_ref, op(source="qbx", qbx_forced_limit=-1))(
+                        actx, sigma=sigma, k=k_val)
             fld = bind(
                 places, op_asymp(source="qbx", qbx_forced_limit=-1))(
                     actx, sigma=sigma, k=k_val)
@@ -205,9 +247,10 @@ def main(case="line", curve_fn=starfish, visualize=True):
             flds_ref.append(fld_ref)
 
         elif case[:6] == "volume":
-            fld_ref = bind(places_ref, op(
-                source="qbx", target="targets", qbx_forced_limit=None))(
-                    actx, sigma=sigma, k=k_val)
+            if 1:
+                fld_ref = bind(places_ref, op(
+                    source="qbx", target="targets", qbx_forced_limit=None))(
+                        actx, sigma=sigma, k=k_val)
             fld = bind(places, op_asymp(
                 source="qbx", target="targets", qbx_forced_limit=None))(
                     actx, sigma=sigma, k=k_val)
@@ -250,11 +293,12 @@ def main(case="line", curve_fn=starfish, visualize=True):
     print(f"Last diff = {last_diff}")
 
     # total length of the boundary curve
-    arclen = bind(places, sym.integral(2, 1, operand=1, dofdesc="qbx"))(actx)
+    arclen = bind(places, sym.integral(dim, dim-1, operand=1, dofdesc="qbx"))(actx)
 
     from pytools.convergence import EOCRecorder
     eocrec = EOCRecorder()
     eocrec_ref = EOCRecorder()
+    eocrec_crossref = EOCRecorder()
     for iexp in range(len(fs) - 1):
         eocrec.add_data_point(
             arclen/ns[iexp],
@@ -262,17 +306,26 @@ def main(case="line", curve_fn=starfish, visualize=True):
         eocrec_ref.add_data_point(
             arclen/ns[iexp],
             inorm(fs_ref[iexp] - fs_ref[-1]) / inorm(fs_ref[-1]))
+        eocrec_crossref.add_data_point(
+            arclen/ns[iexp],
+            inorm(fs[iexp] - fs_ref[-1]) / inorm(fs_ref[-1]))
+
 
     print("\nQBX (without scaling):")
     print(eocrec_ref)
 
-    print("\nTAQBX (with scaling):")
+    print("\nQBMAX against QBX:")
+    print(eocrec_crossref)
+
+    print("\nQBMAX (with scaling):")
     print(eocrec)
 
 
 if __name__ == "__main__":
     import sys
-    if len(sys.argv) > 1:
+    if len(sys.argv) == 2:
         main(sys.argv[1])
+    elif len(sys.argv) == 3:
+        main((sys.argv[1], sys.argv[2]))
     else:
         main()
-- 
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From 3a661814a274e1a673cf43c2873c485f8cbcf2a3 Mon Sep 17 00:00:00 2001
From: xywei <wxy0516@gmail.com>
Date: Sat, 10 Jul 2021 13:34:28 -0500
Subject: [PATCH 38/38] Flake8 fix

---
 examples/boundary-layer.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/examples/boundary-layer.py b/examples/boundary-layer.py
index 96fb0a72..05bedaea 100644
--- a/examples/boundary-layer.py
+++ b/examples/boundary-layer.py
@@ -310,7 +310,6 @@ def main(case="line", curve_fn=starfish, visualize=True):
             arclen/ns[iexp],
             inorm(fs[iexp] - fs_ref[-1]) / inorm(fs_ref[-1]))
 
-
     print("\nQBX (without scaling):")
     print(eocrec_ref)
 
-- 
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