from __future__ import annotations __copyright__ = "Copyright (C) 2017 Andreas Kloeckner" __license__ = """ Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ import logging import sys from collections.abc import Callable from dataclasses import dataclass from typing import Any import numpy as np import numpy.linalg as la import pytest from arraycontext import pytest_generate_tests_for_array_contexts import sumpy.symbolic as sym import sumpy.toys as t from sumpy.array_context import PytestPyOpenCLArrayContextFactory, _acf # noqa: F401 from sumpy.expansion import ( FullExpansionTermsWrangler, LinearPDEBasedExpansionTermsWrangler, ) from sumpy.expansion.diff_op import ( as_scalar_pde, concat, curl, diff, divergence, gradient, laplacian, make_identity_diff_op, ) from sumpy.kernel import ( BiharmonicKernel, ElasticityKernel, ExpressionKernel, HelmholtzKernel, LaplaceKernel, LineOfCompressionKernel, StokesletKernel, StressletKernel, YukawaKernel, ) logger = logging.getLogger(__name__) pytest_generate_tests = pytest_generate_tests_for_array_contexts([ PytestPyOpenCLArrayContextFactory, ]) # {{{ pde check for kernels class KernelInfo: def __init__(self, kernel, **kwargs): self.kernel = kernel self.extra_kwargs = kwargs diff_op = self.kernel.get_pde_as_diff_op() assert len(diff_op.eqs) == 1 eq = diff_op.eqs[0] self.eq = eq def pde_func(self, cp, pot): subs_dict = {sym.Symbol(k): v for k, v in self.extra_kwargs.items()} result = 0 for ident, coeff in self.eq.items(): lresult = pot for axis, nderivs in enumerate(ident.mi): lresult = cp.diff(axis, lresult, nderivs) result += lresult*float(sym.sympify(coeff).xreplace(subs_dict)) return result @property def nderivs(self): return max(sum(ident.mi) for ident in self.eq) @pytest.mark.parametrize("knl_info", [ KernelInfo(BiharmonicKernel(2)), KernelInfo(BiharmonicKernel(3)), KernelInfo(YukawaKernel(2), lam=5), KernelInfo(YukawaKernel(3), lam=5), KernelInfo(LaplaceKernel(2)), KernelInfo(LaplaceKernel(3)), KernelInfo(HelmholtzKernel(2), k=5), KernelInfo(HelmholtzKernel(3), k=5), KernelInfo(StokesletKernel(2, 0, 1), mu=5), KernelInfo(StokesletKernel(2, 1, 1), mu=5), KernelInfo(StokesletKernel(3, 0, 1), mu=5), KernelInfo(StokesletKernel(3, 1, 1), mu=5), KernelInfo(StressletKernel(2, 0, 0, 0), mu=5), KernelInfo(StressletKernel(2, 0, 0, 1), mu=5), KernelInfo(StressletKernel(3, 0, 0, 0), mu=5), KernelInfo(StressletKernel(3, 0, 0, 1), mu=5), KernelInfo(StressletKernel(3, 0, 1, 2), mu=5), KernelInfo(ElasticityKernel(2, 0, 1), mu=5, nu=0.2), KernelInfo(ElasticityKernel(2, 0, 0), mu=5, nu=0.2), KernelInfo(ElasticityKernel(3, 0, 1), mu=5, nu=0.2), KernelInfo(ElasticityKernel(3, 0, 0), mu=5, nu=0.2), KernelInfo(LineOfCompressionKernel(3, 0), mu=5, nu=0.2), KernelInfo(LineOfCompressionKernel(3, 1), mu=5, nu=0.2), ]) def test_pde_check_kernels(actx_factory, knl_info, order=5): actx = actx_factory() dim = knl_info.kernel.dim tctx = t.ToyContext(actx.context, knl_info.kernel, extra_source_kwargs=knl_info.extra_kwargs) rng = np.random.default_rng(42) pt_src = t.PointSources( tctx, rng.random(size=(dim, 50)) - 0.5, np.ones(50)) from pytools.convergence import EOCRecorder from sumpy.point_calculus import CalculusPatch eoc_rec = EOCRecorder() for h in [0.1, 0.05, 0.025]: cp = CalculusPatch(np.array([1, 0, 0])[:dim], h=h, order=order) pot = pt_src.eval(cp.points) pde = knl_info.pde_func(cp, pot) err = la.norm(pde) eoc_rec.add_data_point(h, err) logger.info("eoc:\n%s", eoc_rec) assert eoc_rec.order_estimate() > order - knl_info.nderivs + 1 - 0.1 # }}} # {{{ test_pde_check @pytest.mark.parametrize("dim", [1, 2, 3]) def test_pde_check(dim, order=4): from pytools.convergence import EOCRecorder from sumpy.point_calculus import CalculusPatch for iaxis in range(dim): eoc_rec = EOCRecorder() for h in [0.1, 0.01, 0.001]: cp = CalculusPatch(np.array([3, 0, 0])[:dim], h=h, order=order) df_num = cp.diff(iaxis, np.sin(10*cp.points[iaxis])) df_true = 10*np.cos(10*cp.points[iaxis]) err = la.norm(df_num-df_true) eoc_rec.add_data_point(h, err) logger.info("eoc:\n%s", eoc_rec) assert eoc_rec.order_estimate() > order-2-0.1 # }}} # {{{ test_order_finder @dataclass(frozen=True) class FakeTree: dimensions: int root_extent: float stick_out_factor: float @pytest.mark.parametrize("knl", [ LaplaceKernel(2), HelmholtzKernel(2), LaplaceKernel(3), HelmholtzKernel(3)]) def test_order_finder(knl): from sumpy.expansion.level_to_order import SimpleExpansionOrderFinder ofind = SimpleExpansionOrderFinder(1e-5) tree = FakeTree(knl.dim, 200, 0.5) orders = [ ofind(knl, frozenset([("k", 5)]), tree, level) for level in range(30)] logger.info("orders: %s", orders) # Order should not increase with level assert (np.diff(orders) <= 0).all() @pytest.mark.parametrize("knl", [ LaplaceKernel(2), HelmholtzKernel(2), LaplaceKernel(3), HelmholtzKernel(3)]) def test_fmmlib_order_finder(knl): pytest.importorskip("pyfmmlib") from sumpy.expansion.level_to_order import FMMLibExpansionOrderFinder ofind = FMMLibExpansionOrderFinder(1e-5) tree = FakeTree(knl.dim, 200, 0.5) orders = [ ofind(knl, frozenset([("k", 5)]), tree, level) for level in range(30)] logger.info("orders: %s", orders) # Order should not increase with level assert (np.diff(orders) <= 0).all() # }}} # {{{ expansion toys p2e2e2p test cases def approx_convergence_factor(orders, errors): poly = np.polyfit(orders, np.log(errors), deg=1) return np.exp(poly[0]) @dataclass(frozen=True) class P2E2E2PTestCase: source: np.ndarray target: np.ndarray center1: np.ndarray center2: np.ndarray expansion1: Callable[..., Any] expansion2: Callable[..., Any] conv_factor: str m2l_use_fft: bool = False @property def dim(self): return len(self.source) P2E2E2P_TEST_CASES = ( # local to local, 3D P2E2E2PTestCase( source=np.array([3., 4., 5.]), center1=np.array([1., 0., 0.]), center2=np.array([1., 3., 0.]), target=np.array([1., 1., 1.]), expansion1=t.local_expand, expansion2=t.local_expand, conv_factor="norm(t-c1)/norm(s-c1)"), # multipole to multipole, 3D P2E2E2PTestCase( source=np.array([1., 1., 1.]), center1=np.array([1., 0., 0.]), center2=np.array([1., 0., 3.]), target=np.array([3., 4., 5.]), expansion1=t.multipole_expand, expansion2=t.multipole_expand, conv_factor="norm(s-c2)/norm(t-c2)"), # multipole to local, 3D P2E2E2PTestCase( source=np.array([-2., 2., 1.]), center1=np.array([-2., 5., 3.]), center2=np.array([0., 0., 0.]), target=np.array([0., 0., -1]), expansion1=t.multipole_expand, expansion2=t.local_expand, conv_factor="norm(t-c2)/(norm(c2-c1)-norm(c1-s))"), # multipole to local, 3D with FFT P2E2E2PTestCase( source=np.array([-2., 2., 1.]), center1=np.array([-2., 5., 3.]), center2=np.array([0., 0., 0.]), target=np.array([0., 0., -1]), expansion1=t.multipole_expand, expansion2=t.local_expand, m2l_use_fft=True, conv_factor="norm(t-c2)/(norm(c2-c1)-norm(c1-s))"), ) # }}} # {{{ test_toy_p2e2e2p ORDERS_P2E2E2P = (3, 4, 5) RTOL_P2E2E2P = 1e-2 @pytest.mark.parametrize("case", P2E2E2P_TEST_CASES) def test_toy_p2e2e2p(actx_factory, case): dim = case.dim src = case.source.reshape(dim, -1) tgt = case.target.reshape(dim, -1) from pymbolic import evaluate, parse case_conv_factor = evaluate(parse(case.conv_factor), { "s": case.source, "c1": case.center1, "c2": case.center2, "t": case.target, "norm": la.norm, }) if not 0 <= case_conv_factor <= 1: raise ValueError( f"convergence factor not in valid range: {case_conv_factor}") from sumpy.expansion import VolumeTaylorExpansionFactory actx = actx_factory() ctx = t.ToyContext(actx.context, LaplaceKernel(dim), expansion_factory=VolumeTaylorExpansionFactory(), m2l_use_fft=case.m2l_use_fft) errors = [] src_pot = t.PointSources(ctx, src, weights=np.array([1.])) pot_actual = src_pot.eval(tgt).item() for order in ORDERS_P2E2E2P: expn = case.expansion1(src_pot, case.center1, order=order) expn2 = case.expansion2(expn, case.center2, order=order) pot_p2e2e2p = expn2.eval(tgt).item() errors.append(np.abs(pot_actual - pot_p2e2e2p)) conv_factor = approx_convergence_factor(1 + np.array(ORDERS_P2E2E2P), errors) assert conv_factor <= min(1, case_conv_factor * (1 + RTOL_P2E2E2P)), \ (conv_factor, case_conv_factor * (1 + RTOL_P2E2E2P)) # }}} # {{{ test_cse_matvec def test_cse_matvec(): from sumpy.expansion import CSEMatVecOperator input_coeffs = [ [(0, 2)], [], [(1, 1)], [(1, 9)], ] output_coeffs = [ [], [(0, 3)], [], [(2, 7), (1, 5)], ] op = CSEMatVecOperator(input_coeffs, output_coeffs, shape=(4, 2)) m = np.array([[2, 0], [6, 0], [0, 1], [30, 16]]) rng = np.random.default_rng(42) vec = rng.random(2) expected_result = m @ vec actual_result = op.matvec(vec) assert np.allclose(expected_result, actual_result) vec = rng.random(4) expected_result = m.T @ vec actual_result = op.transpose_matvec(vec) assert np.allclose(expected_result, actual_result) # }}} # {{{ test_diff_op_stokes def test_diff_op_stokes(): from sumpy.symbolic import Function, symbols diff_op = make_identity_diff_op(3, 4) u = diff_op[:3] p = diff_op[3] pde = concat(laplacian(u) - gradient(p), divergence(u)) actual_output = pde.to_sym() x, y, z = syms = symbols("x0, x1, x2") funcs = symbols("f0, f1, f2, f3", cls=Function) u, v, w, p = (f(*syms) for f in funcs) eq1 = u.diff(x, x) + u.diff(y, y) + u.diff(z, z) - p.diff(x) eq2 = v.diff(x, x) + v.diff(y, y) + v.diff(z, z) - p.diff(y) eq3 = w.diff(x, x) + w.diff(y, y) + w.diff(z, z) - p.diff(z) eq4 = u.diff(x) + v.diff(y) + w.diff(z) expected_output = [eq1, eq2, eq3, eq4] assert expected_output == actual_output # }}} # {{{ test_as_scalar_pde_stokes def test_as_scalar_pde_stokes(): diff_op = make_identity_diff_op(3, 4) u = diff_op[:3] p = diff_op[3] pde = concat(laplacian(u) - gradient(p), divergence(u)) # velocity components in Stokes should satisfy Biharmonic for i in range(3): logger.info("pde\n%s", as_scalar_pde(pde, i)) logger.info("\n%s", laplacian(laplacian(u[i]))) assert as_scalar_pde(pde, i) == laplacian(laplacian(u[0])) # pressure should satisfy Laplace assert as_scalar_pde(pde, 3) == laplacian(u[0]) # }}} # {{{ test_as_scalar_pde_maxwell def test_as_scalar_pde_maxwell(): from sumpy.symbolic import symbols op = make_identity_diff_op(3, 6, time_dependent=True) E = op[:3] # noqa: N806 B = op[3:] # noqa: N806 mu, epsilon = symbols("mu, epsilon") t = (0, 0, 0, 1) pde = concat(curl(E) + diff(B, t), curl(B) - mu*epsilon*diff(E, t), divergence(E), divergence(B)) as_scalar_pde(pde, 3) for i in range(6): assert as_scalar_pde(pde, i) == \ laplacian(op[0]) - mu*epsilon*diff(diff(op[0], t), t) # }}} # {{{ test_as_scalar_pde_elasticity def test_as_scalar_pde_elasticity(): # Ref: https://doi.org/10.1006/jcph.1996.0102 diff_op = make_identity_diff_op(2, 5) sigma_x = diff_op[0] sigma_y = diff_op[1] tau = diff_op[2] u = diff_op[3] v = diff_op[4] # Use numeric values as the expressions grow exponentially large otherwise from sumpy.symbolic import symbols lam, mu = symbols("lam, mu") x = (1, 0) y = (0, 1) exprs = [ diff(sigma_x, x) + diff(tau, y), diff(tau, x) + diff(sigma_y, y), sigma_x - (lam + 2*mu)*diff(u, x) - lam*diff(v, y), sigma_y - (lam + 2*mu)*diff(v, y) - lam*diff(u, x), tau - mu*(diff(u, y) + diff(v, x)), ] pde = concat(*exprs) assert pde.order == 1 for i in range(5): scalar_pde = as_scalar_pde(pde, i) assert scalar_pde == laplacian(laplacian(diff_op[0])) assert scalar_pde.order == 4 # }}} # {{{ test_elasticity_new def test_elasticity_new(): from pickle import dumps, loads stokes_knl = StokesletKernel(3, 0, 1, "mu1", 0.5) stokes_knl2 = ElasticityKernel(3, 0, 1, "mu1", 0.5) elasticity_knl = ElasticityKernel(3, 0, 1, "mu1", "nu") elasticity_helper_knl = LineOfCompressionKernel(3, 0, "mu1", "nu") assert isinstance(stokes_knl2, StokesletKernel) assert stokes_knl == stokes_knl2 assert loads(dumps(stokes_knl)) == stokes_knl for knl in [elasticity_knl, elasticity_helper_knl]: assert not isinstance(knl, StokesletKernel) assert loads(dumps(knl)) == knl # }}} # {{{ test_weird_kernel w = make_identity_diff_op(2) pdes = [ diff(w, (1, 1)) + diff(w, (2, 0)), diff(w, (1, 1)) + diff(w, (0, 2)), ] @pytest.mark.parametrize("pde", pdes) def test_weird_kernel(pde): class MyKernel(ExpressionKernel): def __init__(self): super().__init__(dim=2, expression=1, global_scaling_const=1, is_complex_valued=False) def get_pde_as_diff_op(self): return pde from functools import reduce from operator import mul from sumpy.expansion import LinearPDEConformingVolumeTaylorExpansion knl = MyKernel() order = 10 expn = LinearPDEConformingVolumeTaylorExpansion(kernel=knl, order=order, use_rscale=False) coeffs = expn.get_coefficient_identifiers() fft_size = reduce(mul, map(max, *coeffs), 1) assert fft_size == order # }}} # {{{ test_get_storage_index class StorageIndexTestKernel(ExpressionKernel): def __init__(self, dim, max_mi): super().__init__(dim=dim, expression=1, global_scaling_const=1, is_complex_valued=False) self._max_mi = max_mi def get_pde_as_diff_op(self): w = make_identity_diff_op(self.dim) pde = diff(w, tuple(self._max_mi)) return pde @pytest.mark.parametrize("order", [6]) @pytest.mark.parametrize("knl", [ LaplaceKernel(2), LaplaceKernel(3), StorageIndexTestKernel(2, (3, 0)), StorageIndexTestKernel(2, (0, 3)), StorageIndexTestKernel(3, (3, 0, 0)), StorageIndexTestKernel(3, (0, 3, 0)), StorageIndexTestKernel(3, (0, 0, 3)), BiharmonicKernel(2), BiharmonicKernel(3), ]) @pytest.mark.parametrize("compressed", (True, False)) def test_get_storage_index(order, knl, compressed): dim = knl.dim if compressed: wrangler = LinearPDEBasedExpansionTermsWrangler(order, dim, knl=knl) else: wrangler = FullExpansionTermsWrangler(order, dim) for i, mi in enumerate(wrangler.get_coefficient_identifiers()): assert i == wrangler.get_storage_index(mi) # }}} # You can test individual routines by typing # $ python test_misc.py 'test_pde_check_kernels(_acf, # KernelInfo(HelmholtzKernel(2), k=5), order=5)' if __name__ == "__main__": if len(sys.argv) > 1: exec(sys.argv[1]) else: pytest.main([__file__]) # vim: fdm=marker