from __future__ import division, absolute_import, print_function
__copyright__ = "Copyright (C) 2015 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 numpy as np # noqa
import numpy.linalg as la # noqa
import pyopencl as cl # noqa
import pyopencl.array # noqa
import pyopencl.clmath # noqa
import pytest # noqa
from pyopencl.tools import ( # noqa
pytest_generate_tests_for_pyopencl as pytest_generate_tests)
import logging
logger = logging.getLogger(__name__)
from grudge import sym, bind, Discretization
@pytest.mark.parametrize("dim", [2, 3])
def test_inverse_metric(ctx_factory, dim):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5,)*dim, b=(0.5,)*dim,
n=(6,)*dim, order=4)
def m(x):
result = np.empty_like(x)
result[0] = (
1.5*x[0] + np.cos(x[0])
+ 0.1*np.sin(10*x[1]))
result[1] = (
0.05*np.cos(10*x[0])
+ 1.3*x[1] + np.sin(x[1]))
if len(x) == 3:
result[2] = x[2]
return result
from meshmode.mesh.processing import map_mesh
mesh = map_mesh(mesh, m)
discr = Discretization(cl_ctx, mesh, order=4)
sym_op = (
sym.forward_metric_derivative_mat(mesh.dim)
.dot(
sym.inverse_metric_derivative_mat(mesh.dim)
)
.reshape(-1))
op = bind(discr, sym_op)
mat = op(queue).reshape(mesh.dim, mesh.dim)
for i in range(mesh.dim):
for j in range(mesh.dim):
tgt = 1 if i == j else 0
err = np.max(np.abs((mat[i, j] - tgt).get(queue=queue)))
print(i, j, err)
assert err < 1e-12, (i, j, err)
def test_1d_mass_mat_trig(ctx_factory):
"""Check the integral of some trig functions on an interval using the mass
matrix
"""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-4*np.pi,), b=(9*np.pi,),
n=(17,), order=1)
discr = Discretization(cl_ctx, mesh, order=8)
x = sym.nodes(1)
f = bind(discr, sym.cos(x[0])**2)(queue)
ones = bind(discr, sym.Ones(sym.DD_VOLUME))(queue)
mass_op = bind(discr, sym.MassOperator()(sym.var("f")))
num_integral_1 = np.dot(ones.get(), mass_op(queue, f=f).get())
num_integral_2 = np.dot(f.get(), mass_op(queue, f=ones).get())
num_integral_3 = bind(discr, sym.integral(sym.var("f")))(queue, f=f).get()
true_integral = 13*np.pi/2
err_1 = abs(num_integral_1-true_integral)
err_2 = abs(num_integral_2-true_integral)
err_3 = abs(num_integral_3-true_integral)
assert err_1 < 1e-10
assert err_2 < 1e-10
assert err_3 < 1e-10
@pytest.mark.parametrize("dim", [1, 2, 3])
def test_tri_diff_mat(ctx_factory, dim, order=4):
"""Check differentiation matrix along the coordinate axes on a disk
Uses sines as the function to differentiate.
"""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import generate_regular_rect_mesh
from pytools.convergence import EOCRecorder
axis_eoc_recs = [EOCRecorder() for axis in range(dim)]
for n in [10, 20]:
mesh = generate_regular_rect_mesh(a=(-0.5,)*dim, b=(0.5,)*dim,
n=(n,)*dim, order=4)
discr = Discretization(cl_ctx, mesh, order=4)
nabla = sym.nabla(dim)
for axis in range(dim):
x = sym.nodes(dim)
f = bind(discr, sym.sin(3*x[axis]))(queue)
df = bind(discr, 3*sym.cos(3*x[axis]))(queue)
sym_op = nabla[axis](sym.var("f"))
bound_op = bind(discr, sym_op)
df_num = bound_op(queue, f=f)
linf_error = la.norm((df_num-df).get(), np.Inf)
axis_eoc_recs[axis].add_data_point(1/n, linf_error)
for axis, eoc_rec in enumerate(axis_eoc_recs):
print(axis)
print(eoc_rec)
assert eoc_rec.order_estimate() >= order
def test_2d_gauss_theorem(ctx_factory):
"""Verify Gauss's theorem explicitly on a mesh"""
from meshpy.geometry import make_circle, GeometryBuilder
from meshpy.triangle import MeshInfo, build
geob = GeometryBuilder()
geob.add_geometry(*make_circle(1))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info = build(mesh_info)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
discr = Discretization(cl_ctx, mesh, order=2)
def f(x):
return sym.join_fields(
sym.sin(3*x[0])+sym.cos(3*x[1]),
sym.sin(2*x[0])+sym.cos(x[1]))
gauss_err = bind(discr,
sym.integral((
sym.nabla(2) * f(sym.nodes(2))
).sum())
-
sym.integral(
sym.interp("vol", sym.BTAG_ALL)(f(sym.nodes(2)))
.dot(sym.normal(sym.BTAG_ALL, 2)),
dd=sym.BTAG_ALL)
)(queue)
assert abs(gauss_err.get()) < 5e-15
# You can test individual routines by typing
# $ python test_layer_pot.py 'test_routine()'
if __name__ == "__main__":
import sys
if len(sys.argv) > 1:
exec(sys.argv[1])
else:
from py.test.cmdline import main
main([__file__])
# vim: fdm=marker