def test_block_builder(ctx_factory,
ambient_dim,
block_builder_type,
index_sparsity_factor,
op_type,
visualize=False):
"""Test that block builders and full matrix builders actually match."""
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
# prevent cache explosion
from sympy.core.cache import clear_cache
clear_cache()
if ambient_dim == 2:
case = extra.CurveTestCase(
name="ellipse",
target_order=7,
index_sparsity_factor=index_sparsity_factor,
op_type=op_type,
resolutions=[32],
curve_fn=partial(ellipse, 3.0),
)
for i in range(indices.nblocks):
isrc = indices.block_indices(i)
marker[isrc] = 10.0 * (i + 1.0)
from meshmode.dof_array import unflatten
marker = unflatten(actx, discr, actx.from_numpy(marker))
vis = make_visualizer(actx, discr, 10)
filename = "test_partition_{0}_{1}_{3}d_{2}.vtu".format(*args)
vis.write_vtk_file(filename, [("marker", marker)])
PROXY_TEST_CASES = [
extra.CurveTestCase(name="ellipse",
target_order=7,
curve_fn=partial(ellipse, 3.0)),
extra.TorusTestCase(target_order=2, resolutions=[0])
]
@pytest.mark.skip(reason="only useful with visualize=True")
@pytest.mark.parametrize("tree_kind", ['adaptive', None])
@pytest.mark.parametrize("case", PROXY_TEST_CASES)
def test_partition_points(ctx_factory, tree_kind, case, visualize=False):
"""Tests that the points are correctly partitioned (by visualization)."""
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
mesh = merge_disjoint_meshes([mesh, discr.mesh])
discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(4))
vis = make_visualizer(actx, discr)
filename = f"test_proxy_geometry_{suffix}_block_{i:04d}.vtu"
vis.write_vtk_file(filename, [], overwrite=False)
else:
raise ValueError
# }}}
PROXY_TEST_CASES = [
extra.CurveTestCase(name="ellipse",
target_order=7,
curve_fn=partial(ellipse, 3.0)),
extra.CurveTestCase(name="starfish",
target_order=4,
curve_fn=NArmedStarfish(5, 0.25),
resolutions=[32]),
extra.TorusTestCase(target_order=2, resolutions=[0])
]
# {{{ test_partition_points
@pytest.mark.parametrize("tree_kind", ["adaptive", None])
@pytest.mark.parametrize("case", PROXY_TEST_CASES)
def test_partition_points(actx_factory, tree_kind, case, visualize=False):
"""Tests that the points are correctly partitioned."""
def test_build_matrix(ctx_factory, k, curve_fn, op_type, visualize=False):
"""Checks that the matrix built with `symbolic.execution.build_matrix`
gives the same (to tolerance) answer as a direct evaluation.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
case = extra.CurveTestCase(name="curve",
knl_class_or_helmholtz_k=k,
curve_fn=curve_fn,
op_type=op_type,
target_order=7,
qbx_order=4,
resolutions=[30])
logger.info("\n%s", case)
# {{{ geometry
qbx = case.get_layer_potential(actx, case.resolutions[-1],
case.target_order)
from pytential.qbx.refinement import refine_geometry_collection
places = GeometryCollection(qbx, auto_where=case.name)
places = refine_geometry_collection(places,
kernel_length_scale=(5 /
k if k else None))
dd = places.auto_source.to_stage1()
density_discr = places.get_discretization(dd.geometry)
logger.info("nelements: %d", density_discr.mesh.nelements)
logger.info("ndofs: %d", density_discr.ndofs)
# }}}
# {{{ symbolic
sym_u, sym_op = case.get_operator(places.ambient_dim)
bound_op = bind(places, sym_op)
# }}}
# {{{ dense matrix
from pytential.symbolic.execution import build_matrix
mat = actx.to_numpy(
build_matrix(actx,
places,
sym_op,
sym_u,
context=case.knl_concrete_kwargs))
if visualize:
try:
import matplotlib.pyplot as pt
except ImportError:
visualize = False
if visualize:
from sumpy.tools import build_matrix as build_matrix_via_matvec
mat2 = bound_op.scipy_op(actx,
"u",
dtype=mat.dtype,
**case.knl_concrete_kwargs)
mat2 = build_matrix_via_matvec(mat2)
logger.info(
"real %.5e imag %.5e",
la.norm((mat - mat2).real, "fro") / la.norm(mat2.real, "fro"),
la.norm((mat - mat2).imag, "fro") / la.norm(mat2.imag, "fro"))
pt.subplot(121)
pt.imshow(np.log10(np.abs(1.0e-20 + (mat - mat2).real)))
pt.colorbar()
pt.subplot(122)
pt.imshow(np.log10(np.abs(1.0e-20 + (mat - mat2).imag)))
pt.colorbar()
pt.show()
pt.clf()
if visualize:
pt.subplot(121)
pt.imshow(mat.real)
pt.colorbar()
pt.subplot(122)
pt.imshow(mat.imag)
pt.colorbar()
pt.show()
pt.clf()
# }}}
# {{{ check
from pytential.utils import unflatten_from_numpy, flatten_to_numpy
np.random.seed(12)
for i in range(5):
if isinstance(sym_u, np.ndarray):
u = make_obj_array([
np.random.randn(density_discr.ndofs) for _ in range(len(sym_u))
])
else:
u = np.random.randn(density_discr.ndofs)
u_dev = unflatten_from_numpy(actx, density_discr, u)
res_matvec = np.hstack(
flatten_to_numpy(
actx, bound_op(actx, u=u_dev, **case.knl_concrete_kwargs)))
res_mat = mat.dot(np.hstack(u))
abs_err = la.norm(res_mat - res_matvec, np.inf)
rel_err = abs_err / la.norm(res_matvec, np.inf)
logger.info("AbsErr {:.5e} RelErr {:.5e}".format(abs_err, rel_err))
assert rel_err < 1.0e-13, 'iteration: {}'.format(i)
def test_build_matrix_fixed_stage(ctx_factory,
source_discr_stage,
target_discr_stage,
visualize=False):
"""Checks that the block builders match for difference stages."""
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
# prevent cache explosion
from sympy.core.cache import clear_cache
clear_cache()
case = extra.CurveTestCase(
name="starfish",
curve_fn=NArmedStarfish(5, 0.25),
target_order=4,
resolutions=[32],
index_sparsity_factor=0.6,
op_type="scalar",
tree_kind=None,
)
logger.info("\n%s", case)
# {{{ geometry
dd = sym.DOFDescriptor(case.name)
qbx = case.get_layer_potential(actx, case.resolutions[-1],
case.target_order)
places = GeometryCollection(
{case.name: qbx},
auto_where=(dd.copy(discr_stage=source_discr_stage),
dd.copy(discr_stage=target_discr_stage)))
dd = places.auto_source
density_discr = places.get_discretization(dd.geometry, dd.discr_stage)
# }}}
# {{{ symbolic
if source_discr_stage is target_discr_stage:
qbx_forced_limit = -1
else:
qbx_forced_limit = None
sym_u, sym_op = case.get_operator(places.ambient_dim, qbx_forced_limit)
from pytential.symbolic.execution import _prepare_expr
sym_prep_op = _prepare_expr(places, sym_op)
# }}}
# {{{ check
source_discr = places.get_discretization(case.name, source_discr_stage)
target_discr = places.get_discretization(case.name, target_discr_stage)
logger.info("nelements: %d", density_discr.mesh.nelements)
logger.info("ndofs: %d", source_discr.ndofs)
logger.info("ndofs: %d", target_discr.ndofs)
icols = case.get_block_indices(actx, source_discr, matrix_indices=False)
irows = case.get_block_indices(actx, target_discr, matrix_indices=False)
index_set = MatrixBlockIndexRanges(actx.context, icols, irows)
kwargs = dict(
dep_expr=sym_u,
other_dep_exprs=[],
dep_source=places.get_geometry(case.name),
dep_discr=density_discr,
places=places,
context=case.knl_concrete_kwargs,
)
# qbx
from pytential.symbolic import matrix
mat = matrix.MatrixBuilder(actx, **kwargs)(sym_prep_op)
blk = matrix.NearFieldBlockBuilder(actx, index_set=index_set,
**kwargs)(sym_prep_op)
assert mat.shape == (target_discr.ndofs, source_discr.ndofs)
assert extra.max_block_error(mat, blk, index_set.get(queue)) < 1.0e-14
# p2p
mat = matrix.P2PMatrixBuilder(actx, exclude_self=True,
**kwargs)(sym_prep_op)
blk = matrix.FarFieldBlockBuilder(actx,
index_set=index_set,
exclude_self=True,
**kwargs)(sym_prep_op)
assert mat.shape == (target_discr.ndofs, source_discr.ndofs)
assert extra.max_block_error(mat, blk, index_set.get(queue)) < 1.0e-14
def test_build_matrix_conditioning(actx_factory,
side,
op_type,
visualize=False):
"""Checks that :math:`I + K`, where :math:`K` is compact gives a
well-conditioned operator when it should. For example, the exterior Laplace
problem has a nullspace, so we check that and remove it.
"""
actx = actx_factory()
# prevent cache explosion
from sympy.core.cache import clear_cache
clear_cache()
case = extra.CurveTestCase(
name="ellipse",
curve_fn=lambda t: ellipse(3.0, t),
target_order=16,
source_ovsmp=1,
qbx_order=4,
resolutions=[64],
op_type=op_type,
side=side,
)
logger.info("\n%s", case)
# {{{ geometry
qbx = case.get_layer_potential(actx, case.resolutions[-1],
case.target_order)
from pytential.qbx.refinement import refine_geometry_collection
places = GeometryCollection(qbx, auto_where=case.name)
places = refine_geometry_collection(
places, refine_discr_stage=sym.QBX_SOURCE_QUAD_STAGE2)
dd = places.auto_source.to_stage1()
density_discr = places.get_discretization(dd.geometry)
logger.info("nelements: %d", density_discr.mesh.nelements)
logger.info("ndofs: %d", density_discr.ndofs)
# }}}
# {{{ check matrix
from pytential.symbolic.execution import build_matrix
sym_u, sym_op = case.get_operator(places.ambient_dim,
qbx_forced_limit="avg")
mat = actx.to_numpy(
build_matrix(actx,
places,
sym_op,
sym_u,
context=case.knl_concrete_kwargs))
kappa = la.cond(mat)
_, sigma, _ = la.svd(mat)
logger.info("cond: %.5e sigma_max %.5e", kappa, sigma[0])
# NOTE: exterior Laplace has a nullspace
if side == +1 and op_type == "double":
assert kappa > 1.0e+9
assert sigma[-1] < 1.0e-9
else:
assert kappa < 1.0e+1
assert sigma[-1] > 1.0e-2
# remove the nullspace and check that it worked
if side == +1 and op_type == "double":
# NOTE: this adds the "mean" to remove the nullspace for the operator
# See `pytential.symbolic.pde.scalar` for the equivalent formulation
w = actx.to_numpy(
flatten(
bind(places,
sym.sqrt_jac_q_weight(places.ambient_dim)**2)(actx),
actx))
w = np.tile(w.reshape(-1, 1), w.size).T
kappa = la.cond(mat + w)
assert kappa < 1.0e+2
# }}}
# {{{ plot
if not visualize:
return
side = "int" if side == -1 else "ext"
import matplotlib.pyplot as plt
plt.imshow(mat)
plt.colorbar()
plt.title(fr"$\kappa(A) = {kappa:.5e}$")
plt.savefig(f"test_cond_{op_type}_{side}_mat")
plt.clf()
plt.plot(sigma)
plt.ylabel(r"$\sigma$")
plt.grid()
plt.savefig(f"test_cond_{op_type}_{side}_svd")
plt.clf()
