def __call__(self, queue, targets, sources, index_set, **kwargs):
"""Construct a set of blocks of the full P2P interaction matrix.
The blocks are returned as one-dimensional arrays, for performance
and storage reasons. If the two-dimensional form is desired, it can
be obtained using the information in the `index_set` for a block
:math:`i` in the following way:
.. code-block:: python
blkranges = index_set.linear_ranges()
blkshape = index_set.block_shape(i)
block2d = result[blkranges[i]:blkranges[i + 1]].reshape(*blkshape)
:arg targets: target point coordinates.
:arg sources: source point coordinates.
:arg index_set: a :class:`sumpy.tools.MatrixBlockIndexRanges` used
to define the blocks.
:return: a tuple of one-dimensional arrays of kernel evaluations at
target-source pairs described by `index_set`.
"""
from pytools.obj_array import is_obj_array
knl = self.get_cached_optimized_kernel(
targets_is_obj_array=(
is_obj_array(targets) or isinstance(targets, (tuple, list))),
sources_is_obj_array=(
is_obj_array(sources) or isinstance(sources, (tuple, list))))
return knl(queue,
targets=targets,
sources=sources,
tgtindices=index_set.linear_row_indices,
srcindices=index_set.linear_col_indices, **kwargs)
def __call__(self, queue, targets, sources, index_set, **kwargs):
"""Construct a set of blocks of the full P2P interaction matrix.
The blocks are returned as one-dimensional arrays, for performance
and storage reasons. If the two-dimensional form is desired, it can
be obtained using the information in the `index_set` for a block
:math:`i` in the following way:
.. code-block:: python
blkranges = index_set.linear_ranges()
blkshape = index_set.block_shape(i)
block2d = result[blkranges[i]:blkranges[i + 1]].reshape(*blkshape)
:arg targets: target point coordinates.
:arg sources: source point coordinates.
:arg index_set: a :class:`sumpy.tools.MatrixBlockIndexRanges` used
to define the blocks.
:return: a tuple of one-dimensional arrays of kernel evaluations at
target-source pairs described by `index_set`.
"""
from pytools.obj_array import is_obj_array
knl = self.get_cached_optimized_kernel(
targets_is_obj_array=(is_obj_array(targets)
or isinstance(targets, (tuple, list))),
sources_is_obj_array=(is_obj_array(sources)
or isinstance(sources, (tuple, list))))
return knl(queue,
targets=targets,
sources=sources,
tgtindices=index_set.linear_row_indices,
srcindices=index_set.linear_col_indices,
**kwargs)
def field_equal(a, b):
a_is_oa = is_obj_array(a)
assert a_is_oa == is_obj_array(b)
if a_is_oa:
return (a == b).all()
else:
return a == b
def obj_array_equal(a, b):
a_is_oa = is_obj_array(a)
assert a_is_oa == is_obj_array(b)
if a_is_oa:
return np.array_equal(a, b)
else:
return a == b
def obj_array_equal(a, b):
a_is_oa = is_obj_array(a)
assert a_is_oa == is_obj_array(b)
if a_is_oa:
return np.array_equal(a, b)
else:
return a == b
def __call__(self, queue, targets, sources, **kwargs):
from pytools.obj_array import is_obj_array
knl = self.get_cached_optimized_kernel(
targets_is_obj_array=(is_obj_array(targets)
or isinstance(targets, (tuple, list))),
sources_is_obj_array=(is_obj_array(sources)
or isinstance(sources, (tuple, list))))
return knl(queue, sources=sources, targets=targets, **kwargs)
def __call__(self, queue, targets, sources, **kwargs):
from pytools.obj_array import is_obj_array
knl = self.get_cached_optimized_kernel(
targets_is_obj_array=(
is_obj_array(targets) or isinstance(targets, (tuple, list))),
sources_is_obj_array=(
is_obj_array(sources) or isinstance(sources, (tuple, list))))
return knl(queue, sources=sources, targets=targets, **kwargs)
def separate_by_real_and_imag(data, real_only):
for name, field in data:
from pytools.obj_array import log_shape, is_obj_array
ls = log_shape(field)
if is_obj_array(field):
assert len(ls) == 1
from pytools.obj_array import (
oarray_real_copy, oarray_imag_copy,
with_object_array_or_scalar)
if field[0].dtype.kind == "c":
if real_only:
yield (name,
with_object_array_or_scalar(oarray_real_copy, field))
else:
yield (name+"_r",
with_object_array_or_scalar(oarray_real_copy, field))
yield (name+"_i",
with_object_array_or_scalar(oarray_imag_copy, field))
else:
yield (name, field)
else:
# ls == ()
if field.dtype.kind == "c":
yield (name+"_r", field.real.copy())
yield (name+"_i", field.imag.copy())
else:
yield (name, field)
def with_object_array_or_scalar_n_args(f, *args):
oarray_arg_indices = []
for i, arg in enumerate(args):
if is_obj_array(arg):
oarray_arg_indices.append(i)
if not oarray_arg_indices:
return f(*args)
leading_oa_index = oarray_arg_indices[0]
ls = log_shape(args[leading_oa_index])
if ls != ():
from pytools import indices_in_shape
result = np.zeros(ls, dtype=object)
new_args = list(args)
for i in indices_in_shape(ls):
for arg_i in oarray_arg_indices:
new_args[arg_i] = args[arg_i][i]
result[i] = f(*new_args)
return result
else:
return f(*args)
def with_object_array_or_scalar_n_args(f, *args):
oarray_arg_indices = []
for i, arg in enumerate(args):
if is_obj_array(arg):
oarray_arg_indices.append(i)
if not oarray_arg_indices:
return f(*args)
leading_oa_index = oarray_arg_indices[0]
ls = log_shape(args[leading_oa_index])
if ls != ():
from pytools import indices_in_shape
result = np.zeros(ls, dtype=object)
new_args = list(args)
for i in indices_in_shape(ls):
for arg_i in oarray_arg_indices:
new_args[arg_i] = args[arg_i][i]
result[i] = f(*new_args)
return result
else:
return f(*args)
def inverse_mass(self, vec):
if is_obj_array(vec):
return with_object_array_or_scalar(
lambda el: self.inverse_mass(el), vec)
@memoize_in(self, "elwise_linear_knl")
def knl():
knl = lp.make_kernel("""{[k,i,j]:
0<=k<nelements and
0<=i<ndiscr_nodes_out and
0<=j<ndiscr_nodes_in}""",
"result[k,i] = sum(j, mat[i, j] * vec[k, j])",
default_offset=lp.auto,
name="diff")
knl = lp.split_iname(knl, "i", 16, inner_tag="l.0")
return lp.tag_inames(knl, dict(k="g.0"))
discr = self.volume_discr
result = discr.empty(queue=vec.queue, dtype=vec.dtype)
for grp in discr.groups:
matrix = self.get_inverse_mass_matrix(grp, vec.dtype)
knl()(vec.queue,
mat=matrix,
result=grp.view(result),
vec=grp.view(vec))
return result / self.vol_jacobian()
def separate_by_real_and_imag(data, real_only):
for name, field in data:
from pytools.obj_array import log_shape, is_obj_array
ls = log_shape(field)
if is_obj_array(field):
assert len(ls) == 1
from pytools.obj_array import (oarray_real_copy, oarray_imag_copy,
with_object_array_or_scalar)
if field[0].dtype.kind == "c":
if real_only:
yield (name,
with_object_array_or_scalar(oarray_real_copy,
field))
else:
yield (name + "_r",
with_object_array_or_scalar(oarray_real_copy,
field))
yield (name + "_i",
with_object_array_or_scalar(oarray_imag_copy,
field))
else:
yield (name, field)
else:
# ls == ()
if field.dtype.kind == "c":
yield (name + "_r", field.real.copy())
yield (name + "_i", field.imag.copy())
else:
yield (name, field)
def scipy_op(self, queue, arg_name, domains=None, **extra_args):
"""
:arg domains: a list of discretization identifiers or
*None* values indicating the domains on which each component of the
solution vector lives. *None* values indicate that the component
is a scalar. If *None*,
:class:`pytential.symbolic.primitives.DEFAULT_TARGET`, is required
to be a key in :attr:`places`.
"""
from pytools.obj_array import is_obj_array
if domains is None:
from pytential.symbolic.primitives import DEFAULT_TARGET
if DEFAULT_TARGET not in self.places:
raise RuntimeError("'domains is None' requires "
"DEFAULT_TARGET to be defined")
dom_name = DEFAULT_TARGET
if is_obj_array(self.code.result):
domains = len(self.code.result)*[dom_name]
else:
domains = [dom_name]
elif not isinstance(domains, list):
dom_name = domains
if is_obj_array(self.code.result):
domains = len(self.code.result)*[dom_name]
else:
domains = [dom_name]
total_dofs = 0
starts_and_ends = []
for dom_name in domains:
if dom_name is None:
size = 1
else:
size = self.places[dom_name].nnodes
starts_and_ends.append((total_dofs, total_dofs+size))
total_dofs += size
# Hidden assumption: Number of input components
# equals number of output compoments. But IMO that's
# fair, since these operators are usually only used
# for linear system solving, in which case the assumption
# has to be true.
return MatVecOp(self, queue,
arg_name, total_dofs, starts_and_ends, extra_args)
def reorder_potentials(self, potentials):
from pytools.obj_array import is_obj_array, with_object_array_or_scalar
assert is_obj_array(potentials)
def reorder(x):
return x.with_queue(self.queue)[self.tree.sorted_target_ids]
return with_object_array_or_scalar(reorder, potentials)
def reorder_potentials(self, potentials):
from pytools.obj_array import is_obj_array, with_object_array_or_scalar
assert is_obj_array(potentials)
def reorder(x):
return x.with_queue(self.queue)[self.tree.sorted_target_ids]
return with_object_array_or_scalar(reorder, potentials)
def get_array_module(vec):
try:
from pyopencl.tools import array_module
from pytools.obj_array import is_obj_array
if is_obj_array(vec):
return array_module(vec[0])
else:
return array_module(vec)
except ImportError:
return np
def vec_times(self, vec, operand):
from pytools.obj_array import is_obj_array
if is_obj_array(operand):
if len(operand) != self.dimensions:
raise ValueError("operand of vec_times must have %d dimensions"
% self.dimensions)
return np.dot(vec, operand)
else:
return vec*operand
def apply_diff(self, nabla, operand):
from pytools.obj_array import make_obj_array, is_obj_array
if is_obj_array(operand):
if len(operand) != self.dimensions:
raise ValueError("operand of apply_diff must have %d dimensions"
% self.dimensions)
return sum(nabla[i](operand[i]) for i in range(self.dimensions))
else:
return make_obj_array(
[nabla[i](operand) for i in range(self.dimensions)])
def dot_dataflow_graph(code, max_node_label_length=30,
label_wrap_width=50):
origins = {}
node_names = {}
result = [
"initial [label=\"initial\"]"
"result [label=\"result\"]"]
for num, insn in enumerate(code.instructions):
node_name = "node%d" % num
node_names[insn] = node_name
node_label = str(insn)
if max_node_label_length is not None:
node_label = node_label[:max_node_label_length]
if label_wrap_width is not None:
from pytools import word_wrap
node_label = word_wrap(node_label, label_wrap_width,
wrap_using="\n ")
node_label = node_label.replace("\n", "\\l") + "\\l"
result.append("%s [ label=\"p%d: %s\" shape=box ];" % (
node_name, insn.priority, node_label))
for assignee in insn.get_assignees():
origins[assignee] = node_name
def get_orig_node(expr):
from pymbolic.primitives import Variable
if isinstance(expr, Variable):
return origins.get(expr.name, "initial")
else:
return "initial"
def gen_expr_arrow(expr, target_node):
result.append("%s -> %s [label=\"%s\"];"
% (get_orig_node(expr), target_node, expr))
for insn in code.instructions:
for dep in insn.get_dependencies():
gen_expr_arrow(dep, node_names[insn])
from pytools.obj_array import is_obj_array
if is_obj_array(code.result):
for subexp in code.result:
gen_expr_arrow(subexp, "result")
else:
gen_expr_arrow(code.result, "result")
return "digraph dataflow {\n%s\n}\n" % "\n".join(result)
def dot_dataflow_graph(code, max_node_label_length=30, label_wrap_width=50):
origins = {}
node_names = {}
result = ["initial [label=\"initial\"]" "result [label=\"result\"]"]
for num, insn in enumerate(code.instructions):
node_name = "node%d" % num
node_names[insn] = node_name
node_label = str(insn)
if (max_node_label_length is not None
and not isinstance(insn, LoopyKernelInstruction)):
node_label = node_label[:max_node_label_length]
if label_wrap_width is not None:
from pytools import word_wrap
node_label = word_wrap(node_label,
label_wrap_width,
wrap_using="\n ")
node_label = node_label.replace("\n", "\\l") + "\\l"
result.append("%s [ label=\"p%d: %s\" shape=box ];" %
(node_name, insn.priority, node_label))
for assignee in insn.get_assignees():
origins[assignee] = node_name
def get_orig_node(expr):
from pymbolic.primitives import Variable
if isinstance(expr, Variable):
return origins.get(expr.name, "initial")
else:
return "initial"
def gen_expr_arrow(expr, target_node):
result.append("%s -> %s [label=\"%s\"];" %
(get_orig_node(expr), target_node, expr))
for insn in code.instructions:
for dep in insn.get_dependencies():
gen_expr_arrow(dep, node_names[insn])
from pytools.obj_array import is_obj_array
if is_obj_array(code.result):
for subexp in code.result:
gen_expr_arrow(subexp, "result")
else:
gen_expr_arrow(code.result, "result")
return "digraph dataflow {\n%s\n}\n" % "\n".join(result)
def vec_times(self, vec, operand):
from pytools.obj_array import is_obj_array
if is_obj_array(operand):
if len(operand) != self.dimensions:
raise ValueError(
"operand of vec_times must have %d dimensions" %
self.dimensions)
return np.dot(vec, operand)
else:
return vec * operand
def apply_diff(self, nabla, operand):
from pytools.obj_array import make_obj_array, is_obj_array
if is_obj_array(operand):
if len(operand) != self.dimensions:
raise ValueError(
"operand of apply_diff must have %d dimensions" %
self.dimensions)
return sum(nabla[i](operand[i]) for i in range(self.dimensions))
else:
return make_obj_array(
[nabla[i](operand) for i in range(self.dimensions)])
def __call__(self, discr, t, fields, x, make_empty):
result = self.make_func(discr)(t=numpy.float64(t), x=x, fields=fields)
# make sure we return no scalars in the result
from pytools.obj_array import log_shape, is_obj_array
if is_obj_array(result):
from pytools import indices_in_shape
from hedge.optemplate.tools import is_scalar
for i in indices_in_shape(log_shape(result)):
if is_scalar(result[i]):
result[i] = make_empty().fill(result[i])
return result
def __call__(self, operand, *args, **kwargs):
# If the call is handed an object array full of operands,
# return an object array of the operator applied to each of the
# operands.
from pytools.obj_array import is_obj_array, with_object_array_or_scalar
if is_obj_array(operand):
def make_op(operand_i):
return self(operand_i, *args, **kwargs)
return with_object_array_or_scalar(make_op, operand)
else:
return var.__call__(self, operand, *args, **kwargs)
def __call__(self, discr, t, fields, x, make_empty):
result = self.make_func(discr)(
t=numpy.float64(t), x=x, fields=fields)
# make sure we return no scalars in the result
from pytools.obj_array import log_shape, is_obj_array
if is_obj_array(result):
from pytools import indices_in_shape
from hedge.optemplate.tools import is_scalar
for i in indices_in_shape(log_shape(result)):
if is_scalar(result[i]):
result[i] = make_empty().fill(result[i])
return result
def with_object_array_or_scalar(f, field, obj_array_only=False):
if obj_array_only:
if is_obj_array(field):
ls = field.shape
else:
ls = ()
else:
ls = log_shape(field)
if ls != ():
from pytools import indices_in_shape
result = np.zeros(ls, dtype=object)
for i in indices_in_shape(ls):
result[i] = f(field[i])
return result
else:
return f(field)
def with_object_array_or_scalar(f, field, obj_array_only=False):
if obj_array_only:
if is_obj_array(field):
ls = field.shape
else:
ls = ()
else:
ls = log_shape(field)
if ls != ():
from pytools import indices_in_shape
result = np.zeros(ls, dtype=object)
for i in indices_in_shape(ls):
result[i] = f(field[i])
return result
else:
return f(field)
def __init__(self, structured_vec):
from pytools.obj_array import is_obj_array
self.is_structured = is_obj_array(structured_vec)
self.array_module = get_array_module(structured_vec)
if self.is_structured:
self.slices = []
num_dofs = 0
for entry in structured_vec:
if isinstance(entry, self.array_module.ndarray):
length = len(entry)
else:
length = 1
self.slices.append(slice(num_dofs, num_dofs+length))
num_dofs += length
def face_mass(self, vec):
if is_obj_array(vec):
return with_object_array_or_scalar(lambda el: self.face_mass(el),
vec)
@memoize_in(self, "face_mass_knl")
def knl():
knl = lp.make_kernel(
"""{[k,i,f,j]:
0<=k<nelements and
0<=f<nfaces and
0<=i<nvol_nodes and
0<=j<nface_nodes}""",
"result[k,i] = sum(f, sum(j, mat[i, f, j] * vec[f, k, j]))",
default_offset=lp.auto,
name="face_mass")
knl = lp.split_iname(knl, "i", 16, inner_tag="l.0")
return lp.tag_inames(knl, dict(k="g.0"))
all_faces_conn = self.get_connection("vol", "all_faces")
all_faces_discr = all_faces_conn.to_discr
vol_discr = all_faces_conn.from_discr
result = vol_discr.empty(queue=vec.queue, dtype=vec.dtype)
fj = self.face_jacobian("all_faces")
vec = vec * fj
assert len(all_faces_discr.groups) == len(vol_discr.groups)
for afgrp, volgrp in zip(all_faces_discr.groups, vol_discr.groups):
nfaces = volgrp.mesh_el_group.nfaces
matrix = self.get_local_face_mass_matrix(afgrp, volgrp, vec.dtype)
input_view = afgrp.view(vec).reshape(nfaces, volgrp.nelements,
afgrp.nunit_nodes)
knl()(vec.queue,
mat=matrix,
result=volgrp.view(result),
vec=input_view)
return result
def dd_axis(axis, ambient_dim, operand):
"""Return the derivative along (XYZ) axis *axis*
(in *ambient_dim*-dimensional space) of *operand*.
"""
from pytools.obj_array import is_obj_array, with_object_array_or_scalar
if is_obj_array(operand):
def dd_axis_comp(operand_i):
return dd_axis(axis, ambient_dim, operand_i)
return with_object_array_or_scalar(dd_axis_comp, operand)
d = Derivative()
unit_vector = np.zeros(ambient_dim)
unit_vector[axis] = 1
unit_mvector = MultiVector(unit_vector)
return d.resolve(
(unit_mvector.scalar_product(d.dnabla(ambient_dim)))
* d(operand))
def scipy_op(self, queue, arg_name, dtype, domains=None, **extra_args):
"""
:arg domains: a list of discretization identifiers or
*None* values indicating the domains on which each component of the
solution vector lives. *None* values indicate that the component
is a scalar. If *domains* is *None*,
:class:`~pytential.symbolic.primitives.DEFAULT_TARGET` is required
to be a key in :attr:`places`.
:returns: An object that (mostly) satisfies the
:mod:`scipy.linalg.LinearOperator` protocol, except for accepting
and returning :clas:`pyopencl.array.Array` arrays.
"""
from pytools.obj_array import is_obj_array
if is_obj_array(self.code.result):
nresults = len(self.code.result)
else:
nresults = 1
domains = _prepare_domains(nresults, self.places, domains,
self.places.auto_target)
total_dofs = 0
starts_and_ends = []
for dom_name in domains:
if dom_name is None:
size = 1
else:
size = self.places.get_geometry(dom_name).nnodes
starts_and_ends.append((total_dofs, total_dofs + size))
total_dofs += size
# Hidden assumption: Number of input components
# equals number of output compoments. But IMO that's
# fair, since these operators are usually only used
# for linear system solving, in which case the assumption
# has to be true.
return MatVecOp(self, queue, arg_name, dtype, total_dofs,
starts_and_ends, extra_args)
def test_matrix_build(ctx_factory, k, curve_f, lpot_id, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
# prevent cache 'splosion
from sympy.core.cache import clear_cache
clear_cache()
target_order = 7
qbx_order = 4
nelements = 30
mesh = make_curve_mesh(curve_f,
np.linspace(0, 1, nelements + 1),
target_order)
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
pre_density_discr = Discretization(
cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(target_order))
from pytential.qbx import QBXLayerPotentialSource
qbx, _ = QBXLayerPotentialSource(pre_density_discr, 4 * target_order,
qbx_order,
# Don't use FMM for now
fmm_order=False).with_refinement()
density_discr = qbx.density_discr
op, u_sym, knl_kwargs = _build_op(lpot_id, k=k)
bound_op = bind(qbx, op)
from pytential.symbolic.execution import build_matrix
mat = build_matrix(queue, qbx, op, u_sym).get()
if visualize:
from sumpy.tools import build_matrix as build_matrix_via_matvec
mat2 = bound_op.scipy_op(queue, "u", dtype=mat.dtype, **knl_kwargs)
mat2 = build_matrix_via_matvec(mat2)
print(la.norm((mat - mat2).real, "fro") / la.norm(mat2.real, "fro"),
la.norm((mat - mat2).imag, "fro") / la.norm(mat2.imag, "fro"))
import matplotlib.pyplot as pt
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()
if visualize:
import matplotlib.pyplot as pt
pt.subplot(121)
pt.imshow(mat.real)
pt.colorbar()
pt.subplot(122)
pt.imshow(mat.imag)
pt.colorbar()
pt.show()
from sumpy.tools import vector_to_device, vector_from_device
np.random.seed(12)
for i in range(5):
if is_obj_array(u_sym):
u = make_obj_array([
np.random.randn(density_discr.nnodes)
for _ in range(len(u_sym))
])
else:
u = np.random.randn(density_discr.nnodes)
u_dev = vector_to_device(queue, u)
res_matvec = np.hstack(
list(vector_from_device(
queue, bound_op(queue, u=u_dev))))
res_mat = mat.dot(np.hstack(list(u)))
abs_err = la.norm(res_mat - res_matvec, np.inf)
rel_err = abs_err / la.norm(res_matvec, np.inf)
print("AbsErr {:.5e} RelErr {:.5e}".format(abs_err, rel_err))
assert rel_err < 1e-13
def is_field_equal(a, b):
if is_obj_array(a):
return is_obj_array(b) and (a.shape == b.shape) and (a == b).all()
else:
return not is_obj_array(b) and a == b
def aggregate_assignments(inf_mapper, instructions, result,
max_vectors_in_batch_expr):
from pymbolic.primitives import Variable
function_registry = inf_mapper.function_registry
# {{{ aggregation helpers
def get_complete_origins_set(insn, skip_levels=0):
try:
return insn_to_origins_cache[insn]
except KeyError:
pass
if skip_levels < 0:
skip_levels = 0
result = set()
for dep in insn.get_dependencies():
if isinstance(dep, Variable):
dep_origin = origins_map.get(dep.name, None)
if dep_origin is not None:
if skip_levels <= 0:
result.add(dep_origin)
result |= get_complete_origins_set(dep_origin,
skip_levels - 1)
insn_to_origins_cache[insn] = result
return result
var_assignees_cache = {}
def get_var_assignees(insn):
try:
return var_assignees_cache[insn]
except KeyError:
result = set(
Variable(assignee) for assignee in insn.get_assignees())
var_assignees_cache[insn] = result
return result
def aggregate_two_assignments(ass_1, ass_2):
names = ass_1.names + ass_2.names
from pymbolic.primitives import Variable
deps = (ass_1.get_dependencies() | ass_2.get_dependencies()) \
- set(Variable(name) for name in names)
return Assign(names=names,
exprs=ass_1.exprs + ass_2.exprs,
_dependencies=deps,
priority=max(ass_1.priority, ass_2.priority))
# }}}
# {{{ main aggregation pass
insn_to_origins_cache = {}
origins_map = dict((assignee, insn) for insn in instructions
for assignee in insn.get_assignees())
from pytools import partition
from grudge.symbolic.primitives import DTAG_SCALAR
unprocessed_assigns, other_insns = partition(
lambda insn: (isinstance(insn, Assign) and not isinstance(
insn, ToDiscretizationScopedAssign) and not isinstance(
insn, FromDiscretizationScopedAssign) and not is_external_call(
insn.exprs[0], function_registry) and not any(
inf_mapper.infer_for_name(n).domain_tag == DTAG_SCALAR
for n in insn.names)), instructions)
# filter out zero-flop-count assigns--no need to bother with those
processed_assigns, unprocessed_assigns = partition(
lambda ass: ass.flop_count() == 0, unprocessed_assigns)
# filter out zero assignments
from grudge.tools import is_zero
i = 0
while i < len(unprocessed_assigns):
my_assign = unprocessed_assigns[i]
if any(is_zero(expr) for expr in my_assign.exprs):
processed_assigns.append(unprocessed_assigns.pop(i))
else:
i += 1
# greedy aggregation
while unprocessed_assigns:
my_assign = unprocessed_assigns.pop()
my_deps = my_assign.get_dependencies()
my_assignees = get_var_assignees(my_assign)
agg_candidates = []
for i, other_assign in enumerate(unprocessed_assigns):
other_deps = other_assign.get_dependencies()
other_assignees = get_var_assignees(other_assign)
if ((my_deps & other_deps or my_deps & other_assignees
or other_deps & my_assignees)
and my_assign.priority == other_assign.priority):
agg_candidates.append((i, other_assign))
did_work = False
if agg_candidates:
my_indirect_origins = get_complete_origins_set(my_assign,
skip_levels=1)
for other_assign_index, other_assign in agg_candidates:
if max_vectors_in_batch_expr is not None:
new_assignee_count = len(
set(my_assign.get_assignees())
| set(other_assign.get_assignees()))
new_dep_count = len(
my_assign.get_dependencies(each_vector=True)
| other_assign.get_dependencies(each_vector=True))
if (new_assignee_count + new_dep_count >
max_vectors_in_batch_expr):
continue
other_indirect_origins = get_complete_origins_set(
other_assign, skip_levels=1)
if (my_assign not in other_indirect_origins
and other_assign not in my_indirect_origins):
did_work = True
# aggregate the two assignments
new_assignment = aggregate_two_assignments(
my_assign, other_assign)
del unprocessed_assigns[other_assign_index]
unprocessed_assigns.append(new_assignment)
for assignee in new_assignment.get_assignees():
origins_map[assignee] = new_assignment
break
if not did_work:
processed_assigns.append(my_assign)
externally_used_names = set(expr
for insn in processed_assigns + other_insns
for expr in insn.get_dependencies())
from pytools.obj_array import is_obj_array
if is_obj_array(result):
externally_used_names |= set(expr for expr in result)
else:
externally_used_names |= set([result])
def schedule_and_finalize_assignment(ass):
dep_mapper = _make_dep_mapper(include_subscripts=False)
names_exprs = list(zip(ass.names, ass.exprs))
my_assignees = set(name for name, expr in names_exprs)
names_exprs_deps = [
(name, expr,
set(dep.name
for dep in dep_mapper(expr) if isinstance(dep, Variable))
& my_assignees) for name, expr in names_exprs
]
ordered_names_exprs = []
available_names = set()
while names_exprs_deps:
schedulable = []
i = 0
while i < len(names_exprs_deps):
name, expr, deps = names_exprs_deps[i]
unsatisfied_deps = deps - available_names
if not unsatisfied_deps:
schedulable.append((str(expr), name, expr))
del names_exprs_deps[i]
else:
i += 1
# make sure these come out in a constant order
schedulable.sort()
if schedulable:
for key, name, expr in schedulable:
ordered_names_exprs.append((name, expr))
available_names.add(name)
else:
raise RuntimeError("aggregation resulted in an "
"impossible assignment")
return Assign(names=[name for name, expr in ordered_names_exprs],
exprs=[expr for name, expr in ordered_names_exprs],
do_not_return=[
Variable(name) not in externally_used_names
for name, expr in ordered_names_exprs
],
priority=ass.priority)
return [
schedule_and_finalize_assignment(ass) for ass in processed_assigns
] + other_insns
def apply_imag(self, args):
from pytools.obj_array import is_obj_array
arg, = args
result = self.rec(arg)
assert not is_obj_array(result) # numpy bug with obj_array.imag
return result.imag
def hashable_field(f):
if is_obj_array(f):
return tuple(f)
else:
return f
def obj_array_to_hashable(f):
if is_obj_array(f):
return tuple(f)
else:
return f
def apply_imag(self, args):
from pytools.obj_array import is_obj_array
arg, = args
result = self.rec(arg)
assert not is_obj_array(result) # numpy bug with obj_array.imag
return result.imag
def setify_field(f):
from hedge.tools import is_obj_array
if is_obj_array(f):
return set(f)
else:
return set([f])
def gen_len(expr):
from pytools.obj_array import is_obj_array
if is_obj_array(expr):
return len(expr)
else:
return 1
def gmres(op,
rhs,
restart=None,
tol=None,
x0=None,
inner_product=None,
maxiter=None,
hard_failure=None,
no_progress_factor=None,
stall_iterations=None,
callback=None,
progress=False):
"""Solve a linear system Ax=b by means of GMRES
with restarts.
:arg op: a callable to evaluate A(x)
:arg b: the right hand side
:arg restart: the maximum number of iteration after
which GMRES algorithm needs to be restarted
:arg tol: the required decrease in residual norm
:arg inner_product: Must have an interface compatible with
:func:`numpy.vdot`. Must return a host scalar.
:arg maxiter: the maximum number of iteration permitted
:arg hard_failure: If True, raise :exc:`GMRESError` in case of failure.
:arg stall_iterations: Number of iterations with residual decrease
below *no_progress_factor* indicates stall. Set to 0 to disable
stall detection.
:return: a :class:`GMRESResult`
"""
try:
from pyopencl.tools import array_module
amod = array_module(rhs)
except ImportError:
amod = np
from pytools.obj_array import is_obj_array, make_obj_array
if is_obj_array(rhs):
stacked_rhs = amod.hstack(rhs)
slices = []
num_dofs = 0
for entry in rhs:
if isinstance(entry, amod.ndarray):
length = len(entry)
else:
length = 1
slices.append(slice(num_dofs, num_dofs + length))
num_dofs += length
else:
stacked_rhs = rhs
if inner_product is None:
inner_product = amod.vdot
if callback is None:
if progress:
callback = ResidualPrinter(inner_product)
else:
callback = None
result = _gmres(op,
stacked_rhs,
restart=restart,
tol=tol,
x0=x0,
dot=inner_product,
maxiter=maxiter,
hard_failure=hard_failure,
no_progress_factor=no_progress_factor,
stall_iterations=stall_iterations,
callback=callback)
if is_obj_array(rhs):
return result.copy(
solution=make_obj_array([result.solution[slc] for slc in slices]))
else:
return result
def interp(self, src, tgt, vec):
if is_obj_array(vec):
return with_object_array_or_scalar(
lambda el: self.interp(src, tgt, el), vec)
return self.get_connection(src, tgt)(vec.queue, vec)
def is_equal(a, b):
if is_obj_array(a):
return is_obj_array(b) and (a.shape == b.shape) and (a == b).all()
else:
return not is_obj_array(b) and a == b
def gen_len(expr):
from pytools.obj_array import is_obj_array
if is_obj_array(expr):
return len(expr)
else:
return 1
def obj_array_to_hashable(f):
if is_obj_array(f):
return tuple(f)
else:
return f
def setify_field(f):
from hedge.tools import is_obj_array
if is_obj_array(f):
return set(f)
else:
return set([f])
def build_matrix(queue,
places,
exprs,
input_exprs,
domains=None,
auto_where=None,
context=None):
"""
:arg queue: a :class:`pyopencl.CommandQueue`.
:arg places: a :class:`pytential.symbolic.execution.GeometryCollection`.
Alternatively, any list or mapping that is a valid argument for its
constructor can also be used.
:arg exprs: an array of expressions corresponding to the output block
rows of the matrix. May also be a single expression.
:arg input_exprs: an array of expressions corresponding to the
input block columns of the matrix. May also be a single expression.
:arg domains: a list of discretization identifiers (see 'places') or
*None* values indicating the domains on which each component of the
solution vector lives. *None* values indicate that the component
is a scalar. If *None*, *auto_where* or, if it is not provided,
:class:`~pytential.symbolic.primitives.DEFAULT_SOURCE` is required
to be a key in :attr:`places`.
:arg auto_where: For simple source-to-self or source-to-target
evaluations, find 'where' attributes automatically.
"""
if context is None:
context = {}
from pytools.obj_array import is_obj_array, make_obj_array
if not isinstance(places, GeometryCollection):
places = GeometryCollection(places, auto_where=auto_where)
exprs = _prepare_expr(places, exprs)
if not is_obj_array(exprs):
exprs = make_obj_array([exprs])
try:
input_exprs = list(input_exprs)
except TypeError:
# not iterable, wrap in a list
input_exprs = [input_exprs]
domains = _prepare_domains(len(input_exprs), places, domains,
places.auto_source)
from pytential.symbolic.matrix import MatrixBuilder, is_zero
nblock_rows = len(exprs)
nblock_columns = len(input_exprs)
blocks = np.zeros((nblock_rows, nblock_columns), dtype=np.object)
dtypes = []
for ibcol in range(nblock_columns):
mbuilder = MatrixBuilder(
queue,
dep_expr=input_exprs[ibcol],
other_dep_exprs=(input_exprs[:ibcol] + input_exprs[ibcol + 1:]),
dep_source=places.get_geometry(domains[ibcol]),
dep_discr=places.get_discretization(domains[ibcol]),
places=places,
context=context)
for ibrow in range(nblock_rows):
block = mbuilder(exprs[ibrow])
assert is_zero(block) or isinstance(block, np.ndarray)
blocks[ibrow, ibcol] = block
if isinstance(block, np.ndarray):
dtypes.append(block.dtype)
return cl.array.to_device(queue, _bmat(blocks, dtypes))
def build_matrix(queue, places, exprs, input_exprs, domains=None,
auto_where=None, context=None):
"""
:arg queue: a :class:`pyopencl.CommandQueue`.
:arg places: a :class:`pytential.symbolic.execution.GeometryCollection`.
Alternatively, any list or mapping that is a valid argument for its
constructor can also be used.
:arg exprs: an array of expressions corresponding to the output block
rows of the matrix. May also be a single expression.
:arg input_exprs: an array of expressions corresponding to the
input block columns of the matrix. May also be a single expression.
:arg domains: a list of discretization identifiers (see 'places') or
*None* values indicating the domains on which each component of the
solution vector lives. *None* values indicate that the component
is a scalar. If *None*, *auto_where* or, if it is not provided,
:class:`~pytential.symbolic.primitives.DEFAULT_SOURCE` is required
to be a key in :attr:`places`.
:arg auto_where: For simple source-to-self or source-to-target
evaluations, find 'where' attributes automatically.
"""
if context is None:
context = {}
from pytools.obj_array import is_obj_array, make_obj_array
if not isinstance(places, GeometryCollection):
places = GeometryCollection(places, auto_where=auto_where)
exprs = _prepare_expr(places, exprs)
if not is_obj_array(exprs):
exprs = make_obj_array([exprs])
try:
input_exprs = list(input_exprs)
except TypeError:
# not iterable, wrap in a list
input_exprs = [input_exprs]
domains = _prepare_domains(len(input_exprs), places, domains,
places._default_source_place)
from pytential.symbolic.matrix import MatrixBuilder, is_zero
nblock_rows = len(exprs)
nblock_columns = len(input_exprs)
blocks = np.zeros((nblock_rows, nblock_columns), dtype=np.object)
dtypes = []
for ibcol in range(nblock_columns):
mbuilder = MatrixBuilder(
queue,
dep_expr=input_exprs[ibcol],
other_dep_exprs=(input_exprs[:ibcol]
+ input_exprs[ibcol + 1:]),
dep_source=places[domains[ibcol]],
dep_discr=places.get_discretization(domains[ibcol]),
places=places,
context=context)
for ibrow in range(nblock_rows):
block = mbuilder(exprs[ibrow])
assert is_zero(block) or isinstance(block, np.ndarray)
blocks[ibrow, ibcol] = block
if isinstance(block, np.ndarray):
dtypes.append(block.dtype)
return cl.array.to_device(queue, _bmat(blocks, dtypes))
