__copyright__ = """
Copyright (C) 2012 Andreas Kloeckner
Copyright (C) 2018 Alexandru Fikl
"""
__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
import loopy as lp
from loopy.version import MOST_RECENT_LANGUAGE_VERSION
import sumpy.symbolic as sym
from pytools import memoize_method
from pymbolic import parse, var
from sumpy.tools import (
KernelComputation, KernelCacheWrapper, is_obj_array_like)
import logging
logger = logging.getLogger(__name__)
__doc__ = """
QBX for Layer Potentials
------------------------
.. autoclass:: LayerPotentialBase
.. autoclass:: LayerPotential
.. autoclass:: LayerPotentialMatrixGenerator
.. autoclass:: LayerPotentialMatrixSubsetGenerator
"""
def stringify_expn_index(i):
if isinstance(i, tuple):
return "_".join(stringify_expn_index(i_i) for i_i in i)
else:
assert isinstance(i, int)
if i < 0:
return "m%d" % (-i)
else:
return str(i)
# {{{ layer potential computation
# {{{ base class
[docs]class LayerPotentialBase(KernelComputation, KernelCacheWrapper):
def __init__(self, ctx, expansion, strength_usage=None,
value_dtypes=None, name=None, device=None,
source_kernels=None, target_kernels=None):
from pytools import single_valued
KernelComputation.__init__(self, ctx=ctx, target_kernels=target_kernels,
strength_usage=strength_usage, source_kernels=source_kernels,
value_dtypes=value_dtypes, name=name, device=device)
self.dim = single_valued(knl.dim for knl in self.target_kernels)
self.expansion = expansion
def get_cache_key(self):
return (type(self).__name__, self.expansion, tuple(self.target_kernels),
tuple(self.source_kernels), tuple(self.strength_usage),
tuple(self.value_dtypes),
self.device.hashable_model_and_version_identifier)
def _expand(self, sac, avec, bvec, rscale, isrc):
from sumpy.symbolic import PymbolicToSympyMapper
conv = PymbolicToSympyMapper()
strengths = [conv(self.get_strength_or_not(isrc, idx))
for idx in range(len(self.source_kernels))]
coefficients = self.expansion.coefficients_from_source_vec(
self.source_kernels, avec, bvec, rscale=rscale, weights=strengths,
sac=sac)
return coefficients
def _evaluate(self, sac, avec, bvec, rscale, expansion_nr, coefficients):
from sumpy.expansion.local import LineTaylorLocalExpansion
tgt_knl = self.target_kernels[expansion_nr]
if isinstance(tgt_knl, LineTaylorLocalExpansion):
# In LineTaylorLocalExpansion.evaluate, we can't run
# postprocess_at_target because the coefficients are assigned
# symbols and postprocess with a derivative will make them zero.
# Instead run postprocess here before the coeffients are assigned.
coefficients = [tgt_knl.postprocess_at_target(coeff, bvec) for
coeff in coefficients]
assigned_coeffs = [
sym.Symbol(
sac.assign_unique("expn%dcoeff%s" % (
expansion_nr, stringify_expn_index(i)),
coefficients[self.expansion.get_storage_index(i)]))
for i in self.expansion.get_coefficient_identifiers()]
return sac.assign_unique("expn%d_result" % expansion_nr,
self.expansion.evaluate(tgt_knl, assigned_coeffs, bvec, rscale))
def get_loopy_insns_and_result_names(self):
from sumpy.symbolic import make_sym_vector
avec = make_sym_vector("a", self.dim)
bvec = make_sym_vector("b", self.dim)
from sumpy.assignment_collection import SymbolicAssignmentCollection
sac = SymbolicAssignmentCollection()
logger.info("compute expansion expressions: start")
rscale = sym.Symbol("rscale")
isrc_sym = var("isrc")
coefficients = self._expand(sac, avec, bvec, rscale, isrc_sym)
result_names = [self._evaluate(sac, avec, bvec, rscale, i, coefficients)
for i in range(len(self.target_kernels))]
logger.info("compute expansion expressions: done")
sac.run_global_cse()
pymbolic_expr_maps = [knl.get_code_transformer() for knl in (
self.target_kernels + self.source_kernels)]
from sumpy.codegen import to_loopy_insns
loopy_insns = to_loopy_insns(
sac.assignments.items(),
vector_names={"a", "b"},
pymbolic_expr_maps=pymbolic_expr_maps,
retain_names=result_names,
complex_dtype=np.complex128 # FIXME
)
return loopy_insns, result_names
def get_strength_or_not(self, isrc, kernel_idx):
return var("strength_%d_isrc" % self.strength_usage[kernel_idx])
def get_kernel_exprs(self, result_names):
exprs = [var(name) for i, name in enumerate(result_names)]
return [lp.Assignment(id=None,
assignee="pair_result_%d" % i, expression=expr,
temp_var_type=lp.Optional(None))
for i, expr in enumerate(exprs)]
def get_default_src_tgt_arguments(self):
from sumpy.tools import gather_loopy_source_arguments
return ([
lp.GlobalArg("sources", None,
shape=(self.dim, "nsources"), order="C"),
lp.GlobalArg("targets", None,
shape=(self.dim, "ntargets"), order="C"),
lp.GlobalArg("center", None,
shape=(self.dim, "ntargets"), order="C"),
lp.GlobalArg("expansion_radii",
None, shape="ntargets"),
lp.ValueArg("nsources", None),
lp.ValueArg("ntargets", None)]
+ gather_loopy_source_arguments(self.source_kernels))
def get_kernel(self):
raise NotImplementedError
def get_optimized_kernel(self,
targets_is_obj_array, sources_is_obj_array, centers_is_obj_array,
# Used by pytential to override the name of the loop to be
# parallelized. In the case of QBX, that's the loop over QBX
# targets (not global targets).
itgt_name="itgt"):
# FIXME specialize/tune for GPU/CPU
loopy_knl = self.get_kernel()
if targets_is_obj_array:
loopy_knl = lp.tag_array_axes(loopy_knl, "targets", "sep,C")
if sources_is_obj_array:
loopy_knl = lp.tag_array_axes(loopy_knl, "sources", "sep,C")
if centers_is_obj_array:
loopy_knl = lp.tag_array_axes(loopy_knl, "center", "sep,C")
import pyopencl as cl
dev = self.context.devices[0]
if dev.type & cl.device_type.CPU:
loopy_knl = lp.split_iname(loopy_knl, itgt_name, 16, outer_tag="g.0",
inner_tag="l.0")
loopy_knl = lp.split_iname(loopy_knl, "isrc", 256)
loopy_knl = lp.prioritize_loops(loopy_knl,
["isrc_outer", f"{itgt_name}_inner"])
else:
from warnings import warn
warn("don't know how to tune layer potential computation for '%s'" % dev)
loopy_knl = lp.split_iname(loopy_knl, itgt_name, 128, outer_tag="g.0")
loopy_knl = self._allow_redundant_execution_of_knl_scaling(loopy_knl)
return loopy_knl
# }}}
# {{{ direct applier
[docs]class LayerPotential(LayerPotentialBase):
"""Direct applier for the layer potential.
.. automethod:: __call__
"""
default_name = "qbx_apply"
@memoize_method
def get_kernel(self):
loopy_insns, result_names = self.get_loopy_insns_and_result_names()
kernel_exprs = self.get_kernel_exprs(result_names)
arguments = (
self.get_default_src_tgt_arguments()
+ [lp.GlobalArg("strength_%d" % i,
None, shape="nsources", order="C")
for i in range(self.strength_count)]
+ [lp.GlobalArg("result_%d" % i,
None, shape="ntargets", order="C")
for i in range(len(self.target_kernels))])
loopy_knl = lp.make_kernel(["""
{[itgt, isrc, idim]: \
0 <= itgt < ntargets and \
0 <= isrc < nsources and \
0 <= idim < dim}
"""],
self.get_kernel_scaling_assignments()
+ ["for itgt, isrc"]
+ ["<> a[idim] = center[idim, itgt] - sources[idim, isrc] {dup=idim}"]
+ ["<> b[idim] = targets[idim, itgt] - center[idim, itgt] {dup=idim}"]
+ ["<> rscale = expansion_radii[itgt]"]
+ [f"<> strength_{i}_isrc = strength_{i}[isrc]" for i in
range(self.strength_count)]
+ loopy_insns + kernel_exprs
+ ["""
result_{i}[itgt] = knl_{i}_scaling * \
simul_reduce(sum, isrc, pair_result_{i}) \
{{id_prefix=write_lpot,inames=itgt}}
""".format(i=iknl)
for iknl in range(len(self.target_kernels))]
+ ["end"],
arguments,
name=self.name,
assumptions="ntargets>=1 and nsources>=1",
default_offset=lp.auto,
silenced_warnings="write_race(write_lpot*)",
fixed_parameters=dict(dim=self.dim),
lang_version=MOST_RECENT_LANGUAGE_VERSION)
loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
for knl in self.target_kernels + self.source_kernels:
loopy_knl = knl.prepare_loopy_kernel(loopy_knl)
return loopy_knl
[docs] def __call__(self, queue, targets, sources, centers, strengths, expansion_radii,
**kwargs):
"""
:arg strengths: are required to have area elements and quadrature weights
already multiplied in.
"""
knl = self.get_cached_optimized_kernel(
targets_is_obj_array=is_obj_array_like(targets),
sources_is_obj_array=is_obj_array_like(sources),
centers_is_obj_array=is_obj_array_like(centers))
for i, dens in enumerate(strengths):
kwargs["strength_%d" % i] = dens
return knl(queue, sources=sources, targets=targets, center=centers,
expansion_radii=expansion_radii, **kwargs)
# }}}
# {{{ matrix writer
[docs]class LayerPotentialMatrixGenerator(LayerPotentialBase):
"""Generator for layer potential matrix entries."""
default_name = "qbx_matrix"
def get_strength_or_not(self, isrc, kernel_idx):
return 1
@memoize_method
def get_kernel(self):
loopy_insns, result_names = self.get_loopy_insns_and_result_names()
kernel_exprs = self.get_kernel_exprs(result_names)
arguments = (
self.get_default_src_tgt_arguments()
+ [lp.GlobalArg("result_%d" % i,
dtype, shape="ntargets, nsources", order="C")
for i, dtype in enumerate(self.value_dtypes)])
loopy_knl = lp.make_kernel(["""
{[itgt, isrc, idim]: \
0 <= itgt < ntargets and \
0 <= isrc < nsources and \
0 <= idim < dim}
"""],
self.get_kernel_scaling_assignments()
+ ["for itgt, isrc"]
+ ["<> a[idim] = center[idim, itgt] - sources[idim, isrc] {dup=idim}"]
+ ["<> b[idim] = targets[idim, itgt] - center[idim, itgt] {dup=idim}"]
+ ["<> rscale = expansion_radii[itgt]"]
+ loopy_insns + kernel_exprs
+ ["""
result_{i}[itgt, isrc] = \
knl_{i}_scaling * pair_result_{i} \
{{inames=isrc:itgt}}
""".format(i=iknl)
for iknl in range(len(self.target_kernels))]
+ ["end"],
arguments,
name=self.name,
assumptions="ntargets>=1 and nsources>=1",
default_offset=lp.auto,
fixed_parameters=dict(dim=self.dim),
lang_version=MOST_RECENT_LANGUAGE_VERSION)
loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
for expn in self.source_kernels + self.target_kernels:
loopy_knl = expn.prepare_loopy_kernel(loopy_knl)
return loopy_knl
def __call__(self, queue, targets, sources, centers, expansion_radii, **kwargs):
knl = self.get_cached_optimized_kernel(
targets_is_obj_array=is_obj_array_like(targets),
sources_is_obj_array=is_obj_array_like(sources),
centers_is_obj_array=is_obj_array_like(centers))
return knl(queue, sources=sources, targets=targets, center=centers,
expansion_radii=expansion_radii, **kwargs)
# }}}
# {{{ matrix subset generator
[docs]class LayerPotentialMatrixSubsetGenerator(LayerPotentialBase):
"""Generator for a subset of the layer potential matrix entries.
.. automethod:: __call__
"""
default_name = "qbx_subset"
def get_strength_or_not(self, isrc, kernel_idx):
return 1
@memoize_method
def get_kernel(self):
loopy_insns, result_names = self.get_loopy_insns_and_result_names()
kernel_exprs = self.get_kernel_exprs(result_names)
arguments = (
self.get_default_src_tgt_arguments()
+ [
lp.GlobalArg("srcindices", None, shape="nresult"),
lp.GlobalArg("tgtindices", None, shape="nresult"),
lp.ValueArg("nresult", None)
]
+ [lp.GlobalArg("result_%d" % i, dtype, shape="nresult")
for i, dtype in enumerate(self.value_dtypes)])
loopy_knl = lp.make_kernel([
"{[imat, idim]: 0 <= imat < nresult and 0 <= idim < dim}"
],
self.get_kernel_scaling_assignments()
# NOTE: itgt, isrc need to always be defined in case a statement
# in loopy_insns or kernel_exprs needs them (e.g. hardcoded in
# places like get_kernel_exprs)
+ ["""
for imat
<> itgt = tgtindices[imat]
<> isrc = srcindices[imat]
<> a[idim] = center[idim, itgt] - sources[idim, isrc] {dup=idim}
<> b[idim] = targets[idim, itgt] - center[idim, itgt] {dup=idim}
<> rscale = expansion_radii[itgt]
"""]
+ loopy_insns + kernel_exprs
+ ["""
result_{i}[imat] = knl_{i}_scaling * pair_result_{i} \
{{id_prefix=write_lpot}}
""".format(i=iknl)
for iknl in range(len(self.target_kernels))]
+ ["end"],
arguments,
name=self.name,
assumptions="nresult>=1",
default_offset=lp.auto,
silenced_warnings="write_race(write_lpot*)",
fixed_parameters=dict(dim=self.dim),
lang_version=MOST_RECENT_LANGUAGE_VERSION)
loopy_knl = lp.tag_inames(loopy_knl, "idim*:unr")
loopy_knl = lp.add_dtypes(loopy_knl,
dict(nsources=np.int32, ntargets=np.int32))
for knl in self.source_kernels + self.target_kernels:
loopy_knl = knl.prepare_loopy_kernel(loopy_knl)
return loopy_knl
def get_optimized_kernel(self,
targets_is_obj_array, sources_is_obj_array, centers_is_obj_array):
loopy_knl = self.get_kernel()
if targets_is_obj_array:
loopy_knl = lp.tag_array_axes(loopy_knl, "targets", "sep,C")
if sources_is_obj_array:
loopy_knl = lp.tag_array_axes(loopy_knl, "sources", "sep,C")
if centers_is_obj_array:
loopy_knl = lp.tag_array_axes(loopy_knl, "center", "sep,C")
loopy_knl = lp.split_iname(loopy_knl, "imat", 1024, outer_tag="g.0")
loopy_knl = self._allow_redundant_execution_of_knl_scaling(loopy_knl)
return loopy_knl
[docs] def __call__(self, queue, targets, sources, centers, expansion_radii,
tgtindices, srcindices, **kwargs):
"""Evaluate a subset of the QBX matrix interactions.
:arg targets: target point coordinates, which can be an object
:class:`~numpy.ndarray`, :class:`list` or :class:`tuple` of
coordinates or a single stacked array.
:arg sources: source point coordinates, which can also be in any of the
formats of the *targets*,
:arg centers: QBX target expansion center coordinates, which can also
be in any of the formats of the *targets*. The number of centers
must match the number of targets.
:arg expansion_radii: radii for each expansion center.
:arg srcindices: an array of indices into *sources*.
:arg tgtindices: an array of indices into *targets*, of the same size
as *srcindices*.
:returns: a one-dimensional array of interactions, for each index pair
in (*srcindices*, *tgtindices*)
"""
knl = self.get_cached_optimized_kernel(
targets_is_obj_array=is_obj_array_like(targets),
sources_is_obj_array=is_obj_array_like(sources),
centers_is_obj_array=is_obj_array_like(centers))
return knl(queue,
sources=sources,
targets=targets,
center=centers,
expansion_radii=expansion_radii,
tgtindices=tgtindices,
srcindices=srcindices, **kwargs)
# }}}
# }}}
# {{{ jump term handling
def find_jump_term(kernel, arg_provider):
from sumpy.kernel import (
AxisSourceDerivative,
AxisTargetDerivative,
DirectionalSourceDerivative,
DirectionalTargetDerivative,
DerivativeBase)
tgt_derivatives = []
src_derivatives = []
while isinstance(kernel, DerivativeBase):
if isinstance(kernel, AxisTargetDerivative):
tgt_derivatives.append(kernel.axis)
kernel = kernel.kernel
elif isinstance(kernel, DirectionalTargetDerivative):
tgt_derivatives.append(kernel.dir_vec_name)
kernel = kernel.kernel
elif isinstance(kernel, AxisSourceDerivative):
src_derivatives.append(kernel.axis)
kernel = kernel.kernel
elif isinstance(kernel, DirectionalSourceDerivative):
src_derivatives.append(kernel.dir_vec_name)
kernel = kernel.kernel
else:
raise RuntimeError("derivative type '%s' not understood"
% type(kernel))
tgt_count = len(tgt_derivatives)
src_count = len(src_derivatives)
info = arg_provider
if src_count == 0:
if tgt_count == 0:
return 0
elif tgt_count == 1:
tgt_derivative, = tgt_derivatives
if isinstance(tgt_derivative, int):
# axis derivative
return info.side/2 * info.normal[tgt_derivative] * info.density
else:
# directional derivative
return (info.side/2
* np.dot(info.normal, getattr(info, tgt_derivative))
* info.density)
elif tgt_count == 2:
i, j = tgt_derivatives
assert isinstance(i, int)
assert isinstance(j, int)
from pytools import delta
return (
- info.side * info.mean_curvature / 2
* (-delta(i, j) + 2*info.normal[i]*info.normal[j])
* info.density
+ info.side / 2
* (info.normal[i]*info.tangent[j]
+ info.normal[j]*info.tangent[i])
* info.density_prime)
elif src_count == 1:
src_derivative_name, = src_derivatives
if tgt_count == 0:
return (
- info.side/2
* np.dot(info.normal, getattr(info, src_derivative_name))
* info.density)
elif tgt_count == 1:
from warnings import warn
warn("jump terms for mixed derivatives (1 src+1 tgt) only available "
"for the double-layer potential")
i, = tgt_derivatives
assert isinstance(i, int)
return (
- info.side/2
* info.tangent[i]
* info.density_prime)
raise ValueError("don't know jump term for %d "
"target and %d source derivatives" % (tgt_count, src_count))
# {{{ symbolic argument provider
class _JumpTermSymbolicArgumentProvider:
"""This class answers requests by :func:`find_jump_term` for symbolic values
of quantities needed for the computation of the jump terms and tracks what
data was requested. This tracking allows assembling the argument list of the
resulting computational kernel.
"""
def __init__(self, data_args, dim, density_var_name,
density_dtype, geometry_dtype):
# dictionary of loopy arguments
self.arguments = data_args
self.dim = dim
self.density_var_name = density_var_name
self.density_dtype = density_dtype
self.geometry_dtype = geometry_dtype
@property
@memoize_method
def density(self):
self.arguments[self.density_var_name] = \
lp.GlobalArg(self.density_var_name, self.density_dtype,
shape="ntargets", order="C")
return parse("%s[itgt]" % self.density_var_name)
@property
@memoize_method
def density_prime(self):
prime_var_name = self.density_var_name+"_prime"
self.arguments[prime_var_name] = \
lp.GlobalArg(prime_var_name, self.density_dtype,
shape="ntargets", order="C")
return parse("%s[itgt]" % prime_var_name)
@property
@memoize_method
def side(self):
self.arguments["side"] = \
lp.GlobalArg("side", self.geometry_dtype, shape="ntargets")
return parse("side[itgt]")
@property
@memoize_method
def normal(self):
self.arguments["normal"] = \
lp.GlobalArg("normal", self.geometry_dtype,
shape=("ntargets", self.dim), order="C")
from pytools.obj_array import make_obj_array
return make_obj_array([
parse("normal[itgt, %d]" % i)
for i in range(self.dim)])
@property
@memoize_method
def tangent(self):
self.arguments["tangent"] = \
lp.GlobalArg("tangent", self.geometry_dtype,
shape=("ntargets", self.dim), order="C")
from pytools.obj_array import make_obj_array
return make_obj_array([
parse("tangent[itgt, %d]" % i)
for i in range(self.dim)])
@property
@memoize_method
def mean_curvature(self):
self.arguments["mean_curvature"] = \
lp.GlobalArg("mean_curvature",
self.geometry_dtype, shape="ntargets",
order="C")
return parse("mean_curvature[itgt]")
@property
@memoize_method
def src_derivative_dir(self):
self.arguments["src_derivative_dir"] = \
lp.GlobalArg("src_derivative_dir",
self.geometry_dtype, shape=("ntargets", self.dim),
order="C")
from pytools.obj_array import make_obj_array
return make_obj_array([
parse("src_derivative_dir[itgt, %d]" % i)
for i in range(self.dim)])
@property
@memoize_method
def tgt_derivative_dir(self):
self.arguments["tgt_derivative_dir"] = \
lp.GlobalArg("tgt_derivative_dir",
self.geometry_dtype, shape=("ntargets", self.dim),
order="C")
from pytools.obj_array import make_obj_array
return make_obj_array([
parse("tgt_derivative_dir[itgt, %d]" % i)
for i in range(self.dim)])
# }}}
# }}}
# vim: fdm=marker