def transfer_kernel(Pk, P1):
"""Compile a kernel that will map between Pk and P1.
:returns: a PyOP2 kernel.
The prolongation maps a solution in P1 into Pk using the natural
embedding. The restriction maps a residual in the dual of Pk into
the dual of P1 (it is the dual of the prolongation), computed
using linearity of the test function.
"""
# Mapping of a residual in Pk into a residual in P1
from coffee import base as coffee
from tsfc.coffee import generate as generate_coffee, SCALAR_TYPE
from tsfc.parameters import default_parameters
from gem import gem, impero_utils as imp
# Pk should be at least the same size as P1
assert Pk.finat_element.space_dimension() >= P1.finat_element.space_dimension()
# In the general case we should compute this by doing:
# numpy.linalg.solve(Pkmass, PkP1mass)
Pke = Pk.finat_element._element
P1e = P1.finat_element._element
# TODO, rework to use finat.
matrix = numpy.dot(Pke.dual.to_riesz(P1e.get_nodal_basis()),
P1e.get_coeffs().T).T
Vout, Vin = P1, Pk
weights = gem.Literal(matrix)
name = "Pk_P1_mapper"
funargs = []
assert Vin.shape == Vout.shape
shape = (P1e.space_dimension() * Vout.value_size,
Pke.space_dimension() * Vin.value_size)
outarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A", rank=shape))
i = gem.Index()
j = gem.Index()
k = gem.Index()
indices = i, j, k
A = gem.Variable("A", shape)
outgem = [gem.Indexed(gem.reshape(A,
(P1e.space_dimension(), Vout.value_size),
(Pke.space_dimension(), Vin.value_size)),
(i, k, j, k))]
funargs.append(outarg)
expr = gem.Indexed(weights, (i, j))
outgem, = imp.preprocess_gem(outgem)
ir = imp.compile_gem([(outgem, expr)], indices)
index_names = [(i, "i"), (j, "j"), (k, "k")]
body = generate_coffee(ir, index_names, default_parameters()["precision"])
function = coffee.FunDecl("void", name, funargs, body,
pred=["static", "inline"])
return op2.Kernel(function, name=function.name)
def compile_ufl_kernel(expression, to_pts, to_element, fs):
import collections
from ufl.algorithms.apply_function_pullbacks import apply_function_pullbacks
from ufl.algorithms.apply_algebra_lowering import apply_algebra_lowering
from ufl.algorithms.apply_derivatives import apply_derivatives
from ufl.algorithms.apply_geometry_lowering import apply_geometry_lowering
from ufl.algorithms import extract_arguments, extract_coefficients
from gem import gem, impero_utils
from tsfc import fem, ufl_utils
from tsfc.coffee import generate as generate_coffee
from tsfc.kernel_interface import (KernelBuilderBase,
needs_cell_orientations,
cell_orientations_coffee_arg)
# Imitate the compute_form_data processing pipeline
#
# Unfortunately, we cannot call compute_form_data here, since
# we only have an expression, not a form
expression = apply_algebra_lowering(expression)
expression = apply_derivatives(expression)
expression = apply_function_pullbacks(expression)
expression = apply_geometry_lowering(expression)
expression = apply_derivatives(expression)
expression = apply_geometry_lowering(expression)
expression = apply_derivatives(expression)
# Replace coordinates (if any)
if expression.ufl_domain():
assert fs.mesh() == expression.ufl_domain()
expression = ufl_utils.replace_coordinates(expression, fs.mesh().coordinates)
if extract_arguments(expression):
return ValueError("Cannot interpolate UFL expression with Arguments!")
builder = KernelBuilderBase()
args = []
coefficients = extract_coefficients(expression)
for i, coefficient in enumerate(coefficients):
args.append(builder.coefficient(coefficient, "w_%d" % i))
point_index = gem.Index(name='p')
ir = fem.process('cell', fs.mesh().ufl_cell(), to_pts, None,
point_index, (), expression,
builder.coefficient_mapper,
collections.defaultdict(gem.Index))
assert len(ir) == 1
# Deal with non-scalar expressions
tensor_indices = ()
if fs.shape:
tensor_indices = tuple(gem.Index() for s in fs.shape)
ir = [gem.Indexed(ir[0], tensor_indices)]
# Build kernel body
return_var = gem.Variable('A', (len(to_pts),) + fs.shape)
return_expr = gem.Indexed(return_var, (point_index,) + tensor_indices)
impero_c = impero_utils.compile_gem([return_expr], ir, [point_index])
body = generate_coffee(impero_c, index_names={point_index: 'p'})
oriented = needs_cell_orientations(ir)
if oriented:
args.insert(0, cell_orientations_coffee_arg)
# Build kernel
args.insert(0, ast.Decl("double", ast.Symbol('A', rank=(len(to_pts),) + fs.shape)))
kernel_code = builder.construct_kernel("expression_kernel", args, body)
return op2.Kernel(kernel_code, kernel_code.name), oriented, coefficients