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# -*- coding: utf-8 -*-
# Copyright (C) 2019-2022 Michal Habera and Jørgen S. Dokken
#
# This file is part of FFCx.(https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
import basix
import cffi
import ffcx.codegeneration.jit
import numpy as np
import ufl
from ffcx.naming import cdtype_to_numpy, scalar_to_value_type
def float_to_type(name):
"""Map a string name to C and NumPy types"""
if name == "double":
return "double", np.float64
elif name == "double complex":
return "double _Complex", np.complex128
elif name == "float":
return "float", np.float32
elif name == "float complex":
return "float _Complex", np.complex64
elif name == "long double":
return "long double", np.longdouble
else:
raise RuntimeError("Unknown C type for: {}".format(name))
def test_matvec(compile_args):
"""Test evaluation of linear rank-0 form.
Evaluates expression c * A_ij * f_j where c is a Constant,
A_ij is a user specified constant matrix and f_j is j-th component
of user specified vector-valued finite element function (in P1 space).
"""
e = ufl.VectorElement("P", "triangle", 1)
mesh = ufl.Mesh(e)
V = ufl.FunctionSpace(mesh, e)
f = ufl.Coefficient(V)
a_mat = np.array([[1.0, 2.0], [1.0, 1.0]])
a = ufl.as_matrix(a_mat)
expr = ufl.Constant(mesh) * ufl.dot(a, f)
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
obj, module, code = ffcx.codegeneration.jit.compile_expressions(
[(expr, points)], cffi_extra_compile_args=compile_args)
ffi = cffi.FFI()
expression = obj[0]
c_type, np_type = float_to_type("double")
A = np.zeros((3, 2), dtype=np_type)
f_mat = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
# Coefficient storage XYXYXY
w = np.array(f_mat.T.flatten(), dtype=np_type)
c = np.array([0.5], dtype=np_type)
entity_index = np.array([0], dtype=np.intc)
quad_perm = np.array([0], dtype=np.dtype("uint8"))
geom_type = scalar_to_value_type(c_type)
np_gtype = cdtype_to_numpy(geom_type)
# Coords storage XYZXYZXYZ
coords = np.array([[0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0]], dtype=np_gtype)
expression.tabulate_tensor_float64(
ffi.cast('{type} *'.format(type=c_type), A.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), w.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), c.ctypes.data),
ffi.cast(f'{geom_type} *', coords.ctypes.data),
ffi.cast('int *', entity_index.ctypes.data),
ffi.cast('uint8_t *', quad_perm.ctypes.data))
# Check the computation against correct NumPy value
assert np.allclose(A, 0.5 * np.dot(a_mat, f_mat).T)
# Prepare NumPy array of points attached to the expression
length = expression.num_points * expression.topological_dimension
points_kernel = np.frombuffer(ffi.buffer(expression.points, length * ffi.sizeof("double")), np.double)
points_kernel = points_kernel.reshape(points.shape)
assert np.allclose(points, points_kernel)
# Check the value shape attached to the expression
value_shape = np.frombuffer(ffi.buffer(expression.value_shape,
expression.num_components * ffi.sizeof("int")), np.intc)
assert np.allclose(expr.ufl_shape, value_shape)
def test_rank1(compile_args):
"""Tests evaluation of rank-1 form.
Builds a linear operator which takes vector-valued functions in P1 space
and evaluates expression [u_y, u_x] + grad(u_x) at specified points.
"""
e = ufl.VectorElement("P", "triangle", 1)
mesh = ufl.Mesh(e)
V = ufl.FunctionSpace(mesh, e)
u = ufl.TrialFunction(V)
expr = ufl.as_vector([u[1], u[0]]) + ufl.grad(u[0])
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
obj, module, code = ffcx.codegeneration.jit.compile_expressions(
[(expr, points)], cffi_extra_compile_args=compile_args)
ffi = cffi.FFI()
expression = obj[0]
c_type, np_type = float_to_type("double")
geom_type = scalar_to_value_type(c_type)
np_gtype = cdtype_to_numpy(geom_type)
# 2 components for vector components of expression
# 3 points of evaluation
# 6 degrees of freedom for rank1 form
A = np.zeros((3, 2, 6), dtype=np_type)
# Coefficient storage XYXYXY
w = np.array([0.0], dtype=np_type)
c = np.array([0.0], dtype=np_type)
entity_index = np.array([0], dtype=np.intc)
quad_perm = np.array([0], dtype=np.dtype("uint8"))
# Coords storage XYZXYZXYZ
coords = np.zeros((points.shape[0], 3), dtype=np_gtype)
coords[:, :2] = points
expression.tabulate_tensor_float64(
ffi.cast('{type} *'.format(type=c_type), A.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), w.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), c.ctypes.data),
ffi.cast(f'{geom_type} *', coords.ctypes.data),
ffi.cast('int *', entity_index.ctypes.data),
ffi.cast('uint8_t *', quad_perm.ctypes.data))
f = np.array([[1.0, 2.0, 3.0], [-4.0, -5.0, 6.0]])
# Apply the operator on some test input data
u_ffcx = np.einsum("ijk,k", A, f.T.flatten())
# Compute the correct values using NumPy
# Gradf0 is gradient of f[0], each component of the gradient is constant
gradf0 = np.array([[f[0, 1] - f[0, 0], f[0, 1] - f[0, 0], f[0, 1] - f[0, 0]],
[f[0, 2] - f[0, 0], f[0, 2] - f[0, 0], f[0, 2] - f[0, 0]]])
u_correct = np.array([f[1], f[0]]) + gradf0
assert np.allclose(u_ffcx, u_correct.T)
def test_elimiate_zero_tables_tensor(compile_args):
"""
Test elimination of tensor-valued expressions with zero tables
"""
cell = "tetrahedron"
c_el = ufl.VectorElement("P", cell, 1)
mesh = ufl.Mesh(c_el)
e = ufl.FiniteElement("CG", cell, 1)
V = ufl.FunctionSpace(mesh, e)
u = ufl.Coefficient(V)
expr = ufl.sym(ufl.as_tensor([[u, u.dx(0).dx(0), 0],
[u.dx(1), u.dx(1), 0],
[0, 0, 0]]))
# Get vectices of cell
# Coords storage XYZXYZXYZ
basix_c_e = basix.create_element(basix.ElementFamily.P, basix.cell.string_to_type(cell), 1, False)
coords = basix_c_e.points
# Using same basix element for coordinate element and coefficient
coeff_points = basix_c_e.points
# Compile expression at interpolation points of second order Lagrange space
b_el = basix.create_element(basix.ElementFamily.P, basix.cell.string_to_type(cell), 0, True)
points = b_el.points
obj, module, code = ffcx.codegeneration.jit.compile_expressions(
[(expr, points)], cffi_extra_compile_args=compile_args)
ffi = cffi.FFI()
expression = obj[0]
c_type, np_type = float_to_type("double")
output = np.zeros(9 * points.shape[0], dtype=np_type)
# Define coefficients for u = x + 2 * y
u_coeffs = u_coeffs = coeff_points.T[0] + 2 * coeff_points.T[1]
consts = np.array([], dtype=np_type)
entity_index = np.array([0], dtype=np.intc)
quad_perm = np.array([0], dtype=np.dtype("uint8"))
expression.tabulate_tensor_float64(
ffi.cast('{type} *'.format(type=c_type), output.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), u_coeffs.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), consts.ctypes.data),
ffi.cast('double *', coords.ctypes.data),
ffi.cast('int *', entity_index.ctypes.data),
ffi.cast('uint8_t *', quad_perm.ctypes.data))
def exact_expr(x):
val = np.zeros((9, x.shape[1]), dtype=np_type)
val[0] = x[0] + 2 * x[1]
val[1] = 0 + 0.5 * 2
val[3] = 0.5 * 2 + 0
val[4] = 2
return val.T
exact = exact_expr(points.T)
assert np.allclose(exact, output)
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