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"""Unit tests for assembly with Numba and CFFI kernels."""
# Copyright (C) 2018-2014 Chris N. Richardson, Michal Habera and Garth N. Wells
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
import os
import sys
from mpi4py import MPI
import numpy as np
import pytest
import dolfinx
import dolfinx.utils
import ffcx.codegeneration.utils
from dolfinx import cpp as _cpp
from dolfinx import fem, la
from dolfinx.common import TimingType, list_timings
from dolfinx.fem import Form, Function, IntegralType, form_cpp_class, functionspace
from dolfinx.mesh import create_unit_square
numba = pytest.importorskip("numba")
ufcx_signature = ffcx.codegeneration.utils.numba_ufcx_kernel_signature
sys.path.append(os.getcwd())
def tabulate_rank2(dtype, xdtype):
@numba.cfunc(ufcx_signature(dtype, xdtype), nopython=True)
def tabulate(A_, w_, c_, coords_, entity_local_index, cell_orientation):
A = numba.carray(A_, (3, 3), dtype=dtype)
coordinate_dofs = numba.carray(coords_, (3, 3), dtype=xdtype)
# Ke=∫Ωe BTe Be dΩ
x0, y0 = coordinate_dofs[0, :2]
x1, y1 = coordinate_dofs[1, :2]
x2, y2 = coordinate_dofs[2, :2]
# 2x Element area Ae
Ae = abs((x0 - x1) * (y2 - y1) - (y0 - y1) * (x2 - x1))
B = np.array([y1 - y2, y2 - y0, y0 - y1, x2 - x1, x0 - x2, x1 - x0], dtype=dtype).reshape(
2, 3
)
A[:, :] = np.dot(B.T, B) / (2 * Ae)
return tabulate
def tabulate_rank1(dtype, xdtype):
@numba.cfunc(ufcx_signature(dtype, xdtype), nopython=True)
def tabulate(b_, w_, c_, coords_, local_index, orientation):
b = numba.carray(b_, (3), dtype=dtype)
coordinate_dofs = numba.carray(coords_, (3, 3), dtype=xdtype)
x0, y0 = coordinate_dofs[0, :2]
x1, y1 = coordinate_dofs[1, :2]
x2, y2 = coordinate_dofs[2, :2]
# 2x Element area Ae
Ae = abs((x0 - x1) * (y2 - y1) - (y0 - y1) * (x2 - x1))
b[:] = Ae / 6.0
return tabulate
def tabulate_rank1_coeff(dtype, xdtype):
@numba.cfunc(ufcx_signature(dtype, xdtype), nopython=True)
def tabulate(b_, w_, c_, coords_, local_index, orientation):
b = numba.carray(b_, (3), dtype=dtype)
w = numba.carray(w_, (1), dtype=dtype)
coordinate_dofs = numba.carray(coords_, (3, 3), dtype=xdtype)
x0, y0 = coordinate_dofs[0, :2]
x1, y1 = coordinate_dofs[1, :2]
x2, y2 = coordinate_dofs[2, :2]
# 2x Element area Ae
Ae = abs((x0 - x1) * (y2 - y1) - (y0 - y1) * (x2 - x1))
b[:] = w[0] * Ae / 6.0
return tabulate
@pytest.mark.parametrize("dtype", [np.float32, np.float64, np.complex64, np.complex128])
def test_numba_assembly(dtype):
xdtype = np.real(dtype(0)).dtype
k2 = tabulate_rank2(dtype, xdtype)
k1 = tabulate_rank1(dtype, xdtype)
mesh = create_unit_square(MPI.COMM_WORLD, 13, 13, dtype=xdtype)
V = functionspace(mesh, ("Lagrange", 1))
cells = np.arange(mesh.topology.index_map(mesh.topology.dim).size_local, dtype=np.int32)
active_coeffs = np.array([], dtype=np.int8)
integrals = {
IntegralType.cell: [
(-1, k2.address, cells, active_coeffs),
(2, k2.address, np.arange(0), active_coeffs),
(12, k2.address, np.arange(0), active_coeffs),
]
}
formtype = form_cpp_class(dtype)
a = Form(formtype([V._cpp_object, V._cpp_object], integrals, [], [], False, {}, None))
integrals = {IntegralType.cell: [(-1, k1.address, cells, active_coeffs)]}
L = Form(formtype([V._cpp_object], integrals, [], [], False, {}, None))
A = dolfinx.fem.assemble_matrix(a)
A.scatter_reverse()
b = dolfinx.fem.assemble_vector(L)
b.scatter_reverse(dolfinx.la.InsertMode.add)
Anorm = np.sqrt(A.squared_norm())
bnorm = la.norm(b)
assert np.isclose(Anorm, 56.124860801609124)
assert np.isclose(bnorm, 0.0739710713711999)
list_timings(MPI.COMM_WORLD, [TimingType.wall])
@pytest.mark.parametrize("dtype", [np.float32, np.float64, np.complex64, np.complex128])
def test_coefficient(dtype):
xdtype = np.real(dtype(0)).dtype
k1 = tabulate_rank1_coeff(dtype, xdtype)
mesh = create_unit_square(MPI.COMM_WORLD, 13, 13, dtype=xdtype)
V = functionspace(mesh, ("Lagrange", 1))
DG0 = functionspace(mesh, ("DG", 0))
vals = Function(DG0, dtype=dtype)
vals.x.array[: vals.x.index_map.size_local] = 2
tdim = mesh.topology.dim
num_cells = mesh.topology.index_map(tdim).size_local + mesh.topology.index_map(tdim).num_ghosts
active_coeffs = np.array([0], dtype=np.int8)
integrals = {
IntegralType.cell: [(1, k1.address, np.arange(num_cells, dtype=np.int32), active_coeffs)]
}
formtype = form_cpp_class(dtype)
L = Form(formtype([V._cpp_object], integrals, [vals._cpp_object], [], False, {}, None))
b = dolfinx.fem.assemble_vector(L)
b.scatter_reverse(la.InsertMode.add)
bnorm = la.norm(b)
assert np.isclose(bnorm, 2.0 * 0.0739710713711999)
@pytest.mark.skip_in_parallel
def test_cffi_assembly():
pytest.importorskip("cffi")
mesh = create_unit_square(MPI.COMM_WORLD, 13, 13, dtype=np.float64)
V = functionspace(mesh, ("Lagrange", 1))
if mesh.comm.rank == 0:
from cffi import FFI
ffibuilder = FFI()
ffibuilder.set_source(
"_cffi_kernelA",
r"""
#include <math.h>
void tabulate_tensor_poissonA(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation)
{
// Precomputed values of basis functions and precomputations
// FE* dimensions: [entities][points][dofs]
// PI* dimensions: [entities][dofs][dofs] or [entities][dofs]
// PM* dimensions: [entities][dofs][dofs]
static const double FE3_C0_D01_Q1[1][1][2] = { { { -1.0, 1.0 } } };
// Unstructured piecewise computations
const double J_c0 = coordinate_dofs[0] * FE3_C0_D01_Q1[0][0][0]
+ coordinate_dofs[3] * FE3_C0_D01_Q1[0][0][1];
const double J_c3 = coordinate_dofs[1] * FE3_C0_D01_Q1[0][0][0]
+ coordinate_dofs[7] * FE3_C0_D01_Q1[0][0][1];
const double J_c1 = coordinate_dofs[0] * FE3_C0_D01_Q1[0][0][0]
+ coordinate_dofs[6] * FE3_C0_D01_Q1[0][0][1];
const double J_c2 = coordinate_dofs[1] * FE3_C0_D01_Q1[0][0][0]
+ coordinate_dofs[4] * FE3_C0_D01_Q1[0][0][1];
double sp[20];
sp[0] = J_c0 * J_c3;
sp[1] = J_c1 * J_c2;
sp[2] = sp[0] + -1 * sp[1];
sp[3] = J_c0 / sp[2];
sp[4] = -1 * J_c1 / sp[2];
sp[5] = sp[3] * sp[3];
sp[6] = sp[3] * sp[4];
sp[7] = sp[4] * sp[4];
sp[8] = J_c3 / sp[2];
sp[9] = -1 * J_c2 / sp[2];
sp[10] = sp[9] * sp[9];
sp[11] = sp[8] * sp[9];
sp[12] = sp[8] * sp[8];
sp[13] = sp[5] + sp[10];
sp[14] = sp[6] + sp[11];
sp[15] = sp[12] + sp[7];
sp[16] = fabs(sp[2]);
sp[17] = sp[13] * sp[16];
sp[18] = sp[14] * sp[16];
sp[19] = sp[15] * sp[16];
// UFLACS block mode: preintegrated
A[0] = 0.5 * sp[19] + 0.5 * sp[18] + 0.5 * sp[18] + 0.5 * sp[17];
A[1] = -0.5 * sp[19] + -0.5 * sp[18];
A[2] = -0.5 * sp[18] + -0.5 * sp[17];
A[3] = -0.5 * sp[19] + -0.5 * sp[18];
A[4] = 0.5 * sp[19];
A[5] = 0.5 * sp[18];
A[6] = -0.5 * sp[18] + -0.5 * sp[17];
A[7] = 0.5 * sp[18];
A[8] = 0.5 * sp[17];
}
void tabulate_tensor_poissonL(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation)
{
// Precomputed values of basis functions and precomputations
// FE* dimensions: [entities][points][dofs]
// PI* dimensions: [entities][dofs][dofs] or [entities][dofs]
// PM* dimensions: [entities][dofs][dofs]
static const double FE4_C0_D01_Q1[1][1][2] = { { { -1.0, 1.0 } } };
// Unstructured piecewise computations
const double J_c0 = coordinate_dofs[0] * FE4_C0_D01_Q1[0][0][0]
+ coordinate_dofs[3] * FE4_C0_D01_Q1[0][0][1];
const double J_c3 = coordinate_dofs[1] * FE4_C0_D01_Q1[0][0][0]
+ coordinate_dofs[7] * FE4_C0_D01_Q1[0][0][1];
const double J_c1 = coordinate_dofs[0] * FE4_C0_D01_Q1[0][0][0]
+ coordinate_dofs[6] * FE4_C0_D01_Q1[0][0][1];
const double J_c2 = coordinate_dofs[1] * FE4_C0_D01_Q1[0][0][0]
+ coordinate_dofs[4] * FE4_C0_D01_Q1[0][0][1];
double sp[4];
sp[0] = J_c0 * J_c3;
sp[1] = J_c1 * J_c2;
sp[2] = sp[0] + -1 * sp[1];
sp[3] = fabs(sp[2]);
A[0] = 0.1666666666666667 * sp[3];
A[1] = 0.1666666666666667 * sp[3];
A[2] = 0.1666666666666667 * sp[3];
}
""",
)
ffibuilder.cdef(
"""
void tabulate_tensor_poissonA(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation);
void tabulate_tensor_poissonL(double* restrict A, const double* w,
const double* c,
const double* restrict coordinate_dofs,
const int* entity_local_index,
const int* cell_orientation);
"""
)
ffibuilder.compile(verbose=True)
mesh.comm.Barrier()
from _cffi_kernelA import ffi, lib
cells = np.arange(mesh.topology.index_map(mesh.topology.dim).size_local, dtype=np.int32)
ptrA = ffi.cast("intptr_t", ffi.addressof(lib, "tabulate_tensor_poissonA"))
active_coeffs = np.array([], dtype=np.int8)
integrals = {IntegralType.cell: [(-1, ptrA, cells, active_coeffs)]}
a = Form(
_cpp.fem.Form_float64([V._cpp_object, V._cpp_object], integrals, [], [], False, {}, None)
)
ptrL = ffi.cast("intptr_t", ffi.addressof(lib, "tabulate_tensor_poissonL"))
integrals = {IntegralType.cell: [(-1, ptrL, cells, active_coeffs)]}
L = Form(_cpp.fem.Form_float64([V._cpp_object], integrals, [], [], False, {}, None))
A = fem.assemble_matrix(a)
A.scatter_reverse()
assert np.isclose(np.sqrt(A.squared_norm()), 56.124860801609124)
b = fem.assemble_vector(L)
b.scatter_reverse(la.InsertMode.add)
assert np.isclose(la.norm(b), 0.0739710713711999)
|
