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rGOOSEFEM/tests/basic/Matrix.cpp
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Matrix.cpp
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#include <catch2/catch.hpp>
#include <xtensor/xrandom.hpp>
#include <GooseFEM/Matrix.h>
#include <GooseFEM/MeshQuad4.h>
#define ISCLOSE(a,b) REQUIRE_THAT((a), Catch::WithinAbs((b), 1.e-12));
TEST_CASE("GooseFEM::Matrix", "Matrix.h")
{
SECTION("solve")
{
GooseFEM::Mesh::Quad4::Regular mesh(2, 2);
size_t nne = mesh.nne();
size_t ndim = mesh.ndim();
size_t nelem = mesh.nelem();
size_t nnode = mesh.nnode();
xt::xtensor<double, 3> a = xt::empty<double>({nelem, nne * ndim, nne * ndim});
xt::xtensor<double, 1> b = xt::random::rand<double>({nnode * ndim});
for (size_t e = 0; e < nelem; ++e) {
xt::xtensor<double, 2> ae = xt::random::rand<double>({nne * ndim, nne * ndim});
ae = (ae + xt::transpose(ae)) / 2.0;
xt::view(a, e, xt::all(), xt::all()) = ae;
}
GooseFEM::Matrix A(mesh.conn(), mesh.dofs());
GooseFEM::MatrixSolver<> Solver;
A.assemble(a);
xt::xtensor<double, 1> C = A.Dot(b);
xt::xtensor<double, 1> B = Solver.Solve(A, C);
REQUIRE(B.size() == b.size());
REQUIRE(xt::allclose(B, b));
}
SECTION("set/add/dot/solve - dofval")
{
xt::xtensor<double, 2> a = xt::random::rand<double>({10, 10});
xt::xtensor<double, 1> x = xt::random::rand<double>({10});
xt::xtensor<double, 1> b = xt::zeros<double>({10});
xt::xtensor<double, 2> A = a + xt::transpose(a);
for (size_t i = 0; i < A.shape(0); ++i) {
for (size_t j = 0; j < A.shape(1); ++j) {
b(i) += A(i, j) * x(j);
}
}
xt::xtensor<size_t, 2> conn = xt::zeros<size_t>({1, 5});
xt::xtensor<size_t, 2> dofs = xt::arange<size_t>(10).reshape({5, 2});
GooseFEM::Matrix K(conn, dofs);
GooseFEM::MatrixSolver<> Solver;
K.set(xt::arange<size_t>(10), xt::arange<size_t>(10), a);
K.add(xt::arange<size_t>(10), xt::arange<size_t>(10), xt::transpose(a));
REQUIRE(xt::allclose(A, K.Todense()));
REQUIRE(xt::allclose(b, K.Dot(x)));
REQUIRE(xt::allclose(x, Solver.Solve(K, b)));
}
SECTION("set/add/dot/solve - nodevec")
{
xt::xtensor<double, 2> a = xt::random::rand<double>({10, 10});
xt::xtensor<double, 2> x = xt::random::rand<double>({5, 2});
xt::xtensor<double, 2> b = xt::zeros<double>({5, 2});
xt::xtensor<double, 2> A = a + xt::transpose(a);
for (size_t m = 0; m < x.shape(0); ++m) {
for (size_t n = 0; n < x.shape(0); ++n) {
for (size_t i = 0; i < x.shape(1); ++i) {
for (size_t j = 0; j < x.shape(1); ++j) {
b(m, i) += A(m * x.shape(1) + i, n * x.shape(1) + j) * x(n, j);
}
}
}
}
xt::xtensor<size_t, 2> conn = xt::zeros<size_t>({1, 5});
xt::xtensor<size_t, 2> dofs = xt::arange<size_t>(10).reshape({5, 2});
GooseFEM::Matrix K(conn, dofs);
GooseFEM::MatrixSolver<> Solver;
K.set(xt::arange<size_t>(10), xt::arange<size_t>(10), a);
K.add(xt::arange<size_t>(10), xt::arange<size_t>(10), xt::transpose(a));
REQUIRE(xt::allclose(A, K.Todense()));
REQUIRE(xt::allclose(b, K.Dot(x)));
REQUIRE(xt::allclose(x, Solver.Solve(K, b)));
}
}
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