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#define BOOST_TEST_MODULE TestQR
#include <boost/test/unit_test.hpp>
#include <vector>
#include <random>
#include <boost/multi_array.hpp>
#include <amgcl/detail/qr.hpp>
#include <amgcl/value_type/interface.hpp>
#include <amgcl/value_type/complex.hpp>
#include <amgcl/value_type/static_matrix.hpp>
template <class T>
struct make_random {
static T get() {
static std::mt19937 gen;
static std::uniform_real_distribution<T> rnd;
return rnd(gen);
}
};
template <class T>
T random() {
return make_random<T>::get();
}
template <class T>
struct make_random< std::complex<T> > {
static std::complex<T> get() {
return std::complex<T>( random<T>(), random<T>() );
}
};
template <class T, int N, int M>
struct make_random< amgcl::static_matrix<T,N,M> > {
typedef amgcl::static_matrix<T,N,M> matrix;
static matrix get() {
matrix A = amgcl::math::zero<matrix>();
for(int i = 0; i < N; ++i)
for(int j = 0; j < M; ++j)
A(i,j) = make_random<T>::get();
return A;
}
};
template <class value_type, amgcl::detail::storage_order order>
void qr_factorize(int n, int m) {
std::cout << "factorize " << n << " " << m << std::endl;
typedef typename std::conditional<order == amgcl::detail::row_major,
boost::c_storage_order,
boost::fortran_storage_order
>::type ma_storage_order;
boost::multi_array<value_type, 2> A0(boost::extents[n][m], ma_storage_order());
for(int i = 0; i < n; ++i)
for(int j = 0; j < m; ++j)
A0[i][j] = random<value_type>();
boost::multi_array<value_type, 2> A = A0;
amgcl::detail::QR<value_type> qr;
qr.factorize(n, m, A.data(), order);
// Check that A = QR
int p = std::min(n, m);
for(int i = 0; i < n; ++i) {
for(int j = 0; j < m; ++j) {
value_type sum = amgcl::math::zero<value_type>();
for(int k = 0; k < p; ++k)
sum += qr.Q(i,k) * qr.R(k,j);
sum -= A0[i][j];
BOOST_CHECK_SMALL(amgcl::math::norm(sum), 1e-8);
}
}
}
template <class value_type, amgcl::detail::storage_order order>
void qr_solve(int n, int m) {
std::cout << "solve " << n << " " << m << std::endl;
typedef typename std::conditional<order == amgcl::detail::row_major,
boost::c_storage_order,
boost::fortran_storage_order
>::type ma_storage_order;
typedef typename amgcl::math::rhs_of<value_type>::type rhs_type;
boost::multi_array<value_type, 2> A0(boost::extents[n][m], ma_storage_order());
for(int i = 0; i < n; ++i)
for(int j = 0; j < m; ++j)
A0[i][j] = random<value_type>();
boost::multi_array<value_type, 2> A = A0;
amgcl::detail::QR<value_type> qr;
std::vector<rhs_type> f0(n, amgcl::math::constant<rhs_type>(1));
std::vector<rhs_type> f = f0;
std::vector<rhs_type> x(m);
qr.solve(n, m, A.data(), f.data(), x.data(), order);
std::vector<rhs_type> Ax(n);
for(int i = 0; i < n; ++i) {
rhs_type sum = amgcl::math::zero<rhs_type>();
for(int j = 0; j < m; ++j)
sum += A0[i][j] * x[j];
Ax[i] = sum;
if (n < m) {
BOOST_CHECK_SMALL(amgcl::math::norm(sum - f0[i]), 1e-8);
}
}
if (n >= m) {
for(int i = 0; i < m; ++i) {
rhs_type sumx = amgcl::math::zero<rhs_type>();
rhs_type sumf = amgcl::math::zero<rhs_type>();
for(int j = 0; j < n; ++j) {
sumx += amgcl::math::adjoint(A0[j][i]) * Ax[j];
sumf += amgcl::math::adjoint(A0[j][i]) * f0[j];
}
rhs_type delta = sumx - sumf;
BOOST_CHECK_SMALL(amgcl::math::norm(delta), 1e-8);
}
}
}
BOOST_AUTO_TEST_SUITE( test_qr )
BOOST_AUTO_TEST_CASE( test_qr_factorize ) {
const int shape[][2] = {
{3, 3},
{3, 5},
{5, 3},
{5, 5}
};
const int n = sizeof(shape) / sizeof(shape[0]);
for(int i = 0; i < n; ++i) {
qr_factorize<double, amgcl::detail::row_major>(shape[i][0], shape[i][1]);
qr_factorize<double, amgcl::detail::col_major>(shape[i][0], shape[i][1]);
qr_factorize<std::complex<double>, amgcl::detail::row_major>(shape[i][0], shape[i][1]);
qr_factorize<std::complex<double>, amgcl::detail::col_major>(shape[i][0], shape[i][1]);
qr_factorize<amgcl::static_matrix<double, 2, 2>, amgcl::detail::row_major>(shape[i][0], shape[i][1]);
qr_factorize<amgcl::static_matrix<double, 2, 2>, amgcl::detail::col_major>(shape[i][0], shape[i][1]);
}
}
BOOST_AUTO_TEST_CASE( test_qr_solve ) {
const int shape[][2] = {
{3, 3},
{3, 5},
{5, 3},
{5, 5}
};
const int n = sizeof(shape) / sizeof(shape[0]);
for(int i = 0; i < n; ++i) {
qr_solve<double, amgcl::detail::row_major>(shape[i][0], shape[i][1]);
qr_solve<double, amgcl::detail::col_major>(shape[i][0], shape[i][1]);
qr_solve<std::complex<double>, amgcl::detail::row_major>(shape[i][0], shape[i][1]);
qr_solve<std::complex<double>, amgcl::detail::col_major>(shape[i][0], shape[i][1]);
qr_solve<amgcl::static_matrix<double, 2, 2>, amgcl::detail::row_major>(shape[i][0], shape[i][1]);
qr_solve<amgcl::static_matrix<double, 2, 2>, amgcl::detail::col_major>(shape[i][0], shape[i][1]);
}
}
BOOST_AUTO_TEST_CASE( qr_issue_39 ) {
boost::multi_array<double, 2> A0(boost::extents[2][2]);
A0[0][0] = 1e+0;
A0[0][1] = 1e+0;
A0[1][0] = 1e-8;
A0[1][1] = 1e+0;
boost::multi_array<double, 2> A = A0;
amgcl::detail::QR<double> qr;
qr.factorize(2, 2, A.data());
// Check that A = QR
for(int i = 0; i < 2; ++i) {
for(int j = 0; j < 2; ++j) {
double sum = 0;
for(int k = 0; k < 2; ++k)
sum += qr.Q(i,k) * qr.R(k,j);
sum -= A0[i][j];
BOOST_CHECK_SMALL(sum, 1e-8);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
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