void test_svd(const std::string & fn, ScalarType EPS)
{
std::size_t sz1, sz2;
//read matrix
// sz1 = 2048, sz2 = 2048;
// std::vector<ScalarType> in(sz1 * sz2);
// random_fill(in);
// read file
std::fstream f(fn.c_str(), std::fstream::in);
//read size of input matrix
read_matrix_size(f, sz1, sz2);
std::size_t to = std::min(sz1, sz2);
viennacl::matrix<ScalarType> Ai(sz1, sz2), Aref(sz1, sz2), QL(sz1, sz1), QR(sz2, sz2);
read_matrix_body(f, Ai);
std::vector<ScalarType> sigma_ref(to);
read_vector_body(f, sigma_ref);
f.close();
// viennacl::fast_copy(&in[0], &in[0] + in.size(), Ai);
Aref = Ai;
viennacl::tools::timer timer;
timer.start();
viennacl::linalg::svd(Ai, QL, QR);
viennacl::backend::finish();
double time_spend = timer.get();
viennacl::matrix<ScalarType> result1(sz1, sz2), result2(sz1, sz2);
result1 = viennacl::linalg::prod(QL, Ai);
result2 = viennacl::linalg::prod(result1, trans(QR));
ScalarType sigma_diff = sigmas_compare(Ai, sigma_ref);
ScalarType prods_diff = matrix_compare(result2, Aref);
bool sigma_ok = (fabs(sigma_diff) < EPS)
&& (fabs(prods_diff) < std::sqrt(EPS)); //note: computing the product is not accurate down to 10^{-16}, so we allow for a higher tolerance here
printf("%6s [%dx%d] %40s sigma_diff = %.6f; prod_diff = %.6f; time = %.6f\n", sigma_ok?"[[OK]]":"[FAIL]", (int)Aref.size1(), (int)Aref.size2(), fn.c_str(), sigma_diff, prods_diff, time_spend);
if (!sigma_ok)
exit(EXIT_FAILURE);
}
void test_eigen(const std::string& fn, bool is_symm)
{
std::cout << "Reading..." << "\n";
std::size_t sz;
// read file
std::fstream f(fn.c_str(), std::fstream::in);
//read size of input matrix
read_matrix_size(f, sz);
bool is_row = viennacl::is_row_major<MatrixLayout>::value;
if (is_row)
std::cout << "Testing row-major matrix of size " << sz << "-by-" << sz << std::endl;
else
std::cout << "Testing column-major matrix of size " << sz << "-by-" << sz << std::endl;
viennacl::matrix<ScalarType> A_input(sz, sz), A_ref(sz, sz), Q(sz, sz);
// reference vector with reference values from file
std::vector<ScalarType> eigen_ref_re(sz);
// calculated real eigenvalues
std::vector<ScalarType> eigen_re(sz);
// calculated im. eigenvalues
std::vector<ScalarType> eigen_im(sz);
// read input matrix from file
read_matrix_body(f, A_input);
// read reference eigenvalues from file
read_vector_body(f, eigen_ref_re);
f.close();
A_ref = A_input;
std::cout << "Calculation..." << "\n";
Timer timer;
timer.start();
// Start the calculation
if(is_symm)
viennacl::linalg::qr_method_sym(A_input, Q, eigen_re);
else
viennacl::linalg::qr_method_nsm(A_input, Q, eigen_re, eigen_im);
/*
std::cout << "\n\n Matrix A: \n\n";
matrix_print(A_input);
std::cout << "\n\n";
std::cout << "\n\n Matrix Q: \n\n";
matrix_print(Q);
std::cout << "\n\n";
*/
double time_spend = timer.get();
std::cout << "Verification..." << "\n";
bool is_hessenberg = check_hessenberg(A_input);
bool is_tridiag = check_tridiag(A_input);
ublas::matrix<ScalarType> A_ref_ublas(sz, sz), A_input_ublas(sz, sz), Q_ublas(sz, sz), result1(sz, sz), result2(sz, sz);
viennacl::copy(A_ref, A_ref_ublas);
viennacl::copy(A_input, A_input_ublas);
viennacl::copy(Q, Q_ublas);
// compute result1 = ublas::prod(Q_ublas, A_input_ublas); (terribly slow when using ublas directly)
for (std::size_t i=0; i<result1.size1(); ++i)
for (std::size_t j=0; j<result1.size2(); ++j)
{
ScalarType value = 0;
for (std::size_t k=0; k<Q_ublas.size2(); ++k)
value += Q_ublas(i, k) * A_input_ublas(k, j);
result1(i,j) = value;
}
// compute result2 = ublas::prod(A_ref_ublas, Q_ublas); (terribly slow when using ublas directly)
for (std::size_t i=0; i<result2.size1(); ++i)
for (std::size_t j=0; j<result2.size2(); ++j)
{
ScalarType value = 0;
for (std::size_t k=0; k<A_ref_ublas.size2(); ++k)
value += A_ref_ublas(i, k) * Q_ublas(k, j);
result2(i,j) = value;
}
ScalarType prods_diff = matrix_compare(result1, result2);
ScalarType eigen_diff = vector_compare(eigen_re, eigen_ref_re);
bool is_ok = is_hessenberg;
if(is_symm)
is_ok = is_ok && is_tridiag;
is_ok = is_ok && (eigen_diff < EPS);
is_ok = is_ok && (prods_diff < EPS);
// std::cout << A_ref << "\n";
// std::cout << A_input << "\n";
// std::cout << Q << "\n";
// std::cout << eigen_re << "\n";
// std::cout << eigen_im << "\n";
// std::cout << eigen_ref_re << "\n";
// std::cout << eigen_ref_im << "\n";
// std::cout << result1 << "\n";
// std::cout << result2 << "\n";
// std::cout << eigen_ref << "\n";
// std::cout << eigen << "\n";
printf("%6s [%dx%d] %40s time = %.4f\n", is_ok?"[[OK]]":"[FAIL]", (int)A_ref.size1(), (int)A_ref.size2(), fn.c_str(), time_spend);
printf("tridiagonal = %d, hessenberg = %d prod-diff = %f eigen-diff = %f\n", is_tridiag, is_hessenberg, prods_diff, eigen_diff);
std::cout << std::endl << std::endl;
if (!is_ok)
exit(EXIT_FAILURE);
}