bool testGaussTransform (const Ring &F, size_t m, size_t n)
{
commentator.start ("Testing GaussJordan::echelonize", __FUNCTION__);
std::ostream &report = commentator.report (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION);
std::ostream &error = commentator.report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR);
bool pass = true;
DenseMatrix<typename Ring::Element> R (m, n);
RandomDenseStream<Ring, typename DenseMatrix<typename Ring::Element>::Row> A_stream (F, n, m);
DenseMatrix<typename Ring::Element> A (A_stream), A_copy (m, n);
typename GaussJordan<Ring>::Permutation P;
Context<Ring> ctx (F);
Elimination<Ring> elim (ctx);
GaussJordan<Ring> GJ (ctx);
size_t rank;
typename Ring::Element det;
BLAS3::copy (ctx, A, R);
BLAS3::copy (ctx, A, A_copy);
GJ.echelonize (R, P, rank, det);
report << "A = " << std::endl;
BLAS3::write (ctx, report, A);
report << "P = ";
BLAS1::write_permutation (report, P.begin (), P.end ()) << std::endl;
report << "R, L = " << std::endl;
BLAS3::write (ctx, report, R);
BLAS3::permute_rows (ctx, P.begin (), P.end (), A);
report << "PA = " << std::endl;
BLAS3::write (ctx, report, A);
typename DenseMatrix<typename Ring::Element>::SubmatrixType Rp (R, 0, 0, R.rowdim (), R.rowdim ());
BLAS3::trmm (ctx, F.one (), Rp, A, LowerTriangular, true);
report << "LPA = " << std::endl;
BLAS3::write (ctx, report, A);
report << "Computed rank = " << rank << std::endl;
report << "Computed det = ";
F.write (report, det);
report << std::endl;
// Trick to eliminate part below diagonal so that equality-check works
elim.move_L (R, R);
if (!BLAS3::equal (ctx, A, R)) {
error << "ERROR: LPA != R" << std::endl;
pass = false;
}
elim.echelonize (A_copy, P, rank, det, false);
report << "Result of Elimination::echelonize: " << std::endl;
BLAS3::write (ctx, report, A_copy);
if (!BLAS3::equal (ctx, A_copy, R)) {
error << "ERROR: Results from Elimination and GaussJordan not equal" << std::endl;
pass = false;
}
commentator.stop (MSG_STATUS (pass));
return pass;
}
bool testEchelonize (const Ring &F, const char *text, Matrix &A)
{
std::ostringstream str;
str << "Testing Elimination::echelonize for " << text << " matrices" << std::ends;
commentator.start (str.str ().c_str (), __FUNCTION__);
std::ostream &report = commentator.report (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION);
std::ostream &error = commentator.report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR);
bool pass = true;
Context<Ring> ctx (F);
Elimination<Ring> elim (ctx);
typename Matrix::ContainerType PA (A.rowdim (), A.coldim ()), LPA (A.rowdim (), A.coldim ());
BLAS3::copy (ctx, A, PA);
typename Elimination<Ring>::Permutation P;
size_t rank;
typename Ring::Element det;
report << "A = " << std::endl;
BLAS3::write (ctx, report, A, FORMAT_PRETTY);
elim.echelonize (A, P, rank, det, true);
report << "L, R = " << std::endl;
BLAS3::write (ctx, report, A, FORMAT_PRETTY);
report << "P = ";
BLAS1::write_permutation (report, P.begin (), P.end ()) << std::endl;
BLAS3::permute_rows (ctx, P.begin (), P.end (), PA);
report << "PA = " << std::endl;
BLAS3::write (ctx, report, PA, FORMAT_PRETTY);
typename Matrix::ContainerType L (A.rowdim (), A.rowdim ());
typename Matrix::ContainerType::RowIterator i_L;
StandardBasisStream<Ring, typename Matrix::ContainerType::Row> s (ctx.F, A.rowdim ());
for (i_L = L.rowBegin (); i_L != L.rowEnd (); ++i_L)
s >> *i_L;
elim.move_L (L, A);
BLAS3::scal (ctx, F.zero (), LPA);
BLAS3::gemm (ctx, F.one (), L, PA, F.zero (), LPA);
report << "LPA = " << std::endl;
BLAS3::write (ctx, report, LPA);
report << "Computed rank = " << rank << std::endl;
report << "Computed det = ";
F.write (report, det);
report << std::endl;
if (!BLAS3::equal (ctx, LPA, A)) {
error << "LPA != R, not okay" << std::endl;
pass = false;
}
commentator.stop (MSG_STATUS (pass));
return pass;
}
bool testGaussJordanTransform (const Ring &F, size_t m, size_t n)
{
commentator.start ("Testing GaussJordan::echelonize_reduced", __FUNCTION__);
std::ostream &report = commentator.report (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION);
std::ostream &error = commentator.report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR);
bool pass = true;
DenseMatrix<typename Ring::Element> R (m, n);
RandomDenseStream<Ring, typename DenseMatrix<typename Ring::Element>::Row> A_stream (F, n, m);
DenseMatrix<typename Ring::Element> A (A_stream), L (m, m), LPA (m, n);
typename GaussJordan<Ring>::Permutation P;
Context<Ring> ctx (F);
GaussJordan<Ring> GJ (ctx);
size_t rank;
typename Ring::Element det;
BLAS3::copy (ctx, A, R);
GJ.echelonize_reduced (R, L, P, rank, det);
report << "A = " << std::endl;
BLAS3::write (ctx, report, A);
report << "P = ";
BLAS1::write_permutation (report, P.begin (), P.end ()) << std::endl;
report << "R = " << std::endl;
BLAS3::write (ctx, report, R);
report << "L = " << std::endl;
BLAS3::write (ctx, report, L);
BLAS3::permute_rows (ctx, P.begin (), P.end (), A);
report << "PA = " << std::endl;
BLAS3::write (ctx, report, A);
BLAS3::scal (ctx, F.zero (), LPA);
BLAS3::gemm (ctx, F.one (), L, A, F.zero (), LPA);
report << "LPA = " << std::endl;
BLAS3::write (ctx, report, LPA);
report << "Computed rank = " << rank << std::endl;
report << "Computed det = ";
F.write (report, det);
report << std::endl;
// Trick to eliminate part below diagonal so that equality-check works
Elimination<Ring> elim (ctx);
elim.move_L (R, R);
if (!BLAS3::equal (ctx, LPA, R)) {
error << "ERROR: LPA != R" << std::endl;
pass = false;
}
commentator.stop (MSG_STATUS (pass));
return pass;
}
bool testPLUQ (const Ring &F, const char *text, Matrix &A)
{
std::ostringstream str;
str << "Testing Elimination::pluq for " << text << " matrices" << std::ends;
commentator.start (str.str ().c_str (), __FUNCTION__);
std::ostream &report = commentator.report (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION);
std::ostream &error = commentator.report (Commentator::LEVEL_IMPORTANT, INTERNAL_ERROR);
bool pass = true;
Context<Ring> ctx (F);
Elimination<Ring> elim (ctx);
typename Matrix::ContainerType Acopy (A.rowdim (), A.coldim ()), L (A.rowdim (), A.rowdim ());
BLAS3::copy (ctx, A, Acopy);
typename Elimination<Ring>::Permutation P, Q;
size_t rank;
typename Ring::Element det;
report << "A = " << std::endl;
BLAS3::write (ctx, report, A, FORMAT_PRETTY);
elim.pluq (A, P, Q, rank, det);
report << "L, U = " << std::endl;
BLAS3::write (ctx, report, A, FORMAT_PRETTY);
report << "P = ";
BLAS1::write_permutation (report, P.begin (), P.end ()) << std::endl;
report << "Q = ";
BLAS1::write_permutation (report, Q.begin (), Q.end ()) << std::endl;
BLAS3::scal (ctx, ctx.F.zero (), L);
elim.move_L (L, A);
report << "L = " << std::endl;
BLAS3::write (ctx, report, L, FORMAT_PRETTY);
report << "U = " << std::endl;
BLAS3::write (ctx, report, A, FORMAT_PRETTY);
BLAS3::trmm (ctx, F.one (), L, A, LowerTriangular, true);
report << "LU = " << std::endl;
BLAS3::write (ctx, report, A, FORMAT_PRETTY);
BLAS3::permute_rows (ctx, P.begin (), P.end (), A);
report << "PLU = " << std::endl;
BLAS3::write (ctx, report, A);
BLAS3::permute_cols (ctx, Q.begin (), Q.end (), A);
report << "PLUQ = " << std::endl;
BLAS3::write (ctx, report, A);
report << "Computed rank = " << rank << std::endl;
report << "Computed det = ";
F.write (report, det);
report << std::endl;
if (!BLAS3::equal (ctx, A, Acopy)) {
error << "PLUQ != A, not okay" << std::endl;
BLAS3::axpy (ctx, ctx.F.minusOne (), A, Acopy);
error << "Difference is:" << std::endl;
BLAS3::write (ctx, error, Acopy);
pass = false;
}
commentator.stop (MSG_STATUS (pass));
return pass;
}