void DenseMatrix<T>::_svd_lapack (DenseVector<T>& sigma, DenseMatrix<T>& U, DenseMatrix<T>& VT)
{
// The calling sequence for dgetrf is:
// DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO )
// JOBU (input) CHARACTER*1
// Specifies options for computing all or part of the matrix U:
// = 'A': all M columns of U are returned in array U:
// = 'S': the first min(m,n) columns of U (the left singular
// vectors) are returned in the array U;
// = 'O': the first min(m,n) columns of U (the left singular
// vectors) are overwritten on the array A;
// = 'N': no columns of U (no left singular vectors) are
// computed.
char JOBU = 'S';
// JOBVT (input) CHARACTER*1
// Specifies options for computing all or part of the matrix
// V**T:
// = 'A': all N rows of V**T are returned in the array VT;
// = 'S': the first min(m,n) rows of V**T (the right singular
// vectors) are returned in the array VT;
// = 'O': the first min(m,n) rows of V**T (the right singular
// vectors) are overwritten on the array A;
// = 'N': no rows of V**T (no right singular vectors) are
// computed.
char JOBVT = 'S';
std::vector<T> sigma_val;
std::vector<T> U_val;
std::vector<T> VT_val;
_svd_helper(JOBU, JOBVT, sigma_val, U_val, VT_val);
// Load the singular values into sigma, ignore U_val and VT_val
sigma.resize(sigma_val.size());
for(unsigned int i=0; i<sigma_val.size(); i++)
sigma(i) = sigma_val[i];
int M = this->n();
int N = this->m();
int min_MN = (M < N) ? M : N;
U.resize(M,min_MN);
for(unsigned int i=0; i<U.m(); i++)
for(unsigned int j=0; j<U.n(); j++)
{
unsigned int index = i + j*U.n(); // Column major storage
U(i,j) = U_val[index];
}
VT.resize(min_MN,N);
for(unsigned int i=0; i<VT.m(); i++)
for(unsigned int j=0; j<VT.n(); j++)
{
unsigned int index = i + j*U.n(); // Column major storage
VT(i,j) = VT_val[index];
}
}
void DenseMatrix<T>::right_multiply_transpose (const DenseMatrix<T>& B)
{
if (this->use_blas_lapack)
this->_multiply_blas(B, RIGHT_MULTIPLY_TRANSPOSE);
else
{
//Check to see if we are doing B*(B^T)
if (this == &B)
{
//libmesh_here();
DenseMatrix<T> A(*this);
// Simple but inefficient way
// return this->right_multiply_transpose(A);
// More efficient, more code
// If B is mxn, the result will be a square matrix of Size m x m.
const unsigned int n_rows = B.m();
const unsigned int n_cols = B.n();
// resize() *this and also zero out all entries.
this->resize(n_rows,n_rows);
// Compute the lower-triangular part
for (unsigned int i=0; i<n_rows; ++i)
for (unsigned int j=0; j<=i; ++j)
for (unsigned int k=0; k<n_cols; ++k) // inner products are over n_cols
(*this)(i,j) += A(i,k)*A(j,k);
// Copy lower-triangular part into upper-triangular part
for (unsigned int i=0; i<n_rows; ++i)
for (unsigned int j=i+1; j<n_rows; ++j)
(*this)(i,j) = (*this)(j,i);
}
else
{
DenseMatrix<T> A(*this);
this->resize (A.m(), B.m());
libmesh_assert_equal_to (A.n(), B.n());
libmesh_assert_equal_to (this->m(), A.m());
libmesh_assert_equal_to (this->n(), B.m());
const unsigned int m_s = A.m();
const unsigned int p_s = A.n();
const unsigned int n_s = this->n();
// Do it this way because there is a
// decent chance (at least for constraint matrices)
// that B.transpose(k,j) = 0.
for (unsigned int j=0; j<n_s; j++)
for (unsigned int k=0; k<p_s; k++)
if (B.transpose(k,j) != 0.)
for (unsigned int i=0; i<m_s; i++)
(*this)(i,j) += A(i,k)*B.transpose(k,j);
}
}
}
void SparseMatrix<T>::add_block_matrix (const DenseMatrix<T> & dm,
const std::vector<numeric_index_type> & brows,
const std::vector<numeric_index_type> & bcols)
{
libmesh_assert_equal_to (dm.m() / brows.size(), dm.n() / bcols.size());
const numeric_index_type blocksize = cast_int<numeric_index_type>
(dm.m() / brows.size());
libmesh_assert_equal_to (dm.m()%blocksize, 0);
libmesh_assert_equal_to (dm.n()%blocksize, 0);
std::vector<numeric_index_type> rows, cols;
rows.reserve(blocksize*brows.size());
cols.reserve(blocksize*bcols.size());
for (unsigned int ib=0; ib<brows.size(); ib++)
{
numeric_index_type i=brows[ib]*blocksize;
for (unsigned int v=0; v<blocksize; v++)
rows.push_back(i++);
}
for (unsigned int jb=0; jb<bcols.size(); jb++)
{
numeric_index_type j=bcols[jb]*blocksize;
for (unsigned int v=0; v<blocksize; v++)
cols.push_back(j++);
}
this->add_matrix (dm, rows, cols);
}
void
dataStore(std::ostream & stream, DenseMatrix<Real> & v, void * /*context*/)
{
unsigned int m = v.m();
unsigned int n = v.n();
stream.write((char *) &m, sizeof(m));
stream.write((char *) &n, sizeof(n));
for (unsigned int i = 0; i < v.m(); i++)
for (unsigned int j = 0; j < v.n(); j++)
{
Real r = v(i, j);
stream.write((char *) &r, sizeof(r));
}
}
void PetscMatrix<T>::add_block_matrix(const DenseMatrix<T>& dm,
const std::vector<numeric_index_type>& brows,
const std::vector<numeric_index_type>& bcols)
{
libmesh_assert (this->initialized());
const numeric_index_type n_rows = dm.m();
const numeric_index_type n_cols = dm.n();
const numeric_index_type n_brows = brows.size();
const numeric_index_type n_bcols = bcols.size();
const numeric_index_type blocksize = n_rows / n_brows;
libmesh_assert_equal_to (n_cols / n_bcols, blocksize);
libmesh_assert_equal_to (blocksize*n_brows, n_rows);
libmesh_assert_equal_to (blocksize*n_bcols, n_cols);
PetscErrorCode ierr=0;
#ifndef NDEBUG
PetscInt petsc_blocksize;
ierr = MatGetBlockSize(_mat, &petsc_blocksize);
LIBMESH_CHKERRABORT(ierr);
libmesh_assert_equal_to (blocksize, static_cast<numeric_index_type>(petsc_blocksize));
#endif
// These casts are required for PETSc <= 2.1.5
ierr = MatSetValuesBlocked(_mat,
n_brows, (PetscInt*) &brows[0],
n_bcols, (PetscInt*) &bcols[0],
(PetscScalar*) &dm.get_values()[0],
ADD_VALUES);
LIBMESH_CHKERRABORT(ierr);
}
void DenseMatrix<T>::get_transpose (DenseMatrix<T>& dest) const
{
dest.resize(this->n(), this->m());
for (unsigned int i=0; i<dest.m(); i++)
for (unsigned int j=0; j<dest.n(); j++)
dest(i,j) = (*this)(j,i);
}
void LaspackMatrix<T>::add_matrix(const DenseMatrix<T>& dm,
const std::vector<numeric_index_type>& rows,
const std::vector<numeric_index_type>& cols)
{
libmesh_assert (this->initialized());
libmesh_assert_equal_to (dm.m(), rows.size());
libmesh_assert_equal_to (dm.n(), cols.size());
for (numeric_index_type i=0; i<rows.size(); i++)
for (numeric_index_type j=0; j<cols.size(); j++)
this->add(rows[i],cols[j],dm(i,j));
}
void EpetraMatrix<T>::add_matrix(const DenseMatrix<T>& dm,
const std::vector<unsigned int>& rows,
const std::vector<unsigned int>& cols)
{
libmesh_assert (this->initialized());
const unsigned int m = dm.m();
const unsigned int n = dm.n();
libmesh_assert (rows.size() == m);
libmesh_assert (cols.size() == n);
_mat->SumIntoGlobalValues(m, (int *)&rows[0], n, (int *)&cols[0], &dm.get_values()[0]);
}
void EpetraMatrix<T>::add_matrix(const DenseMatrix<T>& dm,
const std::vector<numeric_index_type>& rows,
const std::vector<numeric_index_type>& cols)
{
libmesh_assert (this->initialized());
const numeric_index_type m = dm.m();
const numeric_index_type n = dm.n();
libmesh_assert_equal_to (rows.size(), m);
libmesh_assert_equal_to (cols.size(), n);
_mat->SumIntoGlobalValues(m, (int *)&rows[0], n, (int *)&cols[0], &dm.get_values()[0]);
}
void
dataLoad(std::istream & stream, DenseMatrix<Real> & v, void * /*context*/)
{
unsigned int nr = 0, nc = 0;
stream.read((char *) &nr, sizeof(nr));
stream.read((char *) &nc, sizeof(nc));
v.resize(nr,nc);
for (unsigned int i = 0; i < v.m(); i++)
for (unsigned int j = 0; j < v.n(); j++)
{
Real r = 0;
stream.read((char *) &r, sizeof(r));
v(i, j) = r;
}
}
void EigenSparseMatrix<T>::add_matrix(const DenseMatrix<T> & dm,
const std::vector<numeric_index_type> & rows,
const std::vector<numeric_index_type> & cols)
{
libmesh_assert (this->initialized());
unsigned int n_rows = cast_int<unsigned int>(rows.size());
unsigned int n_cols = cast_int<unsigned int>(cols.size());
libmesh_assert_equal_to (dm.m(), n_rows);
libmesh_assert_equal_to (dm.n(), n_cols);
for (unsigned int i=0; i<n_rows; i++)
for (unsigned int j=0; j<n_cols; j++)
this->add(rows[i],cols[j],dm(i,j));
}
void
Assembly::addJacobianBlock(SparseMatrix<Number> & jacobian, DenseMatrix<Number> & jac_block, const std::vector<dof_id_type> & idof_indices, const std::vector<dof_id_type> & jdof_indices, Real scaling_factor)
{
if ((idof_indices.size() > 0) && (jdof_indices.size() > 0) && jac_block.n() && jac_block.m())
{
std::vector<dof_id_type> di(idof_indices);
std::vector<dof_id_type> dj(jdof_indices);
_dof_map.constrain_element_matrix(jac_block, di, dj, false);
if (scaling_factor != 1.0)
{
_tmp_Ke = jac_block;
_tmp_Ke *= scaling_factor;
jacobian.add_matrix(_tmp_Ke, di, dj);
}
else
jacobian.add_matrix(jac_block, di, dj);
}
}
void PetscMatrix<T>::add_matrix(const DenseMatrix<T>& dm,
const std::vector<numeric_index_type>& rows,
const std::vector<numeric_index_type>& cols)
{
libmesh_assert (this->initialized());
const numeric_index_type n_rows = dm.m();
const numeric_index_type n_cols = dm.n();
libmesh_assert_equal_to (rows.size(), n_rows);
libmesh_assert_equal_to (cols.size(), n_cols);
PetscErrorCode ierr=0;
// These casts are required for PETSc <= 2.1.5
ierr = MatSetValues(_mat,
n_rows, (PetscInt*) &rows[0],
n_cols, (PetscInt*) &cols[0],
(PetscScalar*) &dm.get_values()[0],
ADD_VALUES);
LIBMESH_CHKERRABORT(ierr);
}
void
Assembly::cacheJacobianBlock(DenseMatrix<Number> & jac_block, std::vector<dof_id_type> & idof_indices, std::vector<dof_id_type> & jdof_indices, Real scaling_factor)
{
if ((idof_indices.size() > 0) && (jdof_indices.size() > 0) && jac_block.n() && jac_block.m())
{
std::vector<dof_id_type> di(idof_indices);
std::vector<dof_id_type> dj(jdof_indices);
_dof_map.constrain_element_matrix(jac_block, di, dj, false);
if (scaling_factor != 1.0)
{
_tmp_Ke = jac_block;
_tmp_Ke *= scaling_factor;
for(unsigned int i=0; i<di.size(); i++)
for(unsigned int j=0; j<dj.size(); j++)
{
_cached_jacobian_values.push_back(_tmp_Ke(i, j));
_cached_jacobian_rows.push_back(di[i]);
_cached_jacobian_cols.push_back(dj[j]);
}
}
else
{
for(unsigned int i=0; i<di.size(); i++)
for(unsigned int j=0; j<dj.size(); j++)
{
_cached_jacobian_values.push_back(jac_block(i, j));
_cached_jacobian_rows.push_back(di[i]);
_cached_jacobian_cols.push_back(dj[j]);
}
}
}
jac_block.zero();
}
// This function is called by testEVD for different matrices. The
// Lapack results are compared to known eigenvalue real and
// imaginary parts for the matrix in question, which must also be
// passed in by non-const value, since this routine will sort them
// in-place.
void testEVD_helper(DenseMatrix<Real> & A,
std::vector<Real> true_lambda_real,
std::vector<Real> true_lambda_imag)
{
// Note: see bottom of this file, we only do this test if PETSc is
// available, but this function currently only exists if we're
// using real numbers.
#ifdef LIBMESH_USE_REAL_NUMBERS
// Let's compute the eigenvalues on a copy of A, so that we can
// use the original to check the computation.
DenseMatrix<Real> A_copy = A;
DenseVector<Real> lambda_real, lambda_imag;
DenseMatrix<Real> VR; // right eigenvectors
DenseMatrix<Real> VL; // left eigenvectors
A_copy.evd_left_and_right(lambda_real, lambda_imag, VL, VR);
// The matrix is square and of size N x N.
const unsigned N = A.m();
// Verify left eigen-values.
// Test that the right eigenvalues are self-consistent by computing
// u_j**H * A = lambda_j * u_j**H
// Note that we have to handle real and complex eigenvalues
// differently, since complex eigenvectors share their storage.
for (unsigned eigenval=0; eigenval<N; ++eigenval)
{
// Only check real eigenvalues
if (std::abs(lambda_imag(eigenval)) < TOLERANCE*TOLERANCE)
{
// remove print libMesh::out << "Checking eigenvalue: " << eigenval << std::endl;
DenseVector<Real> lhs(N), rhs(N);
for (unsigned i=0; i<N; ++i)
{
rhs(i) = lambda_real(eigenval) * VL(i, eigenval);
for (unsigned j=0; j<N; ++j)
lhs(i) += A(j, i) * VL(j, eigenval); // Note: A(j,i)
}
// Subtract and assert that the norm of the difference is
// below some tolerance.
lhs -= rhs;
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/0., /*actual=*/lhs.l2_norm(), std::sqrt(TOLERANCE)*TOLERANCE);
}
else
{
// This is a complex eigenvalue, so:
// a.) It occurs in a complex-conjugate pair
// b.) the real part of the eigenvector is stored is VL(:,eigenval)
// c.) the imag part of the eigenvector is stored in VL(:,eigenval+1)
//
// Equating the real and imaginary parts of Ax=lambda*x leads to two sets
// of relations that must hold:
// 1.) A^T x_r = lambda_r*x_r + lambda_i*x_i
// 2.) A^T x_i = -lambda_i*x_r + lambda_r*x_i
// which we can verify.
// 1.)
DenseVector<Real> lhs(N), rhs(N);
for (unsigned i=0; i<N; ++i)
{
rhs(i) = lambda_real(eigenval) * VL(i, eigenval) + lambda_imag(eigenval) * VL(i, eigenval+1);
for (unsigned j=0; j<N; ++j)
lhs(i) += A(j, i) * VL(j, eigenval); // Note: A(j,i)
}
lhs -= rhs;
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/0., /*actual=*/lhs.l2_norm(), std::sqrt(TOLERANCE)*TOLERANCE);
// libMesh::out << "lhs=" << std::endl;
// lhs.print_scientific(libMesh::out, /*precision=*/15);
//
// libMesh::out << "rhs=" << std::endl;
// rhs.print_scientific(libMesh::out, /*precision=*/15);
// 2.)
lhs.zero();
rhs.zero();
for (unsigned i=0; i<N; ++i)
{
rhs(i) = -lambda_imag(eigenval) * VL(i, eigenval) + lambda_real(eigenval) * VL(i, eigenval+1);
for (unsigned j=0; j<N; ++j)
lhs(i) += A(j, i) * VL(j, eigenval+1); // Note: A(j,i)
}
lhs -= rhs;
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/0., /*actual=*/lhs.l2_norm(), std::sqrt(TOLERANCE)*TOLERANCE);
// libMesh::out << "lhs=" << std::endl;
// lhs.print_scientific(libMesh::out, /*precision=*/15);
//
// libMesh::out << "rhs=" << std::endl;
// rhs.print_scientific(libMesh::out, /*precision=*/15);
// We'll skip the second member of the complex conjugate
// pair. If the first one worked, the second one should
// as well...
eigenval += 1;
}
}
// Verify right eigen-values.
// Test that the right eigenvalues are self-consistent by computing
// A * v_j - lambda_j * v_j
// Note that we have to handle real and complex eigenvalues
// differently, since complex eigenvectors share their storage.
for (unsigned eigenval=0; eigenval<N; ++eigenval)
{
// Only check real eigenvalues
if (std::abs(lambda_imag(eigenval)) < TOLERANCE*TOLERANCE)
{
// remove print libMesh::out << "Checking eigenvalue: " << eigenval << std::endl;
DenseVector<Real> lhs(N), rhs(N);
for (unsigned i=0; i<N; ++i)
{
rhs(i) = lambda_real(eigenval) * VR(i, eigenval);
for (unsigned j=0; j<N; ++j)
lhs(i) += A(i, j) * VR(j, eigenval);
}
lhs -= rhs;
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/0., /*actual=*/lhs.l2_norm(), std::sqrt(TOLERANCE)*TOLERANCE);
}
else
{
// This is a complex eigenvalue, so:
// a.) It occurs in a complex-conjugate pair
// b.) the real part of the eigenvector is stored is VR(:,eigenval)
// c.) the imag part of the eigenvector is stored in VR(:,eigenval+1)
//
// Equating the real and imaginary parts of Ax=lambda*x leads to two sets
// of relations that must hold:
// 1.) Ax_r = lambda_r*x_r - lambda_i*x_i
// 2.) Ax_i = lambda_i*x_r + lambda_r*x_i
// which we can verify.
// 1.)
DenseVector<Real> lhs(N), rhs(N);
for (unsigned i=0; i<N; ++i)
{
rhs(i) = lambda_real(eigenval) * VR(i, eigenval) - lambda_imag(eigenval) * VR(i, eigenval+1);
for (unsigned j=0; j<N; ++j)
lhs(i) += A(i, j) * VR(j, eigenval);
}
lhs -= rhs;
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/0., /*actual=*/lhs.l2_norm(), std::sqrt(TOLERANCE)*TOLERANCE);
// 2.)
lhs.zero();
rhs.zero();
for (unsigned i=0; i<N; ++i)
{
rhs(i) = lambda_imag(eigenval) * VR(i, eigenval) + lambda_real(eigenval) * VR(i, eigenval+1);
for (unsigned j=0; j<N; ++j)
lhs(i) += A(i, j) * VR(j, eigenval+1);
}
lhs -= rhs;
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/0., /*actual=*/lhs.l2_norm(), std::sqrt(TOLERANCE)*TOLERANCE);
// We'll skip the second member of the complex conjugate
// pair. If the first one worked, the second one should
// as well...
eigenval += 1;
}
}
// Sort the results from Lapack *individually*.
std::sort(lambda_real.get_values().begin(), lambda_real.get_values().end());
std::sort(lambda_imag.get_values().begin(), lambda_imag.get_values().end());
// Sort the true eigenvalues *individually*.
std::sort(true_lambda_real.begin(), true_lambda_real.end());
std::sort(true_lambda_imag.begin(), true_lambda_imag.end());
// Compare the individually-sorted values.
for (unsigned i=0; i<lambda_real.size(); ++i)
{
// Note: I initially verified the results with TOLERANCE**2,
// but that turned out to be just a bit too tight for some of
// the test problems. I'm not sure what controls the accuracy
// of the eigenvalue computation in LAPACK, there is no way to
// set a tolerance in the LAPACKgeev_ interface.
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/true_lambda_real[i], /*actual=*/lambda_real(i), std::sqrt(TOLERANCE)*TOLERANCE);
CPPUNIT_ASSERT_DOUBLES_EQUAL(/*expected=*/true_lambda_imag[i], /*actual=*/lambda_imag(i), std::sqrt(TOLERANCE)*TOLERANCE);
}
#endif
}
void DenseMatrix<T>::_multiply_blas(const DenseMatrixBase<T>& other,
_BLAS_Multiply_Flag flag)
{
int result_size = 0;
// For each case, determine the size of the final result make sure
// that the inner dimensions match
switch (flag)
{
case LEFT_MULTIPLY:
{
result_size = other.m() * this->n();
if (other.n() == this->m())
break;
}
case RIGHT_MULTIPLY:
{
result_size = other.n() * this->m();
if (other.m() == this->n())
break;
}
case LEFT_MULTIPLY_TRANSPOSE:
{
result_size = other.n() * this->n();
if (other.m() == this->m())
break;
}
case RIGHT_MULTIPLY_TRANSPOSE:
{
result_size = other.m() * this->m();
if (other.n() == this->n())
break;
}
default:
{
libMesh::out << "Unknown flag selected or matrices are ";
libMesh::out << "incompatible for multiplication." << std::endl;
libmesh_error();
}
}
// For this to work, the passed arg. must actually be a DenseMatrix<T>
const DenseMatrix<T>* const_that = libmesh_cast_ptr< const DenseMatrix<T>* >(&other);
// Also, although 'that' is logically const in this BLAS routine,
// the PETSc BLAS interface does not specify that any of the inputs are
// const. To use it, I must cast away const-ness.
DenseMatrix<T>* that = const_cast< DenseMatrix<T>* > (const_that);
// Initialize A, B pointers for LEFT_MULTIPLY* cases
DenseMatrix<T>
*A = this,
*B = that;
// For RIGHT_MULTIPLY* cases, swap the meaning of A and B.
// Here is a full table of combinations we can pass to BLASgemm, and what the answer is when finished:
// pass A B -> (Fortran) -> A^T B^T -> (C++) -> (A^T B^T)^T -> (identity) -> B A "lt multiply"
// pass B A -> (Fortran) -> B^T A^T -> (C++) -> (B^T A^T)^T -> (identity) -> A B "rt multiply"
// pass A B^T -> (Fortran) -> A^T B -> (C++) -> (A^T B)^T -> (identity) -> B^T A "lt multiply t"
// pass B^T A -> (Fortran) -> B A^T -> (C++) -> (B A^T)^T -> (identity) -> A B^T "rt multiply t"
if (flag==RIGHT_MULTIPLY || flag==RIGHT_MULTIPLY_TRANSPOSE)
std::swap(A,B);
// transa, transb values to pass to blas
char
transa[] = "n",
transb[] = "n";
// Integer values to pass to BLAS:
//
// M
// In Fortran, the number of rows of op(A),
// In the BLAS documentation, typically known as 'M'.
//
// In C/C++, we set:
// M = n_cols(A) if (transa='n')
// n_rows(A) if (transa='t')
int M = static_cast<int>( A->n() );
// N
// In Fortran, the number of cols of op(B), and also the number of cols of C.
// In the BLAS documentation, typically known as 'N'.
//
// In C/C++, we set:
// N = n_rows(B) if (transb='n')
// n_cols(B) if (transb='t')
int N = static_cast<int>( B->m() );
// K
// In Fortran, the number of cols of op(A), and also
// the number of rows of op(B). In the BLAS documentation,
// typically known as 'K'.
//
// In C/C++, we set:
// K = n_rows(A) if (transa='n')
// n_cols(A) if (transa='t')
int K = static_cast<int>( A->m() );
// LDA (leading dimension of A). In our cases,
// LDA is always the number of columns of A.
int LDA = static_cast<int>( A->n() );
// LDB (leading dimension of B). In our cases,
// LDB is always the number of columns of B.
int LDB = static_cast<int>( B->n() );
if (flag == LEFT_MULTIPLY_TRANSPOSE)
{
transb[0] = 't';
N = static_cast<int>( B->n() );
}
else if (flag == RIGHT_MULTIPLY_TRANSPOSE)
{
transa[0] = 't';
std::swap(M,K);
}
// LDC (leading dimension of C). LDC is the
// number of columns in the solution matrix.
int LDC = M;
// Scalar values to pass to BLAS
//
// scalar multiplying the whole product AB
T alpha = 1.;
// scalar multiplying C, which is the original matrix.
T beta = 0.;
// Storage for the result
std::vector<T> result (result_size);
// Finally ready to call the BLAS
BLASgemm_(transa, transb, &M, &N, &K, &alpha, &(A->_val[0]), &LDA, &(B->_val[0]), &LDB, &beta, &result[0], &LDC);
// Update the relevant dimension for this matrix.
switch (flag)
{
case LEFT_MULTIPLY: { this->_m = other.m(); break; }
case RIGHT_MULTIPLY: { this->_n = other.n(); break; }
case LEFT_MULTIPLY_TRANSPOSE: { this->_m = other.n(); break; }
case RIGHT_MULTIPLY_TRANSPOSE: { this->_n = other.m(); break; }
default:
{
libMesh::out << "Unknown flag selected." << std::endl;
libmesh_error();
}
}
// Swap my data vector with the result
this->_val.swap(result);
}