cholmod_dense* Cholmod<I>::solve(cholmod_sparse* A, spqr_factor* L,
cholmod_dense* b, double tol, bool norm, double normTol) {
cholmod_sparse* qrJ = cholmod_l_transpose(A, 1, &_cholmod);
cholmod_dense* scaling = NULL;
if (norm) {
scaling =
CholmodIndexTraits<index_t>::allocate_dense(qrJ->ncol, 1, qrJ->ncol,
CHOLMOD_REAL, &_cholmod);
double* values =
reinterpret_cast<double*>(scaling->x);
for (size_t i = 0; i < qrJ->ncol; ++i) {
const double normCol = colNorm(qrJ, i);
if (normCol < normTol)
values[i] = 0.0;
else
values[i] = 1.0 / normCol;
}
SM_ASSERT_TRUE(Exception, scale(scaling, CHOLMOD_COL, qrJ),
"Scaling failed");
}
cholmod_dense* res = NULL;
if (factorize(qrJ, L, tol)) {
cholmod_dense* qrY = SuiteSparseQR_qmult(SPQR_QTX, L, b, &_cholmod);
res = SuiteSparseQR_solve(SPQR_RETX_EQUALS_B, L, qrY, &_cholmod);
CholmodIndexTraits<index_t>::free_dense(&qrY, &_cholmod);
}
if (norm) {
const double* svalues =
reinterpret_cast<const double*>(scaling->x);
double* rvalues =
reinterpret_cast<double*>(res->x);
for (size_t i = 0; i < qrJ->ncol; ++i)
rvalues[i] = svalues[i] * rvalues[i];
CholmodIndexTraits<index_t>::free_dense(&scaling, &_cholmod);
}
CholmodIndexTraits<index_t>::free_sparse(&qrJ, &_cholmod);
return res;
}
int main (int argc, char **argv)
{
cholmod_common Common, *cc ;
cholmod_sparse *A ;
cholmod_dense *X, *B ;
int mtype ;
Long m, n ;
// start CHOLMOD
cc = &Common ;
cholmod_l_start (cc) ;
// A = mread (stdin) ; read in the sparse matrix A
A = (cholmod_sparse *) cholmod_l_read_matrix (stdin, 1, &mtype, cc) ;
if (mtype != CHOLMOD_SPARSE)
{
printf ("input matrix must be sparse\n") ;
exit (1) ;
}
// [m n] = size (A) ;
m = A->nrow ;
n = A->ncol ;
printf ("Matrix %6ld-by-%-6ld nnz: %6ld\n", m, n, cholmod_l_nnz (A, cc)) ;
// B = ones (m,1), a dense right-hand-side of the same type as A
B = cholmod_l_ones (m, 1, A->xtype, cc) ;
// X = A\B ; with default ordering and default column 2-norm tolerance
if (A->xtype == CHOLMOD_REAL)
{
// A, X, and B are all real
X = SuiteSparseQR <double>
(SPQR_ORDERING_DEFAULT, SPQR_DEFAULT_TOL, A, B, cc) ;
}
else
{
// A, X, and B are all complex
X = SuiteSparseQR < std::complex<double> >
(SPQR_ORDERING_DEFAULT, SPQR_DEFAULT_TOL, A, B, cc) ;
}
check_residual (A, X, B, cc) ;
cholmod_l_free_dense (&X, cc) ;
// -------------------------------------------------------------------------
// factorizing once then solving twice with different right-hand-sides
// -------------------------------------------------------------------------
// Just the real case. Complex case is essentially identical
if (A->xtype == CHOLMOD_REAL)
{
SuiteSparseQR_factorization <double> *QR ;
cholmod_dense *Y ;
Long i ;
double *Bx ;
// factorize once
QR = SuiteSparseQR_factorize <double>
(SPQR_ORDERING_DEFAULT, SPQR_DEFAULT_TOL, A, cc) ;
// solve Ax=b, using the same B as before
// Y = Q'*B
Y = SuiteSparseQR_qmult (SPQR_QTX, QR, B, cc) ;
// X = R\(E*Y)
X = SuiteSparseQR_solve (SPQR_RETX_EQUALS_B, QR, Y, cc) ;
// check the results
check_residual (A, X, B, cc) ;
// free X and Y
cholmod_l_free_dense (&Y, cc) ;
cholmod_l_free_dense (&X, cc) ;
// repeat with a different B
Bx = (double *) (B->x) ;
for (i = 0 ; i < m ; i++)
{
Bx [i] = i ;
}
// Y = Q'*B
Y = SuiteSparseQR_qmult (SPQR_QTX, QR, B, cc) ;
// X = R\(E*Y)
X = SuiteSparseQR_solve (SPQR_RETX_EQUALS_B, QR, Y, cc) ;
// check the results
check_residual (A, X, B, cc) ;
// free X and Y
cholmod_l_free_dense (&Y, cc) ;
cholmod_l_free_dense (&X, cc) ;
// free QR
SuiteSparseQR_free (&QR, cc) ;
}
// -------------------------------------------------------------------------
// free everything that remains
// -------------------------------------------------------------------------
cholmod_l_free_sparse (&A, cc) ;
cholmod_l_free_dense (&B, cc) ;
cholmod_l_finish (cc) ;
return (0) ;
}
