int main (int argc, char **argv)
{
cholmod_common Common, *cc ;
cholmod_sparse *A ;
cholmod_dense *X, *B, *Residual ;
double rnorm, one [2] = {1,0}, minusone [2] = {-1,0} ;
int mtype ;
// start CHOLMOD
cc = &Common ;
cholmod_l_start (cc) ;
// load A
A = (cholmod_sparse *) cholmod_l_read_matrix (stdin, 1, &mtype, cc) ;
// B = ones (size (A,1),1)
B = cholmod_l_ones (A->nrow, 1, A->xtype, cc) ;
// X = A\B
X = SuiteSparseQR <double> (A, B, cc) ;
// rnorm = norm (B-A*X)
Residual = cholmod_l_copy_dense (B, cc) ;
cholmod_l_sdmult (A, 0, minusone, one, X, Residual, cc) ;
rnorm = cholmod_l_norm_dense (Residual, 2, cc) ;
printf ("2-norm of residual: %8.1e\n", rnorm) ;
printf ("rank %ld\n", cc->SPQR_istat [4]) ;
// free everything and finish CHOLMOD
cholmod_l_free_dense (&Residual, cc) ;
cholmod_l_free_sparse (&A, cc) ;
cholmod_l_free_dense (&X, cc) ;
cholmod_l_free_dense (&B, cc) ;
cholmod_l_finish (cc) ;
return (0) ;
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
void *G ;
cholmod_dense *X = NULL ;
cholmod_sparse *A = NULL, *Z = NULL ;
cholmod_common Common, *cm ;
Long *Ap = NULL, *Ai ;
double *Ax, *Az = NULL ;
char filename [MAXLEN] ;
Long nz, k, is_complex = FALSE, nrow = 0, ncol = 0, allzero ;
int mtype ;
/* ---------------------------------------------------------------------- */
/* start CHOLMOD and set parameters */
/* ---------------------------------------------------------------------- */
cm = &Common ;
cholmod_l_start (cm) ;
sputil_config (SPUMONI, cm) ;
/* ---------------------------------------------------------------------- */
/* get inputs */
/* ---------------------------------------------------------------------- */
if (nargin < 1 || nargin > 2 || nargout > 2)
{
mexErrMsgTxt ("usage: [A Z] = mread (filename, prefer_binary)") ;
}
if (!mxIsChar (pargin [0]))
{
mexErrMsgTxt ("mread requires a filename") ;
}
mxGetString (pargin [0], filename, MAXLEN) ;
sputil_file = fopen (filename, "r") ;
if (sputil_file == NULL)
{
mexErrMsgTxt ("cannot open file") ;
}
if (nargin > 1)
{
cm->prefer_binary = (mxGetScalar (pargin [1]) != 0) ;
}
/* ---------------------------------------------------------------------- */
/* read the matrix, as either a dense or sparse matrix */
/* ---------------------------------------------------------------------- */
G = cholmod_l_read_matrix (sputil_file, 1, &mtype, cm) ;
fclose (sputil_file) ;
sputil_file = NULL ;
if (G == NULL)
{
mexErrMsgTxt ("could not read file") ;
}
/* get the specific matrix (A or X), and change to ZOMPLEX if needed */
if (mtype == CHOLMOD_SPARSE)
{
A = (cholmod_sparse *) G ;
nrow = A->nrow ;
ncol = A->ncol ;
is_complex = (A->xtype == CHOLMOD_COMPLEX) ;
Ap = A->p ;
Ai = A->i ;
if (is_complex)
{
/* if complex, ensure A is ZOMPLEX */
cholmod_l_sparse_xtype (CHOLMOD_ZOMPLEX, A, cm) ;
}
Ax = A->x ;
Az = A->z ;
}
else if (mtype == CHOLMOD_DENSE)
{
X = (cholmod_dense *) G ;
nrow = X->nrow ;
ncol = X->ncol ;
is_complex = (X->xtype == CHOLMOD_COMPLEX) ;
if (is_complex)
{
/* if complex, ensure X is ZOMPLEX */
cholmod_l_dense_xtype (CHOLMOD_ZOMPLEX, X, cm) ;
}
Ax = X->x ;
Az = X->z ;
}
else
{
mexErrMsgTxt ("invalid file") ;
}
/* ---------------------------------------------------------------------- */
/* if requested, extract the zero entries and place them in Z */
/* ---------------------------------------------------------------------- */
if (nargout > 1)
{
if (mtype == CHOLMOD_SPARSE)
{
/* A is a sparse real/zomplex double matrix */
Z = sputil_extract_zeros (A, cm) ;
}
else
{
/* input is full; just return an empty Z matrix */
Z = cholmod_l_spzeros (nrow, ncol, 0, CHOLMOD_REAL, cm) ;
}
}
/* ---------------------------------------------------------------------- */
/* prune the zero entries from A and set nzmax(A) to nnz(A) */
/* ---------------------------------------------------------------------- */
if (mtype == CHOLMOD_SPARSE)
{
sputil_drop_zeros (A) ;
cholmod_l_reallocate_sparse (cholmod_l_nnz (A, cm), A, cm) ;
}
/* ---------------------------------------------------------------------- */
/* change a complex matrix to real if its imaginary part is all zero */
/* ---------------------------------------------------------------------- */
if (is_complex)
{
if (mtype == CHOLMOD_SPARSE)
{
nz = Ap [ncol] ;
}
else
{
nz = nrow * ncol ;
}
allzero = TRUE ;
for (k = 0 ; k < nz ; k++)
{
if (Az [k] != 0)
{
allzero = FALSE ;
break ;
}
}
if (allzero)
{
/* discard the all-zero imaginary part */
if (mtype == CHOLMOD_SPARSE)
{
cholmod_l_sparse_xtype (CHOLMOD_REAL, A, cm) ;
}
else
{
cholmod_l_dense_xtype (CHOLMOD_REAL, X, cm) ;
}
}
}
/* ---------------------------------------------------------------------- */
/* return results to MATLAB */
/* ---------------------------------------------------------------------- */
if (mtype == CHOLMOD_SPARSE)
{
pargout [0] = sputil_put_sparse (&A, cm) ;
}
else
{
pargout [0] = sputil_put_dense (&X, cm) ;
}
if (nargout > 1)
{
pargout [1] = sputil_put_sparse (&Z, cm) ;
}
/* ---------------------------------------------------------------------- */
/* free workspace */
/* ---------------------------------------------------------------------- */
cholmod_l_finish (cm) ;
cholmod_l_print_common (" ", cm) ;
}
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) ;
}
int main (int argc, char **argv)
{
cholmod_sparse *A, *R ;
cholmod_dense *B, *C ;
SuiteSparse_long *E ;
int mtype ;
long m, n, rnk ;
size_t total_mem, available_mem ;
double t ;
// start CHOLMOD
cholmod_common *cc, Common ;
cc = &Common ;
cholmod_l_start (cc) ;
// warmup the GPU. This can take some time, but only needs
// to be done once
cc->useGPU = false ;
t = SuiteSparse_time ( ) ;
cholmod_l_gpu_memorysize (&total_mem, &available_mem, cc) ;
cc->gpuMemorySize = available_mem ;
t = SuiteSparse_time ( ) - t ;
if (cc->gpuMemorySize <= 1)
{
printf ("no GPU available\n") ;
}
printf ("available GPU memory: %g MB, warmup time: %g\n",
(double) (cc->gpuMemorySize) / (1024 * 1024), t) ;
// A = mread (stdin) ; read in the sparse matrix A
const char *filename = argv[1];
FILE *file = fopen(filename, "r");
A = (cholmod_sparse *) cholmod_l_read_matrix (file, 1, &mtype, cc) ;
fclose(file);
if (mtype != CHOLMOD_SPARSE)
{
printf ("input matrix must be sparse\n") ;
exit (1) ;
}
// [m n] = size (A) ;
m = A->nrow ;
n = A->ncol ;
long ordering = (argc < 3 ? SPQR_ORDERING_DEFAULT : atoi(argv[2]));
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) ;
double tol = SPQR_NO_TOL ;
long econ = 0 ;
// [Q,R,E] = qr (A), but discard Q
// SuiteSparseQR <double> (ordering, tol, econ, A, &R, &E, cc) ;
// [C,R,E] = qr (A,b), but discard Q
SuiteSparseQR <double> (ordering, tol, econ, A, B, &C, &R, &E, cc) ;
// now R'*R-A(:,E)'*A(:,E) should be epsilon
// and C = Q'*b. The solution to the least-squares problem
// should be x=R\C.
// write out R to a file
FILE *f = fopen ("R.mtx", "w") ;
cholmod_l_write_sparse (f, R, NULL, NULL, cc) ;
fclose (f) ;
// write out C to a file
f = fopen ("C.mtx", "w") ;
cholmod_l_write_dense (f, C, NULL, cc) ;
fclose (f) ;
// write out E to a file
f = fopen ("E.txt", "w") ;
for (long i = 0 ; i < n ; i++)
{
fprintf (f, "%ld\n", 1 + E [i]) ;
}
fclose (f) ;
// free everything
cholmod_l_free_sparse (&A, cc) ;
cholmod_l_free_sparse (&R, cc) ;
cholmod_l_free_dense (&C, cc) ;
// cholmod_l_free (&E, cc) ;
cholmod_l_finish (cc) ;
return (0) ;
}
int main (int argc, char **argv)
{
cholmod_sparse *A ;
cholmod_dense *X, *B, *r, *atr ;
double anorm, xnorm, rnorm, one [2] = {1,0}, minusone [2] = {-1,0}, t ;
double zero [2] = {0,0}, atrnorm ;
int mtype ;
long m, n, rnk ;
size_t total_mem, available_mem ;
// start CHOLMOD
cholmod_common *cc, Common ;
cc = &Common ;
cholmod_l_start (cc) ;
// warmup the GPU. This can take some time, but only needs
// to be done once
cc->useGPU = true ;
t = SuiteSparse_time ( ) ;
cholmod_l_gpu_memorysize (&total_mem, &available_mem, cc) ;
cc->gpuMemorySize = available_mem ;
t = SuiteSparse_time ( ) - t ;
if (cc->gpuMemorySize <= 1)
{
printf ("no GPU available\n") ;
}
printf ("available GPU memory: %g MB, warmup time: %g\n",
(double) (cc->gpuMemorySize) / (1024 * 1024), t) ;
// A = mread (stdin) ; read in the sparse matrix A
const char *filename = (argc < 2 ? "Problems/2.mtx" : argv[1]);
FILE *file = fopen(filename, "r");
A = (cholmod_sparse *) cholmod_l_read_matrix (file, 1, &mtype, cc) ;
fclose(file);
if (mtype != CHOLMOD_SPARSE)
{
printf ("input matrix must be sparse\n") ;
exit (1) ;
}
// [m n] = size (A) ;
m = A->nrow ;
n = A->ncol ;
long ordering = (argc < 3 ? SPQR_ORDERING_DEFAULT : atoi(argv[2]));
#if 1
printf ("Matrix %6ld-by-%-6ld nnz: %6ld\n",
m, n, cholmod_l_nnz (A, cc)) ;
#endif
// anorm = norm (A,1) ;
anorm = cholmod_l_norm_sparse (A, 1, 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>(ordering, SPQR_NO_TOL, A, B, cc) ;
}
else
{
#if SUPPORTS_COMPLEX
// A, X, and B are all complex
X = SuiteSparseQR < std::complex<double> >
(SPQR_ORDERING_DEFAULT, SPQR_NO_TOL, A, B, cc) ;
#else
printf("Code doesn't support std::complex<?> types.\n");
#endif
}
// get the rank(A) estimate
rnk = cc->SPQR_istat [4] ;
// compute the residual r, and A'*r, and their norms
r = cholmod_l_copy_dense (B, cc) ; // r = B
cholmod_l_sdmult (A, 0, one, minusone, X, r, cc) ; // r = A*X-r = A*x-b
rnorm = cholmod_l_norm_dense (r, 2, cc) ; // rnorm = norm (r)
atr = cholmod_l_zeros (n, 1, CHOLMOD_REAL, cc) ; // atr = zeros (n,1)
cholmod_l_sdmult (A, 1, one, zero, r, atr, cc) ; // atr = A'*r
atrnorm = cholmod_l_norm_dense (atr, 2, cc) ; // atrnorm = norm (atr)
// xnorm = norm (X)
xnorm = cholmod_l_norm_dense (X, 2, cc) ;
// write out X to a file
FILE *f = fopen ("X.mtx", "w") ;
cholmod_l_write_dense (f, X, NULL, cc) ;
fclose (f) ;
if (m <= n && anorm > 0 && xnorm > 0)
{
// find the relative residual, except for least-squares systems
rnorm /= (anorm * xnorm) ;
}
printf ("\nnorm(Ax-b): %8.1e\n", rnorm) ;
printf ("norm(A'(Ax-b)) %8.1e rank: %ld of %ld\n",
atrnorm, rnk, (m < n) ? m:n) ;
/* Write an info file. */
FILE *info = fopen("gpu_results.txt", "w");
fprintf(info, "%ld\n", cc->SPQR_istat[7]); // ordering method
fprintf(info, "%ld\n", cc->memory_usage); // memory usage (bytes)
fprintf(info, "%30.16e\n", cc->SPQR_flopcount); // flop count
fprintf(info, "%lf\n", cc->SPQR_analyze_time); // analyze time
fprintf(info, "%lf\n", cc->SPQR_factorize_time); // factorize time
fprintf(info, "-1\n") ; // cpu memory (bytes)
fprintf(info, "-1\n") ; // gpu memory (bytes)
fprintf(info, "%32.16e\n", rnorm); // residual
fprintf(info, "%ld\n", cholmod_l_nnz (A, cc)); // nnz(A)
fprintf(info, "%ld\n", cc->SPQR_istat [0]); // nnz(R)
fprintf(info, "%ld\n", cc->SPQR_istat [2]); // # of frontal matrices
fprintf(info, "%ld\n", cc->SPQR_istat [3]); // ntasks, for now
fprintf(info, "%lf\n", cc->gpuKernelTime); // kernel time (ms)
fprintf(info, "%ld\n", cc->gpuFlops); // "actual" gpu flops
fprintf(info, "%d\n", cc->gpuNumKernelLaunches); // # of kernel launches
fprintf(info, "%32.16e\n", atrnorm) ; // norm (A'*(Ax-b))
fclose(info);
// free everything
cholmod_l_free_dense (&r, cc) ;
cholmod_l_free_dense (&atr, cc) ;
cholmod_l_free_sparse (&A, cc) ;
cholmod_l_free_dense (&X, cc) ;
cholmod_l_free_dense (&B, cc) ;
cholmod_l_finish (cc) ;
return (0) ;
}