mxArray *spqr_mx_put_sparse
(
cholmod_sparse **Ahandle, // CHOLMOD version of the matrix
cholmod_common *cc
)
{
mxArray *Amatlab ;
cholmod_sparse *A ;
Long nz, is_complex ;
A = *Ahandle ;
is_complex = (A->xtype != CHOLMOD_REAL) ;
Amatlab = mxCreateSparse (0, 0, 0, is_complex ? mxCOMPLEX: mxREAL) ;
mxSetM (Amatlab, A->nrow) ;
mxSetN (Amatlab, A->ncol) ;
mxSetNzmax (Amatlab, A->nzmax) ;
mxFree (mxGetJc (Amatlab)) ;
mxFree (mxGetIr (Amatlab)) ;
mxFree (mxGetPr (Amatlab)) ;
mxSetJc (Amatlab, (mwIndex *) A->p) ;
mxSetIr (Amatlab, (mwIndex *) A->i) ;
nz = cholmod_l_nnz (A, cc) ;
put_values (nz, Amatlab, (double *) A->x, is_complex, cc) ;
A->p = NULL ;
A->i = NULL ;
A->x = NULL ;
A->z = NULL ;
cholmod_l_free_sparse (Ahandle, cc) ;
return (Amatlab) ;
}
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_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) ;
}
/**
* Copy the contents of a to an appropriate CsparseMatrix object and,
* optionally, free a or free both a and its the pointers to its contents.
*
* @param a (cholmod_sparse) matrix to be converted
* @param dofree 0 - don't free a; > 0 cholmod_free a; < 0 Free a
* @param uploT 0 - not triangular; > 0 upper triangular; < 0 lower
* @param Rkind - vector type to store for a->xtype == CHOLMOD_REAL,
* 0 - REAL; 1 - LOGICAL [unused for other a->xtype]
* @param diag character string suitable for the diag slot of a
* triangular matrix (not accessed if uploT == 0).
* @param dn either R_NilValue or an SEXP suitable for the Dimnames slot.
*
* @return SEXP containing a copy of a
*/
SEXP chm_sparse_to_SEXP(CHM_SP a, int dofree, int uploT, int Rkind,
const char* diag, SEXP dn)
{
SEXP ans;
char *cls = "";/* -Wall */
Rboolean longi = (a->itype) == CHOLMOD_LONG;
int *dims, nnz, *ansp, *ansi;
// if (longi) :
SuiteSparse_long
*ail = (SuiteSparse_long*)(a->i),
*apl = (SuiteSparse_long*)(a->p);
// else ((a->itype) == CHOLMOD_INT) :
int *aii = (int*)(a->i),
*api = (int*)(a->p);
PROTECT(dn); /* dn is usually UNPROTECTed before the call */
/* ensure a is sorted and packed */
if (!a->sorted || !a->packed)
longi ? cholmod_l_sort(a, &cl) : cholmod_sort(a, &c);
/* determine the class of the result */
#define DOFREE_MAYBE \
if (dofree > 0) \
longi ? cholmod_l_free_sparse(&a, &cl) : cholmod_free_sparse(&a, &c); \
else if (dofree < 0) Free(a)
switch(a->xtype) {
case CHOLMOD_PATTERN:
cls = uploT ? "ntCMatrix": ((a->stype) ? "nsCMatrix" : "ngCMatrix");
break;
case CHOLMOD_REAL:
switch(Rkind) {
case 0:
cls = uploT ? "dtCMatrix": ((a->stype) ? "dsCMatrix" : "dgCMatrix");
break;
case 1:
cls = uploT ? "ltCMatrix": ((a->stype) ? "lsCMatrix" : "lgCMatrix");
break;
default:
DOFREE_MAYBE;
error(_("chm_sparse_to_SEXP(<real>, *): invalid 'Rkind' (real kind code)"));
}
break;
case CHOLMOD_COMPLEX:
cls = uploT ? "ztCMatrix": ((a->stype) ? "zsCMatrix" : "zgCMatrix");
break;
default:
DOFREE_MAYBE;
error(_("unknown xtype in cholmod_sparse object"));
}
ans = PROTECT(NEW_OBJECT_OF_CLASS(cls));
/* allocate and copy common slots */
nnz = longi ? cholmod_l_nnz(a, &cl) : cholmod_nnz(a, &c);
dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));
dims[0] = a->nrow; dims[1] = a->ncol;
ansp = INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, a->ncol + 1));
ansi = INTEGER(ALLOC_SLOT(ans, Matrix_iSym, INTSXP, nnz));
for (int j = 0; j <= a->ncol; j++) ansp[j] = longi ? (int)(apl[j]) : api[j];
for (int p = 0; p < nnz; p++) ansi[p] = longi ? (int)(ail[p]) : aii[p];
/* copy data slot if present */
if (a->xtype == CHOLMOD_REAL) {
int i, *m_x;
double *a_x = (double *) a->x;
switch(Rkind) {
case 0:
Memcpy(REAL(ALLOC_SLOT(ans, Matrix_xSym, REALSXP, nnz)),
a_x, nnz);
break;
case 1:
m_x = LOGICAL(ALLOC_SLOT(ans, Matrix_xSym, LGLSXP, nnz));
for (i=0; i < nnz; i++)
m_x[i] = ISNAN(a_x[i]) ? NA_LOGICAL : (a_x[i] != 0);
break;
}
}
else if (a->xtype == CHOLMOD_COMPLEX) {
DOFREE_MAYBE;
error(_("complex sparse matrix code not yet written"));
/* Memcpy(COMPLEX(ALLOC_SLOT(ans, Matrix_xSym, CPLXSXP, nnz)), */
/* (complex *) a->x, nnz); */
}
if (uploT) { /* slots for triangularMatrix */
if (a->stype) error(_("Symmetric and triangular both set"));
SET_SLOT(ans, Matrix_uploSym, mkString((uploT > 0) ? "U" : "L"));
SET_SLOT(ans, Matrix_diagSym, mkString(diag));
}
if (a->stype) /* slot for symmetricMatrix */
SET_SLOT(ans, Matrix_uploSym,
mkString((a->stype > 0) ? "U" : "L"));
DOFREE_MAYBE;
if (dn != R_NilValue)
SET_SLOT(ans, Matrix_DimNamesSym, duplicate(dn));
UNPROTECT(2);
return ans;
}
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 ;
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) ;
}
