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) ;
const Dense& Dense :: operator=( const Dense& A )
{
if( data ) { cholmod_l_free_dense( &data, common ); data = NULL; }
data = cholmod_l_copy_dense( A.data, common );
initializeFromCopy();
return *this;
}
const DenseMatrix& DenseMatrix :: operator=( const DenseMatrix& A )
// copies A
{
if( data ) { cholmod_l_free_dense( &data, context ); data = NULL; }
data = cholmod_l_copy_dense( A.data, context );
initializeFromCopy();
return *this;
}
void check_residual
(
cholmod_sparse *A,
cholmod_dense *X,
cholmod_dense *B,
cholmod_common *cc
)
{
Long m = A->nrow ;
Long n = A->ncol ;
Long rnk ;
double rnorm, anorm, xnorm, atrnorm ;
double one [2] = {1,0}, minusone [2] = {-1,0}, zero [2] = {0,0} ;
cholmod_dense *r, *atr ;
// get the rank(A) estimate
rnk = cc->SPQR_istat [4] ;
// anorm = norm (A,1) ;
anorm = cholmod_l_norm_sparse (A, 1, cc) ;
// rnorm = norm (A*X-B)
r = cholmod_l_copy_dense (B, cc) ;
cholmod_l_sdmult (A, 0, one, minusone, X, r, cc) ;
rnorm = cholmod_l_norm_dense (r, 2, cc) ;
// xnorm = norm (X)
xnorm = cholmod_l_norm_dense (X, 2, cc) ;
// atrnorm = norm (A'*r)
atr = cholmod_l_zeros (n, 1, r->xtype, 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)
if (anorm > 0) atrnorm /= anorm ;
if (m <= n && anorm > 0 && xnorm > 0)
{
// find the relative residual, except for least-squares systems
rnorm /= (anorm * xnorm) ;
}
printf ("relative norm(Ax-b): %8.1e rank: %6ld "
"rel. norm(A'(Ax-b)) %8.1e\n", rnorm, rnk, atrnorm) ;
cholmod_l_free_dense (&r, cc) ;
cholmod_l_free_dense (&atr, cc) ;
}
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) ;
}