int main(int argc, char* argv[])
{
if (argc != 2) return usage(argv[0]);
int n = atoi(argv[1]), n2 = n * n;
if (n <= 0) return usage(argv[0]);
// Generate random matrix.
size_t size = sizeof(float) * n2;
float* A1 = (float*)malloc(size);
int one = 1, seed[4] = { 0, 0, 0, 1 };
slarnv_(&one, seed, &n2, A1);
// Symmetrize and increase the diagonal.
for (int i = 0; i < n; i++)
{
A1[i * n + i] += n;
for (int j = 0; j < i; j++)
A1[i * n + j] = A1[j * n + i];
}
// Clone generated matrix for GPU version
// (we can't use one copy of A, because
// spotrf rewrites the input matrix).
float* A2 = (float*)malloc(size);
memcpy(A2, A1, size);
// Use upper part of input matrix and
// rewrite it with Cholessky factor.
char uplo = 'U';
// The status info (routine must return 0 into info).
int info = 0;
// Perform decomposition on CPU.
printf("Computing on CPU ... "); fflush(stdout);
spotrf_(&uplo, &n, A1, &n, &info);
chkerr(info);
// Perform decomposition on GPU.
printf("Computing on GPU ... "); fflush(stdout);
magma_spotrf(uplo, n, A2, n, &info);
chkerr(info);
// Compare results.
float maxdiff = fabs(A1[0] - A2[0]);
for (int i = 0; i < n; i++)
for (int j = 0; j < i; j++)
{
maxdiff = fmax(maxdiff,
fabs(A1[i * n + j] - A2[i * n + j]));
maxdiff = fmax(maxdiff,
fabs(A1[j * n + i] - A2[j * n + i]));
}
printf("Done! max diff = %f\n", maxdiff);
free(A1); free(A2);
}
void magmaf_spotrf(
magma_uplo_t *uplo, magma_int_t *n,
float *A, magma_int_t *lda,
magma_int_t *info,
magma_queue_t *queue )
{
magma_spotrf(
*uplo, *n,
A, *lda,
info,
queue );
}
extern "C" magma_int_t
magma_sposv ( char uplo, magma_int_t n, magma_int_t nrhs,
float *A, magma_int_t lda,
float *B, magma_int_t ldb, magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
SPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
magma_int_t num_gpus, ldda, lddb;
*info = 0 ;
if( (uplo != 'U') && (uplo != 'u') && (uplo != 'L') && (uplo != 'l') )
*info = -1;
if( n < 0 )
*info = -2;
if( nrhs < 0)
*info = -3;
if ( lda < max(1, n) )
*info = -5;
if ( ldb < max(1, n) )
*info = -7;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if ( (n==0) || (nrhs == 0) ) {
return *info;
}
/* If single-GPU and allocation suceeds, use GPU interface. */
num_gpus = magma_num_gpus();
float *dA, *dB;
if ( num_gpus > 1 ) {
goto CPU_INTERFACE;
}
ldda = ((n+31)/32)*32;
lddb = ldda;
if ( MAGMA_SUCCESS != magma_smalloc( &dA, ldda*n )) {
goto CPU_INTERFACE;
}
if ( MAGMA_SUCCESS != magma_smalloc( &dB, lddb*nrhs )) {
magma_free( dA );
goto CPU_INTERFACE;
}
magma_ssetmatrix( n, n, A, lda, dA, ldda );
magma_spotrf_gpu( uplo, n, dA, ldda, info );
if ( *info == MAGMA_ERR_DEVICE_ALLOC ) {
magma_free( dA );
magma_free( dB );
goto CPU_INTERFACE;
}
magma_sgetmatrix( n, n, dA, ldda, A, lda );
if ( *info == 0 ) {
magma_ssetmatrix( n, nrhs, B, ldb, dB, lddb );
magma_spotrs_gpu( uplo, n, nrhs, dA, ldda, dB, lddb, info );
magma_sgetmatrix( n, nrhs, dB, lddb, B, ldb );
}
magma_free( dA );
magma_free( dB );
return *info;
CPU_INTERFACE:
/* If multi-GPU or allocation failed, use CPU interface and LAPACK.
* Faster to use LAPACK for potrs than to copy A to GPU. */
magma_spotrf( uplo, n, A, lda, info );
if ( *info == 0 ) {
lapackf77_spotrs( &uplo, &n, &nrhs, A, &lda, B, &ldb, info );
}
return *info;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing spotrf
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float *h_A, *h_R;
magma_int_t N, n2, lda, info;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
float work[1], error;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
float tol = opts.tolerance * lapackf77_slamch("E");
printf("ngpu %d, uplo %c\n", (int) opts.ngpu, opts.uplo );
printf(" N CPU GFlop/s (sec) GPU GFlop/s (sec) ||R_magma - R_lapack||_F / ||R_lapack||_F\n");
printf("========================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[i];
lda = N;
n2 = lda*N;
gflops = FLOPS_SPOTRF( N ) / 1e9;
TESTING_MALLOC_CPU( h_A, float, n2 );
TESTING_MALLOC_PIN( h_R, float, n2 );
/* Initialize the matrix */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
magma_smake_hpd( N, h_A, lda );
lapackf77_slacpy( MagmaUpperLowerStr, &N, &N, h_A, &lda, h_R, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_spotrf( opts.uplo, N, h_R, lda, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0)
printf("magma_spotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
if ( opts.lapack ) {
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_spotrf( &opts.uplo, &N, h_A, &lda, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0)
printf("lapackf77_spotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
/* =====================================================================
Check the result compared to LAPACK
=================================================================== */
error = lapackf77_slange("f", &N, &N, h_A, &lda, work);
blasf77_saxpy(&n2, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_slange("f", &N, &N, h_R, &lda, work) / error;
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %8.2e%s\n",
(int) N, cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "" : " failed") );
status |= ! (error < tol);
}
else {
printf("%5d --- ( --- ) %7.2f (%7.2f) --- \n",
(int) N, gpu_perf, gpu_time );
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_PIN( h_R );
}
}
TESTING_FINALIZE();
return status;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ssygst
*/
int main( int argc, char** argv)
{
TESTING_INIT();
// Constants
const float c_neg_one = MAGMA_S_NEG_ONE;
const magma_int_t ione = 1;
// Local variables
real_Double_t gpu_time, cpu_time;
float *h_A, *h_B, *h_R;
magmaFloat_ptr d_A, d_B;
float Anorm, error, work[1];
magma_int_t N, n2, lda, ldda, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
opts.lapack |= opts.check; // check (-c) implies lapack (-l)
float tol = opts.tolerance * lapackf77_slamch("E");
printf("%% uplo = %s\n", lapack_uplo_const(opts.uplo) );
printf("%% itype N CPU time (sec) GPU time (sec) |R| \n");
printf("%%=======================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
ldda = magma_roundup( lda, opts.align );
n2 = N*lda;
TESTING_MALLOC_CPU( h_A, float, lda*N );
TESTING_MALLOC_CPU( h_B, float, lda*N );
TESTING_MALLOC_PIN( h_R, float, lda*N );
TESTING_MALLOC_DEV( d_A, float, ldda*N );
TESTING_MALLOC_DEV( d_B, float, ldda*N );
/* ====================================================================
Initialize the matrix
=================================================================== */
lapackf77_slarnv( &ione, ISEED, &n2, h_A );
lapackf77_slarnv( &ione, ISEED, &n2, h_B );
magma_smake_symmetric( N, h_A, lda );
magma_smake_hpd( N, h_B, lda );
magma_spotrf( opts.uplo, N, h_B, lda, &info );
if (info != 0) {
printf("magma_spotrf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
magma_ssetmatrix( N, N, h_A, lda, d_A, ldda, opts.queue );
magma_ssetmatrix( N, N, h_B, lda, d_B, ldda, opts.queue );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_wtime();
magma_ssygst_gpu( opts.itype, opts.uplo, N, d_A, ldda, d_B, ldda, &info );
gpu_time = magma_wtime() - gpu_time;
if (info != 0) {
printf("magma_ssygst_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
lapackf77_ssygst( &opts.itype, lapack_uplo_const(opts.uplo),
&N, h_A, &lda, h_B, &lda, &info );
cpu_time = magma_wtime() - cpu_time;
if (info != 0) {
printf("lapackf77_ssygst returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
magma_sgetmatrix( N, N, d_A, ldda, h_R, lda, opts.queue );
blasf77_saxpy( &n2, &c_neg_one, h_A, &ione, h_R, &ione );
Anorm = safe_lapackf77_slansy("f", lapack_uplo_const(opts.uplo), &N, h_A, &lda, work );
error = safe_lapackf77_slansy("f", lapack_uplo_const(opts.uplo), &N, h_R, &lda, work )
/ Anorm;
bool okay = (error < tol);
status += ! okay;
printf("%3d %5d %7.2f %7.2f %8.2e %s\n",
(int) opts.itype, (int) N, cpu_time, gpu_time,
error, (okay ? "ok" : "failed"));
}
else {
printf("%3d %5d --- %7.2f\n",
(int) opts.itype, (int) N, gpu_time );
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_PIN( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
SPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H * U, if UPLO = MagmaUpper, or
A = L * L**H, if UPLO = MagmaLower,
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
nrhs INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
@param[in,out]
A REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_sposv_driver
********************************************************************/
extern "C" magma_int_t
magma_sposv(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs,
float *A, magma_int_t lda,
float *B, magma_int_t ldb,
magma_int_t *info )
{
magma_int_t ngpu, ldda, lddb;
*info = 0;
if ( uplo != MagmaUpper && uplo != MagmaLower )
*info = -1;
if ( n < 0 )
*info = -2;
if ( nrhs < 0)
*info = -3;
if ( lda < max(1, n) )
*info = -5;
if ( ldb < max(1, n) )
*info = -7;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if ( (n == 0) || (nrhs == 0) ) {
return *info;
}
/* If single-GPU and allocation suceeds, use GPU interface. */
ngpu = magma_num_gpus();
float *dA, *dB;
if ( ngpu > 1 ) {
goto CPU_INTERFACE;
}
ldda = ((n+31)/32)*32;
lddb = ldda;
if ( MAGMA_SUCCESS != magma_smalloc( &dA, ldda*n )) {
goto CPU_INTERFACE;
}
if ( MAGMA_SUCCESS != magma_smalloc( &dB, lddb*nrhs )) {
magma_free( dA );
goto CPU_INTERFACE;
}
magma_ssetmatrix( n, n, A, lda, dA, ldda );
magma_spotrf_gpu( uplo, n, dA, ldda, info );
if ( *info == MAGMA_ERR_DEVICE_ALLOC ) {
magma_free( dA );
magma_free( dB );
goto CPU_INTERFACE;
}
magma_sgetmatrix( n, n, dA, ldda, A, lda );
if ( *info == 0 ) {
magma_ssetmatrix( n, nrhs, B, ldb, dB, lddb );
magma_spotrs_gpu( uplo, n, nrhs, dA, ldda, dB, lddb, info );
magma_sgetmatrix( n, nrhs, dB, lddb, B, ldb );
}
magma_free( dA );
magma_free( dB );
return *info;
CPU_INTERFACE:
/* If multi-GPU or allocation failed, use CPU interface and LAPACK.
* Faster to use LAPACK for potrs than to copy A to GPU. */
magma_spotrf( uplo, n, A, lda, info );
if ( *info == 0 ) {
lapackf77_spotrs( lapack_uplo_const(uplo), &n, &nrhs, A, &lda, B, &ldb, info );
}
return *info;
}
