/** Perform triangular matrix-vector product.
\f$ x = A x \f$ (trans == MagmaNoTrans), or \n
\f$ x = A^T x \f$ (trans == MagmaTrans), or \n
\f$ x = A^H x \f$ (trans == MagmaConjTrans).
@param[in]
uplo Whether the upper or lower triangle of A is referenced.
@param[in]
trans Operation to perform on A.
@param[in]
diag Whether the diagonal of A is assumed to be unit or non-unit.
@param[in]
n Number of rows and columns of A. n >= 0.
@param[in]
dA COMPLEX array of dimension (ldda,n), ldda >= max(1,n).
The n-by-n matrix A, on GPU device.
@param[in]
ldda Leading dimension of dA.
@param[in]
dx COMPLEX array on GPU device.
The n element vector x of dimension (1 + (n-1)*incx).
@param[in]
incx Stride between consecutive elements of dx. incx != 0.
@ingroup magma_cblas2
*/
extern "C" void
magma_ctrmv(
magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag,
magma_int_t n,
magmaFloatComplex_const_ptr dA, size_t dA_offset, magma_int_t ldda,
magmaFloatComplex_ptr dx, size_t dx_offset, magma_int_t incx,
magma_queue_t queue )
{
if ( n <= 0 )
return;
magmaFloatComplex_ptr dwork;
magma_cmalloc( &dwork, (1 + (n-1)*abs(incx)) );
cl_int err = clblasCtrmv(
clblasColumnMajor,
clblas_uplo_const( uplo ),
clblas_trans_const( trans ),
clblas_diag_const( diag ),
n,
dA, dA_offset, ldda,
dx, dx_offset, incx,
dwork,
1, &queue, 0, NULL, g_event );
clFlush(queue);
check_error( err );
magma_free( dwork );
}
/** Perform Hermitian matrix-vector product, \f$ y = \alpha A x + \beta y \f$.
@param[in]
uplo Whether the upper or lower triangle of A is referenced.
@param[in]
n Number of rows and columns of A. n >= 0.
@param[in]
alpha Scalar \f$ \alpha \f$
@param[in]
dA COMPLEX array of dimension (ldda,n), ldda >= max(1,n).
The n-by-n matrix A, on GPU device.
@param[in]
ldda Leading dimension of dA.
@param[in]
dx COMPLEX array on GPU device.
The m element vector x of dimension (1 + (m-1)*incx).
@param[in]
incx Stride between consecutive elements of dx. incx != 0.
@param[in]
beta Scalar \f$ \beta \f$
@param[in,out]
dy COMPLEX array on GPU device.
The n element vector y of dimension (1 + (n-1)*incy).
@param[in]
incy Stride between consecutive elements of dy. incy != 0.
@ingroup magma_cblas2
*/
extern "C" void
magma_chemv(
magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex alpha,
magmaFloatComplex_const_ptr dA, size_t dA_offset, magma_int_t ldda,
magmaFloatComplex_const_ptr dx, size_t dx_offset, magma_int_t incx,
magmaFloatComplex beta,
magmaFloatComplex_ptr dy, size_t dy_offset, magma_int_t incy,
magma_queue_t queue )
{
if ( n <= 0 )
return;
cl_int err = clblasChemv(
clblasColumnMajor,
clblas_uplo_const( uplo ),
n,
alpha, dA, dA_offset, ldda,
dx, dx_offset, incx,
beta, dy, dy_offset, incy,
1, &queue, 0, NULL, g_event );
clFlush(queue);
check_error( err );
}
/** Solve triangular matrix-matrix system (multiple right-hand sides).
\f$ op(A) X = \alpha B \f$ (side == MagmaLeft), or \n
\f$ X op(A) = \alpha B \f$ (side == MagmaRight), \n
where \f$ A \f$ is triangular.
@param[in]
side Whether A is on the left or right.
@param[in]
uplo Whether A is upper or lower triangular.
@param[in]
trans Operation to perform on A.
@param[in]
diag Whether the diagonal of A is assumed to be unit or non-unit.
@param[in]
m Number of rows of B. m >= 0.
@param[in]
n Number of columns of B. n >= 0.
@param[in]
alpha Scalar \f$ \alpha \f$
@param[in]
dA COMPLEX array on GPU device.
If side == MagmaLeft, the m-by-m triangular matrix A of dimension (ldda,m), ldda >= max(1,m); \n
otherwise, the n-by-n triangular matrix A of dimension (ldda,n), ldda >= max(1,n).
@param[in]
ldda Leading dimension of dA.
@param[in,out]
dB COMPLEX array on GPU device.
On entry, m-by-n matrix B of dimension (lddb,n), lddb >= max(1,m).
On exit, overwritten with the solution matrix X.
@param[in]
lddb Leading dimension of dB.
@ingroup magma_cblas3
*/
extern "C" void
magma_ctrsm(
magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag,
magma_int_t m, magma_int_t n,
magmaFloatComplex alpha,
magmaFloatComplex_const_ptr dA, size_t dA_offset, magma_int_t ldda,
magmaFloatComplex_ptr dB, size_t dB_offset, magma_int_t lddb,
magma_queue_t queue )
{
if (m <= 0 || n <= 0)
return;
cl_int err = clblasCtrsm(
clblasColumnMajor,
clblas_side_const( side ),
clblas_uplo_const( uplo ),
clblas_trans_const( trans ),
clblas_diag_const( diag ),
m, n,
alpha, dA, dA_offset, ldda,
dB, dB_offset, lddb,
1, &queue, 0, NULL, g_event );
clFlush(queue);
check_error( err );
}
/** Perform Hermitian rank-2k update.
\f$ C = \alpha A B^T + \alpha B A^T \beta C \f$ (trans == MagmaNoTrans), or \n
\f$ C = \alpha A^T B + \alpha B^T A \beta C \f$ (trans == MagmaTrans), \n
where \f$ C \f$ is Hermitian.
@param[in]
uplo Whether the upper or lower triangle of C is referenced.
@param[in]
trans Operation to perform on A and B.
@param[in]
n Number of rows and columns of C. n >= 0.
@param[in]
k Number of columns of A and B (for MagmaNoTrans) or rows of A and B (for MagmaTrans). k >= 0.
@param[in]
alpha Scalar \f$ \alpha \f$
@param[in]
dA COMPLEX array on GPU device.
If trans == MagmaNoTrans, the n-by-k matrix A of dimension (ldda,k), ldda >= max(1,n); \n
otherwise, the k-by-n matrix A of dimension (ldda,n), ldda >= max(1,k).
@param[in]
ldda Leading dimension of dA.
@param[in]
dB COMPLEX array on GPU device.
If trans == MagmaNoTrans, the n-by-k matrix B of dimension (lddb,k), lddb >= max(1,n); \n
otherwise, the k-by-n matrix B of dimension (lddb,n), lddb >= max(1,k).
@param[in]
lddb Leading dimension of dB.
@param[in]
beta Scalar \f$ \beta \f$
@param[in,out]
dC COMPLEX array on GPU device.
The n-by-n Hermitian matrix C of dimension (lddc,n), lddc >= max(1,n).
@param[in]
lddc Leading dimension of dC.
@ingroup magma_cblas3
*/
extern "C" void
magma_cher2k(
magma_uplo_t uplo, magma_trans_t trans,
magma_int_t n, magma_int_t k,
magmaFloatComplex alpha,
magmaFloatComplex_const_ptr dA, size_t dA_offset, magma_int_t ldda,
magmaFloatComplex_const_ptr dB, size_t dB_offset, magma_int_t lddb,
float beta,
magmaFloatComplex_ptr dC, size_t dC_offset, magma_int_t lddc,
magma_queue_t queue )
{
if (n <= 0 || k <= 0)
return;
cl_int err = clblasCher2k(
clblasColumnMajor,
clblas_uplo_const( uplo ),
clblas_trans_const( trans ),
n, k,
alpha, dA, dA_offset, ldda,
dB, dB_offset, lddb,
beta, dC, dC_offset, lddc,
1, &queue, 0, NULL, g_event );
clFlush(queue);
check_error( err );
}
/** Perform Hermitian matrix-matrix product.
\f$ C = \alpha A B + \beta C \f$ (side == MagmaLeft), or \n
\f$ C = \alpha B A + \beta C \f$ (side == MagmaRight), \n
where \f$ A \f$ is Hermitian.
@param[in]
side Whether A is on the left or right.
@param[in]
uplo Whether the upper or lower triangle of A is referenced.
@param[in]
m Number of rows of C. m >= 0.
@param[in]
n Number of columns of C. n >= 0.
@param[in]
alpha Scalar \f$ \alpha \f$
@param[in]
dA COMPLEX array on GPU device.
If side == MagmaLeft, the m-by-m Hermitian matrix A of dimension (ldda,m), ldda >= max(1,m); \n
otherwise, the n-by-n Hermitian matrix A of dimension (ldda,n), ldda >= max(1,n).
@param[in]
ldda Leading dimension of dA.
@param[in]
dB COMPLEX array on GPU device.
The m-by-n matrix B of dimension (lddb,n), lddb >= max(1,m).
@param[in]
lddb Leading dimension of dB.
@param[in]
beta Scalar \f$ \beta \f$
@param[in,out]
dC COMPLEX array on GPU device.
The m-by-n matrix C of dimension (lddc,n), lddc >= max(1,m).
@param[in]
lddc Leading dimension of dC.
@ingroup magma_cblas3
*/
extern "C" void
magma_chemm(
magma_side_t side, magma_uplo_t uplo,
magma_int_t m, magma_int_t n,
magmaFloatComplex alpha,
magmaFloatComplex_const_ptr dA, size_t dA_offset, magma_int_t ldda,
magmaFloatComplex_const_ptr dB, size_t dB_offset, magma_int_t lddb,
magmaFloatComplex beta,
magmaFloatComplex_ptr dC, size_t dC_offset, magma_int_t lddc,
magma_queue_t queue )
{
if ( m <= 0 || n <= 0)
return;
cl_int err = clblasChemm(
clblasColumnMajor,
clblas_side_const( side ),
clblas_uplo_const( uplo ),
m, n,
alpha, dA, dA_offset, ldda,
dB, dB_offset, lddb,
beta, dC, dC_offset, lddc,
1, &queue, 0, NULL, g_event );
clFlush(queue);
check_error( err );
}
/** Perform Hermitian rank-1 update, \f$ A = \alpha x x^H + A \f$.
@param[in]
uplo Whether the upper or lower triangle of A is referenced.
@param[in]
n Number of rows and columns of A. n >= 0.
@param[in]
alpha Scalar \f$ \alpha \f$
@param[in]
dx COMPLEX array on GPU device.
The n element vector x of dimension (1 + (n-1)*incx).
@param[in]
incx Stride between consecutive elements of dx. incx != 0.
@param[in,out]
dA COMPLEX array of dimension (ldda,n), ldda >= max(1,n).
The n-by-n matrix A, on GPU device.
@param[in]
ldda Leading dimension of dA.
@ingroup magma_cblas2
*/
extern "C" void
magma_cher(
magma_uplo_t uplo,
magma_int_t n,
float alpha,
magmaFloatComplex_const_ptr dx, size_t dx_offset, magma_int_t incx,
magmaFloatComplex_ptr dA, size_t dA_offset, magma_int_t ldda,
magma_queue_t queue )
{
cl_int err = clblasCher(
clblasColumnMajor,
clblas_uplo_const( uplo ),
n,
alpha, dx, dx_offset, incx,
dA, dA_offset, ldda,
1, &queue, 0, NULL, g_event );
check_error( err );
}
/** Perform symmetric rank-k update.
\f$ C = \alpha A A^T + \beta C \f$ (trans == MagmaNoTrans), or \n
\f$ C = \alpha A^T A + \beta C \f$ (trans == MagmaTrans), \n
where \f$ C \f$ is symmetric.
@param[in]
uplo Whether the upper or lower triangle of C is referenced.
@param[in]
trans Operation to perform on A.
@param[in]
n Number of rows and columns of C. n >= 0.
@param[in]
k Number of columns of A (for MagmaNoTrans) or rows of A (for MagmaTrans). k >= 0.
@param[in]
alpha Scalar \f$ \alpha \f$
@param[in]
dA COMPLEX array on GPU device.
If trans == MagmaNoTrans, the n-by-k matrix A of dimension (ldda,k), ldda >= max(1,n); \n
otherwise, the k-by-n matrix A of dimension (ldda,n), ldda >= max(1,k).
@param[in]
ldda Leading dimension of dA.
@param[in]
beta Scalar \f$ \beta \f$
@param[in,out]
dC COMPLEX array on GPU device.
The n-by-n symmetric matrix C of dimension (lddc,n), lddc >= max(1,n).
@param[in]
lddc Leading dimension of dC.
@ingroup magma_cblas3
*/
extern "C" void
magma_csyrk(
magma_uplo_t uplo, magma_trans_t trans,
magma_int_t n, magma_int_t k,
magmaFloatComplex alpha,
magmaFloatComplex_const_ptr dA, size_t dA_offset, magma_int_t ldda,
magmaFloatComplex beta,
magmaFloatComplex_ptr dC, size_t dC_offset, magma_int_t lddc,
magma_queue_t queue )
{
cl_int err = clblasCsyrk(
clblasColumnMajor,
clblas_uplo_const( uplo ),
clblas_trans_const( trans ),
n, k,
alpha, dA, dA_offset, ldda,
beta, dC, dC_offset, lddc,
1, &queue, 0, NULL, g_event );
check_error( err );
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ctrsm
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf=0, magma_time=0, cublas_perf, cublas_time, cpu_perf=0, cpu_time=0;
float magma_error=0, cublas_error, lapack_error, work[1];
magma_int_t M, N, info;
magma_int_t Ak;
magma_int_t sizeA, sizeB;
magma_int_t lda, ldb, ldda, lddb;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t *ipiv;
magmaFloatComplex *h_A, *h_B, *h_Bcublas, *h_Bmagma, *h_Blapack, *h_X;
magmaFloatComplex_ptr d_A, d_B;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex alpha = MAGMA_C_MAKE( 0.29, -0.86 );
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
float tol = opts.tolerance * lapackf77_slamch("E");
// pass ngpu = -1 to test multi-GPU code using 1 gpu
magma_int_t abs_ngpu = abs( opts.ngpu );
printf("%% side = %s, uplo = %s, transA = %s, diag = %s, ngpu = %d\n",
lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
lapack_trans_const(opts.transA), lapack_diag_const(opts.diag), int(abs_ngpu) );
printf("%% M N MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) CPU Gflop/s (ms) MAGMA CUBLAS LAPACK error\n");
printf("%%============================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
gflops = FLOPS_CTRSM(opts.side, M, N) / 1e9;
if ( opts.side == MagmaLeft ) {
lda = M;
Ak = M;
} else {
lda = N;
Ak = N;
}
ldb = M;
ldda = magma_roundup( lda, opts.align ); // multiple of 32 by default
lddb = magma_roundup( ldb, opts.align ); // multiple of 32 by default
sizeA = lda*Ak;
sizeB = ldb*N;
TESTING_MALLOC_CPU( h_A, magmaFloatComplex, lda*Ak );
TESTING_MALLOC_CPU( h_B, magmaFloatComplex, ldb*N );
TESTING_MALLOC_CPU( h_X, magmaFloatComplex, ldb*N );
TESTING_MALLOC_CPU( h_Blapack, magmaFloatComplex, ldb*N );
TESTING_MALLOC_CPU( h_Bcublas, magmaFloatComplex, ldb*N );
TESTING_MALLOC_CPU( h_Bmagma, magmaFloatComplex, ldb*N );
TESTING_MALLOC_CPU( ipiv, magma_int_t, Ak );
TESTING_MALLOC_DEV( d_A, magmaFloatComplex, ldda*Ak );
TESTING_MALLOC_DEV( d_B, magmaFloatComplex, lddb*N );
/* Initialize the matrices */
/* Factor A into LU to get well-conditioned triangular matrix.
* Copy L to U, since L seems okay when used with non-unit diagonal
* (i.e., from U), while U fails when used with unit diagonal. */
lapackf77_clarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_cgetrf( &Ak, &Ak, h_A, &lda, ipiv, &info );
for( int j = 0; j < Ak; ++j ) {
for( int i = 0; i < j; ++i ) {
*h_A(i,j) = *h_A(j,i);
}
}
lapackf77_clarnv( &ione, ISEED, &sizeB, h_B );
memcpy( h_Blapack, h_B, sizeB*sizeof(magmaFloatComplex) );
magma_csetmatrix( Ak, Ak, h_A, lda, d_A, ldda, opts.queue );
/* =====================================================================
Performs operation using MAGMABLAS
=================================================================== */
#if defined(HAVE_CUBLAS)
magma_csetmatrix( M, N, h_B, ldb, d_B, lddb, opts.queue );
magma_time = magma_sync_wtime( opts.queue );
if (opts.ngpu == 1) {
magmablas_ctrsm( opts.side, opts.uplo, opts.transA, opts.diag,
M, N,
alpha, d_A, ldda,
d_B, lddb, opts.queue );
}
else {
magma_ctrsm_m( abs_ngpu, opts.side, opts.uplo, opts.transA, opts.diag,
M, N,
alpha, d_A, ldda,
d_B, lddb );
}
magma_time = magma_sync_wtime( opts.queue ) - magma_time;
magma_perf = gflops / magma_time;
magma_cgetmatrix( M, N, d_B, lddb, h_Bmagma, ldb, opts.queue );
#endif
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_csetmatrix( M, N, h_B, ldb, d_B, lddb, opts.queue );
cublas_time = magma_sync_wtime( opts.queue );
#if defined(HAVE_CUBLAS)
// opts.handle also uses opts.queue
cublasCtrsm( opts.handle,
cublas_side_const(opts.side), cublas_uplo_const(opts.uplo),
cublas_trans_const(opts.transA), cublas_diag_const(opts.diag),
M, N,
&alpha, d_A, ldda,
d_B, lddb );
#elif defined(HAVE_clBLAS)
clblasCtrsm( clblasColumnMajor,
clblas_side_const(opts.side), clblas_uplo_const(opts.uplo),
clblas_trans_const(opts.transA), clblas_diag_const(opts.diag),
M, N,
alpha, d_A, 0, ldda,
d_B, 0, lddb,
1, &opts.queue, 0, NULL, NULL );
#endif
cublas_time = magma_sync_wtime( opts.queue ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_cgetmatrix( M, N, d_B, lddb, h_Bcublas, ldb, opts.queue );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_ctrsm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
&M, &N,
&alpha, h_A, &lda,
h_Blapack, &ldb );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
// ||b - 1/alpha*A*x|| / (||A||*||x||)
magmaFloatComplex inv_alpha = MAGMA_C_DIV( c_one, alpha );
float normR, normX, normA;
normA = lapackf77_clange( "M", &Ak, &Ak, h_A, &lda, work );
#if defined(HAVE_CUBLAS)
// check magma
memcpy( h_X, h_Bmagma, sizeB*sizeof(magmaFloatComplex) );
blasf77_ctrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
&M, &N,
&inv_alpha, h_A, &lda,
h_X, &ldb );
blasf77_caxpy( &sizeB, &c_neg_one, h_B, &ione, h_X, &ione );
normR = lapackf77_clange( "M", &M, &N, h_X, &ldb, work );
normX = lapackf77_clange( "M", &M, &N, h_Bmagma, &ldb, work );
magma_error = normR/(normX*normA);
#endif
// check cublas
memcpy( h_X, h_Bcublas, sizeB*sizeof(magmaFloatComplex) );
blasf77_ctrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
&M, &N,
&inv_alpha, h_A, &lda,
h_X, &ldb );
blasf77_caxpy( &sizeB, &c_neg_one, h_B, &ione, h_X, &ione );
normR = lapackf77_clange( "M", &M, &N, h_X, &ldb, work );
normX = lapackf77_clange( "M", &M, &N, h_Bcublas, &ldb, work );
cublas_error = normR/(normX*normA);
if ( opts.lapack ) {
// check lapack
// this verifies that the matrix wasn't so bad that it couldn't be solved accurately.
memcpy( h_X, h_Blapack, sizeB*sizeof(magmaFloatComplex) );
blasf77_ctrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
&M, &N,
&inv_alpha, h_A, &lda,
h_X, &ldb );
blasf77_caxpy( &sizeB, &c_neg_one, h_B, &ione, h_X, &ione );
normR = lapackf77_clange( "M", &M, &N, h_X, &ldb, work );
normX = lapackf77_clange( "M", &M, &N, h_Blapack, &ldb, work );
lapack_error = normR/(normX*normA);
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e %8.2e %s\n",
(int) M, (int) N,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
magma_error, cublas_error, lapack_error,
(magma_error < tol && cublas_error < tol? "ok" : "failed"));
status += ! (magma_error < tol && cublas_error < tol);
}
else {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) --- ( --- ) %8.2e %8.2e --- %s\n",
(int) M, (int) N,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
magma_error, cublas_error,
(magma_error < tol && cublas_error < tol ? "ok" : "failed"));
status += ! (magma_error < tol && cublas_error < tol);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_X );
TESTING_FREE_CPU( h_Blapack );
TESTING_FREE_CPU( h_Bcublas );
TESTING_FREE_CPU( h_Bmagma );
TESTING_FREE_CPU( ipiv );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}