/** 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_16 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_16 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_zblas3
*/
extern "C" void
magma_ztrsm(
magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag,
magma_int_t m, magma_int_t n,
magmaDoubleComplex alpha,
magmaDoubleComplex_const_ptr dA, magma_int_t ldda,
magmaDoubleComplex_ptr dB, magma_int_t lddb )
{
cublasZtrsm(
cublas_side_const( side ),
cublas_uplo_const( uplo ),
cublas_trans_const( trans ),
cublas_diag_const( diag ),
m, n,
alpha, dA, ldda,
dB, lddb );
}
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, t1, t2;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_trans_t trans[] = { MagmaNoTrans, MagmaConjTrans, MagmaTrans };
magma_uplo_t uplo [] = { MagmaLower, MagmaUpper };
magma_diag_t diag [] = { MagmaUnit, MagmaNonUnit };
magma_side_t side [] = { MagmaLeft, MagmaRight };
magmaDoubleComplex *A, *B, *C, *C2, *LU;
magmaDoubleComplex *dA, *dB, *dC1, *dC2;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 0.5, 0.1 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( 0.7, 0.2 );
double dalpha = 0.6;
double dbeta = 0.8;
double work[1], error, total_error;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t m, n, k, size, maxn, ld, info;
magma_int_t *piv;
magma_int_t err;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf( "Compares magma wrapper function to cublas function; all diffs should be exactly 0.\n\n" );
total_error = 0.;
for( int itest = 0; itest < opts.ntest; ++itest ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
printf("=========================================================================\n");
printf( "m=%d, n=%d, k=%d\n", (int) m, (int) n, (int) k );
// allocate matrices
// over-allocate so they can be any combination of {m,n,k} x {m,n,k}.
maxn = max( max( m, n ), k );
ld = max( 1, maxn );
size = ld*maxn;
err = magma_malloc_cpu( (void**) &piv, maxn*sizeof(magma_int_t) ); assert( err == 0 );
err = magma_zmalloc_pinned( &A, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &B, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &C, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &C2, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &LU, size ); assert( err == 0 );
err = magma_zmalloc( &dA, size ); assert( err == 0 );
err = magma_zmalloc( &dB, size ); assert( err == 0 );
err = magma_zmalloc( &dC1, size ); assert( err == 0 );
err = magma_zmalloc( &dC2, size ); assert( err == 0 );
// initialize matrices
size = maxn*maxn;
lapackf77_zlarnv( &ione, ISEED, &size, A );
lapackf77_zlarnv( &ione, ISEED, &size, B );
lapackf77_zlarnv( &ione, ISEED, &size, C );
printf( "========== Level 1 BLAS ==========\n" );
// ----- test ZSWAP
// swap columns 2 and 3 of dA, then copy to C2 and compare with A
if ( n >= 3 ) {
magma_zsetmatrix( m, n, A, ld, dA, ld );
magma_zsetmatrix( m, n, A, ld, dB, ld );
magma_zswap( m, dA(0,1), 1, dA(0,2), 1 );
magma_zswap( m, dB(0,1), 1, dB(0,2), 1 );
// check results, storing diff between magma and cuda calls in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dA, 1, dB, 1 );
magma_zgetmatrix( m, n, dB, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &k, C2, &ld, work );
total_error += error;
printf( "zswap diff %.2g\n", error );
}
else {
printf( "zswap skipped for n < 3\n" );
}
// ----- test IZAMAX
// get argmax of column of A
magma_zsetmatrix( m, k, A, ld, dA, ld );
error = 0;
for( int j = 0; j < k; ++j ) {
magma_int_t i1 = magma_izamax( m, dA(0,j), 1 );
int i2; // NOT magma_int_t, for cublas
cublasIzamax( handle, m, dA(0,j), 1, &i2 );
// todo need sync here?
assert( i1 == i2 );
error += abs( i1 - i2 );
}
total_error += error;
gflops = (double)m * k / 1e9;
printf( "izamax diff %.2g\n", error );
printf( "\n" );
printf( "========== Level 2 BLAS ==========\n" );
// ----- test ZGEMV
// c = alpha*A*b + beta*c, with A m*n; b,c m or n-vectors
// try no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
magma_zsetmatrix( m, n, A, ld, dA, ld );
magma_zsetvector( maxn, B, 1, dB, 1 );
magma_zsetvector( maxn, C, 1, dC1, 1 );
magma_zsetvector( maxn, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_zgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZgemv( handle, cublas_trans_const(trans[ia]),
m, n, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
size = (trans[ia] == MagmaNoTrans ? m : n);
cublasZaxpy( handle, size, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( size, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &size, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZGEMV( m, n ) / 1e9;
printf( "zgemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test ZHEMV
// c = alpha*A*b + beta*c, with A m*m symmetric; b,c m-vectors
// try upper/lower
for( int iu = 0; iu < 2; ++iu ) {
magma_zsetmatrix( m, m, A, ld, dA, ld );
magma_zsetvector( m, B, 1, dB, 1 );
magma_zsetvector( m, C, 1, dC1, 1 );
magma_zsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_zhemv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZhemv( handle, cublas_uplo_const(uplo[iu]),
m, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHEMV( m ) / 1e9;
printf( "zhemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test ZTRSV
// solve A*c = c, with A m*m triangular; c m-vector
// try upper/lower, no-trans/trans, unit/non-unit diag
// Factor A into LU to get well-conditioned triangles, else solve yields garbage.
// Still can give garbage if solves aren't consistent with LU factors,
// e.g., using unit diag for U, so copy lower triangle to upper triangle.
// Also used for trsm later.
lapackf77_zlacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld );
lapackf77_zgetrf( &maxn, &maxn, LU, &ld, piv, &info );
for( int j = 0; j < maxn; ++j ) {
for( int i = 0; i < j; ++i ) {
*LU(i,j) = *LU(j,i);
}
}
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
magma_zsetmatrix( m, m, LU, ld, dA, ld );
magma_zsetvector( m, C, 1, dC1, 1 );
magma_zsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_ztrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZtrsv( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
cublas_diag_const(diag[id]), m, dA, ld, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRSM( MagmaLeft, m, 1 ) / 1e9;
printf( "ztrsv( %c, %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]), lapacke_diag_const(diag[id]),
error, gflops/t1, gflops/t2 );
}}}
printf( "\n" );
printf( "========== Level 3 BLAS ==========\n" );
// ----- test ZGEMM
// C = alpha*A*B + beta*C, with A m*k or k*m; B k*n or n*k; C m*n
// try combinations of no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
for( int ib = 0; ib < 3; ++ib ) {
bool nta = (trans[ia] == MagmaNoTrans);
bool ntb = (trans[ib] == MagmaNoTrans);
magma_zsetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld );
magma_zsetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zgemm( trans[ia], trans[ib], m, n, k, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZgemm( handle, cublas_trans_const(trans[ia]), cublas_trans_const(trans[ib]),
m, n, k, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZGEMM( m, n, k ) / 1e9;
printf( "zgemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), lapacke_trans_const(trans[ib]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHEMM
// C = alpha*A*B + beta*C (left) with A m*m symmetric; B,C m*n; or
// C = alpha*B*A + beta*C (right) with A n*n symmetric; B,C m*n
// try left/right, upper/lower
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
magma_zsetmatrix( m, m, A, ld, dA, ld );
magma_zsetmatrix( m, n, B, ld, dB, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zhemm( side[is], uplo[iu], m, n, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZhemm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
m, n, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHEMM( side[is], m, n ) / 1e9;
printf( "zhemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_side_const(side[is]), lapacke_uplo_const(uplo[iu]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHERK
// C = alpha*A*A^H + beta*C (no-trans) with A m*k and C m*m symmetric; or
// C = alpha*A^H*A + beta*C (trans) with A k*m and C m*m symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
magma_zsetmatrix( n, k, A, ld, dA, ld );
magma_zsetmatrix( n, n, C, ld, dC1, ld );
magma_zsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zherk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZherk( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &dalpha, dA, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHERK( k, n ) / 1e9;
printf( "zherk( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHER2K
// C = alpha*A*B^H + ^alpha*B*A^H + beta*C (no-trans) with A,B n*k; C n*n symmetric; or
// C = alpha*A^H*B + ^alpha*B^H*A + beta*C (trans) with A,B k*n; C n*n symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
bool nt = (trans[it] == MagmaNoTrans);
magma_zsetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld );
magma_zsetmatrix( n, n, C, ld, dC1, ld );
magma_zsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zher2k( uplo[iu], trans[it], n, k, alpha, dA, ld, dB, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZher2k( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &alpha, dA, ld, dB, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHER2K( k, n ) / 1e9;
printf( "zher2k( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZTRMM
// C = alpha*A*C (left) with A m*m triangular; C m*n; or
// C = alpha*C*A (right) with A n*n triangular; C m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_zsetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ztrmm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
// note cublas does trmm out-of-place (i.e., adds output matrix C),
// but allows C=B to do in-place.
t2 = magma_sync_wtime( 0 );
cublasZtrmm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRMM( side[is], m, n ) / 1e9;
printf( "ztrmm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// ----- test ZTRSM
// solve A*X = alpha*B (left) with A m*m triangular; B m*n; or
// solve X*A = alpha*B (right) with A n*n triangular; B m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_zsetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ztrsm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZtrsm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRSM( side[is], m, n ) / 1e9;
printf( "ztrsm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// cleanup
magma_free_cpu( piv );
magma_free_pinned( A );
magma_free_pinned( B );
magma_free_pinned( C );
magma_free_pinned( C2 );
magma_free_pinned( LU );
magma_free( dA );
magma_free( dB );
magma_free( dC1 );
magma_free( dC2 );
fflush( stdout );
}
if ( total_error != 0. ) {
printf( "total error %.2g -- ought to be 0 -- some test failed (see above).\n",
total_error );
}
else {
printf( "all tests passed\n" );
}
TESTING_FINALIZE();
int status = (total_error != 0.);
return status;
}
int TEMPLATE2 (CHOLMOD (gpu_lower_potrf))
(
Int nscol2, /* S is nscol2-by-nscol2 */
Int nsrow, /* leading dimension of S */
Int psx, /* S is located at Lx + L_ENTRY*psx */
double *Lx, /* contains S; overwritten with Cholesky factor */
Int *info, /* BLAS info return value */
cholmod_common *Common,
cholmod_gpu_pointers *gpu_p
)
{
double *devPtrA, *devPtrB, *A ;
double alpha, beta ;
cudaError_t cudaStat ;
cublasStatus_t cublasStatus ;
Int j, nsrow2, nb, n, gpu_lda, lda, gpu_ldb ;
int ilda, ijb, iinfo ;
#ifndef NTIMER
double tstart ;
#endif
if (nscol2 * L_ENTRY < CHOLMOD_POTRF_LIMIT)
{
/* too small for the CUDA BLAS; use the CPU instead */
return (0) ;
}
#ifndef NTIMER
tstart = SuiteSparse_time ( ) ;
Common->CHOLMOD_GPU_POTRF_CALLS++ ;
#endif
nsrow2 = nsrow - nscol2 ;
/* ---------------------------------------------------------------------- */
/* heuristic to get the block size depending of the problem size */
/* ---------------------------------------------------------------------- */
nb = 128 ;
if (nscol2 > 4096) nb = 256 ;
if (nscol2 > 8192) nb = 384 ;
n = nscol2 ;
gpu_lda = ((nscol2+31)/32)*32 ;
lda = nsrow ;
A = gpu_p->h_Lx[(Common->ibuffer+CHOLMOD_HOST_SUPERNODE_BUFFERS-1)%
CHOLMOD_HOST_SUPERNODE_BUFFERS];
/* ---------------------------------------------------------------------- */
/* determine the GPU leading dimension of B */
/* ---------------------------------------------------------------------- */
gpu_ldb = 0 ;
if (nsrow2 > 0)
{
gpu_ldb = ((nsrow2+31)/32)*32 ;
}
/* ---------------------------------------------------------------------- */
/* remember where device memory is, to be used by triangular solve later */
/* ---------------------------------------------------------------------- */
devPtrA = gpu_p->d_Lx[0];
devPtrB = gpu_p->d_Lx[1];
/* ---------------------------------------------------------------------- */
/* copy A from device to device */
/* ---------------------------------------------------------------------- */
cudaStat = cudaMemcpy2DAsync ( devPtrA,
gpu_lda * L_ENTRY * sizeof (devPtrA[0]),
gpu_p->d_A[1],
nsrow * L_ENTRY * sizeof (Lx[0]),
nscol2 * L_ENTRY * sizeof (devPtrA[0]),
nscol2,
cudaMemcpyDeviceToDevice,
Common->gpuStream[0] );
if ( cudaStat ) {
ERROR ( CHOLMOD_GPU_PROBLEM, "GPU memcopy device to device");
}
/* ---------------------------------------------------------------------- */
/* copy B in advance, for gpu_triangular_solve */
/* ---------------------------------------------------------------------- */
if (nsrow2 > 0)
{
cudaStat = cudaMemcpy2DAsync (devPtrB,
gpu_ldb * L_ENTRY * sizeof (devPtrB [0]),
gpu_p->d_A[1] + L_ENTRY*nscol2,
nsrow * L_ENTRY * sizeof (Lx [0]),
nsrow2 * L_ENTRY * sizeof (devPtrB [0]),
nscol2,
cudaMemcpyDeviceToDevice,
Common->gpuStream[0]) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ;
}
}
/* ------------------------------------------------------------------ */
/* define the dpotrf stream */
/* ------------------------------------------------------------------ */
cublasStatus = cublasSetStream (Common->cublasHandle,
Common->gpuStream [0]) ;
if (cublasStatus != CUBLAS_STATUS_SUCCESS) {
ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS stream") ;
}
/* ---------------------------------------------------------------------- */
/* block Cholesky factorization of S */
/* ---------------------------------------------------------------------- */
for (j = 0 ; j < n ; j += nb)
{
Int jb = nb < (n-j) ? nb : (n-j) ;
/* ------------------------------------------------------------------ */
/* do the CUDA BLAS dsyrk */
/* ------------------------------------------------------------------ */
alpha = -1.0 ;
beta = 1.0 ;
#ifdef REAL
cublasStatus = cublasDsyrk (Common->cublasHandle,
CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_N, jb, j,
&alpha, devPtrA + j, gpu_lda,
&beta, devPtrA + j + j*gpu_lda, gpu_lda) ;
#else
cublasStatus = cublasZherk (Common->cublasHandle,
CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_N, jb, j,
&alpha, (cuDoubleComplex*)devPtrA + j,
gpu_lda,
&beta,
(cuDoubleComplex*)devPtrA + j + j*gpu_lda,
gpu_lda) ;
#endif
if (cublasStatus != CUBLAS_STATUS_SUCCESS)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ;
}
/* ------------------------------------------------------------------ */
cudaStat = cudaEventRecord (Common->cublasEventPotrf [0],
Common->gpuStream [0]) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event failure") ;
}
cudaStat = cudaStreamWaitEvent (Common->gpuStream [1],
Common->cublasEventPotrf [0], 0) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event failure") ;
}
/* ------------------------------------------------------------------ */
/* copy back the jb columns on two different streams */
/* ------------------------------------------------------------------ */
cudaStat = cudaMemcpy2DAsync (A + L_ENTRY*(j + j*lda),
lda * L_ENTRY * sizeof (double),
devPtrA + L_ENTRY*(j + j*gpu_lda),
gpu_lda * L_ENTRY * sizeof (double),
L_ENTRY * sizeof (double)*jb,
jb,
cudaMemcpyDeviceToHost,
Common->gpuStream [1]) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy from device") ;
}
/* ------------------------------------------------------------------ */
/* do the CUDA BLAS dgemm */
/* ------------------------------------------------------------------ */
if ((j+jb) < n)
{
#ifdef REAL
alpha = -1.0 ;
beta = 1.0 ;
cublasStatus = cublasDgemm (Common->cublasHandle,
CUBLAS_OP_N, CUBLAS_OP_T,
(n-j-jb), jb, j,
&alpha,
devPtrA + (j+jb), gpu_lda,
devPtrA + (j) , gpu_lda,
&beta,
devPtrA + (j+jb + j*gpu_lda), gpu_lda) ;
#else
cuDoubleComplex calpha = {-1.0,0.0} ;
cuDoubleComplex cbeta = { 1.0,0.0} ;
cublasStatus = cublasZgemm (Common->cublasHandle,
CUBLAS_OP_N, CUBLAS_OP_C,
(n-j-jb), jb, j,
&calpha,
(cuDoubleComplex*)devPtrA + (j+jb),
gpu_lda,
(cuDoubleComplex*)devPtrA + (j),
gpu_lda,
&cbeta,
(cuDoubleComplex*)devPtrA +
(j+jb + j*gpu_lda),
gpu_lda ) ;
#endif
if (cublasStatus != CUBLAS_STATUS_SUCCESS)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ;
}
}
cudaStat = cudaStreamSynchronize (Common->gpuStream [1]) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ;
}
/* ------------------------------------------------------------------ */
/* compute the Cholesky factorization of the jbxjb block on the CPU */
/* ------------------------------------------------------------------ */
ilda = (int) lda ;
ijb = jb ;
#ifdef REAL
LAPACK_DPOTRF ("L", &ijb, A + L_ENTRY * (j + j*lda), &ilda, &iinfo) ;
#else
LAPACK_ZPOTRF ("L", &ijb, A + L_ENTRY * (j + j*lda), &ilda, &iinfo) ;
#endif
*info = iinfo ;
if (*info != 0)
{
*info = *info + j ;
break ;
}
/* ------------------------------------------------------------------ */
/* copy the result back to the GPU */
/* ------------------------------------------------------------------ */
cudaStat = cudaMemcpy2DAsync (devPtrA + L_ENTRY*(j + j*gpu_lda),
gpu_lda * L_ENTRY * sizeof (double),
A + L_ENTRY * (j + j*lda),
lda * L_ENTRY * sizeof (double),
L_ENTRY * sizeof (double) * jb,
jb,
cudaMemcpyHostToDevice,
Common->gpuStream [0]) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ;
}
/* ------------------------------------------------------------------ */
/* do the CUDA BLAS dtrsm */
/* ------------------------------------------------------------------ */
if ((j+jb) < n)
{
#ifdef REAL
alpha = 1.0 ;
cublasStatus = cublasDtrsm (Common->cublasHandle,
CUBLAS_SIDE_RIGHT,
CUBLAS_FILL_MODE_LOWER,
CUBLAS_OP_T, CUBLAS_DIAG_NON_UNIT,
(n-j-jb), jb,
&alpha,
devPtrA + (j + j*gpu_lda), gpu_lda,
devPtrA + (j+jb + j*gpu_lda), gpu_lda) ;
#else
cuDoubleComplex calpha = {1.0,0.0};
cublasStatus = cublasZtrsm (Common->cublasHandle,
CUBLAS_SIDE_RIGHT,
CUBLAS_FILL_MODE_LOWER,
CUBLAS_OP_C, CUBLAS_DIAG_NON_UNIT,
(n-j-jb), jb,
&calpha,
(cuDoubleComplex *)devPtrA +
(j + j*gpu_lda),
gpu_lda,
(cuDoubleComplex *)devPtrA +
(j+jb + j*gpu_lda),
gpu_lda) ;
#endif
if (cublasStatus != CUBLAS_STATUS_SUCCESS)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ;
}
/* -------------------------------------------------------------- */
/* Copy factored column back to host. */
/* -------------------------------------------------------------- */
cudaStat = cudaEventRecord (Common->cublasEventPotrf[2],
Common->gpuStream[0]) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event failure") ;
}
cudaStat = cudaStreamWaitEvent (Common->gpuStream[1],
Common->cublasEventPotrf[2], 0) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "CUDA event failure") ;
}
cudaStat = cudaMemcpy2DAsync (A + L_ENTRY*(j + jb + j * lda),
lda * L_ENTRY * sizeof (double),
devPtrA + L_ENTRY*
(j + jb + j * gpu_lda),
gpu_lda * L_ENTRY * sizeof (double),
L_ENTRY * sizeof (double)*
(n - j - jb), jb,
cudaMemcpyDeviceToHost,
Common->gpuStream[1]) ;
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy to device") ;
}
}
}
#ifndef NTIMER
Common->CHOLMOD_GPU_POTRF_TIME += SuiteSparse_time ( ) - tstart ;
#endif
return (1) ;
}
int TEMPLATE2 (CHOLMOD (gpu_triangular_solve))
(
Int nsrow2, /* L1 and S2 are nsrow2-by-nscol2 */
Int nscol2, /* L1 is nscol2-by-nscol2 */
Int nsrow, /* leading dimension of L1, L2, and S2 */
Int psx, /* L1 is at Lx+L_ENTRY*psx;
* L2 at Lx+L_ENTRY*(psx+nscol2)*/
double *Lx, /* holds L1, L2, and S2 */
cholmod_common *Common,
cholmod_gpu_pointers *gpu_p
)
{
double *devPtrA, *devPtrB ;
cudaError_t cudaStat ;
cublasStatus_t cublasStatus ;
Int gpu_lda, gpu_ldb, gpu_rowstep ;
Int gpu_row_start = 0 ;
Int gpu_row_max_chunk, gpu_row_chunk;
int ibuf = 0;
int iblock = 0;
int iHostBuff = (Common->ibuffer+CHOLMOD_HOST_SUPERNODE_BUFFERS-1) %
CHOLMOD_HOST_SUPERNODE_BUFFERS;
int i, j;
Int iidx;
int iwrap;
#ifndef NTIMER
double tstart ;
#endif
#ifdef REAL
double alpha = 1.0 ;
gpu_row_max_chunk = 768;
#else
cuDoubleComplex calpha = {1.0,0.0} ;
gpu_row_max_chunk = 256;
#endif
if ( nsrow2 <= 0 )
{
return (0) ;
}
#ifndef NTIMER
tstart = SuiteSparse_time ( ) ;
Common->CHOLMOD_GPU_TRSM_CALLS++ ;
#endif
gpu_lda = ((nscol2+31)/32)*32 ;
gpu_ldb = ((nsrow2+31)/32)*32 ;
devPtrA = gpu_p->d_Lx[0];
devPtrB = gpu_p->d_Lx[1];
/* make sure the copy of B has completed */
cudaStreamSynchronize( Common->gpuStream[0] );
/* ---------------------------------------------------------------------- */
/* do the CUDA BLAS dtrsm */
/* ---------------------------------------------------------------------- */
while ( gpu_row_start < nsrow2 )
{
gpu_row_chunk = nsrow2 - gpu_row_start;
if ( gpu_row_chunk > gpu_row_max_chunk ) {
gpu_row_chunk = gpu_row_max_chunk;
}
cublasStatus = cublasSetStream ( Common->cublasHandle,
Common->gpuStream[ibuf] );
if ( cublasStatus != CUBLAS_STATUS_SUCCESS )
{
ERROR ( CHOLMOD_GPU_PROBLEM, "GPU CUBLAS stream");
}
#ifdef REAL
cublasStatus = cublasDtrsm (Common->cublasHandle,
CUBLAS_SIDE_RIGHT,
CUBLAS_FILL_MODE_LOWER,
CUBLAS_OP_T,
CUBLAS_DIAG_NON_UNIT,
gpu_row_chunk,
nscol2,
&alpha,
devPtrA,
gpu_lda,
devPtrB + gpu_row_start,
gpu_ldb) ;
#else
cublasStatus = cublasZtrsm (Common->cublasHandle,
CUBLAS_SIDE_RIGHT,
CUBLAS_FILL_MODE_LOWER,
CUBLAS_OP_C,
CUBLAS_DIAG_NON_UNIT,
gpu_row_chunk,
nscol2,
&calpha,
(const cuDoubleComplex *) devPtrA,
gpu_lda,
(cuDoubleComplex *)devPtrB + gpu_row_start ,
gpu_ldb) ;
#endif
if (cublasStatus != CUBLAS_STATUS_SUCCESS)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU CUBLAS routine failure") ;
}
/* ------------------------------------------------------------------ */
/* copy result back to the CPU */
/* ------------------------------------------------------------------ */
cudaStat = cudaMemcpy2DAsync (
gpu_p->h_Lx[iHostBuff] +
L_ENTRY*(nscol2+gpu_row_start),
nsrow * L_ENTRY * sizeof (Lx [0]),
devPtrB + L_ENTRY*gpu_row_start,
gpu_ldb * L_ENTRY * sizeof (devPtrB [0]),
gpu_row_chunk * L_ENTRY *
sizeof (devPtrB [0]),
nscol2,
cudaMemcpyDeviceToHost,
Common->gpuStream[ibuf]);
if (cudaStat)
{
ERROR (CHOLMOD_GPU_PROBLEM, "GPU memcopy from device") ;
}
cudaEventRecord ( Common->updateCBuffersFree[ibuf],
Common->gpuStream[ibuf] );
gpu_row_start += gpu_row_chunk;
ibuf++;
ibuf = ibuf % CHOLMOD_HOST_SUPERNODE_BUFFERS;
iblock ++;
if ( iblock >= CHOLMOD_HOST_SUPERNODE_BUFFERS )
{
Int gpu_row_start2 ;
Int gpu_row_end ;
/* then CHOLMOD_HOST_SUPERNODE_BUFFERS worth of work has been
* scheduled, so check for completed events and copy result into
* Lx before continuing. */
cudaEventSynchronize ( Common->updateCBuffersFree
[iblock%CHOLMOD_HOST_SUPERNODE_BUFFERS] );
/* copy into Lx */
gpu_row_start2 = nscol2 +
(iblock-CHOLMOD_HOST_SUPERNODE_BUFFERS)
*gpu_row_max_chunk;
gpu_row_end = gpu_row_start2+gpu_row_max_chunk;
if ( gpu_row_end > nsrow ) gpu_row_end = nsrow;
#pragma omp parallel for num_threads(CHOLMOD_OMP_NUM_THREADS) \
private(iidx) if ( nscol2 > 32 )
for ( j=0; j<nscol2; j++ ) {
for ( i=gpu_row_start2*L_ENTRY; i<gpu_row_end*L_ENTRY; i++ ) {
iidx = j*nsrow*L_ENTRY+i;
Lx[psx*L_ENTRY+iidx] = gpu_p->h_Lx[iHostBuff][iidx];
}
}
}
}
/* Convenient to copy the L1 block here */
#pragma omp parallel for num_threads(CHOLMOD_OMP_NUM_THREADS) \
private ( iidx ) if ( nscol2 > 32 )
for ( j=0; j<nscol2; j++ ) {
for ( i=j*L_ENTRY; i<nscol2*L_ENTRY; i++ ) {
iidx = j*nsrow*L_ENTRY + i;
Lx[psx*L_ENTRY+iidx] = gpu_p->h_Lx[iHostBuff][iidx];
}
}
/* now account for the last HSTREAMS buffers */
for ( iwrap=0; iwrap<CHOLMOD_HOST_SUPERNODE_BUFFERS; iwrap++ )
{
int i, j;
Int gpu_row_start2 = nscol2 + (iblock-CHOLMOD_HOST_SUPERNODE_BUFFERS)
*gpu_row_max_chunk;
if (iblock-CHOLMOD_HOST_SUPERNODE_BUFFERS >= 0 &&
gpu_row_start2 < nsrow )
{
Int iidx;
Int gpu_row_end = gpu_row_start2+gpu_row_max_chunk;
if ( gpu_row_end > nsrow ) gpu_row_end = nsrow;
cudaEventSynchronize ( Common->updateCBuffersFree
[iblock%CHOLMOD_HOST_SUPERNODE_BUFFERS] );
/* copy into Lx */
#pragma omp parallel for num_threads(CHOLMOD_OMP_NUM_THREADS) \
private(iidx) if ( nscol2 > 32 )
for ( j=0; j<nscol2; j++ ) {
for ( i=gpu_row_start2*L_ENTRY; i<gpu_row_end*L_ENTRY; i++ ) {
iidx = j*nsrow*L_ENTRY+i;
Lx[psx*L_ENTRY+iidx] = gpu_p->h_Lx[iHostBuff][iidx];
}
}
}
iblock++;
}
/* ---------------------------------------------------------------------- */
/* return */
/* ---------------------------------------------------------------------- */
#ifndef NTIMER
Common->CHOLMOD_GPU_TRSM_TIME += SuiteSparse_time ( ) - tstart ;
#endif
return (1) ;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ztrsm
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time, cublas_perf, cublas_time, cpu_perf=0, cpu_time=0;
double magma_error, cublas_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 *piv;
magma_err_t err;
magmaDoubleComplex *h_A, *h_B, *h_Bcublas, *h_Bmagma, *h_B1, *h_X1, *h_X2, *LU, *LUT;
magmaDoubleComplex *d_A, *d_B;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 0.29, -0.86 );
magma_opts opts;
parse_opts( argc, argv, &opts );
printf("If running lapack (option --lapack), MAGMA and CUBLAS error are both computed\n"
"relative to CPU BLAS result. Else, MAGMA error is computed relative to CUBLAS result.\n\n"
"side = %c, uplo = %c, transA = %c, diag = %c \n", opts.side, opts.uplo, opts.transA, opts.diag );
printf(" M N MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) CPU Gflop/s (ms) MAGMA error CUBLAS error\n");
printf("==================================================================================================\n");
for( int i = 0; i < opts.ntest; ++i ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[i];
N = opts.nsize[i];
gflops = FLOPS_ZTRSM(opts.side, M, N) / 1e9;
if ( opts.side == MagmaLeft ) {
lda = M;
Ak = M;
} else {
lda = N;
Ak = N;
}
ldb = M;
ldda = ((lda+31)/32)*32;
lddb = ((ldb+31)/32)*32;
sizeA = lda*Ak;
sizeB = ldb*N;
TESTING_MALLOC( h_A, magmaDoubleComplex, lda*Ak );
TESTING_MALLOC( LU, magmaDoubleComplex, lda*Ak );
TESTING_MALLOC( LUT, magmaDoubleComplex, lda*Ak );
TESTING_MALLOC( h_B, magmaDoubleComplex, ldb*N );
TESTING_MALLOC( h_B1, magmaDoubleComplex, ldb*N );
TESTING_MALLOC( h_X1, magmaDoubleComplex, ldb*N );
TESTING_MALLOC( h_X2, magmaDoubleComplex, ldb*N );
TESTING_MALLOC( h_Bcublas, magmaDoubleComplex, ldb*N );
TESTING_MALLOC( h_Bmagma, magmaDoubleComplex, ldb*N );
TESTING_DEVALLOC( d_A, magmaDoubleComplex, ldda*Ak );
TESTING_DEVALLOC( d_B, magmaDoubleComplex, lddb*N );
/* Initialize the matrices */
lapackf77_zlarnv( &ione, ISEED, &sizeA, LU );
err = magma_malloc_cpu( (void**) &piv, Ak*sizeof(magma_int_t) ); assert( err == 0 );
lapackf77_zgetrf( &Ak, &Ak, LU, &lda, piv, &info );
int i, j;
for(i=0;i<Ak;i++){
for(j=0;j<Ak;j++){
LUT[j+i*lda] = LU[i+j*lda];
}
}
lapackf77_zlacpy(MagmaUpperStr, &Ak, &Ak, LUT, &lda, LU, &lda);
if(opts.uplo == MagmaLower){
lapackf77_zlacpy(MagmaLowerStr, &Ak, &Ak, LU, &lda, h_A, &lda);
}else{
lapackf77_zlacpy(MagmaUpperStr, &Ak, &Ak, LU, &lda, h_A, &lda);
}
lapackf77_zlarnv( &ione, ISEED, &sizeB, h_B );
memcpy(h_B1, h_B, sizeB*sizeof(magmaDoubleComplex));
/* =====================================================================
Performs operation using MAGMA-BLAS
=================================================================== */
magma_zsetmatrix( Ak, Ak, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, N, h_B, ldb, d_B, lddb );
magma_time = magma_sync_wtime( NULL );
magmablas_ztrsm( opts.side, opts.uplo, opts.transA, opts.diag,
M, N,
alpha, d_A, ldda,
d_B, lddb );
magma_time = magma_sync_wtime( NULL ) - magma_time;
magma_perf = gflops / magma_time;
magma_zgetmatrix( M, N, d_B, lddb, h_Bmagma, ldb );
/* =====================================================================
Performs operation using CUDA-BLAS
=================================================================== */
magma_zsetmatrix( M, N, h_B, ldb, d_B, lddb );
cublas_time = magma_sync_wtime( NULL );
cublasZtrsm( opts.side, opts.uplo, opts.transA, opts.diag,
M, N,
alpha, d_A, ldda,
d_B, lddb );
cublas_time = magma_sync_wtime( NULL ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_zgetmatrix( M, N, d_B, lddb, h_Bcublas, ldb );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_ztrsm( &opts.side, &opts.uplo, &opts.transA, &opts.diag,
&M, &N,
&alpha, h_A, &lda,
h_B, &ldb );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
// ||b - Ax|| / (||A||*||x||)
memcpy(h_X1, h_Bmagma, sizeB*sizeof(magmaDoubleComplex));
magmaDoubleComplex alpha2 = MAGMA_Z_DIV( c_one, alpha );
blasf77_ztrmm( &opts.side, &opts.uplo, &opts.transA, &opts.diag,
&M, &N,
&alpha2, h_A, &lda,
h_X1, &ldb );
blasf77_zaxpy( &sizeB, &c_neg_one, h_B1, &ione, h_X1, &ione );
double norm1 = lapackf77_zlange( "M", &M, &N, h_X1, &ldb, work );
double normx = lapackf77_zlange( "M", &M, &N, h_Bmagma, &ldb, work );
double normA = lapackf77_zlange( "M", &Ak, &Ak, h_A, &lda, work );
magma_error = norm1/(normx*normA);
memcpy(h_X2, h_Bcublas, sizeB*sizeof(magmaDoubleComplex));
blasf77_ztrmm( &opts.side, &opts.uplo, &opts.transA, &opts.diag,
&M, &N,
&alpha2, h_A, &lda,
h_X2, &ldb );
blasf77_zaxpy( &sizeB, &c_neg_one, h_B1, &ione, h_X2, &ione );
norm1 = lapackf77_zlange( "M", &M, &N, h_X2, &ldb, work );
normx = lapackf77_zlange( "M", &M, &N, h_Bcublas, &ldb, work );
normA = lapackf77_zlange( "M", &Ak, &Ak, h_A, &lda, work );
cublas_error = norm1/(normx*normA);
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %8.2e\n",
(int) M, (int) N,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
cpu_perf, 1000.*cpu_time,
magma_error, cublas_error );
}
else {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) --- ( --- ) %8.2e %8.2e\n",
(int) M, (int) N,
magma_perf, 1000.*magma_time,
cublas_perf, 1000.*cublas_time,
magma_error, cublas_error );
}
TESTING_FREE( h_A );
TESTING_FREE( LU );
TESTING_FREE( LUT );
TESTING_FREE( h_B );
TESTING_FREE( h_Bcublas );
TESTING_FREE( h_Bmagma );
TESTING_FREE( h_B1 );
TESTING_FREE( h_X1 );
TESTING_FREE( h_X2 );
TESTING_DEVFREE( d_A );
TESTING_DEVFREE( d_B );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return 0;
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ztrsm
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gflops, magma_perf, magma_time=0, cublas_perf, cublas_time, cpu_perf=0, cpu_time=0;
double magma_error, cublas_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;
magmaDoubleComplex *h_A, *h_B, *h_Bcublas, *h_Bmagma, *h_B1, *h_X1, *h_X2;
magmaDoubleComplex *d_A, *d_B;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 0.29, -0.86 );
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("side = %s, uplo = %s, transA = %s, diag = %s \n",
lapack_side_const(opts.side), lapack_uplo_const(opts.uplo),
lapack_trans_const(opts.transA), lapack_diag_const(opts.diag) );
printf(" M N MAGMA Gflop/s (ms) CUBLAS Gflop/s (ms) CPU Gflop/s (ms) MAGMA error CUBLAS 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_ZTRSM(opts.side, M, N) / 1e9;
if ( opts.side == MagmaLeft ) {
lda = M;
Ak = M;
} else {
lda = N;
Ak = N;
}
ldb = M;
ldda = ((lda+31)/32)*32;
lddb = ((ldb+31)/32)*32;
sizeA = lda*Ak;
sizeB = ldb*N;
TESTING_MALLOC_CPU( h_A, magmaDoubleComplex, lda*Ak );
TESTING_MALLOC_CPU( h_B, magmaDoubleComplex, ldb*N );
TESTING_MALLOC_CPU( h_B1, magmaDoubleComplex, ldb*N );
TESTING_MALLOC_CPU( h_X1, magmaDoubleComplex, ldb*N );
TESTING_MALLOC_CPU( h_X2, magmaDoubleComplex, ldb*N );
TESTING_MALLOC_CPU( h_Bcublas, magmaDoubleComplex, ldb*N );
TESTING_MALLOC_CPU( h_Bmagma, magmaDoubleComplex, ldb*N );
TESTING_MALLOC_CPU( ipiv, magma_int_t, Ak );
TESTING_MALLOC_DEV( d_A, magmaDoubleComplex, ldda*Ak );
TESTING_MALLOC_DEV( d_B, magmaDoubleComplex, 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_zlarnv( &ione, ISEED, &sizeA, h_A );
lapackf77_zgetrf( &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_zlarnv( &ione, ISEED, &sizeB, h_B );
memcpy(h_B1, h_B, sizeB*sizeof(magmaDoubleComplex));
/* =====================================================================
Performs operation using MAGMABLAS
=================================================================== */
magma_zsetmatrix( Ak, Ak, h_A, lda, d_A, ldda );
magma_zsetmatrix( M, N, h_B, ldb, d_B, lddb );
magma_time = magma_sync_wtime( NULL );
magmablas_ztrsm( opts.side, opts.uplo, opts.transA, opts.diag,
M, N,
alpha, d_A, ldda,
d_B, lddb );
magma_time = magma_sync_wtime( NULL ) - magma_time;
magma_perf = gflops / magma_time;
magma_zgetmatrix( M, N, d_B, lddb, h_Bmagma, ldb );
/* =====================================================================
Performs operation using CUBLAS
=================================================================== */
magma_zsetmatrix( M, N, h_B, ldb, d_B, lddb );
cublas_time = magma_sync_wtime( NULL );
cublasZtrsm( 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 );
cublas_time = magma_sync_wtime( NULL ) - cublas_time;
cublas_perf = gflops / cublas_time;
magma_zgetmatrix( M, N, d_B, lddb, h_Bcublas, ldb );
/* =====================================================================
Performs operation using CPU BLAS
=================================================================== */
if ( opts.lapack ) {
cpu_time = magma_wtime();
blasf77_ztrsm( 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_B, &ldb );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
}
/* =====================================================================
Check the result
=================================================================== */
// ||b - Ax|| / (||A||*||x||)
memcpy(h_X1, h_Bmagma, sizeB*sizeof(magmaDoubleComplex));
magmaDoubleComplex alpha2 = MAGMA_Z_DIV( c_one, alpha );
blasf77_ztrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
&M, &N,
&alpha2, h_A, &lda,
h_X1, &ldb );
blasf77_zaxpy( &sizeB, &c_neg_one, h_B1, &ione, h_X1, &ione );
double norm1 = lapackf77_zlange( "M", &M, &N, h_X1, &ldb, work );
double normx = lapackf77_zlange( "M", &M, &N, h_Bmagma, &ldb, work );
double normA = lapackf77_zlange( "M", &Ak, &Ak, h_A, &lda, work );
magma_error = norm1/(normx*normA);
memcpy(h_X2, h_Bcublas, sizeB*sizeof(magmaDoubleComplex));
blasf77_ztrmm( lapack_side_const(opts.side), lapack_uplo_const(opts.uplo), lapack_trans_const(opts.transA), lapack_diag_const(opts.diag),
&M, &N,
&alpha2, h_A, &lda,
h_X2, &ldb );
blasf77_zaxpy( &sizeB, &c_neg_one, h_B1, &ione, h_X2, &ione );
norm1 = lapackf77_zlange( "M", &M, &N, h_X2, &ldb, work );
normx = lapackf77_zlange( "M", &M, &N, h_Bcublas, &ldb, work );
normA = lapackf77_zlange( "M", &Ak, &Ak, h_A, &lda, work );
cublas_error = norm1/(normx*normA);
if ( opts.lapack ) {
printf("%5d %5d %7.2f (%7.2f) %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,
cpu_perf, 1000.*cpu_time,
magma_error, cublas_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_B1 );
TESTING_FREE_CPU( h_X1 );
TESTING_FREE_CPU( h_X2 );
TESTING_FREE_CPU( h_Bcublas );
TESTING_FREE_CPU( h_Bmagma );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}