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|
/*
-- MAGMA (version 2.9.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2025
@generated from magmablas/ztrsm_batched.cpp, normal z -> s, Wed Jan 22 14:42:05 2025
@author Peng Du
@author Tingxing Dong
@author Mark Gates
@author Azzam Haidar
*/
#include "magma_internal.h"
#include "batched_kernel_param.h"
/***************************************************************************//**
Purpose
-------
strsm_outofplace solves one of the matrix equations on gpu
op(A)*X = alpha*B, or
X*op(A) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op(A) is one of
op(A) = A, or
op(A) = A^T, or
op(A) = A^H.
The matrix X is overwritten on B.
This is an asynchronous version of magmablas_strsm with flag,
d_dinvA and dX workspaces as arguments.
Arguments
----------
@param[in]
side magma_side_t.
On entry, side specifies whether op(A) appears on the left
or right of X as follows:
- = MagmaLeft: op(A)*X = alpha*B.
- = MagmaRight: X*op(A) = alpha*B.
@param[in]
uplo magma_uplo_t.
On entry, uplo specifies whether the matrix A is an upper or
lower triangular matrix as follows:
- = MagmaUpper: A is an upper triangular matrix.
- = MagmaLower: A is a lower triangular matrix.
@param[in]
transA magma_trans_t.
On entry, transA specifies the form of op(A) to be used in
the matrix multiplication as follows:
- = MagmaNoTrans: op(A) = A.
- = MagmaTrans: op(A) = A^T.
- = MagmaConjTrans: op(A) = A^H.
@param[in]
diag magma_diag_t.
On entry, diag specifies whether or not A is unit triangular
as follows:
- = MagmaUnit: A is assumed to be unit triangular.
- = MagmaNonUnit: A is not assumed to be unit triangular.
@param[in]
flag BOOLEAN.
If flag is true, invert diagonal blocks.
If flag is false, assume diagonal blocks (stored in d_dinvA) are already inverted.
@param[in]
m INTEGER.
On entry, m specifies the number of rows of B. m >= 0.
@param[in]
n INTEGER.
On entry, n specifies the number of columns of B. n >= 0.
@param[in]
alpha REAL.
On entry, alpha specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
@param[in]
dA_array Array of pointers, dimension (batchCount).
Each is a REAL array A of dimension ( ldda, k ), where k is m
when side = MagmaLeft and is n when side = MagmaRight.
Before entry with uplo = MagmaUpper, the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with uplo = MagmaLower, the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when diag = MagmaUnit, the diagonal elements of
A are not referenced either, but are assumed to be unity.
@param[in]
ldda INTEGER.
On entry, ldda specifies the first dimension of each array A.
When side = MagmaLeft, ldda >= max( 1, m ),
when side = MagmaRight, ldda >= max( 1, n ).
@param[in]
dB_array Array of pointers, dimension (batchCount).
Each is a REAL array B of dimension ( lddb, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B.
@param[in]
lddb INTEGER.
On entry, lddb specifies the first dimension of each array B.
lddb >= max( 1, m ).
@param[in,out]
dX_array Array of pointers, dimension (batchCount).
Each is a REAL array X of dimension ( lddx, n ).
On entry, should be set to 0
On exit, the solution matrix X
@param[in]
lddx INTEGER.
On entry, lddx specifies the first dimension of each array X.
lddx >= max( 1, m ).
@param
dinvA_array Array of pointers, dimension (batchCount).
Each is a REAL array dinvA, a workspace on device.
If side == MagmaLeft, dinvA must be of size >= ceil(m/STRTRI_BATCHED_NB)*STRTRI_BATCHED_NB*STRTRI_BATCHED_NB
If side == MagmaRight, dinvA must be of size >= ceil(n/STRTRI_BATCHED_NB)*STRTRI_BATCHED_NB*STRTRI_BATCHED_NB
@param[in]
dinvA_length INTEGER
The size of each workspace matrix dinvA
@param
dA_displ (workspace) Array of pointers, dimension (batchCount).
@param
dB_displ (workspace) Array of pointers, dimension (batchCount).
@param
dX_displ (workspace) Array of pointers, dimension (batchCount).
@param
dinvA_displ (workspace) Array of pointers, dimension (batchCount).
@param[in]
resetozero INTEGER
Used internally by STRTRI_DIAG routine
@param[in]
batchCount INTEGER
The number of matrices to operate on.
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magma_trsm_batched
*******************************************************************************/
extern "C"
void magmablas_strsm_inv_outofplace_batched(
magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag,
magma_int_t flag, magma_int_t m, magma_int_t n,
float alpha,
float** dA_array, magma_int_t ldda,
float** dB_array, magma_int_t lddb,
float** dX_array, magma_int_t lddx,
float** dinvA_array, magma_int_t dinvA_length,
float** dA_displ, float** dB_displ,
float** dX_displ, float** dinvA_displ,
magma_int_t resetozero,
magma_int_t batchCount, magma_queue_t queue)
{
/*
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
#define dB(i_, j_) (dB + (i_) + (j_)*lddb)
#define dX(i_, j_) (dX + (i_) + (j_)*m)
#define d_dinvA(i_) (d_dinvA + (i_)*STRTRI_BATCHED_NB)
*/
const float c_neg_one = MAGMA_S_NEG_ONE;
const float c_one = MAGMA_S_ONE;
const float c_zero = MAGMA_S_ZERO;
magma_int_t i, jb;
magma_int_t nrowA = (side == MagmaLeft ? m : n);
magma_int_t info = 0;
if ( side != MagmaLeft && side != MagmaRight ) {
info = -1;
} else if ( uplo != MagmaUpper && uplo != MagmaLower ) {
info = -2;
} else if ( transA != MagmaNoTrans && transA != MagmaTrans && transA != MagmaConjTrans ) {
info = -3;
} else if ( diag != MagmaUnit && diag != MagmaNonUnit ) {
info = -4;
} else if (m < 0) {
info = -5;
} else if (n < 0) {
info = -6;
} else if (ldda < max(1,nrowA)) {
info = -9;
} else if (lddb < max(1,m)) {
info = -11;
}
magma_int_t size_dinvA;
if ( side == MagmaLeft ) {
size_dinvA = magma_roundup( m, STRTRI_BATCHED_NB )*STRTRI_BATCHED_NB;
}
else {
size_dinvA = magma_roundup( n, STRTRI_BATCHED_NB )*STRTRI_BATCHED_NB;
}
if (dinvA_length < size_dinvA) info = -19;
if (info != 0) {
magma_xerbla( __func__, -(info) );
return;
}
// quick return if possible.
if (m == 0 || n == 0)
return;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, 0, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, 0, batchCount, queue);
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, 0, batchCount, queue);
if (side == MagmaLeft) {
// invert diagonal blocks
if (flag)
magmablas_strtri_diag_batched( uplo, diag, m, dA_displ, ldda, dinvA_displ, resetozero, batchCount, queue );
if (transA == MagmaNoTrans) {
if (uplo == MagmaLower) {
// left, lower no-transpose
// handle first block seperately with alpha
jb = min(STRTRI_BATCHED_NB, m);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, jb, n, jb, alpha, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (STRTRI_BATCHED_NB < m) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, STRTRI_BATCHED_NB, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, STRTRI_BATCHED_NB, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m-STRTRI_BATCHED_NB, n, STRTRI_BATCHED_NB, c_neg_one, dA_displ, ldda, dX_displ, lddx, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=STRTRI_BATCHED_NB; i < m; i += STRTRI_BATCHED_NB ) {
jb = min(m-i, STRTRI_BATCHED_NB);
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i, 0, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, i, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, jb, n, jb, c_one, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (i+STRTRI_BATCHED_NB >= m)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, i+STRTRI_BATCHED_NB, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i+STRTRI_BATCHED_NB, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m-i-STRTRI_BATCHED_NB, n, STRTRI_BATCHED_NB, c_neg_one, dA_displ, ldda, dX_displ, lddx, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
else {
// left, upper no-transpose
// handle first block seperately with alpha
jb = (m % STRTRI_BATCHED_NB == 0) ? STRTRI_BATCHED_NB : (m % STRTRI_BATCHED_NB);
i = m-jb;
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i, 0, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, i, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, jb, n, jb, alpha, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB >= 0) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, i, n, jb, c_neg_one, dA_displ, ldda, dX_displ, lddx, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=m-jb-STRTRI_BATCHED_NB; i >= 0; i -= STRTRI_BATCHED_NB ) {
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i, 0, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, i, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, STRTRI_BATCHED_NB, n, STRTRI_BATCHED_NB, c_one, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB < 0)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, i, n, STRTRI_BATCHED_NB, c_neg_one, dA_displ, ldda, dX_displ, lddx, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
}
else { // transA == MagmaTrans || transA == MagmaConjTrans
if (uplo == MagmaLower) {
// left, lower transpose
// handle first block seperately with alpha
jb = (m % STRTRI_BATCHED_NB == 0) ? STRTRI_BATCHED_NB : (m % STRTRI_BATCHED_NB);
i = m-jb;
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i, 0, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, i, 0, batchCount, queue);
magma_sgemm_batched( transA, MagmaNoTrans, jb, n, jb, alpha, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB >= 0) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, i, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( transA, MagmaNoTrans, i, n, jb, c_neg_one, dA_displ, ldda, dX_displ, lddx, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=m-jb-STRTRI_BATCHED_NB; i >= 0; i -= STRTRI_BATCHED_NB ) {
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, i, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i, 0, batchCount, queue);
magma_sgemm_batched( transA, MagmaNoTrans, STRTRI_BATCHED_NB, n, STRTRI_BATCHED_NB, c_one, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB < 0)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, i, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( transA, MagmaNoTrans, i, n, STRTRI_BATCHED_NB, c_neg_one, dA_displ, ldda, dX_displ, lddx, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
else {
// left, upper transpose
// handle first block seperately with alpha
jb = min(STRTRI_BATCHED_NB, m);
magma_sgemm_batched( transA, MagmaNoTrans, jb, n, jb, alpha, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (STRTRI_BATCHED_NB < m) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, 0, STRTRI_BATCHED_NB, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, STRTRI_BATCHED_NB, 0, batchCount, queue);
magma_sgemm_batched( transA, MagmaNoTrans, m-STRTRI_BATCHED_NB, n, STRTRI_BATCHED_NB, c_neg_one, dA_displ, ldda, dX_displ, lddx, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=STRTRI_BATCHED_NB; i < m; i += STRTRI_BATCHED_NB ) {
jb = min(m-i, STRTRI_BATCHED_NB);
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i, 0, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, i, 0, batchCount, queue);
magma_sgemm_batched( transA, MagmaNoTrans, jb, n, jb, c_one, dinvA_displ, STRTRI_BATCHED_NB, dB_displ, lddb, c_zero, dX_displ, lddx, batchCount, queue );
if (i+STRTRI_BATCHED_NB >= m)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, i, i+STRTRI_BATCHED_NB, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, i+STRTRI_BATCHED_NB, 0, batchCount, queue);
magma_sgemm_batched( transA, MagmaNoTrans, m-i-STRTRI_BATCHED_NB, n, STRTRI_BATCHED_NB, c_neg_one, dA_displ, ldda, dX_displ, lddx, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
}
}
else { // side == MagmaRight
// invert diagonal blocks
if (flag)
magmablas_strtri_diag_batched( uplo, diag, n, dA_displ, ldda, dinvA_displ, resetozero, batchCount, queue);
if (transA == MagmaNoTrans) {
if (uplo == MagmaLower) {
// right, lower no-transpose
// handle first block seperately with alpha
jb = (n % STRTRI_BATCHED_NB == 0) ? STRTRI_BATCHED_NB : (n % STRTRI_BATCHED_NB);
i = n-jb;
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, i, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, jb, jb, alpha, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB >= 0) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, i, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, i, jb, c_neg_one, dX_displ, lddx, dA_displ, ldda, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=n-jb-STRTRI_BATCHED_NB; i >= 0; i -= STRTRI_BATCHED_NB ) {
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, i, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, STRTRI_BATCHED_NB, STRTRI_BATCHED_NB, c_one, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB < 0)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, i, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, i, STRTRI_BATCHED_NB, c_neg_one, dX_displ, lddx, dA_displ, ldda, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
else {
// right, upper no-transpose
// handle first block seperately with alpha
jb = min(STRTRI_BATCHED_NB, n);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, jb, jb, alpha, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (STRTRI_BATCHED_NB < n) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, 0, STRTRI_BATCHED_NB, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, STRTRI_BATCHED_NB, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, n-STRTRI_BATCHED_NB, STRTRI_BATCHED_NB, c_neg_one, dX_displ, lddx, dA_displ, ldda, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=STRTRI_BATCHED_NB; i < n; i += STRTRI_BATCHED_NB ) {
jb = min(STRTRI_BATCHED_NB, n-i);
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, i, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, jb, jb, c_one, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (i+STRTRI_BATCHED_NB >= n)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, i, i+STRTRI_BATCHED_NB, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i+STRTRI_BATCHED_NB, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, MagmaNoTrans, m, n-i-STRTRI_BATCHED_NB, STRTRI_BATCHED_NB, c_neg_one, dX_displ, lddx, dA_displ, ldda, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
}
else { // transA == MagmaTrans || transA == MagmaConjTrans
if (uplo == MagmaLower) {
// right, lower transpose
// handle first block seperately with alpha
jb = min(STRTRI_BATCHED_NB, n);
magma_sgemm_batched( MagmaNoTrans, transA, m, jb, jb, alpha, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (STRTRI_BATCHED_NB < n) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, STRTRI_BATCHED_NB, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, STRTRI_BATCHED_NB, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, transA, m, n-STRTRI_BATCHED_NB, STRTRI_BATCHED_NB, c_neg_one, dX_displ, lddx, dA_displ, ldda, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=STRTRI_BATCHED_NB; i < n; i += STRTRI_BATCHED_NB ) {
jb = min(STRTRI_BATCHED_NB, n-i);
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, i, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, transA, m, jb, jb, c_one, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (i+STRTRI_BATCHED_NB >= n)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, STRTRI_BATCHED_NB+i, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i+STRTRI_BATCHED_NB, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, transA, m, n-i-STRTRI_BATCHED_NB, STRTRI_BATCHED_NB, c_neg_one, dX_displ, lddx, dA_displ, ldda, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
else {
// right, upper transpose
// handle first block seperately with alpha
jb = (n % STRTRI_BATCHED_NB == 0) ? STRTRI_BATCHED_NB : (n % STRTRI_BATCHED_NB);
i = n-jb;
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, i, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, transA, m, jb, jb, alpha, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB >= 0) {
magma_sdisplace_pointers(dA_displ, dA_array, ldda, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, transA, m, i, jb, c_neg_one, dX_displ, lddx, dA_displ, ldda, alpha, dB_displ, lddb, batchCount, queue );
// remaining blocks
for( i=n-jb-STRTRI_BATCHED_NB; i >= 0; i -= STRTRI_BATCHED_NB ) {
magma_sdisplace_pointers(dinvA_displ, dinvA_array, STRTRI_BATCHED_NB, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, i, batchCount, queue);
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, i, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, transA, m, STRTRI_BATCHED_NB, STRTRI_BATCHED_NB, c_one, dB_displ, lddb, dinvA_displ, STRTRI_BATCHED_NB, c_zero, dX_displ, lddx, batchCount, queue );
if (i-STRTRI_BATCHED_NB < 0)
break;
magma_sdisplace_pointers(dA_displ, dA_array, ldda, 0, i, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magma_sgemm_batched( MagmaNoTrans, transA, m, i, STRTRI_BATCHED_NB, c_neg_one, dX_displ, lddx, dA_displ, ldda, c_one, dB_displ, lddb, batchCount, queue );
}
}
}
}
}
}
/***************************************************************************//**
Purpose
-------
strsm_work solves one of the matrix equations on gpu
op(A)*X = alpha*B, or
X*op(A) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op(A) is one of
op(A) = A, or
op(A) = A^T, or
op(A) = A^H.
The matrix X is overwritten on B.
This is an asynchronous version of magmablas_strsm with flag,
d_dinvA and dX workspaces as arguments.
Arguments
----------
@param[in]
side magma_side_t.
On entry, side specifies whether op(A) appears on the left
or right of X as follows:
- = MagmaLeft: op(A)*X = alpha*B.
- = MagmaRight: X*op(A) = alpha*B.
@param[in]
uplo magma_uplo_t.
On entry, uplo specifies whether the matrix A is an upper or
lower triangular matrix as follows:
- = MagmaUpper: A is an upper triangular matrix.
- = MagmaLower: A is a lower triangular matrix.
@param[in]
transA magma_trans_t.
On entry, transA specifies the form of op(A) to be used in
the matrix multiplication as follows:
- = MagmaNoTrans: op(A) = A.
- = MagmaTrans: op(A) = A^T.
- = MagmaConjTrans: op(A) = A^H.
@param[in]
diag magma_diag_t.
On entry, diag specifies whether or not A is unit triangular
as follows:
- = MagmaUnit: A is assumed to be unit triangular.
- = MagmaNonUnit: A is not assumed to be unit triangular.
@param[in]
flag BOOLEAN.
If flag is true, invert diagonal blocks.
If flag is false, assume diagonal blocks (stored in d_dinvA) are already inverted.
@param[in]
m INTEGER.
On entry, m specifies the number of rows of B. m >= 0.
@param[in]
n INTEGER.
On entry, n specifies the number of columns of B. n >= 0.
@param[in]
alpha REAL.
On entry, alpha specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
@param[in]
dA_array Array of pointers, dimension (batchCount).
Each is a REAL array A of dimension ( ldda, k ), where k is m
when side = MagmaLeft and is n when side = MagmaRight.
Before entry with uplo = MagmaUpper, the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with uplo = MagmaLower, the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when diag = MagmaUnit, the diagonal elements of
A are not referenced either, but are assumed to be unity.
@param[in]
ldda INTEGER.
On entry, ldda specifies the first dimension of each array A.
When side = MagmaLeft, ldda >= max( 1, m ),
when side = MagmaRight, ldda >= max( 1, n ).
@param[in,out]
dB_array Array of pointers, dimension (batchCount).
Each is a REAL array B of dimension ( lddb, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B.
\n
On exit, the solution matrix X
@param[in]
lddb INTEGER.
On entry, lddb specifies the first dimension of each array B.
lddb >= max( 1, m ).
@param[in,out]
dX_array Array of pointers, dimension (batchCount).
Each is a REAL array X of dimension ( lddx, n ).
On entry, should be set to 0
On exit, the solution matrix X
@param[in]
lddx INTEGER.
On entry, lddx specifies the first dimension of each array X.
lddx >= max( 1, m ).
@param
dinvA_array Array of pointers, dimension (batchCount).
Each is a REAL array dinvA, a workspace on device.
If side == MagmaLeft, dinvA must be of size >= ceil(m/STRTRI_BATCHED_NB)*STRTRI_BATCHED_NB*STRTRI_BATCHED_NB,
If side == MagmaRight, dinvA must be of size >= ceil(n/STRTRI_BATCHED_NB)*STRTRI_BATCHED_NB*STRTRI_BATCHED_NB,
where STRTRI_BATCHED_NB = 128.
@param[in]
dinvA_length INTEGER
The size of each workspace matrix dinvA
@param
dA_displ (workspace) Array of pointers, dimension (batchCount).
@param
dB_displ (workspace) Array of pointers, dimension (batchCount).
@param
dX_displ (workspace) Array of pointers, dimension (batchCount).
@param
dinvA_displ (workspace) Array of pointers, dimension (batchCount).
@param[in]
resetozero INTEGER
Used internally by STRTRI_DIAG routine
@param[in]
batchCount INTEGER
The number of matrices to operate on.
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magma_trsm_batched
*******************************************************************************/
extern "C"
void magmablas_strsm_inv_work_batched(
magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag,
magma_int_t flag, magma_int_t m, magma_int_t n,
float alpha,
float** dA_array, magma_int_t ldda,
float** dB_array, magma_int_t lddb,
float** dX_array, magma_int_t lddx,
float** dinvA_array, magma_int_t dinvA_length,
float** dA_displ, float** dB_displ,
float** dX_displ, float** dinvA_displ,
magma_int_t resetozero,
magma_int_t batchCount, magma_queue_t queue)
{
magma_int_t nrowA = (side == MagmaLeft ? m : n);
magma_int_t info = 0;
if ( side != MagmaLeft && side != MagmaRight ) {
info = -1;
} else if ( uplo != MagmaUpper && uplo != MagmaLower ) {
info = -2;
} else if ( transA != MagmaNoTrans && transA != MagmaTrans && transA != MagmaConjTrans ) {
info = -3;
} else if ( diag != MagmaUnit && diag != MagmaNonUnit ) {
info = -4;
} else if (m < 0) {
info = -5;
} else if (n < 0) {
info = -6;
} else if (ldda < max(1,nrowA)) {
info = -9;
} else if (lddb < max(1,m)) {
info = -11;
}
if (info != 0) {
magma_xerbla( __func__, -(info) );
return;
}
magmablas_strsm_inv_outofplace_batched(
side, uplo, transA, diag, flag,
m, n, alpha,
dA_array, ldda,
dB_array, lddb,
dX_array, lddx,
dinvA_array, dinvA_length,
dA_displ, dB_displ,
dX_displ, dinvA_displ,
resetozero, batchCount, queue );
// copy X to B
magma_sdisplace_pointers(dX_displ, dX_array, lddx, 0, 0, batchCount, queue);
magma_sdisplace_pointers(dB_displ, dB_array, lddb, 0, 0, batchCount, queue);
magmablas_slacpy_batched( MagmaFull, m, n, dX_displ, lddx, dB_displ, lddb, batchCount, queue );
}
/***************************************************************************//**
Purpose
-------
strsm solves one of the matrix equations on gpu
op(A)*X = alpha*B, or
X*op(A) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op(A) is one of
op(A) = A, or
op(A) = A^T, or
op(A) = A^H.
The matrix X is overwritten on B.
This is an asynchronous version of magmablas_strsm with flag,
d_dinvA and dX workspaces as arguments.
Arguments
----------
@param[in]
side magma_side_t.
On entry, side specifies whether op(A) appears on the left
or right of X as follows:
- = MagmaLeft: op(A)*X = alpha*B.
- = MagmaRight: X*op(A) = alpha*B.
@param[in]
uplo magma_uplo_t.
On entry, uplo specifies whether the matrix A is an upper or
lower triangular matrix as follows:
- = MagmaUpper: A is an upper triangular matrix.
- = MagmaLower: A is a lower triangular matrix.
@param[in]
transA magma_trans_t.
On entry, transA specifies the form of op(A) to be used in
the matrix multiplication as follows:
- = MagmaNoTrans: op(A) = A.
- = MagmaTrans: op(A) = A^T.
- = MagmaConjTrans: op(A) = A^H.
@param[in]
diag magma_diag_t.
On entry, diag specifies whether or not A is unit triangular
as follows:
- = MagmaUnit: A is assumed to be unit triangular.
- = MagmaNonUnit: A is not assumed to be unit triangular.
@param[in]
m INTEGER.
On entry, m specifies the number of rows of B. m >= 0.
@param[in]
n INTEGER.
On entry, n specifies the number of columns of B. n >= 0.
@param[in]
alpha REAL.
On entry, alpha specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
@param[in]
dA_array Array of pointers, dimension (batchCount).
Each is a REAL array A of dimension ( ldda, k ), where k is m
when side = MagmaLeft and is n when side = MagmaRight.
Before entry with uplo = MagmaUpper, the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with uplo = MagmaLower, the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when diag = MagmaUnit, the diagonal elements of
A are not referenced either, but are assumed to be unity.
@param[in]
ldda INTEGER.
On entry, ldda specifies the first dimension of each array A.
When side = MagmaLeft, ldda >= max( 1, m ),
when side = MagmaRight, ldda >= max( 1, n ).
@param[in,out]
dB_array Array of pointers, dimension (batchCount).
Each is a REAL array B of dimension ( lddb, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B.
\n
On exit, the solution matrix X
@param[in]
lddb INTEGER.
On entry, lddb specifies the first dimension of each array B.
lddb >= max( 1, m ).
@param[in]
batchCount INTEGER
The number of matrices to operate on.
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magma_trsm_batched
*******************************************************************************/
extern "C"
void magmablas_strsm_inv_batched(
magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag,
magma_int_t m, magma_int_t n,
float alpha,
float** dA_array, magma_int_t ldda,
float** dB_array, magma_int_t lddb,
magma_int_t batchCount, magma_queue_t queue)
{
magma_int_t nrowA = (side == MagmaLeft ? m : n);
magma_int_t info = 0;
if ( side != MagmaLeft && side != MagmaRight ) {
info = -1;
} else if ( uplo != MagmaUpper && uplo != MagmaLower ) {
info = -2;
} else if ( transA != MagmaNoTrans && transA != MagmaTrans && transA != MagmaConjTrans ) {
info = -3;
} else if ( diag != MagmaUnit && diag != MagmaNonUnit ) {
info = -4;
} else if (m < 0) {
info = -5;
} else if (n < 0) {
info = -6;
} else if (ldda < max(1,nrowA)) {
info = -9;
} else if (lddb < max(1,m)) {
info = -11;
}
if (info != 0) {
magma_xerbla( __func__, -(info) );
return;
}
float **dA_displ = NULL;
float **dB_displ = NULL;
float **dX_displ = NULL;
float **dinvA_displ = NULL;
float **dX_array = NULL;
float **dinvA_array = NULL;
magma_malloc((void**)&dA_displ, batchCount * sizeof(*dA_displ));
magma_malloc((void**)&dB_displ, batchCount * sizeof(*dB_displ));
magma_malloc((void**)&dX_displ, batchCount * sizeof(*dX_displ));
magma_malloc((void**)&dinvA_displ, batchCount * sizeof(*dinvA_displ));
magma_malloc((void**)&dinvA_array, batchCount * sizeof(*dinvA_array));
magma_malloc((void**)&dX_array, batchCount * sizeof(*dX_array));
magma_int_t size_dinvA;
magma_int_t lddx = m;
magma_int_t size_x = lddx*n;
if ( side == MagmaLeft ) {
size_dinvA = magma_roundup( m, STRTRI_BATCHED_NB )*STRTRI_BATCHED_NB;
}
else {
size_dinvA = magma_roundup( n, STRTRI_BATCHED_NB )*STRTRI_BATCHED_NB;
}
float *dinvA=NULL, *dX=NULL;
magma_int_t resetozero = 0;
magma_smalloc( &dinvA, size_dinvA*batchCount );
magma_smalloc( &dX, size_x*batchCount );
if ( dinvA == NULL || dX == NULL ) {
info = MAGMA_ERR_DEVICE_ALLOC;
magma_xerbla( __func__, -(info) );
return;
}
magmablas_slaset(MagmaFull, size_dinvA, batchCount, MAGMA_S_ZERO, MAGMA_S_ZERO, dinvA, size_dinvA, queue);
magmablas_slaset(MagmaFull, lddx, n*batchCount, MAGMA_S_ZERO, MAGMA_S_ZERO, dX, lddx, queue);
magma_sset_pointer( dX_array, dX, lddx, 0, 0, size_x, batchCount, queue );
magma_sset_pointer( dinvA_array, dinvA, STRTRI_BATCHED_NB, 0, 0, size_dinvA, batchCount, queue );
magmablas_strsm_inv_work_batched(
side, uplo, transA, diag, 1,
m, n, alpha,
dA_array, ldda,
dB_array, lddb,
dX_array, lddx,
dinvA_array, size_dinvA,
dA_displ, dB_displ,
dX_displ, dinvA_displ,
resetozero, batchCount, queue );
magma_free( dinvA );
magma_free( dX );
magma_free(dA_displ);
magma_free(dB_displ);
magma_free(dX_displ);
magma_free(dinvA_displ);
magma_free(dinvA_array);
magma_free(dX_array);
}
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