# Name

**HPL_dtrsm**B := A^{-1} * B or B := B * A^{-1}.

# Synopsis

`#include "hpl.h"`

`void`

`HPL_dtrsm(`

`const enum HPL_ORDER`

`ORDER`

,
`const enum HPL_SIDE`

`SIDE`

,
`const enum HPL_UPLO`

`UPLO`

,
`const enum HPL_TRANS`

`TRANS`

,
`const enum HPL_DIAG`

`DIAG`

,
`const int`

`M`

,
`const int`

`N`

,
`const double`

`ALPHA`

,
`const double *`

`A`

,
`const int`

`LDA`

,
`double *`

`B`

,
`const int`

`LDB`

`);`

# Description

**HPL_dtrsm**solves one of the matrix equations 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. The matrix X is overwritten on B. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

# Arguments

ORDER (local input) const enum HPL_ORDER On entry, ORDER specifies the storage format of the operands as follows: ORDER = HplRowMajor, ORDER = HplColumnMajor.

SIDE (local input) const enum HPL_SIDE On entry, SIDE specifies whether op(A) appears on the left or right of X as follows: SIDE==HplLeft op( A ) * X = alpha * B, SIDE==HplRight X * op( A ) = alpha * B.

UPLO (local input) const enum HPL_UPLO On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced. When UPLO==HplUpper, only the upper triangular part of A is to be referenced, otherwise only the lower triangular part of A is to be referenced.

TRANS (local input) const enum HPL_TRANS On entry, TRANSA specifies the form of op(A) to be used in the matrix-matrix operation follows: TRANSA==HplNoTrans : op( A ) = A, TRANSA==HplTrans : op( A ) = A^T, TRANSA==HplConjTrans : op( A ) = A^T.

DIAG (local input) const enum HPL_DIAG On entry, DIAG specifies whether A is unit triangular or not. When DIAG==HplUnit, A is assumed to be unit triangular, and otherwise, A is not assumed to be unit triangular.

M (local input) const int On entry, M specifies the number of rows of the matrix B. M must be at least zero.

N (local input) const int On entry, N specifies the number of columns of the matrix B. N must be at least zero.

ALPHA (local input) const double On entry, ALPHA specifies the scalar alpha. When ALPHA is supplied as zero then the elements of the matrix B need not be set on input.

A (local input) const double * On entry, A points to an array of size equal to or greater than LDA * k, where k is m when SIDE==HplLeft and is n otherwise. Before entry with UPLO==HplUpper, 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. When UPLO==HplLower on entry, 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==HplUnit, the diagonal elements of A not referenced either, but are assumed to be unity.

LDA (local input) const int On entry, LDA specifies the leading dimension of A as declared in the calling (sub) program. LDA must be at least MAX(1,m) when SIDE==HplLeft, and MAX(1,n) otherwise.

B (local input/output) double * On entry, B points to an array of size equal to or greater than LDB * n. Before entry, the leading m by n part of the array B must contain the matrix B, except when beta is zero, in which case B need not be set on entry. On exit, the array B is overwritten by the m by n solution matrix.

LDB (local input) const int On entry, LDB specifies the leading dimension of B as declared in the calling (sub) program. LDB must be at least MAX(1,m).

# Example

`#include "hpl.h"`

int main(int argc, char *argv[]) { double a[2*2], b[2*2]; a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0; b[0] = 2.0; b[1] = 1.0; b[2] = 1.0; b[3] = 2.0; HPL_dtrsm( HplColumnMajor, HplLeft, HplUpper, HplNoTrans, HplNonUnit, 2, 2, 2.0, a, 2, b, 2 ); printf(" [%f,%f]\n", b[0], b[2]); printf("b=[%f,%f]\n", b[1], b[3]); exit(0); return(0); }