# dtrsm (l) - Linux Man Pages

## NAME

DTRSM - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,

## SYNOPSIS

SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)

DOUBLE PRECISION ALPHA

INTEGER LDA,LDB,M,N

CHARACTER DIAG,SIDE,TRANSA,UPLO

DOUBLE PRECISION A(LDA,*),B(LDB,*)

## PURPOSE

DTRSM solves one of the matrix equations

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(   or   op( Aaq.

The matrix X is overwritten on B.

## ARGUMENTS

SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:

SIDE = aqLaq or aqlaq op( A )*X = alpha*B.

SIDE = aqRaq or aqraq X*op( A ) = alpha*B.

Unchanged on exit.

UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows:

UPLO = aqUaq or aquaq A is an upper triangular matrix.

UPLO = aqLaq or aqlaq A is a lower triangular matrix.

Unchanged on exit.

TRANSA - CHARACTER*1. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows:

TRANSA = aqNaq or aqnaq op( A ) = A.

TRANSA = aqTaq or aqtaq op( A ) = Aaq.

TRANSA = aqCaq or aqcaq op( A ) = Aaq.

Unchanged on exit.

DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular as follows:

DIAG = aqUaq or aquaq A is assumed to be unit triangular.

DIAG = aqNaq or aqnaq A is not assumed to be unit triangular.

Unchanged on exit.

M - INTEGER.
On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when SIDE = aqLaq or aqlaq and is n when SIDE = aqRaq or aqraq. Before entry with UPLO = aqUaq or aquaq, 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 = aqLaq or aqlaq, 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 = aqUaq or aquaq, the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = aqLaq or aqlaq then LDA must be at least max( 1, m ), when SIDE = aqRaq or aqraq then LDA must be at least max( 1, n ). Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). Unchanged on exit.

## FURTHER DETAILS

Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.