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

SUBROUTINE ZTRSM

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

CHARACTER*1 SIDE, UPLO, TRANSA, DIAG

INTEGER M, N, LDA, LDB

COMPLEX*16 ALPHA

COMPLEX*16 A( LDA, * ), B( LDB, * )

ZTRSM 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( A ) = A or op( A ) = A' or op( A ) = conjg( A' ).

The matrix X is overwritten on B.

SIDE - CHARACTER*1.

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

SIDE = 'L' or 'l' op( A )*X = alpha*B.

SIDE = 'R' or 'r' 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 = 'U' or 'u' A is an upper triangular matrix.

UPLO = 'L' or 'l' 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 = 'N' or 'n' op( A ) = A.

TRANSA = 'T' or 't' op( A ) = A'.

TRANSA = 'C' or 'c' op( A ) = conjg( A' ).

Unchanged on exit.

DIAG - CHARACTER*1.

On entry, DIAG specifies whether or not A is unit triangular as follows:

DIAG = 'U' or 'u' A is assumed to be unit triangular.

DIAG = 'N' or 'n' 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 - COMPLEX*16 .

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 - COMPLEX*16 array of DIMENSION ( LDA, k ), where k is m

when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', 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 = 'L' or 'l', 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 = 'U' or 'u', 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 = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ). Unchanged on exit.

B - COMPLEX*16 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.

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.