NAME

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

SYNOPSIS

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, ∗ )

PURPOSE

ZTRSM  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’   or   op( A ) = conjg( A’ ).
The matrix X is overwritten on B.
 

PARAMETERS

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.

SunSoft, Inc.  —  Last change: 27 Jun 1995