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NAME
ctrsm - solve one of the matrix equations op( A )*X =
alpha*B, or X*op( A ) = alpha*B
SYNOPSIS
SUBROUTINE CTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A,
LDA, B, LDB )
CHARACTER*1 SIDE, UPLO, TRANSA, DIAG
INTEGER M, N, LDA, LDB
COMPLEX ALPHA
COMPLEX A( LDA, * ), B( LDB, * )
#include <sunperf.h>
void ctrsm ( char side, char uplo, char transa, char diag,
int m,
int n, complex *calpha, complex *ca, int
lda,
complex *cb, int ldb ) ;
PURPOSE
CTRSM 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 mul-
tiplication 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 tri-
angular.
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 .
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 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 lead-
ing 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 refer-
enced.
Before entry with UPLO = 'L' or 'l', the lead-
ing 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 refer-
enced.
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 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.
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