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
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 multi
plication as follows:
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 trian
gular.
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
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 Har
well. Jeremy Du Croz, Numerical Algorithms Group
Ltd. Sven Hammarling, Numerical Algorithms Group
Ltd.
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