NAME
CTRMM - perform one of the matrix-matrix operations B := alpha*op( A
)*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n
matrix, 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’
)
SYNOPSIS
SUBROUTINE CTRMM ( 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, * )
PURPOSE
CTRMM performs one of the matrix-matrix operations
PARAMETERS
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) multiplies B from the
left or right as follows:
SIDE = ’L’ or ’l’ B := alpha*op( A )*B.
SIDE = ’R’ or ’r’ B := alpha*B*op( A ).
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 .
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 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 array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the matrix B, and on exit is overwritten by the
transformed matrix.
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.