# ctrmm

```CTRMM(l)                         BLAS routine                         CTRMM(l)

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.

BLAS routine                    16 October 1992                       CTRMM(l)```