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# dtrmm

```
NAME
DTRMM - perform one of the matrix-matrix operations   B :=
alpha*op( A )*B, or B := alpha*B*op( A ),

SYNOPSIS
SUBROUTINE DTRMM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A,
LDA, B, LDB )

CHARACTER*1  SIDE, UPLO, TRANSA, DIAG

INTEGER      M, N, LDA, LDB

DOUBLE       PRECISION ALPHA

DOUBLE       PRECISION A( LDA, * ), B( LDB, * )

PURPOSE
DTRMM  performs one of the matrix-matrix operations

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'.

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 multiplica-
tion as follows:

TRANSA = 'N' or 'n'   op( A ) = A.

TRANSA = 'T' or 't'   op( A ) = A'.

TRANSA = 'C' or 'c'   op( A ) = 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 triangu-
lar.

DIAG = 'N' or 'n'   A is not assumed to be unit tri-
angular.

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  - DOUBLE PRECISION.
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.

is m
A      -
DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k
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 refer-
enced.  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 refer-
enced.  Note that when  DIAG = 'U' or 'u',  the diag-
onal 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      - DOUBLE PRECISION 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.
```