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# strsm

```
NAME
STRSM - solve one of the matrix equations   op( A )*X =
alpha*B, or X*op( A ) = alpha*B,

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

CHARACTER*1  SIDE, UPLO, TRANSA, DIAG

INTEGER      M, N, LDA, LDB

REAL         ALPHA

REAL         A( LDA, * ), B( LDB, * )

PURPOSE
STRSM  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'.

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 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  - REAL            .
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      -
REAL             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      - REAL             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
Harwell.  Jeremy Du Croz, Numerical Algorithms Group
Ltd.  Sven Hammarling, Numerical Algorithms Group
Ltd.
```