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NAME

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

```

SYNOPSIS

```       SUBROUTINE CTRSM ( 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

```       CTRSM  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 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   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.
```