Provided by: libblas-doc_1.2.20110419-2ubuntu1_all #### NAME

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

```

#### SYNOPSIS

```       SUBROUTINE ZTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB )

CHARACTER*1  SIDE, UPLO, TRANSA, DIAG

INTEGER      M, N, LDA, LDB

COMPLEX*16   ALPHA

COMPLEX*16   A( LDA, * ), B( LDB, * )

```

#### PURPOSE

```       ZTRSM  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*16      .
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*16       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*16       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.
```