## MA02GZ

### Column interchanges in a complex matrix

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To perform a series of column interchanges on the matrix A.
One column interchange is initiated for each of columns K1 through
K2 of A. This is useful for solving linear systems X*A = B, when
the matrix A has already been factored by LAPACK Library routine
DGETRF.

```
Specification
```      SUBROUTINE MA02GZ( N, A, LDA, K1, K2, IPIV, INCX )
C     .. Scalar Arguments ..
INTEGER            INCX, K1, K2, LDA, N
C     .. Array Arguments ..
INTEGER            IPIV( * )
COMPLEX*16         A( LDA, * )

```
Arguments

Input/Output Parameters

```  N       (input) INTEGER
The number of rows of the matrix A.  N >= 0.

A       (input/output) COMPLEX*16 array, dimension (LDA,*)
On entry, the leading N-by-M part of this array must
contain the matrix A to which the column interchanges will
be applied, where M is the largest element of IPIV(K), for
K = K1, ..., K2.
On exit, the leading N-by-M part of this array contains
the permuted matrix.

LDA     INTEGER
The leading dimension of the array A.  LDA >= MAX(1,N).

K1      (input) INTEGER
The first element of IPIV for which a column interchange
will be done.

K2      (input) INTEGER
The last element of IPIV for which a column interchange
will be done.

IPIV    (input) INTEGER array, dimension (K1+(K2-K1)*abs(INCX))
The vector of interchanging (pivot) indices.  Only the
elements in positions K1 through K2 of IPIV are accessed.
IPIV(K) = L implies columns K and L are to be
interchanged.

INCX    (input) INTEGER
The increment between successive values of IPIV.
If INCX is negative, the interchanges are applied in
reverse order.

```
Method
```  The columns IPIV(K) and K are swapped for K = K1, ..., K2, for
INCX = 1 (and similarly, for INCX <> 1).

```
```  This routine is the column-oriented counterpart of the LAPACK
Library routine DLASWP. The LAPACK Library routine DLAPMT cannot
be used in this context. To solve the system X*A = B, where A and
B are N-by-N and M-by-N, respectively, the following statements
can be used:

CALL DGETRF( N, N, A, LDA, IPIV, INFO )
CALL DTRSM( 'R', 'U', 'N', 'N', M, N, ONE, A, LDA, B, LDB )
CALL DTRSM( 'R', 'L', 'N', 'U', M, N, ONE, A, LDA, B, LDB )
CALL MA02GZ( M, B, LDB, 1, N, IPIV, -1 )

```
Example

Program Text

```  None
```
Program Data
```  None
```
Program Results
```  None
```