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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).

**Further Comments**
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

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