ztgex2.f - Man Page

subroutine ztgex2 (WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.  

Purpose:

 ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
 in an upper triangular matrix pair (A, B) by an unitary equivalence
 transformation.

 (A, B) must be in generalized Schur canonical form, that is, A and
 B are both upper triangular.

 Optionally, the matrices Q and Z of generalized Schur vectors are
 updated.

        Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
        Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H

Parameters:

WANTQ

          WANTQ is LOGICAL
          .TRUE. : update the left transformation matrix Q;
          .FALSE.: do not update Q.

WANTZ

          WANTZ is LOGICAL
          .TRUE. : update the right transformation matrix Z;
          .FALSE.: do not update Z.

N

          N is INTEGER
          The order of the matrices A and B. N >= 0.

A

          A is COMPLEX*16 array, dimensions (LDA,N)
          On entry, the matrix A in the pair (A, B).
          On exit, the updated matrix A.

LDA

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

B

          B is COMPLEX*16 array, dimensions (LDB,N)
          On entry, the matrix B in the pair (A, B).
          On exit, the updated matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).

Q

          Q is COMPLEX*16 array, dimension (LDQ,N)
          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,
          the updated matrix Q.
          Not referenced if WANTQ = .FALSE..

LDQ

          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= 1;
          If WANTQ = .TRUE., LDQ >= N.

Z

          Z is COMPLEX*16 array, dimension (LDZ,N)
          If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,
          the updated matrix Z.
          Not referenced if WANTZ = .FALSE..

LDZ

          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= 1;
          If WANTZ = .TRUE., LDZ >= N.

J1

          J1 is INTEGER
          The index to the first block (A11, B11).

INFO

          INFO is INTEGER
           =0:  Successful exit.
           =1:  The transformed matrix pair (A, B) would be too far
                from generalized Schur form; the problem is ill-
                conditioned.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

June 2017

Further Details:

In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.

Contributors:

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

References:

Definition at line 192 of file ztgex2.f.