---
name: "ztgexc"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/ztgexc/3lapack"
---

# ztgexc(3lapack)

reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q \* (A, B) \* Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST

## NAME

ZTGEXC - reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q \* (A, B) \* Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST

## SYNOPSIS

- SUBROUTINE ZTGEXC(

  WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, INFO )

- LOGICAL

  WANTQ, WANTZ

- INTEGER

  IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N

- COMPLEX\*16

  A( LDA, \* ), B( LDB, \* ), Q( LDQ, \* ), Z( LDZ, \* )

## PURPOSE

ZTGEXC reorders the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q \* (A, B) \* Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST. (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)' = Q(out) \* A(out) \* Z(out)'\
        Q(in) \* B(in) \* Z(in)' = Q(out) \* B(out) \* Z(out)'

## ARGUMENTS

- WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix Q;

  - WANTZ (input) LOGICAL

  - N (input) INTEGER

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

- A (input/output) COMPLEX\*16 array, dimension (LDA,N)

  On entry, the upper triangular matrix A in the pair (A, B). On exit, the updated matrix A.

- LDA (input) INTEGER

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

- B (input/output) COMPLEX\*16 array, dimension (LDB,N)

  On entry, the upper triangular matrix B in the pair (A, B). On exit, the updated matrix B.

- LDB (input) INTEGER

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

- Q (input/output) COMPLEX\*16 array, dimension (LDZ,N)

  On entry, if WANTQ = .TRUE., the unitary matrix Q. On exit, the updated matrix Q. If WANTQ = .FALSE., Q is not referenced.

- LDQ (input) INTEGER

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

- Z (input/output) COMPLEX\*16 array, dimension (LDZ,N)

  On entry, if WANTZ = .TRUE., the unitary matrix Z. On exit, the updated matrix Z. If WANTZ = .FALSE., Z is not referenced.

- LDZ (input) INTEGER

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

- IFST (input) INTEGER

  ILST    (input/output) INTEGER Specify the reordering of the diagonal blocks of (A, B). The block with row index IFST is moved to row ILST, by a sequence of swapping between adjacent blocks.

- INFO (output) INTEGER

  \=0:  Successful exit.\
   \<0:  if INFO = -i, the i-th argument had an illegal value.\
   \=1:  The transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill- conditioned. (A, B) may have been partially reordered, and ILST points to the first row of the current position of the block being moved.

## FURTHER DETAILS

Based on contributions by\
\
    Bo Kagstrom and Peter Poromaa, Department of Computing Science,\
    Umea University, S-901 87 Umea, Sweden.\
 \[1\] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the\
     Generalized Real Schur Form of a Regular Matrix Pair (A, B), in\
     M.S. Moonen et al (eds), Linear Algebra for Large Scale and\
     Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. \[2\] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified\
     Eigenvalues of a Regular Matrix Pair (A, B) and Condition\
     Estimation: Theory, Algorithms and Software, Report\
\
     UMINF - 94.04, Department of Computing Science, Umea University,\
     S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.\
     To appear in Numerical Algorithms, 1996.\
 \[3\] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software\
     for Solving the Generalized Sylvester Equation and Estimating the\
     Separation between Regular Matrix Pairs, Report UMINF - 93.23,\
     Department of Computing Science, Umea University, S-901 87 Umea,\
     Sweden, December 1993, Revised April 1994, Also as LAPACK working\
     Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,\
     1996\.\