---
name: "ctgex2"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/ctgex2.f"
---

# ctgex2(3)

Part of [ctgex2.f(3)](/ctgex2.f/3.md).

## NAME

SRC/ctgex2.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ctgex2** (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, j1, info)\
 **CTGEX2** swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

## Function/Subroutine Documentation

### subroutine ctgex2 (logical wantq, logical wantz, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldb, \* ) b, integer ldb, complex, dimension( ldq, \* ) q, integer ldq, complex, dimension( ldz, \* ) z, integer ldz, integer j1, integer info)

**CTGEX2** swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

**Purpose:**

```
!>
!> CTGEX2 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 array, dimension (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 array, dimension (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 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 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.

**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:**

\[1\] 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.

Definition at line **188** of file **ctgex2.f**.

## Author

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