# ctgex2.f man page

ctgex2.f —

## Synopsis

### Functions/Subroutines

subroutinectgex2(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)CTGEX2swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equivalence transformation.

## Function/Subroutine Documentation

### subroutine ctgex2 (logicalWANTQ, logicalWANTZ, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldq, * )Q, integerLDQ, complex, dimension( ldz, * )Z, integerLDZ, integerJ1, integerINFO)

**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 arrays, 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 arrays, 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 array, dimension (LDZ,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.

**Date:**

September 2012

**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 190 of file ctgex2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

ctgex2(3) is an alias of ctgex2.f(3).