---
name: "dtgexc.f"
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/dtgexc.f"
---

# dtgexc.f(3)

## NAME

SRC/dtgexc.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dtgexc** (wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, work, lwork, info)\
 **DTGEXC**

## Function/Subroutine Documentation

### subroutine dtgexc (logical wantq, logical wantz, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( ldq, \* ) q, integer ldq, double precision, dimension( ldz, \* ) z, integer ldz, integer ifst, integer ilst, double precision, dimension( \* ) work, integer lwork, integer info)

**DTGEXC**

**Purpose:**

```
!>
!> DTGEXC reorders the generalized real Schur decomposition of a real
!> matrix pair (A,B) using an orthogonal equivalence transformation
!>
!>                (A, B) = Q * (A, B) * Z**T,
!>
!> so that the diagonal block of (A, B) with row index IFST is moved
!> to row ILST.
!>
!> (A, B) must be in generalized real Schur canonical form (as returned
!> by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
!> diagonal blocks. B is upper triangular.
!>
!> Optionally, the matrices Q and Z of generalized Schur vectors are
!> updated.
!>
!>        Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
!>        Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
!>
!>
```

**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 DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the matrix A in generalized real Schur canonical
!>          form.
!>          On exit, the updated matrix A, again in generalized
!>          real Schur canonical form.
!>
```

*LDA*

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

*B*

```
!>          B is DOUBLE PRECISION array, dimension (LDB,N)
!>          On entry, the matrix B in generalized real Schur canonical
!>          form (A,B).
!>          On exit, the updated matrix B, again in generalized
!>          real Schur canonical form (A,B).
!>
```

*LDB*

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

*Q*

```
!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!>          On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
!>          On exit, the updated matrix Q.
!>          If WANTQ = .FALSE., Q is not referenced.
!>
```

*LDQ*

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

*Z*

```
!>          Z is DOUBLE PRECISION array, dimension (LDZ,N)
!>          On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
!>          On exit, the updated matrix Z.
!>          If WANTZ = .FALSE., Z is not referenced.
!>
```

*LDZ*

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

*IFST*

```
!>          IFST is INTEGER
!>
```

*ILST*

```
!>          ILST is 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.
!>          On exit, if IFST pointed on entry to the second row of
!>          a 2-by-2 block, it is changed to point to the first row;
!>          ILST always points to the first row of the block in its
!>          final position (which may differ from its input value by
!>          +1 or -1). 1 <= IFST, ILST <= N.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>
```

*INFO*

```
!>          INFO is 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.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**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.
!>
```

Definition at line **218** of file **dtgexc.f**.

## Author

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