---
name: "dtrexc.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/dtrexc.f"
---

# dtrexc.f(3)

## NAME

SRC/dtrexc.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dtrexc** (compq, n, t, ldt, q, ldq, ifst, ilst, work, info)\
 **DTREXC**

## Function/Subroutine Documentation

### subroutine dtrexc (character compq, integer n, double precision, dimension( ldt, \* ) t, integer ldt, double precision, dimension( ldq, \* ) q, integer ldq, integer ifst, integer ilst, double precision, dimension( \* ) work, integer info)

**DTREXC**

**Purpose:**

```
!>
!> DTREXC reorders the real Schur factorization of a real matrix
!> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
!> moved to row ILST.
!>
!> The real Schur form T is reordered by an orthogonal similarity
!> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
!> is updated by postmultiplying it with Z.
!>
!> T must be in Schur canonical form (as returned by DHSEQR), that is,
!> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
!> 2-by-2 diagonal block has its diagonal elements equal and its
!> off-diagonal elements of opposite sign.
!>
```

**Parameters**

*COMPQ*

```
!>          COMPQ is CHARACTER*1
!>          = 'V':  update the matrix Q of Schur vectors;
!>          = 'N':  do not update Q.
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix T. N >= 0.
!>          If N == 0 arguments ILST and IFST may be any value.
!>
```

*T*

```
!>          T is DOUBLE PRECISION array, dimension (LDT,N)
!>          On entry, the upper quasi-triangular matrix T, in Schur
!>          Schur canonical form.
!>          On exit, the reordered upper quasi-triangular matrix, again
!>          in Schur canonical form.
!>
```

*LDT*

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

*Q*

```
!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!>          On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
!>          On exit, if COMPQ = 'V', Q has been postmultiplied by the
!>          orthogonal transformation matrix Z which reorders T.
!>          If COMPQ = 'N', Q is not referenced.
!>
```

*LDQ*

```
!>          LDQ is INTEGER
!>          The leading dimension of the array Q.  LDQ >= 1, and if
!>          COMPQ = 'V', LDQ >= max(1,N).
!>
```

*IFST*

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

*ILST*

```
!>          ILST is INTEGER
!>
!>          Specify the reordering of the diagonal blocks of T.
!>          The block with row index IFST is moved to row ILST, by a
!>          sequence of transpositions 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 <= N; 1 <= ILST <= N.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          = 1:  two adjacent blocks were too close to swap (the problem
!>                is very ill-conditioned); T 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.

Definition at line **146** of file **dtrexc.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.