# dtrexc.f man page

dtrexc.f —

## Synopsis

### Functions/Subroutines

subroutinedtrexc(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO)DTREXC

## Function/Subroutine Documentation

### subroutine dtrexc (characterCOMPQ, integerN, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( ldq, * )Q, integerLDQ, integerIFST, integerILST, double precision, dimension( * )WORK, integerINFO)

**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.
```

*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 >= 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.

**Date:**

November 2011

Definition at line 146 of file dtrexc.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK