# dtrexc.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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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