# dlaexc.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlaexc.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlaexc (WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO)
DLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation.

## Function/Subroutine Documentation

### subroutine dlaexc (logical WANTQ, integer N, double precision, dimension( ldt, * ) T, integer LDT, double precision, dimension( ldq, * ) Q, integer LDQ, integer J1, integer N1, integer N2, double precision, dimension( * ) WORK, integer INFO)

DLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation.

Purpose:

``` DLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in
an upper quasi-triangular matrix T by an orthogonal similarity
transformation.

T must be in Schur canonical form, that is, block upper triangular
with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block
has its diagonal elemnts equal and its off-diagonal elements of
opposite sign.
```

Parameters:

WANTQ

```          WANTQ is LOGICAL
= .TRUE. : accumulate the transformation in the matrix Q;
= .FALSE.: do not accumulate the transformation.
```

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
canonical form.
On exit, the updated matrix T, 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 WANTQ is .TRUE., the orthogonal matrix Q.
On exit, if WANTQ is .TRUE., the updated matrix Q.
If WANTQ is .FALSE., Q is not referenced.
```

LDQ

```          LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N.
```

J1

```          J1 is INTEGER
The index of the first row of the first block T11.
```

N1

```          N1 is INTEGER
The order of the first block T11. N1 = 0, 1 or 2.
```

N2

```          N2 is INTEGER
The order of the second block T22. N2 = 0, 1 or 2.
```

WORK

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

INFO

```          INFO is INTEGER
= 0: successful exit
= 1: the transformed matrix T would be too far from Schur
form; the blocks are not swapped and T and Q are
unchanged.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 140 of file dlaexc.f.

## Author

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