# laexc - Man Page

laexc: reorder Schur form

## Synopsis

### Functions

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.
subroutine slaexc (wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info)
SLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation.

## Function 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 elements 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

NAG Ltd.

Definition at line 136 of file dlaexc.f.

### subroutine slaexc (logical wantq, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldq, * ) q, integer ldq, integer j1, integer n1, integer n2, real, dimension( * ) work, integer info)

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

Purpose:

``` SLAEXC 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 elements 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 REAL 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 REAL 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 REAL 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