man slaexc (Fonctions bibliothèques) - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation

NAME

SLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation

SYNOPSIS

SUBROUTINE SLAEXC(
WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO )
LOGICAL WANTQ
INTEGER INFO, J1, LDQ, LDT, N, N1, N2
REAL Q( LDQ, * ), T( LDT, * ), WORK( * )

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 elemnts equal and its off-diagonal elements of opposite sign.

ARGUMENTS

WANTQ (input) LOGICAL
= .TRUE. : accumulate the transformation in the matrix Q;

= .FALSE.: do not accumulate the transformation.
N (input) INTEGER
The order of the matrix T. N >= 0.
T (input/output) 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 (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q (input/output) 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 (input) INTEGER
The leading dimension of the array Q. LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N.
J1 (input) INTEGER
The index of the first row of the first block T11.
N1 (input) INTEGER
The order of the first block T11. N1 = 0, 1 or 2.
N2 (input) INTEGER
The order of the second block T22. N2 = 0, 1 or 2.
WORK (workspace) REAL array, dimension (N)
INFO (output) 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.