.TH DLAEXC 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLAEXC - adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation .SH SYNOPSIS .TP 19 SUBROUTINE DLAEXC( WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO ) .TP 19 .ti +4 LOGICAL WANTQ .TP 19 .ti +4 INTEGER INFO, J1, LDQ, LDT, N, N1, N2 .TP 19 .ti +4 DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) .SH 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. .br .SH ARGUMENTS .TP 8 WANTQ (input) LOGICAL = .TRUE. : accumulate the transformation in the matrix Q; .br = .FALSE.: do not accumulate the transformation. .TP 8 N (input) INTEGER The order of the matrix T. N >= 0. .TP 8 T (input/output) 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. .TP 8 LDT (input) INTEGER The leading dimension of the array T. LDT >= max(1,N). .TP 8 Q (input/output) 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. .TP 8 LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N. .TP 8 J1 (input) INTEGER The index of the first row of the first block T11. .TP 8 N1 (input) INTEGER The order of the first block T11. N1 = 0, 1 or 2. .TP 8 N2 (input) INTEGER The order of the second block T22. N2 = 0, 1 or 2. .TP 8 WORK (workspace) DOUBLE PRECISION array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br = 1: the transformed matrix T would be too far from Schur form; the blocks are not swapped and T and Q are unchanged.