LAPACK

NAME¶

laexc - 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.

Detailed Description¶

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 is INTEGER


          The order of the matrix T. N >= 0.



          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 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 is INTEGER


          The index of the first row of the first block T11.



          N1 is INTEGER


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



          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.

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.