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

                     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.

   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

           Univ. of Colorado Denver

           NAG Ltd.

Author

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