dtgexc (3p)

Name

dtgexc - reorder the generalized Schur decomposition of a real matrix pair using an orthogonal or unitary equivalence transformation

Synopsis

SUBROUTINE DTGEXC(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
IFST, ILST, WORK, LWORK, INFO)

INTEGER N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL WANTQ, WANTZ
DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)

SUBROUTINE DTGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
IFST, ILST, WORK, LWORK, INFO)

INTEGER*8 N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL*8 WANTQ, WANTZ
DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)




F95 INTERFACE
SUBROUTINE TGEXC(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
LDZ, IFST, ILST, WORK, LWORK, INFO)

INTEGER :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL :: WANTQ, WANTZ
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B, Q, Z

SUBROUTINE TGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
LDZ, IFST, ILST, WORK, LWORK, INFO)

INTEGER(8) :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
LOGICAL(8) :: WANTQ, WANTZ
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B, Q, Z




C INTERFACE
#include <sunperf.h>

void dtgexc(int wantq, int wantz, int n, double *a, int lda, double *b,
int  ldb,  double *q, int ldq, double *z, int ldz, int *ifst,
int *ilst, int *info);

void dtgexc_64(long wantq, long wantz, long n,  double  *a,  long  lda,
double  *b,  long  ldb,  double *q, long ldq, double *z, long
ldz, long *ifst, long *ilst, long *info);

Description

Oracle Solaris Studio Performance Library                           dtgexc(3P)



NAME
       dtgexc  -  reorder the generalized Schur decomposition of a real matrix
       pair using an orthogonal or unitary equivalence transformation


SYNOPSIS
       SUBROUTINE DTGEXC(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
             IFST, ILST, WORK, LWORK, INFO)

       INTEGER N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
       LOGICAL WANTQ, WANTZ
       DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)

       SUBROUTINE DTGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
             IFST, ILST, WORK, LWORK, INFO)

       INTEGER*8 N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
       LOGICAL*8 WANTQ, WANTZ
       DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)




   F95 INTERFACE
       SUBROUTINE TGEXC(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
              LDZ, IFST, ILST, WORK, LWORK, INFO)

       INTEGER :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
       LOGICAL :: WANTQ, WANTZ
       REAL(8), DIMENSION(:) :: WORK
       REAL(8), DIMENSION(:,:) :: A, B, Q, Z

       SUBROUTINE TGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
              LDZ, IFST, ILST, WORK, LWORK, INFO)

       INTEGER(8) :: N, LDA, LDB, LDQ, LDZ, IFST, ILST, LWORK, INFO
       LOGICAL(8) :: WANTQ, WANTZ
       REAL(8), DIMENSION(:) :: WORK
       REAL(8), DIMENSION(:,:) :: A, B, Q, Z




   C INTERFACE
       #include <sunperf.h>

       void dtgexc(int wantq, int wantz, int n, double *a, int lda, double *b,
                 int  ldb,  double *q, int ldq, double *z, int ldz, int *ifst,
                 int *ilst, int *info);

       void dtgexc_64(long wantq, long wantz, long n,  double  *a,  long  lda,
                 double  *b,  long  ldb,  double *q, long ldq, double *z, long
                 ldz, long *ifst, long *ilst, long *info);



PURPOSE
       dtgexc reorders the generalized real  Schur  decomposition  of  a  real
       matrix pair (A,B) using an orthogonal equivalence transformation

            (A, B) = Q * (A, B) * Z**T,

       so  that  the  diagonal block of (A, B) with row index IFST is moved to
       row ILST.

       (A, B) must be in generalized real Schur canonical form (as returned by
       DGGES),  i.e. A is block upper triangular with 1-by-1 and 2-by-2 diago-
       nal blocks. B is upper triangular.

       Optionally, the matrices Q and  Z  of  generalized  Schur  vectors  are
       updated.

              Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
              Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'


ARGUMENTS
       WANTQ (input) LOGICAL
                  .TRUE. : update the left transformation matrix Q;
                  .FALSE.: do not update Q.


       WANTZ (input) LOGICAL
                  .TRUE. : update the right transformation matrix Z;
                  .FALSE.: do not update Z.


       N (input) The order of the matrices A and B. N >= 0.


       A (input/output)
                 On  entry,  the  matrix A in generalized real Schur canonical
                 form.  On exit, the updated matrix A,  again  in  generalized
                 real Schur canonical form.


       LDA (input)
                 The leading dimension of the array A. LDA >= max(1,N).


       B (input/output)
                 On  entry,  the  matrix B in generalized real Schur canonical
                 form (A,B).  On exit, the updated matrix B, again in general-
                 ized real Schur canonical form (A,B).


       LDB (input)
                 The leading dimension of the array B. LDB >= max(1,N).


       Q (input/output)
                 On  entry,  if  WANTQ  = .TRUE., the orthogonal matrix Q.  On
                 exit, the updated matrix Q.  If WANTQ =  .FALSE.,  Q  is  not
                 referenced.


       LDQ (input)
                 The  leading  dimension of the array Q. LDQ >= 1.  If WANTQ =
                 .TRUE., LDQ >= N.


       Z (input/output)
                 On entry, if WANTZ = .TRUE., the  orthogonal  matrix  Z.   On
                 exit,  the  updated  matrix  Z.  If WANTZ = .FALSE., Z is not
                 referenced.


       LDZ (input)
                 The leading dimension of the array Z. LDZ >= 1.  If  WANTZ  =
                 .TRUE., LDZ >= N.


       IFST (input/output)
                 Specify the reordering of the diagonal blocks of (A, B).  The
                 block with row index IFST is moved to row ILST, by a sequence
                 of  swapping  between  adjacent  blocks.   On  exit,  if IFST
                 pointed on entry to the second row of a 2-by-2 block,  it  is
                 changed  to point to the first row; ILST always points to the
                 first row of the block in its final position (which may  dif-
                 fer  from its input value by +1 or -1). 1 <= IFST, ILST <= N.


       ILST (input/output)
                 See the description of IFST.


       WORK (workspace)
                 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


       LWORK (input)
                 The dimension of the array WORK. LWORK >= 4*N + 16.

                 If LWORK = -1, then a workspace query is assumed; the routine
                 only  calculates  the optimal size of the WORK array, returns
                 this value as the first entry of the WORK array, and no error
                 message related to LWORK is issued by XERBLA.


       INFO (output)
                 =0:  successful exit.
                 <0:  if INFO = -i, the i-th argument had an illegal value.
                 =1:  The transformed matrix pair (A, B) would be too far from
                 generalized Schur form; the problem is ill- conditioned.  (A,
                 B)  may have been partially reordered, and ILST points to the
                 first row of the current position of the block being moved.

FURTHER DETAILS
       Based on contributions by
          Bo Kagstrom and Peter Poromaa, Department of Computing Science,
          Umea University, S-901 87 Umea, Sweden.

       [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
           Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
           M.S. Moonen et al (eds), Linear Algebra for Large Scale and
           Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.




                                  7 Nov 2015                        dtgexc(3P)