ztgexc (3p)

Name

ztgexc - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST

Synopsis

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

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

SUBROUTINE ZTGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
IFST, ILST, INFO)

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




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

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

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

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




C INTERFACE
#include <sunperf.h>

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

void ztgexc_64(long wantq, long wantz, long n, doublecomplex  *a,  long
lda,  doublecomplex *b, long ldb, doublecomplex *q, long ldq,
doublecomplex *z, long ldz,  long  *ifst,  long  *ilst,  long
*info);

Description

Oracle Solaris Studio Performance Library                           ztgexc(3P)



NAME
       ztgexc  -  reorder  the  generalized  Schur  decomposition of a complex
       matrix pair (A,B), using an unitary equivalence transformation  (A,  B)
       := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index
       IFST is moved to row ILST


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

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

       SUBROUTINE ZTGEXC_64(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
             IFST, ILST, INFO)

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




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

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

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

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




   C INTERFACE
       #include <sunperf.h>

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

       void ztgexc_64(long wantq, long wantz, long n, doublecomplex  *a,  long
                 lda,  doublecomplex *b, long ldb, doublecomplex *q, long ldq,
                 doublecomplex *z, long ldz,  long  *ifst,  long  *ilst,  long
                 *info);



PURPOSE
       ztgexc reorders the generalized Schur decomposition of a complex matrix
       pair (A,B), using an unitary equivalence transformation (A, B) :=  Q  *
       (A,  B)  * Z', so that the diagonal block of (A, B) with row index IFST
       is moved to row ILST.

       (A, B) must be in generalized Schur canonical form, that is,  A  and  B
       are both 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 upper triangular matrix A in the pair  (A,  B).
                 On exit, the updated matrix A.


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


       B (input/output)
                 On  entry,  the upper triangular matrix B in the pair (A, B).
                 On exit, the updated matrix B.


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


       Q (input/output)
                 On entry, if WANTQ = .TRUE., the unitary matrix Q.  On  exit,
                 the  updated  matrix  Q.  If WANTQ = .FALSE., Q is not refer-
                 enced.


       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 unitary matrix Z.  On exit,
                 the updated matrix Z.  If WANTZ = .FALSE., Z  is  not  refer-
                 enced.


       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.


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


       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.

       [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
           Eigenvalues of a Regular Matrix Pair (A, B) and Condition
           Estimation: Theory, Algorithms and Software, Report
           UMINF - 94.04, Department of Computing Science, Umea University,
           S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
           To appear in Numerical Algorithms, 1996.

       [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
           for Solving the Generalized Sylvester Equation and Estimating the
           Separation between Regular Matrix Pairs, Report UMINF - 93.23,
           Department of Computing Science, Umea University, S-901 87 Umea,
           Sweden, December 1993, Revised April 1994, Also as LAPACK working
           Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
           1996.




                                  7 Nov 2015                        ztgexc(3P)