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Updated: June 2017
 
 

cgges (3p)

Name

cgges - N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR)

Synopsis

SUBROUTINE CGGES(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
BWORK, INFO)

CHARACTER*1 JOBVSL, JOBVSR, SORT
COMPLEX    A(LDA,*),   B(LDB,*),   ALPHA(*),   BETA(*),   VSL(LDVSL,*),
VSR(LDVSR,*), WORK(*)
INTEGER N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
LOGICAL SELCTG
LOGICAL BWORK(*)
REAL RWORK(*)

SUBROUTINE CGGES_64(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
BWORK, INFO)

CHARACTER*1 JOBVSL, JOBVSR, SORT
COMPLEX   A(LDA,*),   B(LDB,*),   ALPHA(*),   BETA(*),    VSL(LDVSL,*),
VSR(LDVSR,*), WORK(*)
INTEGER*8 N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
LOGICAL*8 SELCTG
LOGICAL*8 BWORK(*)
REAL RWORK(*)




F95 INTERFACE
SUBROUTINE GGES(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK,
RWORK, BWORK, INFO)

CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT
COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR
INTEGER :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
LOGICAL :: SELCTG
LOGICAL, DIMENSION(:) :: BWORK
REAL, DIMENSION(:) :: RWORK

SUBROUTINE GGES_64(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
LWORK, RWORK, BWORK, INFO)

CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT
COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR
INTEGER(8) :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
LOGICAL(8) :: SELCTG
LOGICAL(8), DIMENSION(:) :: BWORK
REAL, DIMENSION(:) :: RWORK




C INTERFACE
#include <sunperf.h>

void  cgges(char  jobvsl,  char  jobvsr,  char  sort, int(*selctg)(com-
plex,complex), int n, complex *a, int lda,  complex  *b,  int
ldb,  int *sdim, complex *alpha, complex *beta, complex *vsl,
int ldvsl, complex *vsr, int ldvsr, int *info);

void cgges_64(char jobvsl, char jobvsr, char  sort,  long(*selctg)(com-
plex,complex), long n, complex *a, long lda, complex *b, long
ldb, long *sdim, complex *alpha, complex *beta, complex *vsl,
long ldvsl, complex *vsr, long ldvsr, long *info);

Description

Oracle Solaris Studio Performance Library                            cgges(3P)



NAME
       cgges  -  compute  for  a  pair of N-by-N complex nonsymmetric matrices
       (A,B), the generalized eigenvalues, the generalized complex Schur  form
       (S, T), and optionally left and/or right Schur vectors (VSL and VSR)


SYNOPSIS
       SUBROUTINE CGGES(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
             SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
             BWORK, INFO)

       CHARACTER*1 JOBVSL, JOBVSR, SORT
       COMPLEX    A(LDA,*),   B(LDB,*),   ALPHA(*),   BETA(*),   VSL(LDVSL,*),
       VSR(LDVSR,*), WORK(*)
       INTEGER N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
       LOGICAL SELCTG
       LOGICAL BWORK(*)
       REAL RWORK(*)

       SUBROUTINE CGGES_64(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
             SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK,
             BWORK, INFO)

       CHARACTER*1 JOBVSL, JOBVSR, SORT
       COMPLEX   A(LDA,*),   B(LDB,*),   ALPHA(*),   BETA(*),    VSL(LDVSL,*),
       VSR(LDVSR,*), WORK(*)
       INTEGER*8 N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
       LOGICAL*8 SELCTG
       LOGICAL*8 BWORK(*)
       REAL RWORK(*)




   F95 INTERFACE
       SUBROUTINE GGES(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB,
              SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK,
              RWORK, BWORK, INFO)

       CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT
       COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
       COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR
       INTEGER :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
       LOGICAL :: SELCTG
       LOGICAL, DIMENSION(:) :: BWORK
       REAL, DIMENSION(:) :: RWORK

       SUBROUTINE GGES_64(JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B,
              LDB, SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK,
              LWORK, RWORK, BWORK, INFO)

       CHARACTER(LEN=1) :: JOBVSL, JOBVSR, SORT
       COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
       COMPLEX, DIMENSION(:,:) :: A, B, VSL, VSR
       INTEGER(8) :: N, LDA, LDB, SDIM, LDVSL, LDVSR, LWORK, INFO
       LOGICAL(8) :: SELCTG
       LOGICAL(8), DIMENSION(:) :: BWORK
       REAL, DIMENSION(:) :: RWORK




   C INTERFACE
       #include <sunperf.h>

       void  cgges(char  jobvsl,  char  jobvsr,  char  sort, int(*selctg)(com-
                 plex,complex), int n, complex *a, int lda,  complex  *b,  int
                 ldb,  int *sdim, complex *alpha, complex *beta, complex *vsl,
                 int ldvsl, complex *vsr, int ldvsr, int *info);

       void cgges_64(char jobvsl, char jobvsr, char  sort,  long(*selctg)(com-
                 plex,complex), long n, complex *a, long lda, complex *b, long
                 ldb, long *sdim, complex *alpha, complex *beta, complex *vsl,
                 long ldvsl, complex *vsr, long ldvsr, long *info);



PURPOSE
       cgges  computes  for  a  pair  of  N-by-N complex nonsymmetric matrices
       (A,B), the generalized eigenvalues, the generalized complex Schur  form
       (S,  T),  and optionally left and/or right Schur vectors (VSL and VSR).
       This gives the generalized Schur factorization

               (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )

       where (VSR)**H is the conjugate-transpose of VSR.

       Optionally, it also orders the eigenvalues so that a  selected  cluster
       of eigenvalues appears in the leading diagonal blocks of the upper tri-
       angular matrix S and the upper triangular matrix T. The leading columns
       of  VSL  and  VSR then form an unitary basis for the corresponding left
       and right eigenspaces (deflating subspaces).

       (If only the generalized eigenvalues are needed, use the  driver  CGGEV
       instead, which is faster.)

       A  generalized eigenvalue for a pair of matrices (A,B) is a scalar w or
       a ratio alpha/beta = w, such that  A - w*B is singular.  It is  usually
       represented  as  the pair (alpha,beta), as there is a reasonable inter-
       pretation for beta=0, and even for both being zero.

       A pair of matrices (S,T) is in generalized complex Schur form if S  and
       T are upper triangular and, in addition, the diagonal elements of T are
       non-negative real numbers.


ARGUMENTS
       JOBVSL (input)
                 = 'N':  do not compute the left Schur vectors;
                 = 'V':  compute the left Schur vectors.


       JOBVSR (input)
                 = 'N':  do not compute the right Schur vectors;
                 = 'V':  compute the right Schur vectors.


       SORT (input)
                 Specifies whether or not to  order  the  eigenvalues  on  the
                 diagonal  of the generalized Schur form.  = 'N':  Eigenvalues
                 are not ordered;
                 = 'S':  Eigenvalues are ordered (see SELCTG).


       SELCTG (input)
                 LOGICAL FUNCTION of two  COMPLEX  arguments  SELCTG  must  be
                 declared  EXTERNAL in the calling subroutine.  If SORT = 'N',
                 SELCTG is not referenced.  If SORT = 'S', SELCTG is  used  to
                 select eigenvalues to sort to the top left of the Schur form.
                 An    eigenvalue    ALPHA(j)/BETA(j)    is    selected     if
                 SELCTG(ALPHA(j),BETA(j)) is true.

                 Note that a selected complex eigenvalue may no longer satisfy
                 SELCTG(ALPHA(j),BETA(j))  =  .TRUE.  after  ordering,   since
                 ordering  may  change the value of complex eigenvalues (espe-
                 cially if the eigenvalue is ill-conditioned),  in  this  case
                 INFO is set to N+2 (See INFO below).


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


       A (input/output)
                 On  entry, the first of the pair of matrices.  On exit, A has
                 been overwritten by its generalized Schur form S.


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


       B (input/output)
                 On entry, the second of the pair of matrices.  On exit, B has
                 been overwritten by its generalized Schur form T.


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


       SDIM (output)
                 If SORT = 'N', SDIM = 0.  If SORT = 'S', SDIM = number of ei-
                 genvalues (after sorting) for which SELCTG is true.


       ALPHA (output)
                 On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be  the  general-
                 ized   eigenvalues.    ALPHA(j),   j=1,...,N   and   BETA(j),
                 j=1,...,N  are the diagonals of the complex Schur form  (A,B)
                 output by CGGES. The  BETA(j) will be non-negative real.

                 Note:  the  quotients  ALPHA(j)/BETA(j)  may  easily over- or
                 underflow, and BETA(j) may even  be  zero.   Thus,  the  user
                 should  avoid  naively  computing the ratio alpha/beta.  How-
                 ever, ALPHA will be always less than and  usually  comparable
                 with norm(A) in magnitude, and BETA always less than and usu-
                 ally comparable with norm(B).


       BETA (output)
                 See description of ALPHA.


       VSL (output)
                 If JOBVSL = 'V', VSL will contain  the  left  Schur  vectors.
                 Not referenced if JOBVSL = 'N'.


       LDVSL (input)
                 The  leading  dimension of the matrix VSL. LDVSL >= 1, and if
                 JOBVSL = 'V', LDVSL >= N.


       VSR (output)
                 If JOBVSR = 'V', VSR will contain the  right  Schur  vectors.
                 Not referenced if JOBVSR = 'N'.


       LDVSR (input)
                 The  leading  dimension of the matrix VSR. LDVSR >= 1, and if
                 JOBVSR = 'V', LDVSR >= N.


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


       LWORK (input)
                 The dimension of the array WORK.  LWORK >=  max(1,2*N).   For
                 good performance, LWORK must generally be larger.

                 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.


       RWORK (workspace)
                 dimension(8*N)

       BWORK (workspace)
                 dimension(N) Not referenced if SORT = 'N'.


       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value.
                 =1,...,N: The QZ iteration failed.  (A,B) are  not  in  Schur
                 form,   but  ALPHA(j)  and  BETA(j)  should  be  correct  for
                 j=INFO+1,...,N.  > N:  =N+1: other than QZ  iteration  failed
                 in CHGEQZ
                 =N+2:  after reordering, roundoff changed values of some com-
                 plex eigenvalues so that leading eigenvalues in the  General-
                 ized  Schur  form no longer satisfy SELCTG=.TRUE.  This could
                 also be caused due to scaling.  =N+3:  reordering  falied  in
                 CTGSEN.




                                  7 Nov 2015                         cgges(3P)