• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

cggev - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

SYNOPSIS

  SUBROUTINE CGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, 
 *      LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
  CHARACTER * 1 JOBVL, JOBVR
  COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER N, LDA, LDB, LDVL, LDVR, LWORK, INFO
  REAL RWORK(*)

  SUBROUTINE CGGEV_64( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, 
 *      VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
  CHARACTER * 1 JOBVL, JOBVR
  COMPLEX A(LDA,*), B(LDB,*), ALPHA(*), BETA(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER*8 N, LDA, LDB, LDVL, LDVR, LWORK, INFO
  REAL RWORK(*)

F95 INTERFACE

  SUBROUTINE GGEV( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHA, BETA, 
 *       VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: JOBVL, JOBVR
  COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
  COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
  INTEGER :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
  REAL, DIMENSION(:) :: RWORK

  SUBROUTINE GGEV_64( JOBVL, JOBVR, [N], A, [LDA], B, [LDB], ALPHA, 
 *       BETA, VL, [LDVL], VR, [LDVR], [WORK], [LWORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: JOBVL, JOBVR
  COMPLEX, DIMENSION(:) :: ALPHA, BETA, WORK
  COMPLEX, DIMENSION(:,:) :: A, B, VL, VR
  INTEGER(8) :: N, LDA, LDB, LDVL, LDVR, LWORK, INFO
  REAL, DIMENSION(:) :: RWORK

C INTERFACE

#include <sunperf.h>

void cggev(char jobvl, char jobvr, int n, complex *a, int lda, complex *b, int ldb, complex *alpha, complex *beta, complex *vl, int ldvl, complex *vr, int ldvr, int *info);

void cggev_64(char jobvl, char jobvr, long n, complex *a, long lda, complex *b, long ldb, complex *alpha, complex *beta, complex *vl, long ldvl, complex *vr, long ldvr, long *info);

PURPOSE

cggev computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

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

The right generalized eigenvector v(j) corresponding to the generalized eigenvalue lambda(j) of (A,B) satisfies

             A * v(j) = lambda(j) * B * v(j).

The left generalized eigenvector u(j) corresponding to the generalized eigenvalues lambda(j) of (A,B) satisfies

             u(j)**H * A = lambda(j) * u(j)**H * B

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

ARGUMENTS

• JOBVL (input)
  

   = 'N':  do not compute the left generalized eigenvectors;

   = 'V':  compute the left generalized eigenvectors.

• JOBVR (input)
  

   = 'N':  do not compute the right generalized eigenvectors;

   = 'V':  compute the right generalized eigenvectors.

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

• A (input/output)
  On entry, the matrix A in the pair (A,B). On exit, A has been overwritten.

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

• B (input/output)
  On entry, the matrix B in the pair (A,B). On exit, B has been overwritten.

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

• ALPHA (output)
  On exit, ALPHA(j)/BETA(j), j =1,...,N, will be the generalized eigenvalues.

  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. However, ALPHA will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).

• BETA (output)
  See description of ALPHA.

• VL (output)
  If JOBVL = 'V', the left generalized eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. Each eigenvector will be scaled so the largest component will have abs(real part) + abs(imag. part) = 1. Not referenced if JOBVL = 'N'.

• LDVL (input)
  The leading dimension of the matrix VL. LDVL > = 1, and if JOBVL = 'V', LDVL > = N.

• VR (output)
  If JOBVR = 'V', the right generalized eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. Each eigenvector will be scaled so the largest component will have abs(real part) + abs(imag. part) = 1. Not referenced if JOBVR = 'N'.

• LDVR (input)
  The leading dimension of the matrix VR. LDVR > = 1, and if JOBVR = 'V', LDVR > = 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)

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value.

   =1,...,N:
  The QZ iteration failed.  No eigenvectors have been
  calculated, but ALPHA(j) and BETA(j) should be
  correct for j =INFO+1,...,N.
   > N:   =N+1: other then QZ iteration failed in SHGEQZ,

   =N+2: error return from STGEVC.