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

NAME

cgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

SYNOPSIS

  SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, 
 *      WORK, LDWORK, WORK2, INFO)
  CHARACTER * 1 JOBVL, JOBVR
  COMPLEX A(LDA,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER N, LDA, LDVL, LDVR, LDWORK, INFO
  REAL WORK2(*)

  SUBROUTINE CGEEV_64( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, 
 *      WORK, LDWORK, WORK2, INFO)
  CHARACTER * 1 JOBVL, JOBVR
  COMPLEX A(LDA,*), W(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
  INTEGER*8 N, LDA, LDVL, LDVR, LDWORK, INFO
  REAL WORK2(*)

F95 INTERFACE

  SUBROUTINE GEEV( JOBVL, JOBVR, [N], A, [LDA], W, VL, [LDVL], VR, 
 *       [LDVR], [WORK], [LDWORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: JOBVL, JOBVR
  COMPLEX, DIMENSION(:) :: W, WORK
  COMPLEX, DIMENSION(:,:) :: A, VL, VR
  INTEGER :: N, LDA, LDVL, LDVR, LDWORK, INFO
  REAL, DIMENSION(:) :: WORK2

  SUBROUTINE GEEV_64( JOBVL, JOBVR, [N], A, [LDA], W, VL, [LDVL], VR, 
 *       [LDVR], [WORK], [LDWORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: JOBVL, JOBVR
  COMPLEX, DIMENSION(:) :: W, WORK
  COMPLEX, DIMENSION(:,:) :: A, VL, VR
  INTEGER(8) :: N, LDA, LDVL, LDVR, LDWORK, INFO
  REAL, DIMENSION(:) :: WORK2

C INTERFACE

#include <sunperf.h>

void cgeev(char jobvl, char jobvr, int n, complex *a, int lda, complex *w, complex *vl, int ldvl, complex *vr, int ldvr, int *info);

void cgeev_64(char jobvl, char jobvr, long n, complex *a, long lda, complex *w, complex *vl, long ldvl, complex *vr, long ldvr, long *info);

PURPOSE

cgeev computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

The right eigenvector v(j) of A satisfies

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

where lambda(j) is its eigenvalue.

The left eigenvector u(j) of A satisfies

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

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

The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.

ARGUMENTS

• JOBVL (input)
  

   = 'N': left eigenvectors of A are not computed;

   = 'V': left eigenvectors of are computed.

• JOBVR (input)
  

   = 'N': right eigenvectors of A are not computed;

   = 'V': right eigenvectors of A are computed.

• N (input)
  The order of the matrix A. N > = 0.

• A (input/output)
  On entry, the N-by-N matrix A. On exit, A has been overwritten.

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

• W (output)
  W contains the computed eigenvalues.

• VL (output)
  If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If JOBVL = 'N', VL is not referenced. u(j) = VL(:,j), the j-th column of VL.

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

• VR (output)
  If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If JOBVR = 'N', VR is not referenced. v(j) = VR(:,j), the j-th column of VR.

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

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

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

  If LDWORK = -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 LDWORK is issued by XERBLA.

• WORK2 (workspace)
  dimension(2*N)

• INFO (output)
  

   = 0:  successful exit

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

   > 0:  if INFO  = i, the QR algorithm failed to compute all the
  eigenvalues, and no eigenvectors have been computed;
  elements and i+1:N of W contain eigenvalues which have
  converged.