NAME

SYNOPSIS

  SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, 
 *      LDVR, WORK, LDWORK, INFO)
  CHARACTER * 1 JOBVL, JOBVR
  INTEGER N, LDA, LDVL, LDVR, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
 
  SUBROUTINE DGEEV_64( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR, 
 *      LDVR, WORK, LDWORK, INFO)
  CHARACTER * 1 JOBVL, JOBVR
  INTEGER*8 N, LDA, LDVL, LDVR, LDWORK, INFO
  DOUBLE PRECISION A(LDA,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*), WORK(*)
 

F95 INTERFACE

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

C INTERFACE

void dgeev(char jobvl, char jobvr, int n, double *a, int lda, double *wr, double *wi, double *vl, int ldvl, double *vr, int ldvr, int *info);

void dgeev_64(char jobvl, char jobvr, long n, double *a, long lda, double *wr, double *wi, double *vl, long ldvl, double *vr, long ldvr, long *info);

PURPOSE

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)

* JOBVR (input)

* 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).

* WR (output)

WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.

* WI (output)

See the description for WR.

* 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. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and

u(j+1) = VL(:,j) - i*VL(:,j+1).

* LDVL (input)

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

* VR (input)

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. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and

v(j+1) = VR(:,j) - i*VR(:,j+1).

* 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(1,3*N), and if JOBVL = 'V' or JOBVR = 'V', LDWORK >= 4*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.

* INFO (output)