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

NAME

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

SYNOPSIS

  SUBROUTINE SGEEV( 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
  REAL A(LDA,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*), WORK(*)

  SUBROUTINE SGEEV_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
  REAL 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, DIMENSION(:) :: WR, WI, WORK
  REAL, 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, DIMENSION(:) :: WR, WI, WORK
  REAL, DIMENSION(:,:) :: A, VL, VR

C INTERFACE

#include <sunperf.h>

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

void sgeev_64(char jobvl, char jobvr, long n, float *a, long lda, float *wr, float *wi, float *vl, long ldvl, float *vr, long ldvr, long *info);

PURPOSE

sgeev computes for an N-by-N real 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 A 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).

• 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 (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. 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)
  

   = 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 i+1:N of WR and WI contain eigenvalues which
  have converged.