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zgeev.f(3) LAPACK zgeev.f(3)

zgeev.f -


subroutine zgeev (JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
 
ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Purpose:
 ZGEEV 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.
Parameters:
JOBVL
          JOBVL is CHARACTER*1
          = 'N': left eigenvectors of A are not computed;
          = 'V': left eigenvectors of are computed.
JOBVR
          JOBVR is CHARACTER*1
          = 'N': right eigenvectors of A are not computed;
          = 'V': right eigenvectors of A are computed.
N
          N is INTEGER
          The order of the matrix A. N >= 0.
A
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the N-by-N matrix A.
          On exit, A has been overwritten.
LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
W
          W is COMPLEX*16 array, dimension (N)
          W contains the computed eigenvalues.
VL
          VL is COMPLEX*16 array, dimension (LDVL,N)
          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
          LDVL is INTEGER
          The leading dimension of the array VL.  LDVL >= 1; if
          JOBVL = 'V', LDVL >= N.
VR
          VR is COMPLEX*16 array, dimension (LDVR,N)
          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
          LDVR is INTEGER
          The leading dimension of the array VR.  LDVR >= 1; if
          JOBVR = 'V', LDVR >= N.
WORK
          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
          LWORK is INTEGER
          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
          RWORK is DOUBLE PRECISION array, dimension (2*N)
INFO
          INFO is INTEGER
          = 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 177 of file zgeev.f.

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