cgeev (l)  Linux Manuals
cgeev: computes for an NbyN complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
NAME
CGEEV  computes for an NbyN complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectorsSYNOPSIS
 SUBROUTINE CGEEV(
 JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )
 CHARACTER JOBVL, JOBVR
 INTEGER INFO, LDA, LDVL, LDVR, LWORK, N
 REAL RWORK( * )
 COMPLEX A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ), WORK( * )
PURPOSE
CGEEV computes for an NbyN complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. The right eigenvector v(j) of A satisfieswhere lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
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) CHARACTER*1

= aqNaq: left eigenvectors of A are not computed;
= aqVaq: left eigenvectors of are computed.  JOBVR (input) CHARACTER*1

= aqNaq: right eigenvectors of A are not computed;
= aqVaq: right eigenvectors of A are computed.  N (input) INTEGER
 The order of the matrix A. N >= 0.
 A (input/output) COMPLEX array, dimension (LDA,N)
 On entry, the NbyN matrix A. On exit, A has been overwritten.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,N).
 W (output) COMPLEX array, dimension (N)
 W contains the computed eigenvalues.
 VL (output) COMPLEX array, dimension (LDVL,N)
 If JOBVL = aqVaq, the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If JOBVL = aqNaq, VL is not referenced. u(j) = VL(:,j), the jth column of VL.
 LDVL (input) INTEGER
 The leading dimension of the array VL. LDVL >= 1; if JOBVL = aqVaq, LDVL >= N.
 VR (output) COMPLEX array, dimension (LDVR,N)
 If JOBVR = aqVaq, the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If JOBVR = aqNaq, VR is not referenced. v(j) = VR(:,j), the jth column of VR.
 LDVR (input) INTEGER
 The leading dimension of the array VR. LDVR >= 1; if JOBVR = aqVaq, LDVR >= N.
 WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 LWORK (input) 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 (workspace) REAL array, dimension (2*N)
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith 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.