ZGEEV(l) LAPACK driver routine (version 1.1) ZGEEV(l) NAME ZGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigen- values and, optionally, the left and/or right eigenvectors SYNOPSIS SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) CHARACTER JOBVL, JOBVR INTEGER INFO, LDA, LDVL, LDVR, LWORK, N DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), W( * ), WORK( * ) PURPOSE ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. The left eigenvectors of A are the same as the right eigenvectors of A**H. If u(j) and v(j) are the left and right eigenvectors, respectively, corresponding to the eigenvalue lambda(j), then (u(j)**H)*A = lambda(j)*(u(j)**H) and A*v(j) = lambda(j) * v(j). The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real. ARGUMENTS JOBVL (input) CHARACTER*1 = 'N': left eigenvectors of A are not computed; = 'V': left eigenvectors of are computed. JOBVR (input) CHARACTER*1 = 'N': right eigenvectors of A are not computed; = 'V': right eigenvectors of A are computed. N (input) INTEGER The order of the matrix A. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the N-by-N 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*16 array, dimension (N) W contains the computed eigenvalues. VL (output) 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 eigen- values. If JOBVL = 'N', VL is not referenced. u(j) = VL(:,j), the j-th column of VL. LDVL (input) INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N. VR (output) 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 eigen- values. If JOBVR = 'N', VR is not referenced. v(j) = VR(:,j), the j-th column of VR. LDVR (input) INTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N. WORK (workspace/output) COMPLEX*16 array, dimension (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. RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) INFO (output) 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.

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