zgegv (3)  Linux Manuals
NAME
zgegv.f 
SYNOPSIS
Functions/Subroutines
subroutine zgegv (JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO)
ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Function/Subroutine Documentation
subroutine zgegv (characterJOBVL, characterJOBVR, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )ALPHA, complex*16, dimension( * )BETA, complex*16, dimension( ldvl, * )VL, integerLDVL, complex*16, dimension( ldvr, * )VR, integerLDVR, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)
ZGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
Purpose:

This routine is deprecated and has been replaced by routine ZGGEV. ZGEGV computes the eigenvalues and, optionally, the left and/or right eigenvectors of a complex matrix pair (A,B). Given two square matrices A and B, the generalized nonsymmetric eigenvalue problem (GNEP) is to find the eigenvalues lambda and corresponding (nonzero) eigenvectors x such that A*x = lambda*B*x. An alternate form is to find the eigenvalues mu and corresponding eigenvectors y such that mu*A*y = B*y. These two forms are equivalent with mu = 1/lambda and x = y if neither lambda nor mu is zero. In order to deal with the case that lambda or mu is zero or small, two values alpha and beta are returned for each eigenvalue, such that lambda = alpha/beta and mu = beta/alpha. The vectors x and y in the above equations are right eigenvectors of the matrix pair (A,B). Vectors u and v satisfying u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B are left eigenvectors of (A,B). Note: this routine performs "full balancing" on A and B
Parameters:

JOBVL
JOBVL is CHARACTER*1 = 'N': do not compute the left generalized eigenvectors; = 'V': compute the left generalized eigenvectors (returned in VL).
JOBVRJOBVR is CHARACTER*1 = 'N': do not compute the right generalized eigenvectors; = 'V': compute the right generalized eigenvectors (returned in VR).
NN is INTEGER The order of the matrices A, B, VL, and VR. N >= 0.
AA is COMPLEX*16 array, dimension (LDA, N) On entry, the matrix A. If JOBVL = 'V' or JOBVR = 'V', then on exit A contains the Schur form of A from the generalized Schur factorization of the pair (A,B) after balancing. If no eigenvectors were computed, then only the diagonal elements of the Schur form will be correct. See ZGGHRD and ZHGEQZ for details.
LDALDA is INTEGER The leading dimension of A. LDA >= max(1,N).
BB is COMPLEX*16 array, dimension (LDB, N) On entry, the matrix B. If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the upper triangular matrix obtained from B in the generalized Schur factorization of the pair (A,B) after balancing. If no eigenvectors were computed, then only the diagonal elements of B will be correct. See ZGGHRD and ZHGEQZ for details.
LDBLDB is INTEGER The leading dimension of B. LDB >= max(1,N).
ALPHAALPHA is COMPLEX*16 array, dimension (N) The complex scalars alpha that define the eigenvalues of GNEP.
BETABETA is COMPLEX*16 array, dimension (N) The complex scalars beta that define the eigenvalues of GNEP. Together, the quantities alpha = ALPHA(j) and beta = BETA(j) represent the jth eigenvalue of the matrix pair (A,B), in one of the forms lambda = alpha/beta or mu = beta/alpha. Since either lambda or mu may overflow, they should not, in general, be computed.
VLVL is COMPLEX*16 array, dimension (LDVL,N) If JOBVL = 'V', the left eigenvectors u(j) are stored in the columns of VL, in the same order as their eigenvalues. Each eigenvector is scaled so that its largest component has abs(real part) + abs(imag. part) = 1, except for eigenvectors corresponding to an eigenvalue with alpha = beta = 0, which are set to zero. Not referenced if JOBVL = 'N'.
LDVLLDVL is INTEGER The leading dimension of the matrix VL. LDVL >= 1, and if JOBVL = 'V', LDVL >= N.
VRVR is COMPLEX*16 array, dimension (LDVR,N) If JOBVR = 'V', the right eigenvectors x(j) are stored in the columns of VR, in the same order as their eigenvalues. Each eigenvector is scaled so that its largest component has abs(real part) + abs(imag. part) = 1, except for eigenvectors corresponding to an eigenvalue with alpha = beta = 0, which are set to zero. Not referenced if JOBVR = 'N'.
LDVRLDVR is INTEGER The leading dimension of the matrix VR. LDVR >= 1, and if JOBVR = 'V', LDVR >= N.
WORKWORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,2*N). For good performance, LWORK must generally be larger. To compute the optimal value of LWORK, call ILAENV to get blocksizes (for ZGEQRF, ZUNMQR, and ZUNGQR.) Then compute: NB  MAX of the blocksizes for ZGEQRF, ZUNMQR, and ZUNGQR; The optimal LWORK is MAX( 2*N, N*(NB+1) ). 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.
RWORKRWORK is DOUBLE PRECISION array, dimension (8*N)
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. =1,...,N: The QZ iteration failed. No eigenvectors have been calculated, but ALPHA(j) and BETA(j) should be correct for j=INFO+1,...,N. > N: errors that usually indicate LAPACK problems: =N+1: error return from ZGGBAL =N+2: error return from ZGEQRF =N+3: error return from ZUNMQR =N+4: error return from ZUNGQR =N+5: error return from ZGGHRD =N+6: error return from ZHGEQZ (other than failed iteration) =N+7: error return from ZTGEVC =N+8: error return from ZGGBAK (computing VL) =N+9: error return from ZGGBAK (computing VR) =N+10: error return from ZLASCL (various calls)
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Further Details:

Balancing  This driver calls ZGGBAL to both permute and scale rows and columns of A and B. The permutations PL and PR are chosen so that PL*A*PR and PL*B*R will be upper triangular except for the diagonal blocks A(i:j,i:j) and B(i:j,i:j), with i and j as close together as possible. The diagonal scaling matrices DL and DR are chosen so that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to one (except for the elements that start out zero.) After the eigenvalues and eigenvectors of the balanced matrices have been computed, ZGGBAK transforms the eigenvectors back to what they would have been (in perfect arithmetic) if they had not been balanced. Contents of A and B on Exit        If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or both), then on exit the arrays A and B will contain the complex Schur form[*] of the "balanced" versions of A and B. If no eigenvectors are computed, then only the diagonal blocks will be correct. [*] In other words, upper triangular form.
Definition at line 282 of file zgegv.f.
Author
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