GSP
Quick Navigator

Search Site

Unix VPS
A - Starter
B - Basic
C - Preferred
D - Commercial
MPS - Dedicated
Previous VPSs
* Sign Up! *

Support
Contact Us
Online Help
Handbooks
Domain Status
Man Pages

FAQ
Virtual Servers
Pricing
Billing
Technical

Network
Facilities
Connectivity
Topology Map

Miscellaneous
Server Agreement
Year 2038
Credits
 

USA Flag

 

 

Man Pages
zgegv.f(3) LAPACK zgegv.f(3)

zgegv.f -


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

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 This routine is deprecated and has been replaced by routine ZGGEV.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 (non-zero) 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).
JOBVR
          JOBVR is CHARACTER*1
          = 'N':  do not compute the right generalized eigenvectors;
          = 'V':  compute the right generalized eigenvectors (returned
                  in VR).
N
          N is INTEGER
          The order of the matrices A, B, VL, and VR.  N >= 0.
A
          A 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.
LDA
          LDA is INTEGER
          The leading dimension of A.  LDA >= max(1,N).
B
          B 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.
LDB
          LDB is INTEGER
          The leading dimension of B.  LDB >= max(1,N).
ALPHA
          ALPHA is COMPLEX*16 array, dimension (N)
          The complex scalars alpha that define the eigenvalues of
          GNEP.
BETA
          BETA 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 j-th 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.
VL
          VL 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'.
LDVL
          LDVL is INTEGER
          The leading dimension of the matrix VL. LDVL >= 1, and
          if JOBVL = 'V', LDVL >= N.
VR
          VR 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'.
LDVR
          LDVR is INTEGER
          The leading dimension of the matrix VR. LDVR >= 1, and
          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.
          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.
RWORK
          RWORK is DOUBLE PRECISION array, dimension (8*N)
INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th 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.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

Search for    or go to Top of page |  Section 3 |  Main Index

Powered by GSP Visit the GSP FreeBSD Man Page Interface.
Output converted with ManDoc.