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
zhgeqz.f(3) LAPACK zhgeqz.f(3)

zhgeqz.f -


subroutine zhgeqz (JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, RWORK, INFO)
 
ZHGEQZ

ZHGEQZ
Purpose:
 ZHGEQZ computes the eigenvalues of a complex matrix pair (H,T),
 where H is an upper Hessenberg matrix and T is upper triangular,
 using the single-shift QZ method.
 Matrix pairs of this type are produced by the reduction to
 generalized upper Hessenberg form of a complex matrix pair (A,B):
 
    A = Q1*H*Z1**H,  B = Q1*T*Z1**H,
 
 as computed by ZGGHRD.
 
 If JOB='S', then the Hessenberg-triangular pair (H,T) is
 also reduced to generalized Schur form,
 
    H = Q*S*Z**H,  T = Q*P*Z**H,
 
 where Q and Z are unitary matrices and S and P are upper triangular.
 
 Optionally, the unitary matrix Q from the generalized Schur
 factorization may be postmultiplied into an input matrix Q1, and the
 unitary matrix Z may be postmultiplied into an input matrix Z1.
 If Q1 and Z1 are the unitary matrices from ZGGHRD that reduced
 the matrix pair (A,B) to generalized Hessenberg form, then the output
 matrices Q1*Q and Z1*Z are the unitary factors from the generalized
 Schur factorization of (A,B):
 
    A = (Q1*Q)*S*(Z1*Z)**H,  B = (Q1*Q)*P*(Z1*Z)**H.
 
 To avoid overflow, eigenvalues of the matrix pair (H,T)
 (equivalently, of (A,B)) are computed as a pair of complex values
 (alpha,beta).  If beta is nonzero, lambda = alpha / beta is an
 eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP)
    A*x = lambda*B*x
 and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the
 alternate form of the GNEP
    mu*A*y = B*y.
 The values of alpha and beta for the i-th eigenvalue can be read
 directly from the generalized Schur form:  alpha = S(i,i),
 beta = P(i,i).
Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), pp. 241--256.
Parameters:
JOB
          JOB is CHARACTER*1
          = 'E': Compute eigenvalues only;
          = 'S': Computer eigenvalues and the Schur form.
COMPQ
          COMPQ is CHARACTER*1
          = 'N': Left Schur vectors (Q) are not computed;
          = 'I': Q is initialized to the unit matrix and the matrix Q
                 of left Schur vectors of (H,T) is returned;
          = 'V': Q must contain a unitary matrix Q1 on entry and
                 the product Q1*Q is returned.
COMPZ
          COMPZ is CHARACTER*1
          = 'N': Right Schur vectors (Z) are not computed;
          = 'I': Q is initialized to the unit matrix and the matrix Z
                 of right Schur vectors of (H,T) is returned;
          = 'V': Z must contain a unitary matrix Z1 on entry and
                 the product Z1*Z is returned.
N
          N is INTEGER
          The order of the matrices H, T, Q, and Z.  N >= 0.
ILO
          ILO is INTEGER
IHI
          IHI is INTEGER
          ILO and IHI mark the rows and columns of H which are in
          Hessenberg form.  It is assumed that A is already upper
          triangular in rows and columns 1:ILO-1 and IHI+1:N.
          If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0.
H
          H is COMPLEX*16 array, dimension (LDH, N)
          On entry, the N-by-N upper Hessenberg matrix H.
          On exit, if JOB = 'S', H contains the upper triangular
          matrix S from the generalized Schur factorization.
          If JOB = 'E', the diagonal of H matches that of S, but
          the rest of H is unspecified.
LDH
          LDH is INTEGER
          The leading dimension of the array H.  LDH >= max( 1, N ).
T
          T is COMPLEX*16 array, dimension (LDT, N)
          On entry, the N-by-N upper triangular matrix T.
          On exit, if JOB = 'S', T contains the upper triangular
          matrix P from the generalized Schur factorization.
          If JOB = 'E', the diagonal of T matches that of P, but
          the rest of T is unspecified.
LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max( 1, N ).
ALPHA
          ALPHA is COMPLEX*16 array, dimension (N)
          The complex scalars alpha that define the eigenvalues of
          GNEP.  ALPHA(i) = S(i,i) in the generalized Schur
          factorization.
BETA
          BETA is COMPLEX*16 array, dimension (N)
          The real non-negative scalars beta that define the
          eigenvalues of GNEP.  BETA(i) = P(i,i) in the generalized
          Schur factorization.
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.
Q
          Q is COMPLEX*16 array, dimension (LDQ, N)
          On entry, if COMPZ = 'V', the unitary matrix Q1 used in the
          reduction of (A,B) to generalized Hessenberg form.
          On exit, if COMPZ = 'I', the unitary matrix of left Schur
          vectors of (H,T), and if COMPZ = 'V', the unitary matrix of
          left Schur vectors of (A,B).
          Not referenced if COMPZ = 'N'.
LDQ
          LDQ is INTEGER
          The leading dimension of the array Q.  LDQ >= 1.
          If COMPQ='V' or 'I', then LDQ >= N.
Z
          Z is COMPLEX*16 array, dimension (LDZ, N)
          On entry, if COMPZ = 'V', the unitary matrix Z1 used in the
          reduction of (A,B) to generalized Hessenberg form.
          On exit, if COMPZ = 'I', the unitary matrix of right Schur
          vectors of (H,T), and if COMPZ = 'V', the unitary matrix of
          right Schur vectors of (A,B).
          Not referenced if COMPZ = 'N'.
LDZ
          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1.
          If COMPZ='V' or 'I', then LDZ >= 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,N).
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 (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 did not converge.  (H,T) is not
                     in Schur form, but ALPHA(i) and BETA(i),
                     i=INFO+1,...,N should be correct.
          = N+1,...,2*N: the shift calculation failed.  (H,T) is not
                     in Schur form, but ALPHA(i) and BETA(i),
                     i=INFO-N+1,...,N should be correct.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
Further Details:
  We assume that complex ABS works as long as its value is less than
  overflow.
Definition at line 283 of file zhgeqz.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.