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
zlahqr.f(3) LAPACK zlahqr.f(3)

zlahqr.f -


subroutine zlahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO)
 
ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.

ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.
Purpose:
    ZLAHQR is an auxiliary routine called by CHSEQR to update the
    eigenvalues and Schur decomposition already computed by CHSEQR, by
    dealing with the Hessenberg submatrix in rows and columns ILO to
    IHI.
Parameters:
WANTT
          WANTT is LOGICAL
          = .TRUE. : the full Schur form T is required;
          = .FALSE.: only eigenvalues are required.
WANTZ
          WANTZ is LOGICAL
          = .TRUE. : the matrix of Schur vectors Z is required;
          = .FALSE.: Schur vectors are not required.
N
          N is INTEGER
          The order of the matrix H.  N >= 0.
ILO
          ILO is INTEGER
IHI
          IHI is INTEGER
          It is assumed that H is already upper triangular in rows and
          columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
          ZLAHQR works primarily with the Hessenberg submatrix in rows
          and columns ILO to IHI, but applies transformations to all of
          H if WANTT is .TRUE..
          1 <= ILO <= max(1,IHI); IHI <= N.
H
          H is COMPLEX*16 array, dimension (LDH,N)
          On entry, the upper Hessenberg matrix H.
          On exit, if INFO is zero and if WANTT is .TRUE., then H
          is upper triangular in rows and columns ILO:IHI.  If INFO
          is zero and if WANTT is .FALSE., then the contents of H
          are unspecified on exit.  The output state of H in case
          INF is positive is below under the description of INFO.
LDH
          LDH is INTEGER
          The leading dimension of the array H. LDH >= max(1,N).
W
          W is COMPLEX*16 array, dimension (N)
          The computed eigenvalues ILO to IHI are stored in the
          corresponding elements of W. If WANTT is .TRUE., the
          eigenvalues are stored in the same order as on the diagonal
          of the Schur form returned in H, with W(i) = H(i,i).
ILOZ
          ILOZ is INTEGER
IHIZ
          IHIZ is INTEGER
          Specify the rows of Z to which transformations must be
          applied if WANTZ is .TRUE..
          1 <= ILOZ <= ILO; IHI <= IHIZ <= N.
Z
          Z is COMPLEX*16 array, dimension (LDZ,N)
          If WANTZ is .TRUE., on entry Z must contain the current
          matrix Z of transformations accumulated by CHSEQR, and on
          exit Z has been updated; transformations are applied only to
          the submatrix Z(ILOZ:IHIZ,ILO:IHI).
          If WANTZ is .FALSE., Z is not referenced.
LDZ
          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= max(1,N).
INFO
          INFO is INTEGER
           =   0: successful exit
          .GT. 0: if INFO = i, ZLAHQR failed to compute all the
                  eigenvalues ILO to IHI in a total of 30 iterations
                  per eigenvalue; elements i+1:ihi of W contain
                  those eigenvalues which have been successfully
                  computed.
If INFO .GT. 0 and WANTT is .FALSE., then on exit, the remaining unconverged eigenvalues are the eigenvalues of the upper Hessenberg matrix rows and columns ILO thorugh INFO of the final, output value of H.
If INFO .GT. 0 and WANTT is .TRUE., then on exit (*) (initial value of H)*U = U*(final value of H) where U is an orthognal matrix. The final value of H is upper Hessenberg and triangular in rows and columns INFO+1 through IHI.
If INFO .GT. 0 and WANTZ is .TRUE., then on exit (final value of Z) = (initial value of Z)*U where U is the orthogonal matrix in (*) (regardless of the value of WANTT.)
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
     02-96 Based on modifications by
     David Day, Sandia National Laboratory, USA
12-04 Further modifications by Ralph Byers, University of Kansas, USA This is a modified version of ZLAHQR from LAPACK version 3.0. It is (1) more robust against overflow and underflow and (2) adopts the more conservative Ahues & Tisseur stopping criterion (LAWN 122, 1997).
Definition at line 195 of file zlahqr.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.