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
zpteqr.f(3) LAPACK zpteqr.f(3)

zpteqr.f -


subroutine zpteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO)
 
ZPTEQR

ZPTEQR
Purpose:
 ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a
 symmetric positive definite tridiagonal matrix by first factoring the
 matrix using DPTTRF and then calling ZBDSQR to compute the singular
 values of the bidiagonal factor.
This routine computes the eigenvalues of the positive definite tridiagonal matrix to high relative accuracy. This means that if the eigenvalues range over many orders of magnitude in size, then the small eigenvalues and corresponding eigenvectors will be computed more accurately than, for example, with the standard QR method.
The eigenvectors of a full or band positive definite Hermitian matrix can also be found if ZHETRD, ZHPTRD, or ZHBTRD has been used to reduce this matrix to tridiagonal form. (The reduction to tridiagonal form, however, may preclude the possibility of obtaining high relative accuracy in the small eigenvalues of the original matrix, if these eigenvalues range over many orders of magnitude.)
Parameters:
COMPZ
          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'V':  Compute eigenvectors of original Hermitian
                  matrix also.  Array Z contains the unitary matrix
                  used to reduce the original matrix to tridiagonal
                  form.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
N
          N is INTEGER
          The order of the matrix.  N >= 0.
D
          D is DOUBLE PRECISION array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal matrix.
          On normal exit, D contains the eigenvalues, in descending
          order.
E
          E is DOUBLE PRECISION array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix.
          On exit, E has been destroyed.
Z
          Z is COMPLEX*16 array, dimension (LDZ, N)
          On entry, if COMPZ = 'V', the unitary matrix used in the
          reduction to tridiagonal form.
          On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
          original Hermitian matrix;
          if COMPZ = 'I', the orthonormal eigenvectors of the
          tridiagonal matrix.
          If INFO > 0 on exit, Z contains the eigenvectors associated
          with only the stored eigenvalues.
          If  COMPZ = 'N', then Z is not referenced.
LDZ
          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          COMPZ = 'V' or 'I', LDZ >= max(1,N).
WORK
          WORK is DOUBLE PRECISION array, dimension (4*N)
INFO
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if INFO = i, and i is:
                <= N  the Cholesky factorization of the matrix could
                      not be performed because the i-th principal minor
                      was not positive definite.
                > N   the SVD algorithm failed to converge;
                      if INFO = N+i, i off-diagonal elements of the
                      bidiagonal factor did not converge to zero.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Definition at line 146 of file zpteqr.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.