[ новости /+++ | форум | теги | ]

NAME
     slaed1 - compute  the  updated  eigensystem  of  a  diagonal
     matrix after modification by a rank-one symmetric matrix

SYNOPSIS
     SUBROUTINE SLAED1( N, D, Q, LDQ, INDXQ, RHO,  CUTPNT,  WORK,
               IWORK, INFO )

     INTEGER CUTPNT, INFO, LDQ, N

     REAL RHO

     INTEGER INDXQ( * ), IWORK( * )

     REAL D( * ), Q( LDQ, * ), WORK( * )



     #include <sunperf.h>

     void slaed1(int n, float *d, float *q, int ldq, int  *indxq,
               float srho, int cutpnt, int *info) ;

PURPOSE
     SLAED1 computes the updated eigensystem of a diagonal matrix
     after  modification  by  a  rank-one symmetric matrix.  This
     routine is used only for the eigenproblem which requires all
     eigenvalues   and  eigenvectors  of  a  tridiagonal  matrix.
     SLAED7 handles the case in which eigenvalues only or  eigen-
     values  and  eigenvectors  of a full symmetric matrix (which
     was reduced to tridiagonal form) are desired.

       T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) *  D(out)
     * Q'(out)

     where Z = Q'u, u is a vector of length N with  ones  in  the
     CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.

     The eigenvectors of the original matrix are stored in Q, and
     the  eigenvalues  are in D.  The algorithm consists of three
     stages:

     The first stage consists of deflating the size of the  prob-
     lem  when  there  are  multiple eigenvalues or if there is a
     zero in the Z vector.  For each such occurence the dimension
     of  the  secular  equation  problem is reduced by one.  This
     stage is performed by the routine SLAED2.

     The second stage consists of calculating the updated  eigen-
     values.  This  is  done  by finding the roots of the secular
     equation via the routine SLAED4 (as called by SLAED3).  This
     routine  also  calculates  the  eigenvectors  of the current
     problem.

     The final stage consists of computing the updated  eigenvec-
     tors  directly using the updated eigenvalues.  The eigenvec-
     tors for the current problem are multiplied with the  eigen-
     vectors from the overall problem.


ARGUMENTS
     N         (input) INTEGER
               The dimension of the symmetric tridiagonal matrix.
               N >= 0.

     D         (input/output) REAL array, dimension (N)
               On entry, the eigenvalues of the  rank-1-perturbed
               matrix.   On exit, the eigenvalues of the repaired
               matrix.

     Q         (input/output) REAL array, dimension (LDQ,N)
               On entry, the eigenvectors of the rank-1-perturbed
               matrix.  On exit, the eigenvectors of the repaired
               tridiagonal matrix.

     LDQ       (input) INTEGER
               The leading dimension of  the  array  Q.   LDQ  >=
               max(1,N).

     INDXQ     (input/output) INTEGER array, dimension (N)
               On entry, the permutation which  separately  sorts
               the two subproblems in D into ascending order.  On
               exit, the permutation which will  reintegrate  the
               subproblems back into sorted order, i.e. D( INDXQ(
               I = 1, N ) ) will be in ascending order.

     RHO       (input) REAL
               The subdiagonal entry used to  create  the  rank-1
               modification.

               CUTPNT (input) INTEGER The location  of  the  last
               eigenvalue in the leading sub-matrix.  min(1,N) <=
               CUTPNT <= N.

     WORK      (workspace) REAL array, dimension (3*N+2*N**2)

     IWORK     (workspace) INTEGER array, dimension (4*N)

     INFO      (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.
               > 0:  if INFO = 1, an eigenvalue did not converge

Партнёры:

Хостинг: