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RedHat 9 (Linux i386) - man page for slaed3 (redhat section l)

SLAED3(l)					)					SLAED3(l)

NAME
       SLAED3  -  find	the  roots of the secular equation, as defined by the values in D, W, and
       RHO, between 1 and K

SYNOPSIS
       SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO )

	   INTEGER	  INFO, K, LDQ, N, N1

	   REAL 	  RHO

	   INTEGER	  CTOT( * ), INDX( * )

	   REAL 	  D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), S( * ), W( * )

PURPOSE
       SLAED3 finds the roots of the secular equation, as defined by the values in D, W, and RHO,
       between	1  and K. It makes the appropriate calls to SLAED4 and then updates the eigenvec-
       tors by multiplying the matrix of eigenvectors of the pair of eigensystems being  combined
       by the matrix of eigenvectors of the K-by-K system which is solved here.

       This  code  makes  very	mild assumptions about floating point arithmetic. It will work on
       machines with a guard digit in add/subtract, or on those  binary  machines  without  guard
       digits  which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.  It could con-
       ceivably fail on hexadecimal or decimal machines without guard  digits,	but  we  know  of
       none.

ARGUMENTS
       K       (input) INTEGER
	       The number of terms in the rational function to be solved by SLAED4.  K >= 0.

       N       (input) INTEGER
	       The  number  of rows and columns in the Q matrix.  N >= K (deflation may result in
	       N>K).

       N1      (input) INTEGER
	       The location of the last eigenvalue in the leading submatrix.  min(1,N) <=  N1  <=
	       N/2.

       D       (output) REAL array, dimension (N)
	       D(I) contains the updated eigenvalues for 1 <= I <= K.

       Q       (output) REAL array, dimension (LDQ,N)
	       Initially the first K columns are used as workspace.  On output the columns 1 to K
	       contain the updated eigenvectors.

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

       RHO     (input) REAL
	       The value of the parameter in the rank one update equation.  RHO >= 0 required.

       DLAMDA  (input/output) REAL array, dimension (K)
	       The first K elements of this array contain the old roots of the deflated  updating
	       problem.  These are the poles of the secular equation. May be changed on output by
	       having lowest order bit set to zero on Cray X-MP, Cray Y-MP, Cray-2, or Cray C-90,
	       as described above.

       Q2      (input) REAL array, dimension (LDQ2, N)
	       The  first  K columns of this matrix contain the non-deflated eigenvectors for the
	       split problem.

       INDX    (input) INTEGER array, dimension (N)
	       The permutation used to arrange the columns of the deflated Q  matrix  into  three
	       groups  (see  SLAED2).  The rows of the eigenvectors found by SLAED4 must be like-
	       wise permuted before the matrix multiply can take place.

       CTOT    (input) INTEGER array, dimension (4)
	       A count of the total number of the various types of columns in Q, as described  in
	       INDX.  The fourth column type is any column which has been deflated.

       W       (input/output) REAL array, dimension (K)
	       The  first  K  elements	of  this  array  contain the components of the deflation-
	       adjusted updating vector. Destroyed on output.

       S       (workspace) REAL array, dimension (N1 + 1)*K
	       Will contain the eigenvectors of the repaired matrix which will be  multiplied  by
	       the previously accumulated eigenvectors to update the system.

       LDS     (input) INTEGER
	       The leading dimension of S.  LDS >= max(1,K).

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

FURTHER DETAILS
       Based on contributions by
	  Jeff Rutter, Computer Science Division, University of California
	  at Berkeley, USA
       Modified by Francoise Tisseur, University of Tennessee.

LAPACK version 3.0			   15 June 2000 				SLAED3(l)


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