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SLAED9(l)					)					SLAED9(l)

NAME
       SLAED9  -  find	the  roots of the secular equation, as defined by the values in D, Z, and
       RHO, between KSTART and KSTOP

SYNOPSIS
       SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO )

	   INTEGER	  INFO, K, KSTART, KSTOP, LDQ, LDS, N

	   REAL 	  RHO

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

PURPOSE
       SLAED9 finds the roots of the secular equation, as defined by the values in D, Z, and RHO,
       between KSTART and KSTOP. It makes the appropriate calls to SLAED4 and then stores the new
       matrix of eigenvectors for use in calculating the next level of Z vectors.

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

       KSTART  (input) INTEGER
	       KSTOP   (input) INTEGER The updated eigenvalues Lambda(I), KSTART <=  I	<=  KSTOP
	       are to be computed.  1 <= KSTART <= KSTOP <= K.

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

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

       Q       (workspace) REAL array, dimension (LDQ,N)

       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) 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.

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

       S       (output) REAL array, dimension (LDS, K)
	       Will contain the eigenvectors of the repaired matrix which will be stored for sub-
	       sequent	Z  vector calculation and multiplied by the previously accumulated eigen-
	       vectors 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

LAPACK version 3.0			   15 June 2000 				SLAED9(l)
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