equation calculation on Unix Post: 302096547

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slaed9

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 appropri-
       ate 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 subsequent Z vector calculation and 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

LAPACK version 3.0						   15 June 2000 							 SLAED9(l)