dlaed9-f(3)

dlaed9.f –

Synopsis

Functions/Subroutines

subroutine dlaed9 (K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO)
DLAED9 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

Function/Subroutine Documentation

subroutine dlaed9 (integerK, integerKSTART, integerKSTOP, integerN, double precision, dimension( * )D, double precision, dimension( ldq, * )Q, integerLDQ, double precisionRHO, double precision, dimension( * )DLAMDA, double precision, dimension( * )W, double precision, dimension( lds, * )S, integerLDS, integerINFO)

DLAED9 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

Purpose:

 DLAED9 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 DLAED4 and then stores the new matrix of
 eigenvectors for use in calculating the next level of Z vectors.

Parameters:

 K is INTEGER
 The number of terms in the rational function to be solved by
 DLAED4. K >= 0.

KSTART

 KSTART is INTEGER

KSTOP

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

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

 D is DOUBLE PRECISION array, dimension (N)
 D(I) contains the updated eigenvalues
 for KSTART <= I <= KSTOP.

 Q is DOUBLE PRECISION array, dimension (LDQ,N)

LDQ

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

RHO

 RHO is DOUBLE PRECISION
 The value of the parameter in the rank one update equation.
 RHO >= 0 required.

DLAMDA

 DLAMDA is DOUBLE PRECISION 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 is DOUBLE PRECISION array, dimension (K)
 The first K elements of this array contain the components
 of the deflation-adjusted updating vector.

 S is DOUBLE PRECISION 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

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

INFO

 INFO is 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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 156 of file dlaed9.f.

Author

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