SLAED9(3F)SLAED9(3F)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.
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SLAED9(3F)SLAED9(3F)
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
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