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DLASD4Run Method

Purpose ======= This subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 .LE. D(i) .LT. D(j) for i .LT. j and that RHO .GT. 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus diag( D ) * diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.

Namespace: DotNumerics.LinearAlgebra.CSLapack
Assembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
Copy
public void Run(
	int N,
	int I,
	double[] D,
	int offset_d,
	double[] Z,
	int offset_z,
	ref double[] DELTA,
	int offset_delta,
	double RHO,
	ref double SIGMA,
	ref double[] WORK,
	int offset_work,
	ref int INFO
)
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Parameters

N  Int32
(input) INTEGER The length of all arrays.
I  Int32
(input) INTEGER The index of the eigenvalue to be computed. 1 .LE. I .LE. N.
D  Double
(input) DOUBLE PRECISION array, dimension ( N ) The original eigenvalues. It is assumed that they are in order, 0 .LE. D(I) .LT. D(J) for I .LT. J.
offset_d  Int32
 
Z  Double
(input) DOUBLE PRECISION array, dimension ( N ) The components of the updating vector.
offset_z  Int32
 
DELTA  Double
(output) DOUBLE PRECISION array, dimension ( N ) If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the (singular) eigenvectors.
offset_delta  Int32
 
RHO  Double
(input) DOUBLE PRECISION The scalar in the symmetric updating formula.
SIGMA  Double
(output) DOUBLE PRECISION The computed sigma_I, the I-th updated eigenvalue.
WORK  Double
(workspace) DOUBLE PRECISION array, dimension ( N ) If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th component. If N = 1, then WORK( 1 ) = 1.
offset_work  Int32
 
INFO  Int32
(output) INTEGER = 0: successful exit .GT. 0: if INFO = 1, the updating process failed.
See Also