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DLAIC1Run Method

Purpose ======= DLAIC1 applies one step of incremental condition estimation in its simplest version: Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j lower triangular matrix L, such that twonorm(L*x) = sest Then DLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w' gamma ] in the sense that twonorm(Lhat*xhat) = sestpr. Depending on JOB, an estimate for the largest or smallest singular value is computed. Note that [s c]' and sestpr**2 is an eigenpair of the system diag(sest*sest, 0) + [alpha gamma] * [ alpha ] [ gamma ] where alpha = x'*w.

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 JOB,
	int J,
	double[] X,
	int offset_x,
	double SEST,
	double[] W,
	int offset_w,
	double GAMMA,
	ref double SESTPR,
	ref double S,
	ref double C
)
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Parameters

JOB  Int32
(input) INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed.
J  Int32
(input) INTEGER Length of X and W
X  Double
(input) DOUBLE PRECISION array, dimension (J) The j-vector x.
offset_x  Int32
 
SEST  Double
(input) DOUBLE PRECISION Estimated singular value of j by j matrix L
W  Double
(input) DOUBLE PRECISION array, dimension (J) The j-vector w.
offset_w  Int32
 
GAMMA  Double
(input) DOUBLE PRECISION The diagonal element gamma.
SESTPR  Double
(output) DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat.
S  Double
(output) DOUBLE PRECISION Sine needed in forming xhat.
C  Double
(output) DOUBLE PRECISION Cosine needed in forming xhat.
See Also