claic1 (3)  Linux Man Pages
NAME
claic1.f 
SYNOPSIS
Functions/Subroutines
subroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
CLAIC1 applies one step of incremental condition estimation.
Function/Subroutine Documentation
subroutine claic1 (integerJOB, integerJ, complex, dimension( j )X, realSEST, complex, dimension( j )W, complexGAMMA, realSESTPR, complexS, complexC)
CLAIC1 applies one step of incremental condition estimation.
Purpose:

CLAIC1 applies one step of incremental condition estimation in its simplest version: Let x, twonorm(x) = 1, be an approximate singular vector of an jbyj lower triangular matrix L, such that twonorm(L*x) = sest Then CLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w**H 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]**H and sestpr**2 is an eigenpair of the system diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ] [ conjg(gamma) ] where alpha = x**H*w.
Parameters:

JOB
JOB is INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed.
JJ is INTEGER Length of X and W
XX is COMPLEX array, dimension (J) The jvector x.
SESTSEST is REAL Estimated singular value of j by j matrix L
WW is COMPLEX array, dimension (J) The jvector w.
GAMMAGAMMA is COMPLEX The diagonal element gamma.
SESTPRSESTPR is REAL Estimated singular value of (j+1) by (j+1) matrix Lhat.
SS is COMPLEX Sine needed in forming xhat.
CC is COMPLEX Cosine needed in forming xhat.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Definition at line 136 of file claic1.f.
Author
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