subroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
CLAIC1 applies one step of incremental condition estimation.
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 j-by-j 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 is INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed.
J
J is INTEGER Length of X and W
X
X is COMPLEX array, dimension (J) The j-vector x.
SEST
SEST is REAL Estimated singular value of j by j matrix L
W
W is COMPLEX array, dimension (J) The j-vector w.
GAMMA
GAMMA is COMPLEX The diagonal element gamma.
SESTPR
SESTPR is REAL Estimated singular value of (j+1) by (j+1) matrix Lhat.
S
S is COMPLEX Sine needed in forming xhat.
C
C is COMPLEX Cosine needed in forming xhat.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 137 of file claic1.f.
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