CLAIC1(1) LAPACK auxiliary routine (version 3.2) CLAIC1(1)NAME
CLAIC1 - applies one step of incremental condition estimation in its
simplest version
SYNOPSIS
SUBROUTINE CLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
INTEGER J, JOB
REAL SEST, SESTPR
COMPLEX C, GAMMA, S
COMPLEX W( J ), X( J )
PURPOSE
CLAIC1 applies one step of incremental condition estimation in its sim‐
plest 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' 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] * [ conjg(alpha) ]
[ conjg(gamma) ] where alpha
= conjg(x)'*w.
ARGUMENTS
JOB (input) INTEGER
= 1: an estimate for the largest singular value is computed.
= 2: an estimate for the smallest singular value is computed.
J (input) INTEGER
Length of X and W
X (input) COMPLEX array, dimension (J)
The j-vector x.
SEST (input) REAL
Estimated singular value of j by j matrix L
W (input) COMPLEX array, dimension (J)
The j-vector w.
GAMMA (input) COMPLEX
The diagonal element gamma.
SESTPR (output) REAL
Estimated singular value of (j+1) by (j+1) matrix Lhat.
S (output) COMPLEX
Sine needed in forming xhat.
C (output) COMPLEX
Cosine needed in forming xhat.
LAPACK auxiliary routine (versioNovember 2008 CLAIC1(1)
