NAME

claic1 - apply 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 )

#include <sunperf.h>

void claic1(int job, int j, complex ∗cx, float sest, complex ∗w, complex ∗gamma, float ∗sestpr, complex ∗s, complex ∗c) ;

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’ 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.

SunOS 5.0  —  Last change: 10 Dec 1998