claic1-f(3)

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 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

 JOB is INTEGER
 = 1: an estimate for the largest singular value is computed.
 = 2: an estimate for the smallest singular value is computed.

 J is INTEGER
 Length of X and W

 X is COMPLEX array, dimension (J)
 The j-vector x.

SEST

 SEST is REAL
 Estimated singular value of j by j matrix L

 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 is COMPLEX
 Sine needed in forming xhat.

 C 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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