dlaic1-f(3)

dlaic1.f –

Synopsis

Functions/Subroutines

subroutine dlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
DLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

subroutine dlaic1 (integerJOB, integerJ, double precision, dimension( j )X, double precisionSEST, double precision, dimension( j )W, double precisionGAMMA, double precisionSESTPR, double precisionS, double precisionC)

DLAIC1 applies one step of incremental condition estimation.

Purpose:

 DLAIC1 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 DLAIC1 computes sestpr, s, c such that
 the vector
 [ s*x ]
 xhat = [ c ]
 is an approximate singular vector of
 [ L 0 ]
 Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system
 diag(sest*sest, 0) + [alpha gamma] * [ alpha ]
 [ gamma ]
 where alpha = x**T*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 DOUBLE PRECISION array, dimension (J)
 The j-vector x.

SEST

 SEST is DOUBLE PRECISION
 Estimated singular value of j by j matrix L

 W is DOUBLE PRECISION array, dimension (J)
 The j-vector w.

GAMMA

 GAMMA is DOUBLE PRECISION
 The diagonal element gamma.

SESTPR

 SESTPR is DOUBLE PRECISION
 Estimated singular value of (j+1) by (j+1) matrix Lhat.

 S is DOUBLE PRECISION
 Sine needed in forming xhat.

 C is DOUBLE PRECISION
 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 135 of file dlaic1.f.

Author

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