dlaic1.f man page

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

J is INTEGER
Length of X and W

X

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

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

S is DOUBLE PRECISION
Sine needed in forming xhat.

C

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

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dlaic1(3) is an alias of dlaic1.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK