slaic1.f man page

slaic1.f —

Synopsis

Functions/Subroutines

subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
SLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

subroutine slaic1 (integerJOB, integerJ, real, dimension( j )X, realSEST, real, dimension( j )W, realGAMMA, realSESTPR, realS, realC)

SLAIC1 applies one step of incremental condition estimation.

Purpose:

SLAIC1 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 SLAIC1 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 REAL array, dimension (J)
The j-vector x.

SEST

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

W

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

GAMMA

GAMMA is REAL
The diagonal element gamma.

SESTPR

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

S

S is REAL
Sine needed in forming xhat.

C

C is REAL
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 slaic1.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

slaic1(3) is an alias of slaic1.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK