zlaic1.f man page

zlaic1.f —

Synopsis

Functions/Subroutines

subroutine zlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
ZLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

subroutine zlaic1 (integerJOB, integerJ, complex*16, dimension( j )X, double precisionSEST, complex*16, dimension( j )W, complex*16GAMMA, double precisionSESTPR, complex*16S, complex*16C)

ZLAIC1 applies one step of incremental condition estimation.

Purpose:

ZLAIC1 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 ZLAIC1 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

J is INTEGER
Length of X and W

X

X is COMPLEX*16 array, dimension (J)
The j-vector x.

SEST

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

W

W is COMPLEX*16 array, dimension (J)
The j-vector w.

GAMMA

GAMMA is COMPLEX*16
The diagonal element gamma.

SESTPR

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

S

S is COMPLEX*16
Sine needed in forming xhat.

C

C is COMPLEX*16
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 zlaic1.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zlaic1(3) is an alias of zlaic1.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK