zlaic1.f(3) LAPACK zlaic1.f(3)
NAME
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.
Version 3.4.2 Tue Sep 25 2012 zlaic1.f(3)