LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
zlaic1.f File Reference

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## 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 ( integer JOB, integer J, complex*16, dimension( j ) X, double precision SEST, complex*16, dimension( j ) W, complex*16 GAMMA, double precision SESTPR, complex*16 S, complex*16 C )

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:
 [in] JOB ``` JOB is INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed.``` [in] J ``` J is INTEGER Length of X and W``` [in] X ``` X is COMPLEX*16 array, dimension (J) The j-vector x.``` [in] SEST ``` SEST is DOUBLE PRECISION Estimated singular value of j by j matrix L``` [in] W ``` W is COMPLEX*16 array, dimension (J) The j-vector w.``` [in] GAMMA ``` GAMMA is COMPLEX*16 The diagonal element gamma.``` [out] SESTPR ``` SESTPR is DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat.``` [out] S ``` S is COMPLEX*16 Sine needed in forming xhat.``` [out] C ``` C is COMPLEX*16 Cosine needed in forming xhat.```
Date:
September 2012

Definition at line 136 of file zlaic1.f.

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