LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
claic1.f File Reference

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Functions/Subroutines

subroutine CLAIC1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
 CLAIC1

Function/Subroutine Documentation

subroutine CLAIC1 ( INTEGER  JOB,
INTEGER  J,
COMPLEX, dimension( j )  X,
REAL  SEST,
COMPLEX, dimension( j )  W,
COMPLEX  GAMMA,
REAL  SESTPR,
COMPLEX  S,
COMPLEX  C 
)

CLAIC1

Download CLAIC1 + dependencies [TGZ] [ZIP] [TXT]
Purpose:

 CLAIC1 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 CLAIC1 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 array, dimension (J)
          The j-vector x.
 
[in]SEST
          SEST is REAL
          Estimated singular value of j by j matrix L
 
[in]W
          W is COMPLEX array, dimension (J)
          The j-vector w.
 
[in]GAMMA
          GAMMA is COMPLEX
          The diagonal element gamma.
 
[out]SESTPR
          SESTPR is REAL
          Estimated singular value of (j+1) by (j+1) matrix Lhat.
 
[out]S
          S is COMPLEX
          Sine needed in forming xhat.
 
[out]C
          C is COMPLEX
          Cosine needed in forming xhat.
 
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

Definition at line 136 of file claic1.f.

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