LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dlaic1.f File Reference

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Functions/Subroutines

subroutine DLAIC1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
 DLAIC1

Function/Subroutine Documentation

subroutine DLAIC1 ( INTEGER  JOB,
INTEGER  J,
DOUBLE PRECISION, dimension( j )  X,
DOUBLE PRECISION  SEST,
DOUBLE PRECISION, dimension( j )  W,
DOUBLE PRECISION  GAMMA,
DOUBLE PRECISION  SESTPR,
DOUBLE PRECISION  S,
DOUBLE PRECISION  C 
)

DLAIC1

Download DLAIC1 + dependencies [TGZ] [ZIP] [TXT]
Purpose:

 DLAIC1 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 DLAIC1 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:
[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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (J)
          The j-vector w.
 
[in]GAMMA
          GAMMA is DOUBLE PRECISION
          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 DOUBLE PRECISION
          Sine needed in forming xhat.
 
[out]C
          C is DOUBLE PRECISION
          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 135 of file dlaic1.f.

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