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dlaic1.f File Reference

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Functions/Subroutines

subroutine dlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
 DLAIC1 applies one step of incremental condition estimation. More...
 

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 applies one step of incremental condition estimation.

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
September 2012

Definition at line 135 of file dlaic1.f.

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