dlaic1.f(3)

NAME
dlaic1.f -

SYNOPSIS

  Functions/Subroutines

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

Function/Subroutine Documentation

  subroutine dlaic1 (integerJOB, integerJ, double precision, dimension( j )X, double precisionSEST, double precision, dimension( j )W, double precisionGAMMA, double precisionSESTPR, double precisionS, double precisionC)

DLAIC1 applies one step of incremental condition estimation.

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:
    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 DOUBLE PRECISION array, dimension (J)
              The j-vector x.

    SEST

              SEST is DOUBLE PRECISION
              Estimated singular value of j by j matrix L

    W

              W is DOUBLE PRECISION array, dimension (J)
              The j-vector w.

    GAMMA

              GAMMA is DOUBLE PRECISION
              The diagonal element gamma.

    SESTPR

              SESTPR is DOUBLE PRECISION
              Estimated singular value of (j+1) by (j+1) matrix Lhat.

    S

              S is DOUBLE PRECISION
              Sine needed in forming xhat.

    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.

Author

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