zlaic1.f(3)

NAME
zlaic1.f -

SYNOPSIS

  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 (integerJOB, integerJ, complex*16, dimension( j )X, double precisionSEST, complex*16, dimension( j )W, complex*16GAMMA, double precisionSESTPR, complex*16S, complex*16C)

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:
    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 COMPLEX*16 array, dimension (J)
              The j-vector x.

    SEST

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

    W

              W is COMPLEX*16 array, dimension (J)
              The j-vector w.

    GAMMA

              GAMMA is COMPLEX*16
              The diagonal element gamma.

    SESTPR

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

    S

              S is COMPLEX*16
              Sine needed in forming xhat.

    C

              C is COMPLEX*16
              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 136 of file zlaic1.f.

Author

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