claic1.f(3)

NAME
claic1.f

SYNOPSIS

  Functions/Subroutines
subroutine claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
CLAIC1 applies one step of incremental condition estimation.

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)

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

    SEST

              SEST is REAL
              Estimated singular value of j by j matrix L

    W

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

    GAMMA

              GAMMA is COMPLEX
              The diagonal element gamma.

    SESTPR

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

    S

              S is COMPLEX
              Sine needed in forming xhat.

    C

              C is COMPLEX
              Cosine needed in forming xhat.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 134 of file claic1.f.

Author

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