SRC/slaic1.f(3)

NAME
SRC/slaic1.f

SYNOPSIS

  Functions/Subroutines
subroutine slaic1 (job, j, x, sest, w, gamma, sestpr, s, c)
SLAIC1 applies one step of incremental condition estimation.

Function/Subroutine Documentation

  subroutine slaic1 (integer job, integer j, real, dimension( j ) x, real sest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)

SLAIC1 applies one step of incremental condition estimation.

Purpose:

    !>
    !> SLAIC1 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 SLAIC1 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 REAL array, dimension (J)
    !>          The j-vector x.
    !>

    SEST

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

    W

    !>          W is REAL array, dimension (J)
    !>          The j-vector w.
    !>

    GAMMA

    !>          GAMMA is REAL
    !>          The diagonal element gamma.
    !>

    SESTPR

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

    S

    !>          S is REAL
    !>          Sine needed in forming xhat.
    !>

    C

    !>          C is REAL
    !>          Cosine needed in forming xhat.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 133 of file slaic1.f.

Author

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