SRC/slaic1.f(3)            Library Functions Manual            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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/slaic1.f(3)