SRC/dlaic1.f(3)            Library Functions Manual            SRC/dlaic1.f(3)

NAME
       SRC/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 (integer job, integer j, double precision, dimension( j )
       x, double precision sest, double precision, dimension( j ) w, double
       precision gamma, double precision sestpr, double precision s, double
       precision c)
       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.

       Definition at line 133 of file dlaic1.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/dlaic1.f(3)