SRC/claic1.f(3)            Library Functions Manual            SRC/claic1.f(3)

NAME
       SRC/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)
       CLAIC1 applies one step of incremental condition estimation.

       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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/claic1.f(3)