Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - applies one step of incremental condition estimation in its simplest version

SYNOPSIS

       SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )

           INTEGER        J, JOB

           DOUBLE         PRECISION C, GAMMA, S, SEST, SESTPR

           DOUBLE         PRECISION W( J ), X( J )

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.

ARGUMENTS

        JOB     (input) INTEGER
                = 1: an estimate for the largest singular value is computed.
                = 2: an estimate for the smallest singular value is computed.

        J       (input) INTEGER
                Length of X and W

        X       (input) DOUBLE PRECISION array, dimension (J)
                The j-vector x.

        SEST    (input) DOUBLE PRECISION
                Estimated singular value of j by j matrix L

        W       (input) DOUBLE PRECISION array, dimension (J)
                The j-vector w.

        GAMMA   (input) DOUBLE PRECISION
                The diagonal element gamma.

        SESTPR  (output) DOUBLE PRECISION
                Estimated singular value of (j+1) by (j+1) matrix Lhat.

        S       (output) DOUBLE PRECISION
                Sine needed in forming xhat.

        C       (output) DOUBLE PRECISION
                Cosine needed in forming xhat.

 LAPACK auxiliary routine (version 3.3.1)   April 2011                            DLAIC1(3lapack)