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    #include "cs.h"
    /* apply the ith Householder vector to x */
    CS_INT cs_happly (const cs *V, CS_INT i, double beta, CS_ENTRY *x)
    {
        CS_INT p, *Vp, *Vi ;
        CS_ENTRY *Vx, tau = 0 ;
        if (!CS_CSC (V) || !x) return (0) ;     /* check inputs */
        Vp = V->p ; Vi = V->i ; Vx = V->x ;
        for (p = Vp [i] ; p < Vp [i+1] ; p++)   /* tau = v'*x */
        {
            tau += CS_CONJ (Vx [p]) * x [Vi [p]] ;
        }
        tau *= beta ;                           /* tau = beta*(v'*x) */
        for (p = Vp [i] ; p < Vp [i+1] ; p++)   /* x = x - v*tau */
        {
            x [Vi [p]] -= Vx [p] * tau ;
        }
        return (1) ;
    }