kv

-

kernel handle of type MKernelVector

hf

-

an hfdata structure

    #include <math.h>

    #include "maplec.h"

    ALGEB MyNewtonData( MKernelVector kv, ALGEB *args )

    {

    M_INT i;

    FLOAT64 tolerance, newguess, res;

    hfdata guess[2];

    ALGEB f, fprime, x;

    if( 3 != MapleNumArgs(kv,(ALGEB)args) ) {

        MapleRaiseError(kv,"three arguments expected");

        return( NULL );

    }

    if( IsMapleProcedure(kv,args[1]) ) {

        f = args[1];

    }

    else {

        ALGEB indets;

        indets = EvalMapleProc(kv,ToMapleName(kv,"indets",TRUE),1,args[1]);

        if( !IsMapleSet(kv,indets) || MapleNumArgs(kv,indets) != 1 ) {

        MapleRaiseError(kv,"unable to find roots");

        return( NULL );

        }

        i = 1;

        f = EvalMapleProc(kv,ToMapleName(kv,"unapply",TRUE),2,args[1],

             MapleSelectIndexed(kv,indets,1,&i));

        if( !f || !IsMapleProcedure(kv,f) ) {

        MapleRaiseError(kv,"unable to convert first arg to a procedure");

        return( NULL );

        }

    }

    x = ToMapleName(kv,"x",FALSE);

    fprime = EvalMapleProc(kv,ToMapleName(kv,"unapply",TRUE),2,

            EvalMapleProc(kv,ToMapleName(kv,"diff",TRUE),2,

            ToMapleFunction(kv,f,1,x),x),x);

    if( !fprime || !IsMapleProcedure(kv,fprime) ) {

        MapleRaiseError(kv,"unable to compute derivative");

        return( NULL );

    }

    DoubleTohfData( kv, MapleEvalhf( kv, args[2] ), 0, guess+1 );

    tolerance = MapleEvalhf(kv,args[3]);

    res = 0.0;

    for( i=0; i<500; ++i ) {

        res = RealhfData( kv, EvalhfDataProc(kv,f,1,guess) );

        if( fabs( res ) <= tolerance )

        break;

        newguess = RealhfData( kv, guess[1] ) -

        res / RealhfData( kv, EvalhfDataProc(kv,fprime,1,guess) );

        DoubleTohfData( kv, newguess, 0, guess+1 );

    }

    if( i == 500 ) {

        MapleRaiseError(kv,"unable to find root after 500 iterations");

        return( NULL );

    }

    return( ToMapleFloat(kv, RealhfData( kv, guess[1] ) ) );

    }