Subversion Repositories programming

/* Copyright: Ira W. Snyder

 * Start Date: 2005-11-13

 * End Date: 2005-11-13

 * License: Public Domain

 *

 * Changelog Follows:

 *

 * 2005-11-13

 * - Implemented Functions 1-3 from the Project #3 Handout.

 * - Implemented Algorithm 7 (LaGrange) from Notes Set #3.

 * - Implemented Algorithm 8-9 (Newton Divided Diff) from Notes Set #3.

 *

 */

#include <cstdio>

#include <cmath>

using namespace std;

#define X_MIN = -5.0

#define X_MAX = 5.0

double func1 (double x)

{

    return 1.0 / (1.0 + pow(x, 2));

}

double func2 (double x)

{

    // NOTE: M_E is the value of e defined by the math.h header

    return (pow(M_E, x) + pow(M_E, -x)) / 2.0;

}

double func3 (double x)

{

    return pow(x, 14) + pow(x, 10) + pow(x, 4) + x + 1;

}

double LaGrangeMethod (double *x, double *y, int n, double point)

{

    double value = 0;

    double term  = 0;

    int i, j;

    for (i=0; i<n; i++)

    {

        term = y[i];

        for (j=0; j<n; j++)

        {

            if (i != j)

                term *= (point - x[j])/(x[i] - x[j]);

        }

        value += term;

    }

    return value;

}

double NewtonMethod (double *x, double *y, int n, double point)

{

    int i, j;

    double a[n];

    for (i=0; i<n; i++)

        a[i] = y[i];

    for (i=1; i<n; i++)

        for (j=n-1; j>=i; j--)

            a[j] = (a[j] - a[j-1]) / (x[j] - x[j-i]);

    // At this point, all of the a[i]'s have been calculated,

    // using a Divided Difference Table.

    double xterm = 1.0;

    double value = 0.0;

    for (i=0; i<n; i++)

    {

        value += a[i] * xterm;

        xterm *= (point - x[i]);

    }

    return value;

}

int main (void)

{

    double x[] = {-2, -1, 0, 2, 3};

    double y[] = {15, -3, -5, 15, 85};

    int size = 5;

    double point = 2.0;

    printf ("LaGrange = %e\n", LaGrangeMethod(x, y, size, point));

    printf ("Newton = %e\n", NewtonMethod(x, y, size, point));

    return 0;

}