d5r8.cpp

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#include "iostream.h"
#include "math.h"

double func(double x)
{
    return (x * x) * (x * x - 2.0) * sin(x);
}
void chebft(double a, double b, double c[], int n)
{
    int k,nmax = 50;
    double f[51];
    const double pi = 3.14159265358979;
	double bma,bpa,y,sum,fac;
    bma = 0.5 * (b - a);
    bpa = 0.5 * (b + a);
    for (k = 1; k<=n; k++)
	{
        y = cos(pi * (k - 0.5) / n);
        f[k] = func(y * bma + bpa);
    }
    fac = 2.0 / n;
    for (int j = 1; j<=n; j++)
	{
        sum = 0.0;
        for (k = 1; k<=n; k++)
		{
            sum = sum + f[k] * cos((pi * (j - 1)) * ((k - 0.5) / n));
        }
        c[j] = fac * sum;
    }
}

void chebpc(double c[], double d[], int n)
{
    double dd[51];
	int j;
	double sv;
    for (j = 1; j<=n; j++)
	{
        d[j] = 0.0;
        dd[j] = 0.0;
    }
    d[1] = c[n];
    for (j = n - 1; j>=2; j--)
	{
        for ( int k = n - j + 1; k>=2; k--)
		{
            sv = d[k];
            d[k] = 2.0 * d[k - 1] - dd[k];
            dd[k] = sv;
        }
        sv = d[1];
        d[1] = -dd[1] + c[j];
        dd[1] = sv;
    }
    for (j = n; j>=2; j--)
	{
        d[j] = d[j - 1] - dd[j];
    }
    d[1] = -dd[1] + 0.5 * c[1];
}

void main()
{
    //program d5r8
    //driver for routine chebpc
    int nval = 40;
    double a,b,x,y,poly,pio2 = 1.5707963;
    double c[41], d[41];
    a = -pio2;
    b = pio2;
    chebft(a, b, c, nval);
    cout<<endl;
    cout<<"How many terms in chebyshev evaluation?"<<endl;
    //input mval , between 6 and 40, mval=0 to end
    int mval = 20;
    cout<<mval<<endl;
    if ((mval <= 0) || (mval > nval))
	{
		return;
	}
    chebpc(c, d, mval);
    //test polynomial
    cout<<"        x          Actual     Polynomial"<<endl;
	cout.setf(ios::fixed|ios::right);
	cout.precision(6);
    for (int i = -8; i<=8; i++)
	{
        x = i * pio2 / 10.0;
        y = (x - (0.5 * (b + a))) / (0.5 * (b - a));
        poly = d[mval];
        for (int j = mval - 1; j>=1; j--)
		{
            poly = poly * y + d[j];
        }
		cout.width(13);
        cout<<x;
		cout.width(13);
        cout<<func(x);
		cout.width(13);
        cout<<poly<<endl;
    }
}