d2r1.cpp

拉各朗日插值方法

# include<iostream.h>
# include<math.h>
# include<iomanip.h>

void main()
{
	//program d2r1
    //river for routine polint
	int nfunc,i;
	int n=9;
	double xa[11], ya[11], x,f,y=0.0,dy=0.0;
    n = 9;    //输入插值节点个数
    const double pi = 3.1415926;
    cout<<"Generation of interpolation tables;"<<endl;
    cout<<" ... sin(x)    0 < x < pi"<<endl;
    cout<<" ... exp(x)    0 < x < 1"<<endl;
    cout<<"How many entries go in these tables?(note: n<10)"<<endl;
    cout<<n<<endl;
    for( nfunc = 1; nfunc<=2; nfunc++)
	{
        if(nfunc == 1 )
		{
            cout<<"sine function from 0 to pi"<<endl;
            for( i = 1; i<=n; i++)
			{
                xa[i] = double(i) * pi / n;
                ya[i] = sin(xa[i]);
            }
		}
        else
		{
			if (nfunc == 2 )
			{
            cout<< "exponential function from 0 to 1"<<endl;
            for ( i = 1; i<=n; i++)
				{
					xa[i] = double(i) * 1 / n;
					ya[i] = exp(xa[i]);
				}
			}
			else
            return;
		}
        cout<<"     x           f(x)   interpolated      error"<<endl;
        for ( i = 1; i<=10; i++)
		{
            if( nfunc == 1 )
			{
                x = (-0.05 + double(i) / 10) * pi;
                f = sin(x);
			}
            else if( nfunc == 2) 
			{
                x = (-0.05 + double(i) / 10);
                f = exp(x);
            }
            polint(xa, ya, n, x, y, dy);
            cout<<setw(10)<<setiosflags(ios::fixed)<<setprecision(6)<<x;
            cout<<setw(12)<<setiosflags(ios::fixed)<<setprecision(6)<<f;
            cout<<setw(12)<<setiosflags(ios::fixed)<<setprecision(6)<<y;
            cout<<setw(16)<<setiosflags(ios::scientific)<<dy<<endl; 
		}
	}    
}