d2r10.cpp

用vc＋＋平台开发的双三次样条插值函数

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

void spline(double x[], double y[], int n, double yp1,double  ypn, double y2[])
{
    double u[101],aaa,sig,p,bbb,ccc,qn,un;
	int i,k;
    if( yp1 > 9.9e+29 )
	{
        y2[1] = 0;
        u[1] = 0;
	}
    else
	{
        y2[1] = -0.5;
        aaa = (y[2] - y[1]) / (x[2] - x[1]);
        u[1] = (3.0 / (x[2] - x[1])) * (aaa - yp1);
    }
    for (i = 2;i<=n-1;i++)
	{
        sig = (x[i] - x[i - 1]) / (x[i + 1] - x[i - 1]);
        p = sig * y2[i - 1] + 2.0;
        y2[i] = (sig - 1.0) / p;
        aaa = (y[i + 1] - y[i]) / (x[i + 1] - x[i]);
        bbb = (y[i] - y[i - 1]) / (x[i] - x[i - 1]);
        ccc = x[i + 1] - x[i - 1];
        u[i] = (6.0 * (aaa - bbb) / ccc - sig * u[i - 1]) / p;
    }
    if (ypn > 9.9e+29 )
	{
        qn = 0.0;
        un = 0.0;
	}
    else
	{
        qn = 0.5;
        aaa = ypn - (y[n] - y[n - 1]) / (x[n] - x[n - 1]);
        un = (3.0/ (x[n] - x[n - 1])) * aaa;
    }
    y2[n] = (un - qn * u[n - 1]) / (qn * y2[n - 1] + 1.0);
    for (k = n - 1;k>=1;k--)
        y2[k] = y2[k] * y2[k + 1] + u[k];
}

void splie2(double x1a[], double x2a[], double ya[][11], int m, int n, double y2a[][11])
{
    double ytmp[101], y2tmp[101];
	int j,k;
    for (j = 1; j<=m; j++)
	{
        for (k = 1; k<=n; k++)
            ytmp[k] = ya[j][k];
        spline(x2a, ytmp, n, 1e+30, 1e+30, y2tmp);
        for (k = 1; k<=n; k++)
            y2a[j][k] = y2tmp[k];
    }
}

void main()
{
    //program d2r10
    //driver for routine splie2
	double x1[11], x2[11], y[11][11], y2[11][11],x1x2;
	int m,n,i,j;
    m = 10;
    n = 10;
    for (i = 1; i<=m; i++)
        x1[i] = 0.2 * i;
    for (i = 1; i<=n; i++)
        x2[i] = 0.2 * i;
    for (i = 1; i<=m; i++)
	{
        for (j = 1; j<=n; j++)
		{
            x1x2 = x1[i] * x2[j];
            y[i][j] = x1x2*x1x2;
        }
    }
    splie2(x1, x2, y, m, n, y2);
	cout<<setprecision(6)<<setiosflags(ios::fixed);
    cout<<endl;
    cout<<"Second derivatives from splie2"<<endl;
    cout<<"Natural spline assumed"<<endl;
	cout<<endl;
    for (i = 1; i<=5; i++)
	{
        for (j = 1; j<=5; j++)
            cout<<setw(12)<<y2[i][j];
        cout<<endl;
    }
    cout<<endl;
    cout<<"Actual second derivatives"<<endl;
	cout<<endl;
    for (i = 1; i<=5; i++)
	{
        for (j = 1; j<=5; j++)
            y2[i][j] = 2.0* (x1[i] *x1[i]);
        for (j = 1; j<=5; j++)
            cout<<setw(12)<<y2[i][j];
        cout<<endl;
    }
}