三次样条函数源代码
void yangtiao(){
cin_f.open(sr_f1);
int i = 0, j = 0, k = 0, n = 0, l = 0;
double s3 = 0;
double y[100], h[100], x[100], z[100], a[100], b[100], m[100];
///////////////////////////////////////////////////////////////////
cin_f >> n >> k;
for(i = 0; i < n; i++){
cin_f >> x[i] >> y[i];
x[i] = i - 5;
x[i + 1] = i - 4;
h[i] = x[i + 1] - x[i];
};
for(i = 0; i < k; i++)
cin_f >> z[i];
cin_f.close();
///////////////////////////////////////////////////////////////////
for(i = 0; i < n; i++){
a[i] = h[i - 1] / (h[i - 1] + h[i]);
b[i] = 3 * ((1 - a[i]) * (y[i] - y[i - 1]) / h[i - 1] + a[i] * (y[i + 1] - y[i]) / h[i]);
};
cout_f.open(sc_f1);
cout_f <<n - 1 << endl;
for(i = 0; i < n - 1; i++){
for(j = 0; j < n - 1; j++)
if(i - j == 1) cout_f << 1 - a[i] << " ";
else if(i == j) cout_f << 2 << " ";
else if(j - i == 1) cout_f << a[i] << " ";
cout_f << endl;
};
for(i = 0; i < n - 1; i++){
if(i == 0 || i == n - 1) cout_f <<setprecision(10)<< b[i] - (1 - a[i]) * ((-4 * x[i] )/( (1 + x[i] * x[i]) * (1 + x[i] * x[i] ))) << " ";
else {cout_f<<setprecision(10)<< b[i] <<" ";cout<<setprecision(10)<< b[i] <<" ";}
}; cout_f << endl;
cout_f.close();
//cout<<"!"<<endl;
//////////////////////////////////////////
zhuigan();
//////////////////////////////////////////
//cout<<"!!"<<endl;
ifstream cin_f2;
ofstream cout_f2;
cin_f2.open(sr_f3);
cout_f2.open(sc_f3);
for(i = 0; i < n - 1; i++){
cin_f2 >> m[i];
//cout << m[i] <<endl;
}
//cout<<endl;
for(i = 0; i < k; i++){
for(j = 0; j < n; j++)
if(z[i] >= x[j] && z[i] < x[j + 1]){
l = j;
break;
};
s3 = p0((z[i] - x[l]) / h[l]) * y[l] + p1((z[i] - x[l]) / h[l]) * y[l + 1] + h[l] * q0((z[i] - x[l]) / h[l]) * m[l] + h[l] * q1((z[i] - x[l]) / h[l]) * m[l + 1];
cout_f2 <<setprecision(10)<< s3 <<endl;
};
cin_f.close();
cout_f.close();
};
