include iostream include vector using namespace std typedef vector dou

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#include <iostream>
#include <vector>
using namespace std;
typedef vector<double> Vec;
typedef vector<Vec> Matrix;
int n;
double h(Vec x, int k)
{
return x[k] - x[k - 1];
}
double fff(Vec x, Vec y, int k)
{
return y[k - 1] / (x[k - 1] - x[k]) / (x[k - 1] - x[k + 1]) +
y[k] / (x[k] - x[k - 1]) / (x[k] - x[k + 1]) +
y[k + 1] / (x[k + 1] - x[k - 1]) / (x[k + 1] - x[k]);
}
double ff(Vec x, Vec y, int k)
{
return y[k - 1] / (x[k - 1] - x[k]) + y[k] / (x[k] - x[k - 1]);
}
void SolveTridiagonal(Vec A, Vec B, Vec C, Vec b, Vec &x)
{
int n = A.size();
Vec B1(n);
Vec b1(n);
B1[0] = B[0];
b1[0] = b[0];
for (int i = 1; i < n; ++i)
{
B1[i] = B[i] - A[i] * C[i - 1] / B1[i - 1];
b1[i] = b[i] - A[i] * b1[i - 1] / B1[i - 1];
}
x.resize(n);
x[n - 1] = b1[n - 1] / B1[n - 1];
for (int i = n - 2; i >= 0; --i)
{
x[i] = (b1[i] - C[i] * x[i + 1]) / B1[i];
}
}
void BuildSpline(Vec &knotX, Vec knotY, Matrix &Coef, double A, double B)
{
Vec a(n-2);
Vec b(n-2);
Vec c(n-2);
Vec f(n - 2);
for (int i = 2; i <= n - 1; ++i)
{
int id = i - 2;
if (i != n - 1)
c[id] = h(knotX, i - 1) / (h(knotX, i - 1) + h(knotX, i));
if (i != 2)
B = h(knotX, i) / (h(knotX, i - 1) + h(knotX, i));
b[id] = 3;
if (i == 2)
f[id] = 4 * fff(knotX, knotY, i - 1) - A * h(knotX, 1) / 2 / (h(knotX, 1) + h(knotX, 2));
else if (i == n - 3)
f[id] = 4 * fff(knotX, knotY, i - 1) - B* h(knotX, n - 1) / 2 / (h(knotX, n - 2) + h(knotX, n - 1));
else
f[id] = 4 * fff(knotX, knotY, i - 1);
}
Vec x;
SolveTridiagonal(a, b, c, f, x);
Vec coeffA(n);
Vec coeffB(n);
Vec coeffC(n);
Vec X(n);
for (int i = 0; i < n - 1; ++i)
X[i] = (knotX[i] + knotX[i + 1]) / 2;
X[n-1] = knotX[n-1];
coeffC[n - 1] = B / 2;
coeffC[0] = A / 2;
for (int i = 1; i < n - 1; ++i)
{
coeffC[i] = x[i - 1];
}
for (int i = 0; i < n - 1; ++i)
{
coeffB[i] = h(knotX,i+1) / 4 * (coeffC[i] - coeffC[i + 1]) + ff(knotX, knotY,i+1);
}
coeffB[n - 1] = coeffB[n - 2] + B / 2 * h(knotX, n - 1);
for (int i = 0; i < n - 1; ++i)
{
coeffA[i] = h(knotX, i+1) / 2 * (coeffB[i] - h(knotX,i+1) / 2 * coeffC[i]) + knotY[i];
}
coeffA[n - 1] = knotY[n - 1];
for (int j = 0; j < n; j++)
{
Coef[j][0] = coeffA[j];
Coef[j][1] = coeffB[j];
Coef[j][2] = coeffC[j];
}
knotX = X;
}
double Interpolate(double x, Vec knotX, Matrix Coef)
{
int ind = 0;
if (x <= knotX[0])
ind = 1;
else if (x >= knotX[n - 1])
ind = n - 1;
else
{
int i = 0, j = n - 1;
while (i + 1 < j)
{
std::size_t k = i + (j - i) / 2;
if (x <= knotX[k])
j = k;
else
i = k;
}
ind = j;
}
double dx = x - knotX[ind];
return Coef[ind][0] + Coef[ind][1] * dx + Coef[ind][2] * dx*dx;
}
int main()
{
freopen("output.txt", "w", stdout);
Vec knotX = { -3.14, -2.44, -1.74, -1.04, -0.34, 0.36, 1.06, 1.76, 2.46 };
Vec knotY = { -0.0016, -0.6454, -0.9857, -0.8624, -0.3335, 0.3523, 0.8724, 0.9822, 0.6300 };
n = knotX.size();
Matrix Coef(n, Vec(3, 0));
BuildSpline(knotX, knotY, Coef, 0, 0);
cout << "[ ";
for (double x = -3.14; x <= 2.46; x += 0.1)
{
cout << x << " ";
double temp = Interpolate(x, knotX, Coef);
cout << temp << endl;
}
cout << " ]";
return 0;
}