c语言 多项式拟合函数

多项式拟合函数可以使用最小二乘法进行求解。以下是一个简单的 C 语言多项式拟合函数的示例代码，其中假设要拟合的多项式为二次函数：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

void polyfit(double x[], double y[], int n, int degree, double coeff[]);
double evaluate(double x, double coeff[], int degree);

int main()
{
    int n = 5; // 数据点数目
    double x[] = {1.0, 2.0, 3.0, 4.0, 5.0}; // X 值
    double y[] = {1.0, 4.0, 9.0, 16.0, 25.0}; // Y 值
    int degree = 2; // 多项式次数
    double coeff[degree + 1]; // 存储拟合系数

    polyfit(x, y, n, degree, coeff);

    printf("拟合的二次函数为：y = %.2fx^2 + %.2fx + %.2f\n", coeff[2], coeff[1], coeff[0]);

    double x_test = 6.0; // 预测值
    double y_test = evaluate(x_test, coeff, degree);
    printf("当 x = %.2f 时，预测的 y 值为：%.2f\n", x_test, y_test);

    return 0;
}

void polyfit(double x[], double y[], int n, int degree, double coeff[])
{
    int i, j, k;
    double X[2 * degree + 1];
    double B[degree + 1][degree + 2];
    double Y[degree + 1];

    for (i = 0; i < 2 * degree + 1; i++)
    {
        X[i] = 0;

        for (j = 0; j < n; j++)
        {
            X[i] = X[i] + pow(x[j], i);
        }
    }

    for (i = 0; i <= degree; i++)
    {
        for (j = 0; j <= degree; j++)
        {
            B[i][j] = X[i + j];
        }

        Y[i] = 0;

        for (j = 0; j < n; j++)
        {
            Y[i] = Y[i] + pow(x[j], i) * y[j];
        }
    }

    int m = degree + 1;
    int p = 2 * m - 1;
    double A[m][m + 1];

    for (i = 0; i < m; i++)
    {
        for (j = 0; j < m; j++)
        {
            A[i][j] = B[i][j];
        }

        A[i][p] = Y[i];
    }

    for (k = 0; k < m; k++)
    {
        for (i = 0; i < m; i++)
        {
            if (i != k)
            {
                double c = A[i][k] / A[k][k];

                for (j = 0; j <= p; j++)
                {
                    A[i][j] = A[i][j] - c * A[k][j];
                }
            }
        }
    }

    for (i = 0; i < m; i++)
    {
        coeff[i] = A[i][p] / A[i][i];
    }
}

double evaluate(double x, double coeff[], int degree)
{
    double y = 0;

    for (int i = 0; i <= degree; i++)
    {
        y = y + coeff[i] * pow(x, i);
    }

    return y;
}

代码中 `polyfit()` 函数使用最小二乘法求解多项式拟合系数，`evaluate()` 函数用于计算预测的 y 值。在主函数中，我们传入了五个数据点，拟合一个二次函数，并计算了当 x 等于 6 时的预测值。