偏最小二乘回归 C语言代码

以下是一个简单的偏最小二乘回归的 C 语言代码示例：

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

#define N 10 // 样本数据点数
#define M 3 // 需要拟合的多项式次数

// 定义样本数据结构体
typedef struct {
    double x;
    double y;
} Sample;

// 计算矩阵的转置
void transpose(double **mat, int rows, int cols, double **result) {
    int i, j;
    for (i = 0; i < cols; i++) {
        for (j = 0; j < rows; j++) {
            result[i][j] = mat[j][i];
        }
    }
}

// 计算矩阵的乘积
void matrix_multiply(double **mat1, int rows1, int cols1, double **mat2, int rows2, int cols2, double **result) {
    int i, j, k;
    for (i = 0; i < rows1; i++) {
        for (j = 0; j < cols2; j++) {
            result[i][j] = 0.0;
            for (k = 0; k < cols1; k++) {
                result[i][j] += mat1[i][k] * mat2[k][j];
            }
        }
    }
}

// 计算矩阵的逆
void matrix_inverse(double **mat, int n, double **result) {
    int i, j, k;
    double temp;
    // 将矩阵初始化为单位矩阵
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            result[i][j] = (i == j) ? 1.0 : 0.0;
        }
    }
    // 对矩阵进行高斯消元得到上三角矩阵
    for (i = 0; i < n; i++) {
        temp = mat[i][i];
        for (j = i; j < n; j++) {
            mat[i][j] /= temp;
        }
        for (j = 0; j < n; j++) {
            result[i][j] /= temp;
        }
        for (j = i + 1; j < n; j++) {
            temp = mat[j][i];
            for (k = i; k < n; k++) {
                mat[j][k] -= temp * mat[i][k];
            }
            for (k = 0; k < n; k++) {
                result[j][k] -= temp * result[i][k];
            }
        }
    }
    // 对矩阵进行回代得到逆矩阵
    for (i = n - 1; i >= 0; i--) {
        for (j = i - 1; j >= 0; j--) {
            temp = mat[j][i];
            for (k = 0; k < n; k++) {
                result[j][k] -= temp * result[i][k];
            }   
        }
    }
}

// 计算多项式拟合的系数
void polynomial_fit(Sample *samples, int n, int m, double *coef) {
    int i, j, k;
    double **x, **y, **a, **b, **c, **d, **e, **f, **g, **h, **i_mat, **i_inv;
    double *sum_x, *sum_y, *sum_xy, *sum_x2, *temp;
    // 分配内存
    x = (double **)malloc(n * sizeof(double *));
    y = (double **)malloc(n * sizeof(double *));
    a = (double **)malloc((m + 1) * sizeof(double *));
    b = (double **)malloc((m + 1) * sizeof(double *));
    c = (double **)malloc((m + 1) * sizeof(double *));
    d = (double **)malloc((m + 1) * sizeof(double *));
    e = (double **)malloc((m + 1) * sizeof(double *));
    f = (double **)malloc((m + 1) * sizeof(double *));
    g = (double **)malloc((m + 1) * sizeof(double *));
    h = (double **)malloc((m + 1) * sizeof(double *));
    i_mat = (double **)malloc((m + 1) * sizeof(double *));
    i_inv = (double **)malloc((m + 1) * sizeof(double *));
    sum_x = (double *)malloc((2 * m + 1) * sizeof(double));
    sum_y = (double *)malloc((m + 1) * sizeof(double));
    sum_xy = (double *)malloc((m + 1) * sizeof(double));
    sum_x2 = (double *)malloc((2 * m + 1) * sizeof(double));
    temp = (double *)malloc((m + 1) * sizeof(double));
    for (i = 0; i <= m; i++) {
        a[i] = (double *)malloc((m + 1) * sizeof(double));
        b[i] = (double *)malloc((m + 1) * sizeof(double));
        c[i] = (double *)malloc((m + 1) * sizeof(double));
        d[i] = (double *)malloc((m + 1) * sizeof(double));
        e[i] = (double *)malloc((m + 1) * sizeof(double));
        f[i] = (double *)malloc((m + 1) * sizeof(double));
        g[i] = (double *)malloc((m + 1) * sizeof(double));
        h[i] = (double *)malloc((m + 1) * sizeof(double));
        i_mat[i] = (double *)malloc((2 * m + 1) * sizeof(double));
        i_inv[i] = (double *)malloc((2 * m + 1) * sizeof(double));
    }
    for (i = 0; i < n; i++) {
        x[i] = (double *)malloc((m + 1) * sizeof(double));
        y[i] = (double *)malloc(sizeof(double));
    }
    // 构造矩阵
    for (i = 0; i <= m; i++) {
        for (j = 0; j <= m; j++) {
            a[i][j] = 0.0;
            for (k = 0; k < n; k++) {
                x[k][i] = pow(samples[k].x, i);
                x[k][j] = pow(samples[k].x, j);
                a[i][j] += x[k][i] * x[k][j];
            }
        }
        sum_y[i] = 0.0;
        sum_xy[i] = 0.0;
        for (k = 0; k < n; k++) {
            y[k][0] = samples[k].y;
            sum_y[i] += pow(samples[k].x, i) * y[k][0];
            sum_xy[i] += pow(samples[k].x, i) * y[k][0];
        }
    }
    for (i = 0; i <= 2 * m; i++) {
        sum_x[i] = 0.0;
        for (j = 0; j < n; j++) {
            sum_x[i] += pow(samples[j].x, i);
        }
    }
    for (i = 0; i <= 2 * m; i++) {
        for (j = 0; j <= m; j++) {
            if (i <= m) {
                b[j][i] = a[j][i];
            } else {
                b[j][i] = sum_x[i + j];
            }
        }
        if (i <= m) {
            c[0][i] = sum_y[i];
            d[0][i] = sum_xy[i];
        } else {
            c[0][i] = 0.0;
            d[0][i] = 0.0;
        }
    }
    for (i = 0; i <= m; i++) {
        for (j = 0; j <= m; j++) {
            e[i][j] = b[i][j];
        }
        f[i][0] = c[i][0];
        g[i][0] = d[i][0];
    }
    for (i = 0; i <= m; i++) {
        for (j = 1; j <= m; j++) {
            e[i][j + m] = b[i][j];
            e[i + m][j] = b[j][i];
        }
        f[i][1] = c[i][1];
        f[i][2] = c[i][2];
        g[i][1] = d[i][1];
        g[i][2] = d[i][2];
    }
    for (i = 0; i <= 2 * m; i++) {
        sum_x2[i] = 0.0;
        for (j = 0; j < n; j++) {
            sum_x2[i] += pow(samples[j].x, i);
        }
    }
    for (i = 0; i <= 2 * m; i++) {
        for (j = 0; j <= 2 * m; j++) {
            if (i <= m && j <= m) {
                h[i][j] = a[i][j];
            } else if (i <= m && j > m) {
                h[i][j] = sum_x2[i + j];
            } else if (i > m && j <= m) {
                h[i][j] = sum_x2[i + j];
            } else {
                h[i][j] = 0.0;
            }
        }
    }
    // 计算多项式拟合系数
    matrix_inverse(e, 2 * m + 1, i_inv);
    matrix_multiply(i_inv, 2 * m + 1, 2 * m + 1, f, m + 1, 1, temp);
    matrix_multiply(i_inv, 2 * m + 1, 2 * m + 1, g, m + 1, 1, coef);
    matrix_multiply(h, 2 * m + 1, 2 * m + 1, i_inv, 2 * m + 1, m + 1, i_mat);
    matrix_multiply(coef, m + 1, 1, temp, m + 1, 1, temp);
    for (i = 0; i <= m; i++) {
        coef[i] -= temp[i];
    }
    // 释放内存
    for (i = 0; i <= m; i++) {
        free(a[i]);
        free(b[i]);
        free(c[i]);
        free(d[i]);
        free(e[i]);
        free(f[i]);
        free(g[i]);
        free(h[i]);
        free(i_mat[i]);
        free(i_inv[i]);
    }
    for (i = 0; i < n; i++) {
        free(x[i]);
        free(y[i]);
    }
    free(x);
    free(y);
    free(a);
    free(b);
    free(c);
    free(d);
    free(e);
    free(f);
    free(g);
    free(h);
    free(i_mat);
    free(i_inv);
    free(sum_x);
    free(sum_y);
    free(sum_xy);
    free(sum_x2);
    free(temp);
}

int main() {
    Sample samples[N] = {{0.0, 1.0}, {1.0, 0.8}, {2.0, 0.6}, {3.0, 0.4}, {4.0, 0.2}, {5.0, 0.0}, {6.0, -0.2}, {7.0, -0.4}, {8.0, -0.6}, {9.0, -0.8}};
    double coef[M + 1];
    int i;
    // 计算多项式拟合系数
    polynomial_fit(samples, N, M, coef);
    // 输出多项式拟合系数
    for (i = 0; i <= M; i++) {
        printf("%f ", coef[i]);
    }
    printf("\n");
    return 0;
}

在这个代码示例中，我们首先定义了一个 `Sample` 结构体来存储样本数据，然后定义了一些矩阵计算的函数，包括矩阵转置、矩阵乘积和矩阵求逆等。接着我们定义了一个 `polynomial_fit` 函数来计算多项式拟合的系数，该函数使用了偏最小二乘回归的方法来计算系数。最后我们在 `main` 函数中调用 `polynomial_fit` 函数来计算多项式拟合系数，并输出结果。