偏最小二乘回归c语言实现

偏最小二乘回归（Partial Least Squares Regression，PLSR）是一种统计回归方法，用于处理多元回归问题。与普通最小二乘回归相比，PLSR可以在存在多个自变量之间的共线性或高维数据情况下，减小模型的复杂度，提高预测性能。

实现偏最小二乘回归的C语言代码如下：

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

#define MAX_ROWS 100
#define MAX_COLS 100

void PLSR(double X[MAX_ROWS][MAX_COLS], double y[MAX_ROWS], int n, int p, int m) {
    double T[MAX_ROWS][MAX_COLS]; // Score matrix
    double P[MAX_COLS][MAX_COLS]; // Loading matrix
    double W[MAX_COLS][MAX_COLS]; // Weight matrix
    double C[MAX_COLS][MAX_COLS]; // Regression coefficient matrix
    double B[MAX_COLS]; // Regression coefficient vector
    double E[MAX_ROWS]; // Residuals vector
    double w[MAX_COLS]; // Current weight vector
    double t[MAX_ROWS]; // Current score vector
    double p[MAX_COLS]; // Current loading vector
    double c[MAX_COLS]; // Current regression coefficient vector
    int i, j, k;

    // Initializing matrices
    for (i = 0; i < m; i++) {
        for (j = 0; j < p; j++) {
            W[i][j] = 0.0;
        }
    }

    // Performing PLSR iterations
    for (k = 0; k < m; k++) {
        for (i = 0; i < p; i++) {
            w[i] = 0.0;
            for (j = 0; j < n; j++) {
                w[i] += X[j][i] * y[j];
            }
            for (j = 0; j < i; j++) {
                w[i] -= p[j] * W[k][j];
            }
            for (j = 0; j < i; j++) {
                w[i] /= sqrt(P[j][j]);
            }
        }

        double w_norm = 0.0;
        for (i = 0; i < p; i++) {
            w_norm += w[i] * w[i];
        }
        w_norm = sqrt(w_norm);

        for (i = 0; i < p; i++) {
            w[i] = w[i] / w_norm;
        }

        for (i = 0; i < n; i++) {
            t[i] = 0.0;
            for (j = 0; j < p; j++) {
                t[i] += X[i][j] * w[j];
            }
        }

        double t_norm = 0.0;
        for (i = 0; i < n; i++) {
            t_norm += t[i] * t[i];
        }
        t_norm = sqrt(t_norm);

        for (i = 0; i < n; i++) {
            t[i] = t[i] / t_norm;
        }

        for (i = 0; i < p; i++) {
            p[i] = 0.0;
            for (j = 0; j < n; j++) {
                p[i] += X[j][i] * t[j];
            }
            for (j = 0; j < k; j++) {
                p[i] -= P[j][i] * W[k][j];
            }
            p[i] = p[i] / (t_norm * t_norm);
        }

        for (i = 0; i < n; i++) {
            for (j = 0; j < p; j++) {
                X[i][j] -= t[i] * p[j];
            }
        }

        for (i = 0; i < p; i++) {
            P[k][i] = p[i];
            W[k][i] = w[i];
        }

        c[k] = 0.0;
        for (i = 0; i < n; i++) {
            c[k] += y[i] * t[i];
        }
        c[k] = c[k] / (t_norm * t_norm);

        for (i = 0; i < n; i++) {
            y[i] -= c[k] * t[i];
        }
    }

    for (i = 0; i < m; i++) {
        B[i] = 0.0;
        for (j = 0; j < m; j++) {
            B[i] += W[i][j] * c[j];
        }
    }

    // Print the regression coefficient vector
    printf("Regression Coefficient Vector: ");
    for (i = 0; i < m; i++) {
        printf("%lf ", B[i]);
    }
    printf("\n");
}

int main() {
    // Sample data
    double X[MAX_ROWS][MAX_COLS] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    double y[MAX_ROWS] = {10, 11, 12};
    int n = 3; // Number of data points
    int p = 3; // Number of independent variables
    int m = 1; // Number of components

    PLSR(X, y, n, p, m); // Perform PLSR

    return 0;
}

这是一个简单的实现，可根据实际需求进行修改和优化。请注意，以上代码仅用于示范，并不包含完整的错误处理和边界情况处理。