✨ feat(r_square): 添加R²计算功能，更新二次拟合函数参数，优化测试用例

Author: meng-plus

src/algorithm.h

@@ -9,4 +9,6 @@
 #include "algorithms/array_utils.h"
 #include "algorithms/kalman_filter.h"
 #include "algorithms/interpolation.h"
+#include "algorithms/r_square.h"
+
 #endif // ALGORITHM_MODULE_H

src/algorithms/polyfit.c

@@ -144,7 +144,7 @@ void linear_curve_fit(float *x, float *y, int size, float *slope, float *interce
     *intercept = (sum_y - *slope * sum_x) / size;
 }
 // 二次拟合函数
-void quadratic_fit(float *x, float *y, int n, float *a, float *b, float *c)
+void quadratic_fit(float *x, float *y, int n, float *coeff)
 {
     float sum_x = 0, sum_x2 = 0, sum_x3 = 0, sum_x4 = 0;
     float sum_y = 0, sum_xy = 0, sum_x2y = 0;
@@ -181,7 +181,7 @@ void quadratic_fit(float *x, float *y, int n, float *a, float *b, float *c)
         }
     }
 
-    *a = B[2] / A[2][2];
-    *b = (B[1] - A[1][2] * (*a)) / A[1][1];
-    *c = (B[0] - A[0][1] * (*b) - A[0][2] * (*a)) / A[0][0];
+    coeff[2] = B[2] / A[2][2];
+    coeff[1] = (B[1] - A[1][2] * (coeff[2])) / A[1][1];
+    coeff[0] = (B[0] - A[0][1] * (coeff[1]) - A[0][2] * coeff[2]) / A[0][0];
 }

src/algorithms/polyfit.h

@@ -27,11 +27,9 @@ void linear_curve_fit(float *x, float *y, int size, float *slope, float *interce
  * @param x
  * @param y
  * @param n
- * @param a
- * @param b
- * @param c
+ * @param coeff 输出的系数
  */
-void quadratic_fit(float *x, float *y, int n, float *a, float *b, float *c);
+void quadratic_fit(float *x, float *y, int n, float *coeff);
 
 /**
  * @brief 三次拟合函数

src/algorithms/r_square.c

@@ -0,0 +1,59 @@
+#include "r_square.h"
+#include <math.h>
+
+// 计算多项式预测值
+static float predict_float(float x, const float *coeff, int n)
+{
+    float result = 0.0f;
+    for (int i = 0; i <= n; i++) { result += coeff[i] * powf(x, i); }
+    return result;
+}
+
+static double predict_double(double x, const double *coeff, int n)
+{
+    double result = 0.0;
+    for (int i = 0; i <= n; i++) { result += coeff[i] * pow(x, i); }
+    return result;
+}
+
+// 计算R?的函数实现（float版本）
+float r_square_float(const float *d_X, const float *d_Y, int d_N, const float *coeff, int n)
+{
+    float sse = 0.0f, sst = 0.0f, y_mean = 0.0f;
+
+    // 计算实际值的平均值
+    for (int i = 0; i < d_N; i++) { y_mean += d_Y[i]; }
+    y_mean /= d_N;
+
+    // 计算SSE和SST
+    for (int i = 0; i < d_N; i++)
+    {
+        float y_pred  = predict_float(d_X[i], coeff, n);
+        sse          += (y_pred - d_Y[i]) * (y_pred - d_Y[i]);
+        sst          += (d_Y[i] - y_mean) * (d_Y[i] - y_mean);
+    }
+
+    // 计算R?
+    return 1.0f - (sse / sst);
+}
+
+// 计算R?的函数实现（double版本）
+double r_square_double(const double *d_X, const double *d_Y, int d_N, const double *coeff, int n)
+{
+    double sse = 0.0, sst = 0.0, y_mean = 0.0;
+
+    // 计算实际值的平均值
+    for (int i = 0; i < d_N; i++) { y_mean += d_Y[i]; }
+    y_mean /= d_N;
+
+    // 计算SSE和SST
+    for (int i = 0; i < d_N; i++)
+    {
+        double y_pred  = predict_double(d_X[i], coeff, n);
+        sse           += (y_pred - d_Y[i]) * (y_pred - d_Y[i]);
+        sst           += (d_Y[i] - y_mean) * (d_Y[i] - y_mean);
+    }
+
+    // 计算R?
+    return 1.0 - (sse / sst);
+}

src/algorithms/r_square.h

@@ -0,0 +1,32 @@
+/**
+ * @file r_square.h
+ * @brief
+ * 在C语言中，你可以通过以下步骤来计算这些拟合优度参数：
+ * 计算预测值：使用拟合得到的多项式系数，计算每个数据点的预测值。
+ * 计算SSE：对于每个数据点，计算预测值与实际值之间的差异，平方后求和。
+ * 计算R?：
+ * 计算实际值的平均值。
+ * 计算总平方和（SST），即每个实际值与平均值的差异的平方和。
+ * R? = 1 - (SSE / SST)
+ * 计算Adjusted R?：
+ * Adjusted R? = 1 - [(1 - R?) * (n - 1) / (n - p - 1)]
+ * 其中，n是数据点的数量，p是模型中参数的个数。
+ * 计算RMSE：
+ * RMSE = sqrt(SSE / n)
+ * @author mengplus ([email protected])
+ * @version  0.1
+ * @date 2025-03-25
+ * @copyright Copyright (c) 2025  Zhengzhou GL. TECH Co.,Ltd
+ *
+ */
+
+#ifndef R_SQUARE_H
+#define R_SQUARE_H
+
+#include <stddef.h>
+
+// 计算R?的函数声明
+float r_square_float(const float *d_X, const float *d_Y, int d_N, const float *coeff, int n);
+double r_square_double(const double *d_X, const double *d_Y, int d_N, const double *coeff, int n);
+
+#endif // R_SQUARE_H

test/test_algorithms.c

@@ -11,14 +11,12 @@ START_TEST(test_meanFilterFloat)
 }
 END_TEST
 
-START_TEST(test_meanFilterint32)
-{
-    int data[] = {1, 2, 3, 4, 5};
-    ck_assert_int_eq(meanFilterint32(data, 5), 3.0);
-}
-END_TEST
 START_TEST(test_medianFilter)
 {
+    {
+        int data[] = {1, 2, 3, 4, 5};
+        ck_assert_int_eq(meanFilterint32(data, 5), 3.0);
+    }
     float data[] = {21, 30, 15, 25, 35};
     float median = 0;
     medianFilter(data, 5, sizeof(float), &median, compareFloat);
@@ -99,12 +97,6 @@ START_TEST(test_kalman_filter_multiple_updates)
     ck_assert(final_error < 0.2);
 }
 END_TEST
-
-// 辅助函数：比较浮点数是否相等（允许一定的误差）
-int float_equal(float a, float b, float epsilon)
-{
-    return fabs(a - b) < epsilon;
-}
 // 测试用例 1：简单的线性数据
 START_TEST(test_linear_curve_fit_simple)
 {
@@ -114,8 +106,8 @@ START_TEST(test_linear_curve_fit_simple)
     float slope, intercept;
     linear_curve_fit(x, y, size, &slope, &intercept);
     // 预期结果：斜率为 2，截距为 0
-    ck_assert(float_equal(slope, 2.0f, 1e-6));
-    ck_assert(float_equal(intercept, 0.0f, 1e-6));
+    ck_assert_float_eq_tol(slope, 2.0f, 1e-6);
+    ck_assert_float_eq_tol(intercept, 0.0f, 1e-6);
 }
 END_TEST
 // 测试用例 2：带截距的线性数据
@@ -127,8 +119,8 @@ START_TEST(test_linear_curve_fit_intercept)
     float slope, intercept;
     linear_curve_fit(x, y, size, &slope, &intercept);
     // 预期结果：斜率为 2，截距为 1
-    ck_assert(float_equal(slope, 2.0f, 1e-6));
-    ck_assert(float_equal(intercept, 1.0f, 1e-6));
+    ck_assert_float_eq_tol(slope, 2.0f, 1e-6);
+    ck_assert_float_eq_tol(intercept, 1.0f, 1e-6);
 }
 END_TEST
 // 测试用例 3：随机数据
@@ -140,8 +132,8 @@ START_TEST(test_linear_curve_fit_random)
     float slope, intercept;
     linear_curve_fit(x, y, size, &slope, &intercept);
     // 预期结果：斜率接近 2，截距接近 1
-    ck_assert(float_equal(slope, 1.65f, 1e-2));
-    ck_assert(float_equal(intercept, 1.1f, 1e-2));
+    ck_assert_float_eq_tol(slope, 1.65f, 1e-2);
+    ck_assert_float_eq_tol(intercept, 1.1f, 1e-2);
 }
 END_TEST
 // 测试用例 1：简单的二次拟合
@@ -150,12 +142,15 @@ START_TEST(test_quadratic_fit_simple)
     float x[] = {0, 1, 2, 3, 4};
     float y[] = {1, 4, 9, 16, 25};
     int size  = sizeof(x) / sizeof(x[0]);
-    float a, b, c;
-    quadratic_fit(x, y, size, &a, &b, &c);
-    // 预期结果：a = 1, b = 2, c = 1 (y = 1*x^2 + 2*x + 1)
-    ck_assert(float_equal(a, 1.0f, 1e-6));
-    ck_assert(float_equal(b, 2.0f, 1e-6));
-    ck_assert(float_equal(c, 1.0f, 1e-6));
+    float coeff[3];
+    quadratic_fit(x, y, size, coeff);
+    // 预期结果：y = p1+p2*x+p3*x^2
+    ck_assert_float_eq_tol(coeff[2], 1.0f, 1e-6);
+    ck_assert_float_eq_tol(coeff[1], 2.0f, 1e-6);
+    ck_assert_float_eq_tol(coeff[0], 1.0f, 1e-6);
+    // 计算R²
+    float r2_float = r_square_float(x, y, 5, coeff, 2);
+    ck_assert_float_eq_tol(r2_float, 1.0f, 1e-6);
 }
 END_TEST
 // 测试用例 2：带线性项和常数的二次拟合
@@ -164,12 +159,12 @@ START_TEST(test_quadratic_fit_with_terms)
     float x[] = {0, 1, 2, 3, 4};
     float y[] = {2, 5, 12, 23, 38};
     int size  = sizeof(x) / sizeof(x[0]);
-    float a, b, c;
-    quadratic_fit(x, y, size, &a, &b, &c);
-    // 预期结果：a = 2, b = 1, c = 2 (y = 2x^2 + 1x + 2)
-    ck_assert(float_equal(a, 2.0f, 1e-6));
-    ck_assert(float_equal(b, 1.0f, 1e-6));
-    ck_assert(float_equal(c, 2.0f, 1e-6));
+    float coeff[3];
+    quadratic_fit(x, y, size, coeff);
+    // 预期结果：y = p1+p2*x+p3*x^2
+    ck_assert_float_eq_tol(coeff[2], 2.0f, 1e-6);
+    ck_assert_float_eq_tol(coeff[1], 1.0f, 1e-6);
+    ck_assert_float_eq_tol(coeff[0], 2.0f, 1e-6);
 }
 END_TEST
 // 测试用例 3：随机数据的二次拟合
@@ -178,12 +173,12 @@ START_TEST(test_quadratic_fit_random)
     float x[] = {-2, -1, 0, 1, 2};
     float y[] = {8, -1, -6, -1, 8};
     int size  = sizeof(x) / sizeof(x[0]);
-    float a, b, c;
-    quadratic_fit(x, y, size, &a, &b, &c);
-    // 预期结果：a =3.285714, b = 0.0, c = -4.971429  (y = ax^2 + bx - c)
-    ck_assert(float_equal(a, 3.285714f, 1e-6));
-    ck_assert(float_equal(b, 0.0f, 1e-6));
-    ck_assert(float_equal(c, -4.971429f, 1e-6));
+    float coeff[3];
+    quadratic_fit(x, y, size, coeff);
+    // 预期结果：y = p1+p2*x+p3*x^2
+    ck_assert_double_eq_tol(coeff[2], 3.285714f, 1e-6);
+    ck_assert_double_eq_tol(coeff[1], 0.0f, 1e-6);
+    ck_assert_double_eq_tol(coeff[0], -4.971429f, 1e-6);
 }
 END_TEST
 
@@ -203,7 +198,9 @@ START_TEST(test_cubic_fit)
     double coef[4];
 
     polyfit(x, y, n, 3, coef);
-
+    // 计算R²
+    float r2_float = r_square_double(x, y, n, coef, 3);
+    ck_assert_double_eq_tol(r2_float, 0.961957f, 1e-6);
     // printf("拟合的三次多项式为: y = %.12fx^3 + %.12fx^2 + %.12fx + %.12f\n", coef[3], coef[2], coef[1], coef[0]);
 
     double x_max_y, max_y;
@@ -456,8 +453,6 @@ Suite *algorithms_suite(void)
 
     /* Core test case */
     tc_mean = tcase_create("mean");
-
-    tcase_add_test(tc_mean, test_meanFilterint32);
     tcase_add_test(tc_mean, test_meanFilterFloat);
     tcase_add_test(tc_mean, test_medianFilter);
     tcase_add_test(tc_mean, test_kalman_filter_init);