chore: import upstream snapshot with attribution

math/realtime_stats.cpp

@@ -0,0 +1,193 @@
+/**
+ * \file
+ * \brief Compute statistics for data entered in rreal-time
+ *
+ * This algorithm is really beneficial to compute statistics on data read in
+ * realtime. For example, devices reading biometrics data. The algorithm is
+ * simple enough to be easily implemented in an embedded system.
+ * \author [Krishna Vedala](https://github.com/kvedala)
+ */
+#include <cassert>
+#include <cmath>
+#include <iostream>
+
+/**
+ * \namespace statistics
+ * \brief Statistical algorithms
+ */
+namespace statistics {
+
+/**
+ * continuous mean and variance computance using
+ * first value as an approximation for the mean.
+ * If the first number is much far form the mean, the algorithm becomes very
+ * inaccurate to compute variance and standard deviation.
+ */
+template <typename T>
+class stats_computer1 {
+ public:
+    /** Constructor
+     * \param[in] x new data sample
+     */
+    void new_val(T x) {
+        if (n == 0)
+            K = x;
+        n++;
+        T tmp = x - K;
+        Ex += tmp;
+        Ex2 += static_cast<double>(tmp) * tmp;
+    }
+
+    /** return sample mean computed till last sample */
+    double mean() const { return K + Ex / n; }
+
+    /** return data variance computed till last sample */
+    double variance() const { return (Ex2 - (Ex * Ex) / n) / (n - 1); }
+
+    /** return sample standard deviation computed till last sample */
+    double std() const { return std::sqrt(this->variance()); }
+
+    /** short-hand operator to read new sample from input stream
+     * \n e.g.: `std::cin >> stats1;`
+     */
+    friend std::istream &operator>>(std::istream &input,
+                                    stats_computer1 &stat) {
+        T val;
+        input >> val;
+        stat.new_val(val);
+        return input;
+    }
+
+ private:
+    unsigned int n = 0;
+    double Ex, Ex2;
+    T K;
+};
+
+/**
+ * continuous mean and variance computance using
+ * Welford's algorithm  (very accurate)
+ */
+template <typename T>
+class stats_computer2 {
+ public:
+    /** Constructor
+     * \param[in] x new data sample
+     */
+    void new_val(T x) {
+        n++;
+        double delta = x - mu;
+        mu += delta / n;
+        double delta2 = x - mu;
+        M += delta * delta2;
+    }
+
+    /** return sample mean computed till last sample */
+    double mean() const { return mu; }
+
+    /** return data variance computed till last sample */
+    double variance() const { return M / n; }
+
+    /** return sample standard deviation computed till last sample */
+    double std() const { return std::sqrt(this->variance()); }
+
+    /** short-hand operator to read new sample from input stream
+     * \n e.g.: `std::cin >> stats1;`
+     */
+    friend std::istream &operator>>(std::istream &input,
+                                    stats_computer2 &stat) {
+        T val;
+        input >> val;
+        stat.new_val(val);
+        return input;
+    }
+
+ private:
+    unsigned int n = 0;
+    double mu = 0, var = 0, M = 0;
+};
+
+}  // namespace statistics
+
+using statistics::stats_computer1;
+using statistics::stats_computer2;
+
+/** Test the algorithm implementation
+ * \param[in] test_data array of data to test the algorithms
+ */
+void test_function(const float *test_data, const int number_of_samples) {
+    float mean = 0.f, variance = 0.f;
+
+    stats_computer1<float> stats01;
+    stats_computer2<float> stats02;
+
+    for (int i = 0; i < number_of_samples; i++) {
+        stats01.new_val(test_data[i]);
+        stats02.new_val(test_data[i]);
+        mean += test_data[i];
+    }
+
+    mean /= number_of_samples;
+
+    for (int i = 0; i < number_of_samples; i++) {
+        float temp = test_data[i] - mean;
+        variance += temp * temp;
+    }
+    variance /= number_of_samples;
+
+    std::cout << "<<<<<<<< Test Function >>>>>>>>" << std::endl
+              << "Expected: Mean: " << mean << "\t Variance: " << variance
+              << std::endl;
+    std::cout << "\tMethod 1:"
+              << "\tMean: " << stats01.mean()
+              << "\t Variance: " << stats01.variance()
+              << "\t Std: " << stats01.std() << std::endl;
+    std::cout << "\tMethod 2:"
+              << "\tMean: " << stats02.mean()
+              << "\t Variance: " << stats02.variance()
+              << "\t Std: " << stats02.std() << std::endl;
+
+    assert(std::abs(stats01.mean() - mean) < 0.01);
+    assert(std::abs(stats02.mean() - mean) < 0.01);
+    assert(std::abs(stats02.variance() - variance) < 0.01);
+
+    std::cout << "(Tests passed)" << std::endl;
+}
+
+/** Main function */
+int main() {
+    const float test_data1[] = {3, 4, 5, -1.4, -3.6, 1.9, 1.};
+    test_function(test_data1, sizeof(test_data1) / sizeof(test_data1[0]));
+
+    std::cout
+        << "Enter data. Any non-numeric data will terminate the data input."
+        << std::endl;
+
+    stats_computer1<float> stats1;
+    stats_computer2<float> stats2;
+
+    while (1) {
+        double val;
+        std::cout << "Enter number: ";
+        std::cin >> val;
+
+        // check for failure to read input. Happens for
+        // non-numeric data
+        if (std::cin.fail())
+            break;
+
+        stats1.new_val(val);
+        stats2.new_val(val);
+
+        std::cout << "\tMethod 1:"
+                  << "\tMean: " << stats1.mean()
+                  << "\t Variance: " << stats1.variance()
+                  << "\t Std: " << stats1.std() << std::endl;
+        std::cout << "\tMethod 2:"
+                  << "\tMean: " << stats2.mean()
+                  << "\t Variance: " << stats2.variance()
+                  << "\t Std: " << stats2.std() << std::endl;
+    }
+
+    return 0;
+}