statistics.cpp

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// Copyright (c) 2024 anabrid GmbH
// Contact: https://www.anabrid.com/licensing/
//
// SPDX-License-Identifier: MIT OR GPL-2.0-or-later
 
#include "utils/statistics.h"
 
#include <cmath>
 
// Input pairs consist of <x, y>
// Returns y = a + b * x
// where a is the first element, b the second and the third element is R^2
std::tuple<float, float, float> regression(const std::vector<std::pair<float, float>> &data) {
  float a = 0.0f, b = 0.0f;
  float x_avg = 0.0f, y_avg = 0.0f;
 
  for (size_t i = 0; i < data.size(); i++) {
    x_avg += data[i].first;
    y_avg += data[i].second;
  }
 
  x_avg /= data.size();
  y_avg /= data.size();
 
  float p = 0.0f, q = 0.0f;
 
  for (size_t i = 0; i < data.size(); i++) {
    p += (data[i].first - x_avg) * (data[i].second - y_avg);
    q += (data[i].first - x_avg) * (data[i].first - x_avg);
  }
 
  b = p / q;
  a = y_avg - b * x_avg;
 
  float r_sq = 1.0f;
 
  p = q = 0.0f;
 
  for (size_t i = 0; i < data.size(); i++) {
    p += (data[i].second - (a + data[i].first * b)) * (data[i].second - (a + data[i].first * b));
    q += (data[i].second - y_avg) * (data[i].second - y_avg);
  }
 
  r_sq -= p / q;
 
  return {a, b, r_sq};
}
 
// Standard deviation
// Returns <average, standard deviation>
std::tuple<float, float> std_dev(const std::vector<float> &data) {
  float avg = vector_sum(data);
  avg /= data.size();
 
  float dev = 0.0f;
  for (size_t i = 0; i < data.size(); i++)
    dev += (data[i] - avg) * (data[i] - avg);
 
  dev /= data.size();
  dev = sqrt(dev);
 
  return std::make_tuple(avg, dev);
}
 
// Calculates the mean square error of a data set, compared to an expected value data set
float mean_sq_error(const std::vector<float> &data, const std::vector<float> &expected) {
  if (data.size() != expected.size())
    return -1;
 
  float sum = 0.0f;
 
  for (size_t i = 0; i < data.size(); i++)
    sum += (data[i] - expected[i]) * (data[i] - expected[i]);
 
  return sum / data.size();
}