prho.hpp

// Copyright © 2020 Thomas Nagler
//
// This file is part of the wdm library and licensed under the terms of
// the MIT license. For a copy, see the LICENSE file in the root directory
// or https://github.com/tnagler/wdm/blob/master/LICENSE.
 
#pragma once
 
#include "utils.hpp"
 
namespace wdm {
 
namespace impl {
 
inline double
prho(std::vector<double> x,
     std::vector<double> y,
     std::vector<double> weights = std::vector<double>())
{
  utils::check_sizes(x, y, weights);
  size_t n = x.size();
  if (weights.size() == 0)
    weights = std::vector<double>(x.size(), 1.0);
 
  // calculate means of x and y
  double mu_x = 0.0, mu_y = 0.0, w_sum = 0.0;
  for (size_t i = 0; i < n; i++) {
    mu_x += x[i] * weights[i];
    mu_y += y[i] * weights[i];
    w_sum += weights[i];
  }
  mu_x /= w_sum;
  mu_y /= w_sum;
 
  // substract mean from x and y
  for (size_t i = 0; i < n; i++) {
    x[i] -= mu_x;
    y[i] -= mu_y;
  }
 
  // compute variances and covariance
  double v_x = 0.0, v_y = 0.0, cov = 0.0;
  for (size_t i = 0; i < n; i++) {
    v_x += x[i] * x[i] * weights[i];
    v_y += y[i] * y[i] * weights[i];
    cov += x[i] * y[i] * weights[i];
  }
 
  // compute correlation
  return cov / std::sqrt(v_x * v_y);
}
 
}
 
}