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/*
* Copyright Nick Thompson, 2019
* Copyright Matt Borland, 2021
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#include "math_unit_test.hpp"
#include <vector>
#include <random>
#include <utility>
#include <tuple>
#include <algorithm>
#include <boost/math/statistics/linear_regression.hpp>
using boost::math::statistics::simple_ordinary_least_squares;
using boost::math::statistics::simple_ordinary_least_squares_with_R_squared;
template<typename Real>
void test_line()
{
std::vector<Real> x(128);
std::vector<Real> y(128);
Real expected_c0 = 7;
Real expected_c1 = 12;
for (size_t i = 0; i < x.size(); ++i) {
x[i] = i;
y[i] = expected_c0 + expected_c1*x[i];
}
std::pair<Real, Real> temp = simple_ordinary_least_squares(x, y);
Real computed_c0 = std::get<0>(temp);
Real computed_c1 = std::get<1>(temp);
CHECK_ULP_CLOSE(expected_c0, computed_c0, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1, 0);
std::tuple<Real, Real, Real> temp_with_R = simple_ordinary_least_squares_with_R_squared(x, y);
Real computed_c0_R = std::get<0>(temp_with_R);
Real computed_c1_R = std::get<1>(temp_with_R);
Real Rsquared = std::get<2>(temp_with_R);
Real expected_Rsquared = 1;
CHECK_ULP_CLOSE(expected_c0, computed_c0_R, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1_R, 0);
CHECK_ULP_CLOSE(expected_Rsquared, Rsquared, 0);
}
template<typename Z>
void test_integer_line()
{
std::vector<Z> x(128);
std::vector<Z> y(128);
double expected_c0 = 7;
double expected_c1 = 12;
for (size_t i = 0; i < x.size(); ++i) {
x[i] = i;
y[i] = expected_c0 + expected_c1*x[i];
}
std::pair<double, double> temp = simple_ordinary_least_squares(x, y);
double computed_c0 = std::get<0>(temp);
double computed_c1 = std::get<1>(temp);
CHECK_ULP_CLOSE(expected_c0, computed_c0, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1, 0);
std::tuple<double, double, double> temp_with_R = simple_ordinary_least_squares_with_R_squared(x, y);
double computed_c0_R = std::get<0>(temp_with_R);
double computed_c1_R = std::get<1>(temp_with_R);
double Rsquared = std::get<2>(temp_with_R);
double expected_Rsquared = 1;
CHECK_ULP_CLOSE(expected_c0, computed_c0_R, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1_R, 0);
CHECK_ULP_CLOSE(expected_Rsquared, Rsquared, 0);
}
template<typename Real>
void test_constant()
{
std::vector<Real> x(128);
std::vector<Real> y(128);
Real expected_c0 = 7;
Real expected_c1 = 0;
for (size_t i = 0; i < x.size(); ++i) {
x[i] = i;
y[i] = expected_c0 + expected_c1*x[i];
}
std::pair<Real, Real> temp = simple_ordinary_least_squares(x, y);
Real computed_c0 = std::get<0>(temp);
Real computed_c1 = std::get<1>(temp);
CHECK_ULP_CLOSE(expected_c0, computed_c0, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1, 0);
std::tuple<Real, Real, Real> temp_with_R = simple_ordinary_least_squares_with_R_squared(x, y);
Real computed_c0_R = std::get<0>(temp_with_R);
Real computed_c1_R = std::get<1>(temp_with_R);
Real Rsquared = std::get<2>(temp_with_R);
Real expected_Rsquared = 1;
CHECK_ULP_CLOSE(expected_c0, computed_c0_R, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1_R, 0);
CHECK_ULP_CLOSE(expected_Rsquared, Rsquared, 0);
}
template<typename Z>
void test_integer_constant()
{
std::vector<Z> x(128);
std::vector<Z> y(128);
double expected_c0 = 7;
double expected_c1 = 0;
for (size_t i = 0; i < x.size(); ++i) {
x[i] = i;
y[i] = expected_c0 + expected_c1*x[i];
}
std::pair<double, double> temp = simple_ordinary_least_squares(x, y);
double computed_c0 = std::get<0>(temp);
double computed_c1 = std::get<1>(temp);
CHECK_ULP_CLOSE(expected_c0, computed_c0, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1, 0);
std::tuple<double, double, double> temp_with_R = simple_ordinary_least_squares_with_R_squared(x, y);
double computed_c0_R = std::get<0>(temp_with_R);
double computed_c1_R = std::get<1>(temp_with_R);
double Rsquared = std::get<2>(temp_with_R);
double expected_Rsquared = 1;
CHECK_ULP_CLOSE(expected_c0, computed_c0_R, 0);
CHECK_ULP_CLOSE(expected_c1, computed_c1_R, 0);
CHECK_ULP_CLOSE(expected_Rsquared, Rsquared, 0);
}
template<typename Real>
void test_permutation_invariance()
{
std::vector<Real> x(256);
std::vector<Real> y(256);
std::mt19937_64 gen{123456};
std::normal_distribution<Real> dis(0, 0.1);
Real expected_c0 = -7.2;
Real expected_c1 = -13.5;
x[0] = 0;
y[0] = expected_c0 + dis(gen);
for(size_t i = 1; i < x.size(); ++i) {
Real t = dis(gen);
x[i] = x[i-1] + t*t;
y[i] = expected_c0 + expected_c1*x[i] + dis(gen);
}
std::tuple<Real, Real, Real> temp = simple_ordinary_least_squares_with_R_squared(x, y);
Real c0 = std::get<0>(temp);
Real c1 = std::get<1>(temp);
Real Rsquared = std::get<2>(temp);
CHECK_MOLLIFIED_CLOSE(expected_c0, c0, 0.003);
CHECK_MOLLIFIED_CLOSE(expected_c1, c1, 0.002);
int j = 0;
std::mt19937_64 gen1{12345};
std::mt19937_64 gen2{12345};
while(j++ < 10) {
std::shuffle(x.begin(), x.end(), gen1);
std::shuffle(y.begin(), y.end(), gen2);
std::tuple<Real, Real, Real> temp_ = simple_ordinary_least_squares_with_R_squared(x, y);
Real c0_ = std::get<0>(temp_);
Real c1_ = std::get<1>(temp_);
Real Rsquared_ = std::get<2>(temp_);
CHECK_ULP_CLOSE(c0, c0_, 100);
CHECK_ULP_CLOSE(c1, c1_, 100);
CHECK_ULP_CLOSE(Rsquared, Rsquared_, 65);
}
}
template<typename Real>
void test_scaling_relations()
{
std::vector<Real> x(256);
std::vector<Real> y(256);
std::mt19937_64 gen{123456};
std::normal_distribution<Real> dis(0, 0.1);
Real expected_c0 = 3.2;
Real expected_c1 = -13.5;
x[0] = 0;
y[0] = expected_c0 + dis(gen);
for(size_t i = 1; i < x.size(); ++i) {
Real t = dis(gen);
x[i] = x[i-1] + t*t;
y[i] = expected_c0 + expected_c1*x[i] + dis(gen);
}
std::tuple<Real, Real, Real> temp = simple_ordinary_least_squares_with_R_squared(x, y);
Real c0 = std::get<0>(temp);
Real c1 = std::get<1>(temp);
Real Rsquared = std::get<2>(temp);
CHECK_MOLLIFIED_CLOSE(expected_c0, c0, 0.006);
CHECK_MOLLIFIED_CLOSE(expected_c1, c1, 0.005);
// If y -> lambda y, then c0 -> lambda c0 and c1 -> lambda c1.
Real lambda = 6;
for (auto& s : y) {
s *= lambda;
}
temp = simple_ordinary_least_squares_with_R_squared(x, y);
Real c0_lambda = std::get<0>(temp);
Real c1_lambda = std::get<1>(temp);
Real Rsquared_lambda = std::get<2>(temp);
CHECK_ULP_CLOSE(lambda*c0, c0_lambda, 70);
CHECK_ULP_CLOSE(lambda*c1, c1_lambda, 30);
CHECK_ULP_CLOSE(Rsquared, Rsquared_lambda, 3);
// If x -> lambda x, then c0 -> c0 and c1 -> c1/lambda
for (auto& s : x) {
s *= lambda;
}
// Put y back into it's original state:
for (auto& s : y) {
s /= lambda;
}
temp = simple_ordinary_least_squares_with_R_squared(x, y);
Real c0_ = std::get<0>(temp);
Real c1_ = std::get<1>(temp);
Real Rsquared_ = std::get<2>(temp);
CHECK_ULP_CLOSE(c0, c0_, 100);
CHECK_ULP_CLOSE(c1, c1_*lambda, 50);
CHECK_ULP_CLOSE(Rsquared, Rsquared_, 50);
}
int main()
{
test_line<float>();
test_line<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_line<long double>();
#endif
test_integer_line<int>();
test_integer_line<int32_t>();
test_integer_line<int64_t>();
test_integer_line<uint32_t>();
test_constant<float>();
test_constant<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_constant<long double>();
#endif
test_integer_constant<int>();
test_integer_constant<int32_t>();
test_integer_constant<int64_t>();
test_integer_constant<uint32_t>();
test_permutation_invariance<float>();
test_permutation_invariance<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_permutation_invariance<long double>();
#endif
test_scaling_relations<float>();
test_scaling_relations<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_scaling_relations<long double>();
#endif
return boost::math::test::report_errors();
}
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