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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Klaus Spanderen
Copyright (C) 2010 Slava Mazur
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/math/randomnumbers/rngtraits.hpp>
#include <ql/math/linearleastsquaresregression.hpp>
#include <boost/circular_buffer.hpp>
#include <functional>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(LinearLeastSquaresRegressionTests)
BOOST_AUTO_TEST_CASE(testRegression) {
BOOST_TEST_MESSAGE("Testing linear least-squares regression...");
const Real tolerance = 0.05;
const Size nr=100000;
PseudoRandom::rng_type rng(PseudoRandom::urng_type(1234U));
std::vector<std::function<Real(Real)>> v = {
[](Real x) -> Real { return 1.0; },
[](Real x) -> Real { return x; },
[](Real x) -> Real { return x*x; },
[](Real x) -> Real { return std::sin(x); }
};
std::vector<std::function<Real(Real)>> w(v);
w.emplace_back([](Real x){ return x*x; });
for (Size k=0; k<3; ++k) {
Size i;
const Real a[] = {
rng.next().value,
rng.next().value,
rng.next().value,
rng.next().value
};
std::vector<Real> x(nr), y(nr);
for (i=0; i<nr; ++i) {
x[i] = rng.next().value;
// regression in y = a_1 + a_2*x + a_3*x^2 + a_4*sin(x) + eps
y[i] = a[0]*v[0](x[i]) + a[1]*v[1](x[i]) + a[2]*v[2](x[i])
+ a[3]*v[3](x[i]) + rng.next().value;
}
LinearRegression m(x, y, v);
for (i=0; i<v.size(); ++i) {
if (m.standardErrors()[i] > tolerance) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n error: " << m.standardErrors()[i]
<< "\n tolerance: " << tolerance);
}
if (std::fabs(m.coefficients()[i]-a[i]) > 3*m.standardErrors()[i]) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n calculated: " << m.coefficients()[i]
<< "\n error: " << m.standardErrors()[i]
<< "\n expected: " << a[i]);
}
}
m = LinearRegression(x, y, w);
const Real ma[] = {m.coefficients()[0], m.coefficients()[1],
m.coefficients()[2]+m.coefficients()[4],
m.coefficients()[3]};
const Real err[] = {m.standardErrors()[0], m.standardErrors()[1],
std::sqrt( m.standardErrors()[2]*m.standardErrors()[2]
+m.standardErrors()[4]*m.standardErrors()[4]),
m.standardErrors()[3]};
for (i=0; i<v.size(); ++i) {
if (std::fabs(ma[i] - a[i]) > 3*err[i]) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n calculated: " << ma[i]
<< "\n error: " << err[i]
<< "\n expected: " << a[i]);
}
}
}
}
struct get_item {
Size i;
explicit get_item(Size i) : i(i) {}
Real operator()(const Array& a) const {
return a[i];
}
};
BOOST_AUTO_TEST_CASE(testMultiDimRegression) {
BOOST_TEST_MESSAGE(
"Testing multi-dimensional linear least-squares regression...");
const Size nr=100000;
const Size dims = 4;
const Real tolerance = 0.01;
PseudoRandom::rng_type rng(PseudoRandom::urng_type(1234U));
std::vector<std::function<Real(Array)> > v;
v.emplace_back([](const Array& x) { return 1.0; });
for (Size i=0; i < dims; ++i) {
v.emplace_back(get_item(i));
}
Array coeff(v.size());
for (Size i=0; i < v.size(); ++i) {
coeff[i] = rng.next().value;
}
std::vector<Real> y(nr, 0.0);
std::vector<Array> x(nr, Array(dims));
for (Size i=0; i < nr; ++i) {
for (Size j=0; j < dims; ++j) {
x[i][j] = rng.next().value;
}
for (Size j=0; j < v.size(); ++j) {
y[i] += coeff[j]*v[j](x[i]);
}
y[i] += rng.next().value;
}
LinearRegression m(x, y, v);
for (Size i=0; i < v.size(); ++i) {
if (m.standardErrors()[i] > tolerance) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n error: " << m.standardErrors()[i]
<< "\n tolerance: " << tolerance);
}
if (std::fabs(m.coefficients()[i]-coeff[i]) > 3*tolerance) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n calculated: " << m.coefficients()[i]
<< "\n error: " << m.standardErrors()[i]
<< "\n expected: " << coeff[i]);
}
}
// much simpler
LinearRegression m1(x, y, Real(1.0));
for (Size i=0; i < m1.dim(); ++i) {
if (m1.standardErrors()[i] > tolerance) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n error: " << m1.standardErrors()[i]
<< "\n tolerance: " << tolerance);
}
if (std::fabs(m1.coefficients()[i]-coeff[i]) > 3*tolerance) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n calculated: " << m1.coefficients()[i]
<< "\n error: " << m1.standardErrors()[i]
<< "\n expected: " << coeff[i]);
}
}
}
BOOST_AUTO_TEST_CASE(test1dLinearRegression) {
BOOST_TEST_MESSAGE("Testing 1D simple linear least-squares regression...");
/* Example taken from the QuantLib-User list, see posting
* Multiple linear regression/weighted regression, Boris Skorodumov */
std::vector<Real> x = {2.4, 1.8, 2.5, 3.0, 2.1, 1.2, 2.0, 2.7, 3.6};
std::vector<Real> y = {7.8, 5.5, 8.0, 9.0, 6.5, 4.0, 6.3, 8.4, 10.2};
std::vector<std::function<Real(Real)>> v = {
[](Real x) { return 1.0; },
[](Real x) { return x; }
};
LinearRegression m(x, y);
const Real tol = 0.0002;
const Real coeffExpected[] = { 0.9448, 2.6853 };
const Real errorsExpected[] = { 0.3654, 0.1487 };
for (Size i=0; i < 2; ++i) {
if (std::fabs(m.standardErrors()[i]-errorsExpected[i]) > tol) {
BOOST_ERROR("Failed to reproduce linear regression standard errors"
<< "\n calculated: " << m.standardErrors()[i]
<< "\n expected: " << errorsExpected[i]
<< "\n tolerance: " << tol);
}
if (std::fabs(m.coefficients()[i]-coeffExpected[i]) > tol) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n calculated: " << m.coefficients()[i]
<< "\n expected: " << coeffExpected[i]
<< "\n tolerance: " << tol);
}
}
// an alternative container type
boost::circular_buffer<Real> cx(x.begin(), x.end()), cy(y.begin(), y.end());
LinearRegression m1(cx, cy);
for (Size i=0; i < 2; ++i) {
if (std::fabs(m1.standardErrors()[i]-errorsExpected[i]) > tol) {
BOOST_ERROR("Failed to reproduce linear regression standard errors"
<< "\n calculated: " << m1.standardErrors()[i]
<< "\n expected: " << errorsExpected[i]
<< "\n tolerance: " << tol);
}
if (std::fabs(m1.coefficients()[i]-coeffExpected[i]) > tol) {
BOOST_ERROR("Failed to reproduce linear regression coef."
<< "\n calculated: " << m1.coefficients()[i]
<< "\n expected: " << coeffExpected[i]
<< "\n tolerance: " << tol);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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