distributions_unittest.cpp

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/* +---------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)               |
   |                          http://www.mrpt.org/                             |
   |                                                                           |
   | Copyright (c) 2005-2017, Individual contributors, see AUTHORS file        |
   | See: http://www.mrpt.org/Authors - All rights reserved.                   |
   | Released under BSD License. See details in http://www.mrpt.org/License    |
   +---------------------------------------------------------------------------+ */


#include <mrpt/math/distributions.h>
#include <mrpt/random.h>
#include <gtest/gtest.h>

using namespace mrpt;
using namespace mrpt::utils;
using namespace mrpt::math;
using namespace mrpt::random;
using namespace std;

const double eps = 1e-12;

TEST(distributions,normalPDF_1d)
{
        EXPECT_NEAR( normalPDF(0,0,1),0.398942280401433, eps);
        EXPECT_NEAR( normalPDF(5,5,1),0.398942280401433, eps);
        EXPECT_NEAR( normalPDF(0,0,2),0.199471140200716, eps);
        EXPECT_NEAR( normalPDF(1,0,1),0.241970724519143, eps);
}

TEST(distributions,normalPDF_vector)
{
        const double cov_vals [3*3] = {
                4.0,  2.0,  1.0,
                2.0,  3.0,  0.5,
                1.0,  0.5,  1.0
        };
        const double x1_vals[3] = {1.0, 0.0, 0.0};
        const double x2_vals[3] = {1.0, 2.0, 3.0};

        const CMatrixDouble33  COV(cov_vals);
        const CMatrixFixedNumeric<double,3,1> x0;
        const CMatrixFixedNumeric<double,3,1> x1(x1_vals);
        const CMatrixFixedNumeric<double,3,1> x2(x2_vals);

        EXPECT_NEAR( normalPDF(x0,x0,COV), 0.02592116832548877620, eps); // sprintf('%.20f',mvnpdf([0;0;0],[0;0;0],S))
        EXPECT_NEAR( normalPDF(x2,x2,COV), 0.02592116832548877620, eps); // sprintf('%.20f',mvnpdf([0;0;0],[0;0;0],S))

        EXPECT_NEAR( normalPDF(x1,x0,COV), 0.02061240910323311470, eps); // sprintf('%.20f',mvnpdf([1;0;0],[0;0;0],S))
        EXPECT_NEAR( normalPDF(x2,x0,COV), 0.00008423820480102986, eps); // sprintf('%.20f',mvnpdf([1;2;3],[0;0;0],S))

        EXPECT_NEAR( normalPDF(x1,COV), 0.02061240910323311470, eps); // sprintf('%.20f',mvnpdf([1;0;0],[0;0;0],S))
        EXPECT_NEAR( normalPDF(x2,COV), 0.00008423820480102986, eps); // sprintf('%.20f',mvnpdf([1;0;0],[0;0;0],S))
}

TEST(distributions,erfc)
{
        const double eps2 = 1e-7;

        EXPECT_NEAR( mrpt::math::erfc(0), 1, eps );
        EXPECT_NEAR( mrpt::math::erfc(1), 0.157299207050285, eps2 );
        EXPECT_NEAR( mrpt::math::erfc(2), 0.004677734981047, eps2 );
}

TEST(distributions,erf)
{
        const double eps2 = 1e-7;

        EXPECT_NEAR( mrpt::math::erf(0), 0, eps );
        EXPECT_NEAR( mrpt::math::erf(1), 0.842700792949715, eps2 );
        EXPECT_NEAR( mrpt::math::erf(2), 0.995322265018953, eps2 );
}

TEST(distributions,normalCDF)
{
        EXPECT_NEAR( mrpt::math::normalCDF(0), 0.5 , eps );
        EXPECT_NEAR( mrpt::math::normalCDF(1), 0.841344746068543 , eps );
        EXPECT_NEAR( mrpt::math::normalCDF(2), 0.977249868051821 , eps );
        EXPECT_NEAR( mrpt::math::normalCDF(3), 0.998650101968370 , eps );
}

TEST(distributions,chi2inv)
{
        EXPECT_NEAR( mrpt::math::chi2inv(0.0, 1), 0 , eps );
        EXPECT_NEAR( mrpt::math::chi2inv(0.5, 3),   2.365973884375338 , 0.1 );
        EXPECT_NEAR( mrpt::math::chi2inv(0.95, 3), 7.814727903251178 , 0.1 );
}

TEST(distributions,chi2PDF)
{
        EXPECT_NEAR( mrpt::math::chi2PDF(1, 1.0), 0.241970724519143 , eps );
        EXPECT_NEAR( mrpt::math::chi2PDF(1, 2.0), 0.103776874355149 , eps );
        EXPECT_NEAR( mrpt::math::chi2PDF(1, 3.0), 0.051393443267923 , eps );
        EXPECT_NEAR( mrpt::math::chi2PDF(1, 4.0), 0.026995483256594 , eps );

        EXPECT_NEAR( mrpt::math::chi2PDF(4, 1.0), 0.151632664928158 , eps );
}

TEST(distributions,noncentralChi2PDF_CDF)
{
        const double eps2 = 1e-7;

        // ncx2cdf(arg,degreesOfFreedom,noncentrality)
        // noncentralChi2PDF_CDF(degreesOfFreedom,noncentrality,arg)
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 1.0, 0).first, 0 , eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 2.0, 0).first, 0 , eps2 );

        // MATLAB: ncx2cdf(1:3,1,1)
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 1, 1.0).second, 0.477249868051821, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 1, 2.0).second, 0.652756536682270, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 1, 3.0).second, 0.764784149631031, eps2 );
        // MATLAB: ncx2pdf(1:3,1,1)
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 1, 1.0).first, 0.226466623457311, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 1, 2.0).first, 0.137103272271503, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(1, 1, 3.0).first, 0.090852330823658, eps2 );

        // MATLAB: ncx2cdf(1:3,2,3)
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(2, 3, 1.0).second, 0.121825497229364, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(2, 3, 2.0).second, 0.252206942426039, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(2, 3, 3.0).second, 0.378499822919087, eps2 );
        // MATLAB: ncx2pdf(1:3,2,3)
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(2, 3, 1.0).first, 0.128765424775546, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(2, 3, 2.0).first, 0.129923687128879, eps2 );
        EXPECT_NEAR( mrpt::math::noncentralChi2PDF_CDF(2, 3, 3.0).first, 0.121500177080913, eps2 );
}