chi2test.cpp

/*
    This file is part of Nori, a simple educational ray tracer
 
    Copyright (c) 2015 by Wenzel Jakob
 
    Nori is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License Version 3
    as published by the Free Software Foundation.
 
    Nori 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
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
 
#include <nori/bsdf.h>
#include <nori/warp.h>
#include <pcg32.h>
#include <hypothesis.h>
#include <fstream>
#include <memory>
 
/*
 * =======================================================================
 *   WARNING    WARNING    WARNING    WARNING    WARNING    WARNING
 * =======================================================================
 *   Remember to put on SAFETY GOGGLES before looking at this file. You
 *   are most certainly not expected to read or understand any of it.
 * =======================================================================
 */
 
NORI_NAMESPACE_BEGIN
 
class ChiSquareTest : public NoriObject {
public:
    ChiSquareTest(const PropertyList &propList) {
        /* The null hypothesis will be rejected when the associated
           p-value is below the significance level specified here. */
        m_significanceLevel = propList.getFloat("significanceLevel", 0.01f);
 
        /* Number of cells along the latitudinal axis. The azimuthal
           resolution is twice this value. */
        m_cosThetaResolution = propList.getInteger("resolution", 10);
 
        /* Minimum expected bin frequency. The chi^2 test does not
           work reliably when the expected frequency in a cell is
           low (e.g. less than 5), because normality assumptions
           break down in this case. Therefore, the implementation
           will merge such low-frequency cells when they fall below
           the threshold specified here. */
        m_minExpFrequency = propList.getInteger("minExpFrequency", 5);
 
        /* Number of samples that should be taken (-1: automatic) */
        m_sampleCount = propList.getInteger("sampleCount", -1);
 
        /* Each provided BSDF will be tested for a few different
           incident directions. The value specified here determines
           how many tests will be executed per BSDF */
        m_testCount = propList.getInteger("testCount", 5);
 
        m_phiResolution = 2 * m_cosThetaResolution;
 
        if (m_sampleCount < 0) // ~5K samples per bin
            m_sampleCount = m_cosThetaResolution * m_phiResolution * 5000;
    }
 
    virtual ~ChiSquareTest() {
        for (auto bsdf : m_bsdfs)
            delete bsdf;
    }
 
    virtual void addChild(NoriObject *obj) override {
        switch (obj->getClassType()) {
            case EBSDF:
                m_bsdfs.push_back(static_cast<BSDF *>(obj));
                break;
 
            default:
                throw NoriException("ChiSquareTest::addChild(<%s>) is not supported!",
                    classTypeName(obj->getClassType()));
        }
    }
 
    virtual void activate() override {
        int passed = 0, total = 0, res = m_cosThetaResolution*m_phiResolution;
        pcg32 random; /* Pseudorandom number generator */
 
        std::unique_ptr<double[]> obsFrequencies(new double[res]);
        std::unique_ptr<double[]> expFrequencies(new double[res]);
 
 
        /* Test each registered BSDF */
        for (auto bsdf : m_bsdfs) {
            /* Run several tests per BSDF to be on the safe side */
            for (int l = 0; l<m_testCount; ++l) {
                memset(obsFrequencies.get(), 0, res*sizeof(double));
                memset(expFrequencies.get(), 0, res*sizeof(double));
 
                cout << "------------------------------------------------------" << endl;
                cout << "Testing: " << bsdf->toString() << endl;
                ++total;
 
                float cosTheta = random.nextFloat();
                float sinTheta = std::sqrt(std::max((float) 0, 1-cosTheta*cosTheta));
                float sinPhi, cosPhi;
                sincosf(2.0f * M_PI * random.nextFloat(), &sinPhi, &cosPhi);
                Vector3f wi(cosPhi * sinTheta, sinPhi * sinTheta, cosTheta);
 
                cout << "Accumulating " << m_sampleCount << " samples into a " << m_cosThetaResolution
                     << "x" << m_phiResolution << " contingency table .. ";
                cout.flush();
 
                /* Generate many samples from the BSDF and create
                   a histogram / contingency table */
                BSDFQueryRecord bRec(wi, Point2f());
                bool belowSurface = false;
                for (int i=0; i<m_sampleCount; ++i) {
                    Point2f sample(random.nextFloat(), random.nextFloat());
                    Color3f result = bsdf->sample(bRec, sample);
 
                    if ((result.array() == 0).all())
                        continue;
 
                    // Raise a warning if the sample is below the surface, i.e. wo.z < 0
                    if (bRec.wo.z() < 0)
                        belowSurface = true;
 
                    int cosThetaBin = std::min(std::max(0, (int) std::floor((bRec.wo.z()*0.5f+0.5f)
                            * m_cosThetaResolution)), m_cosThetaResolution-1);
 
                    float scaledPhi = std::atan2(bRec.wo.y(), bRec.wo.x()) * INV_TWOPI;
                    if (scaledPhi < 0)
                        scaledPhi += 1;
 
                    int phiBin = std::min(std::max(0,
                        (int) std::floor(scaledPhi * m_phiResolution)), m_phiResolution-1);
                    obsFrequencies[cosThetaBin * m_phiResolution + phiBin] += 1;
                }
                if (belowSurface)
                    cerr << "Warning: some samples are below the surface (wo.z < 0). "
                         << "Make sure the `sample` method returns Color3f(0) in such cases to reject these bad samples!" << endl;
                cout << "done." << endl;
 
                /* Numerically integrate the probability density
                   function over rectangles in spherical coordinates. */
                double *ptr = expFrequencies.get();
                cout << "Integrating expected frequencies .. ";
                cout.flush();
                for (int i=0; i<m_cosThetaResolution; ++i) {
                    double cosThetaStart = -1.0 + i     * 2.0 / m_cosThetaResolution;
                    double cosThetaEnd   = -1.0 + (i+1) * 2.0 / m_cosThetaResolution;
                    for (int j=0; j<m_phiResolution; ++j) {
                        double phiStart = j     * 2*M_PI / m_phiResolution;
                        double phiEnd   = (j+1) * 2*M_PI / m_phiResolution;
 
                        auto integrand = [&](double cosTheta, double phi) -> double {
                            double sinTheta = std::sqrt(1 - cosTheta * cosTheta);
                            double sinPhi = std::sin(phi), cosPhi = std::cos(phi);
 
                            Vector3f wo((float) (sinTheta * cosPhi),
                                        (float) (sinTheta * sinPhi),
                                        (float) cosTheta);
 
                            BSDFQueryRecord bRec(wi, wo, ESolidAngle, Point2f());
                            return bsdf->pdf(bRec);
                        };
 
                        double integral = hypothesis::adaptiveSimpson2D(
                            integrand, cosThetaStart, phiStart, cosThetaEnd,
                            phiEnd);
 
                        *ptr++ = integral * m_sampleCount;
                    }
                }
                cout << "done." << endl;
 
                /* Write the test input data to disk for debugging */
                hypothesis::chi2_dump(m_cosThetaResolution, m_phiResolution, obsFrequencies.get(), expFrequencies.get(),
                    tfm::format("chi2test_%i.py", total));
 
                /* Perform the Chi^2 test */
                std::pair<bool, std::string> result =
                    hypothesis::chi2_test(m_cosThetaResolution*m_phiResolution, obsFrequencies.get(), expFrequencies.get(),
                        m_sampleCount, m_minExpFrequency, m_significanceLevel, m_testCount * (int) m_bsdfs.size());
 
                if (result.first)
                    ++passed;
 
                cout << result.second << endl;
            }
        }
 
        cout << "Passed " << passed << "/" << total << " tests." << endl;
 
        if (passed < total) {
            throw std::runtime_error("Failed some of the tests");
        }
    }
 
    virtual std::string toString() const override {
        return tfm::format("ChiSquareTest[\n"
            "  thetaResolution = %i,\n"
            "  phiResolution = %i,\n"
            "  minExpFrequency = %i,\n"
            "  sampleCount = %i,\n"
            "  testCount = %i,\n"
            "  significanceLevel = %f\n"
            "]",
            m_cosThetaResolution,
            m_phiResolution,
            m_minExpFrequency,
            m_sampleCount,
            m_testCount,
            m_significanceLevel
        );
    }
 
    virtual EClassType getClassType() const override { return ETest; }
private:
    int m_cosThetaResolution;
    int m_phiResolution;
    int m_minExpFrequency;
    int m_sampleCount;
    int m_testCount;
    float m_significanceLevel;
    std::vector<BSDF *> m_bsdfs;
};
 
NORI_REGISTER_CLASS(ChiSquareTest, "chi2test");
NORI_NAMESPACE_END