CPosePDFGaussian.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2020, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */

#include "poses-precomp.h"  // Precompiled headers

#include <mrpt/math/CMatrixF.h>
#include <mrpt/math/distributions.h>
#include <mrpt/math/matrix_serialization.h>
#include <mrpt/math/wrap2pi.h>
#include <mrpt/poses/CPoint2DPDFGaussian.h>
#include <mrpt/poses/CPose3D.h>
#include <mrpt/poses/CPose3DPDF.h>
#include <mrpt/poses/CPosePDFGaussian.h>
#include <mrpt/random.h>
#include <mrpt/serialization/CArchive.h>
#include <mrpt/serialization/CSchemeArchiveBase.h>
#include <mrpt/system/os.h>
#include <Eigen/Dense>

using namespace mrpt;
using namespace mrpt::poses;
using namespace mrpt::math;
using namespace mrpt::random;
using namespace mrpt::system;
using namespace std;

IMPLEMENTS_SERIALIZABLE(CPosePDFGaussian, CPosePDF, mrpt::poses)

/*---------------------------------------------------------------
    Constructor
  ---------------------------------------------------------------*/
CPosePDFGaussian::CPosePDFGaussian() : mean(0, 0, 0), cov() {}
/*---------------------------------------------------------------
    Constructor
  ---------------------------------------------------------------*/
CPosePDFGaussian::CPosePDFGaussian(
    const CPose2D& init_Mean, const CMatrixDouble33& init_Cov)
    : mean(init_Mean), cov(init_Cov)
{
}

/*---------------------------------------------------------------
    Constructor
  ---------------------------------------------------------------*/
CPosePDFGaussian::CPosePDFGaussian(const CPose2D& init_Mean)
    : mean(init_Mean), cov()
{
    cov.setZero();
}

uint8_t CPosePDFGaussian::serializeGetVersion() const { return 2; }
void CPosePDFGaussian::serializeTo(mrpt::serialization::CArchive& out) const
{
    out << mean;
    mrpt::math::serializeSymmetricMatrixTo(cov, out);
}
void CPosePDFGaussian::serializeFrom(
    mrpt::serialization::CArchive& in, uint8_t version)
{
    switch (version)
    {
        case 2:
        {
            in >> mean;
            mrpt::math::deserializeSymmetricMatrixFrom(cov, in);
        }
        break;
        case 1:
        {
            in >> mean;
            CMatrixFloat33 m;
            mrpt::math::deserializeSymmetricMatrixFrom(m, in);
            cov = m.cast_double();
        }
        break;
        case 0:
        {
            CMatrixF auxCov;
            in >> mean >> auxCov;
            cov = auxCov.cast_double();
        }
        break;
        default:
            MRPT_THROW_UNKNOWN_SERIALIZATION_VERSION(version);
    };
}

void CPosePDFGaussian::serializeTo(
    mrpt::serialization::CSchemeArchiveBase& out) const
{
    SCHEMA_SERIALIZE_DATATYPE_VERSION(1);
    out["mean"] = mean;
    out["cov"] = CMatrixD(cov);
}
void CPosePDFGaussian::serializeFrom(
    mrpt::serialization::CSchemeArchiveBase& in)
{
    uint8_t version;
    SCHEMA_DESERIALIZE_DATATYPE_VERSION();
    switch (version)
    {
        case 1:
        {
            in["mean"].readTo(mean);
            CMatrixD m;
            in["cov"].readTo(m);
            cov = m;
        }
        break;
        default:
            MRPT_THROW_UNKNOWN_SERIALIZATION_VERSION(version);
    }
}

/*---------------------------------------------------------------
                        copyFrom
  ---------------------------------------------------------------*/
void CPosePDFGaussian::copyFrom(const CPosePDF& o)
{
    if (this == &o) return;  // It may be used sometimes

    // Convert to gaussian pdf:
    o.getMean(mean);
    o.getCovariance(cov);
}

/*---------------------------------------------------------------
                        copyFrom 3D
  ---------------------------------------------------------------*/
void CPosePDFGaussian::copyFrom(const CPose3DPDF& o)
{
    // Convert to gaussian pdf:
    mean = CPose2D(o.getMeanVal());
    CMatrixDouble66 C;
    o.getCovariance(C);

    // Clip to 3x3:
    C(2, 0) = C(0, 2) = C(0, 3);
    C(2, 1) = C(1, 2) = C(1, 3);
    C(2, 2) = C(3, 3);
    cov = C.block<3, 3>(0, 0);
}

/*---------------------------------------------------------------

  ---------------------------------------------------------------*/
bool CPosePDFGaussian::saveToTextFile(const std::string& file) const
{
    FILE* f = os::fopen(file.c_str(), "wt");
    if (!f) return false;

    os::fprintf(f, "%f %f %f\n", mean.x(), mean.y(), mean.phi());

    os::fprintf(f, "%f %f %f\n", cov(0, 0), cov(0, 1), cov(0, 2));
    os::fprintf(f, "%f %f %f\n", cov(1, 0), cov(1, 1), cov(1, 2));
    os::fprintf(f, "%f %f %f\n", cov(2, 0), cov(2, 1), cov(2, 2));

    os::fclose(f);
    return true;
}

/*---------------------------------------------------------------
                        changeCoordinatesReference
 ---------------------------------------------------------------*/
void CPosePDFGaussian::changeCoordinatesReference(
    const CPose3D& newReferenceBase_)
{
    const CPose2D newReferenceBase = CPose2D(newReferenceBase_);

    // The mean:
    mean.composeFrom(newReferenceBase, mean);

    // The covariance:
    rotateCov(newReferenceBase.phi());
}

/*---------------------------------------------------------------
                        changeCoordinatesReference
 ---------------------------------------------------------------*/
void CPosePDFGaussian::changeCoordinatesReference(
    const CPose2D& newReferenceBase)
{
    // The mean:
    mean.composeFrom(newReferenceBase, mean);
    // The covariance:
    rotateCov(newReferenceBase.phi());
}

/*---------------------------------------------------------------
                        changeCoordinatesReference
 ---------------------------------------------------------------*/
void CPosePDFGaussian::rotateCov(const double ang)
{
    const double ccos = cos(ang);
    const double ssin = sin(ang);

    alignas(MRPT_MAX_STATIC_ALIGN_BYTES)
        const double rot_vals[] = {ccos, -ssin, 0., ssin, ccos, 0., 0., 0., 1.};

    const CMatrixFixed<double, 3, 3> rot(rot_vals);
    cov = (rot.asEigen() * cov.asEigen() * rot.asEigen().transpose()).eval();
}

/*---------------------------------------------------------------
                    drawSingleSample
 ---------------------------------------------------------------*/
void CPosePDFGaussian::drawSingleSample(CPose2D& outPart) const
{
    MRPT_START

    CVectorDouble v;
    getRandomGenerator().drawGaussianMultivariate(v, cov);

    outPart.x(mean.x() + v[0]);
    outPart.y(mean.y() + v[1]);
    outPart.phi(mean.phi() + v[2]);

    // Range -pi,pi
    outPart.normalizePhi();

    MRPT_END_WITH_CLEAN_UP(
        cov.saveToTextFile("__DEBUG_EXC_DUMP_drawSingleSample_COV.txt"););
}

/*---------------------------------------------------------------
                    drawManySamples
 ---------------------------------------------------------------*/
void CPosePDFGaussian::drawManySamples(
    size_t N, std::vector<CVectorDouble>& outSamples) const
{
    MRPT_START

    std::vector<CVectorDouble> rndSamples;

    getRandomGenerator().drawGaussianMultivariateMany(rndSamples, N, cov);
    outSamples.resize(N);
    for (size_t i = 0; i < N; i++)
    {
        outSamples[i].resize(3);
        outSamples[i][0] = mean.x() + rndSamples[i][0];
        outSamples[i][1] = mean.y() + rndSamples[i][1];
        outSamples[i][2] = mean.phi() + rndSamples[i][2];

        wrapToPiInPlace(outSamples[i][2]);
    }

    MRPT_END
}

/*---------------------------------------------------------------
                    bayesianFusion
 ---------------------------------------------------------------*/
void CPosePDFGaussian::bayesianFusion(
    const CPosePDF& p1_, const CPosePDF& p2_,
    [[maybe_unused]] const double minMahalanobisDistToDrop)
{
    MRPT_START

    ASSERT_(p1_.GetRuntimeClass() == CLASS_ID(CPosePDFGaussian));
    ASSERT_(p2_.GetRuntimeClass() == CLASS_ID(CPosePDFGaussian));

    const auto* p1 = dynamic_cast<const CPosePDFGaussian*>(&p1_);
    const auto* p2 = dynamic_cast<const CPosePDFGaussian*>(&p2_);

    const CMatrixDouble33 C1 = p1->cov;
    const CMatrixDouble33 C2 = p2->cov;

    const CMatrixDouble33 C1_inv = C1.inverse_LLt();
    const CMatrixDouble33 C2_inv = C2.inverse_LLt();

    auto x1 = CMatrixDouble31(p1->mean);
    auto x2 = CMatrixDouble31(p2->mean);

    CMatrixDouble33 auxC = C1_inv + C2_inv;
    this->cov = auxC.inverse_LLt();
    this->enforceCovSymmetry();

    auto x = CMatrixDouble31(this->cov.asEigen() * (C1_inv * x1 + C2_inv * x2));

    this->mean.x(x(0, 0));
    this->mean.y(x(1, 0));
    this->mean.phi(x(2, 0));
    this->mean.normalizePhi();

    MRPT_END
}

/*---------------------------------------------------------------
                    inverse
 ---------------------------------------------------------------*/
void CPosePDFGaussian::inverse(CPosePDF& o) const
{
    ASSERT_(o.GetRuntimeClass() == CLASS_ID(CPosePDFGaussian));
    auto* out = dynamic_cast<CPosePDFGaussian*>(&o);

    // The mean:
    out->mean = CPose2D(0, 0, 0) - mean;

    // The covariance:
    const double ccos = ::cos(mean.phi());
    const double ssin = ::sin(mean.phi());

    // jacobian:
    alignas(MRPT_MAX_STATIC_ALIGN_BYTES) const double H_values[] = {
        -ccos, -ssin, mean.x() * ssin - mean.y() * ccos,
        ssin,  -ccos, mean.x() * ccos + mean.y() * ssin,
        0,   0,  -1};
    const CMatrixFixed<double, 3, 3> H(H_values);

    out->cov.asEigen().noalias() =
        (H.asEigen() * cov.asEigen() * H.transpose()).eval();
}

/*---------------------------------------------------------------
                            +=
 ---------------------------------------------------------------*/
void CPosePDFGaussian::operator+=(const CPose2D& Ap)
{
    mean = mean + Ap;
    rotateCov(Ap.phi());
}

/*---------------------------------------------------------------
                        evaluatePDF
 ---------------------------------------------------------------*/
double CPosePDFGaussian::evaluatePDF(const CPose2D& x) const
{
    auto X = CMatrixDouble31(x);
    auto MU = CMatrixDouble31(mean);

    return math::normalPDF(X, MU, this->cov);
}

/*---------------------------------------------------------------
                        evaluateNormalizedPDF
 ---------------------------------------------------------------*/
double CPosePDFGaussian::evaluateNormalizedPDF(const CPose2D& x) const
{
    auto X = CMatrixDouble31(x);
    auto MU = CMatrixDouble31(mean);

    return math::normalPDF(X, MU, this->cov) /
           math::normalPDF(MU, MU, this->cov);
}

/*---------------------------------------------------------------
                        enforceCovSymmetry
 ---------------------------------------------------------------*/
void CPosePDFGaussian::enforceCovSymmetry()
{
    // Differences, when they exist, appear in the ~15'th significant
    //  digit, so... just take one of them arbitrarily!
    cov(0, 1) = cov(1, 0);
    cov(0, 2) = cov(2, 0);
    cov(1, 2) = cov(2, 1);
}

/*---------------------------------------------------------------
                        mahalanobisDistanceTo
 ---------------------------------------------------------------*/
double CPosePDFGaussian::mahalanobisDistanceTo(const CPosePDFGaussian& theOther)
{
    MRPT_START

    auto MU = CVectorFixedDouble<3>(mean);
    MU -= CVectorFixedDouble<3>(theOther.mean);

    wrapToPiInPlace(MU[2]);

    if (MU[0] == 0 && MU[1] == 0 && MU[2] == 0)
        return 0;  // This is the ONLY case where we know the result, whatever
    // COVs are.

    CMatrixDouble33 COV_ = cov;
    COV_ += theOther.cov;

    const CMatrixDouble33 COV_inv = COV_.inverse_LLt();

    // (~MU) * (!COV_) * MU
    return std::sqrt(mrpt::math::multiply_HtCH_scalar(MU.asEigen(), COV_inv));

    MRPT_END
}

/*---------------------------------------------------------------
                        operator <<
 ---------------------------------------------------------------*/
std::ostream& mrpt::poses::operator<<(
    std::ostream& out, const CPosePDFGaussian& obj)
{
    out << "Mean: " << obj.mean << "\n";
    out << "Covariance:\n" << obj.cov << "\n";

    return out;
}

/*---------------------------------------------------------------
                        operator +
 ---------------------------------------------------------------*/
poses::CPosePDFGaussian operator+(
    const mrpt::poses::CPose2D& A, const mrpt::poses::CPosePDFGaussian& B)
{
    poses::CPosePDFGaussian ret(B);
    ret.changeCoordinatesReference(A);
    return ret;
}

/*---------------------------------------------------------------
                        assureMinCovariance
 ---------------------------------------------------------------*/
void CPosePDFGaussian::assureMinCovariance(double minStdXY, double minStdPhi)
{
    cov(0, 0) = max(cov(0, 0), square(minStdXY));
    cov(1, 1) = max(cov(1, 1), square(minStdXY));
    cov(2, 2) = max(cov(2, 2), square(minStdPhi));
}

/*---------------------------------------------------------------
                        inverseComposition
  Set 'this' = 'x' - 'ref', computing the mean using the "-"
    operator and the covariances through the corresponding Jacobians.
 ---------------------------------------------------------------*/
void CPosePDFGaussian::inverseComposition(
    const CPosePDFGaussian& xv, const CPosePDFGaussian& xi)
{
    // COV:
    double cpi = cos(xi.mean.phi());
    double spi = sin(xi.mean.phi());

    // jacob: dh_xv
    CMatrixDouble33 dh_xv;

    dh_xv(0, 0) = cpi;
    dh_xv(0, 1) = spi;
    dh_xv(1, 0) = -spi;
    dh_xv(1, 1) = cpi;
    dh_xv(2, 2) = 1;

    // jacob: dh_xi
    CMatrixDouble33 dh_xi;

    double xv_xi = xv.mean.x() - xi.mean.x();
    double yv_yi = xv.mean.y() - xi.mean.y();

    dh_xi(0, 0) = -cpi;
    dh_xi(0, 1) = -spi;
    dh_xi(0, 2) = -xv_xi * spi + yv_yi * cpi;
    dh_xi(1, 0) = spi;
    dh_xi(1, 1) = -cpi;
    dh_xi(1, 2) = -xv_xi * cpi - yv_yi * spi;
    dh_xi(2, 2) = -1;

    // Build the cov:
    //  Y = dh_xv * XV * dh_xv^T  + dh_xi * XI * dh_xi^T
    this->cov = mrpt::math::multiply_HCHt(dh_xv, xv.cov) +
                mrpt::math::multiply_HCHt(dh_xi, xi.cov);

    // Mean:
    mean = xv.mean - xi.mean;
}

/*---------------------------------------------------------------
                        inverseComposition
  Set \f$ this = x1 \ominus x0 \f$ , computing the mean using
   the "-" operator and the covariances through the corresponding
    Jacobians (Given the 3x3 cross-covariance matrix of variables x0 and x0).
 ---------------------------------------------------------------*/
void CPosePDFGaussian::inverseComposition(
    const CPosePDFGaussian& x1, const CPosePDFGaussian& x0,
    const CMatrixDouble33& COV_01)
{
    double cp0 = cos(x0.mean.phi());
    double sp0 = sin(x0.mean.phi());

    // jacob: dh_x1
    CMatrixDouble33 dh_x1;

    dh_x1(0, 0) = cp0;
    dh_x1(0, 1) = sp0;
    dh_x1(1, 0) = -sp0;
    dh_x1(1, 1) = cp0;
    dh_x1(2, 2) = 1;

    // jacob: dh_x0
    CMatrixDouble33 dh_x0;

    double xv_xi = x1.mean.x() - x0.mean.x();
    double yv_yi = x1.mean.y() - x0.mean.y();

    dh_x0(0, 0) = -cp0;
    dh_x0(0, 1) = -sp0;
    dh_x0(0, 2) = -xv_xi * sp0 + yv_yi * cp0;
    dh_x0(1, 0) = sp0;
    dh_x0(1, 1) = -cp0;
    dh_x0(1, 2) = -xv_xi * cp0 - yv_yi * sp0;
    dh_x0(2, 2) = -1;

    // Build the cov:
    //  Y = dh_xv * XV * dh_xv^T  + dh_xi * XI * dh_xi^T +  A + At
    //     being A = dh_dx0 * COV01 * dh_dx1^t
    this->cov = mrpt::math::multiply_HCHt(dh_x0, x0.cov) +
                mrpt::math::multiply_HCHt(dh_x1, x1.cov);

    auto M =
        CMatrixDouble33(dh_x0.asEigen() * COV_01.asEigen() * dh_x1.asEigen());

    this->cov.asEigen() += (M.asEigen() * M.transpose()).eval();

    // mean
    mean = x1.mean - x0.mean;
}

/*---------------------------------------------------------------
                            +=
 ---------------------------------------------------------------*/
void CPosePDFGaussian::operator+=(const CPosePDFGaussian& Ap)
{
    // COV:
    const CMatrixDouble33 OLD_COV = this->cov;
    CMatrixDouble33 df_dx(UNINITIALIZED_MATRIX), df_du(UNINITIALIZED_MATRIX);

    CPosePDF::jacobiansPoseComposition(
        this->mean,  // x
        Ap.mean,  // u
        df_dx, df_du);

    this->cov = mrpt::math::multiply_HCHt(df_dx, OLD_COV) +
                mrpt::math::multiply_HCHt(df_du, Ap.cov);

    // MEAN:
    this->mean = this->mean + Ap.mean;
}

/** Returns the PDF of the 2D point \f$ g = q \oplus l\f$ with "q"=this pose and
 * "l" a point without uncertainty */
void CPosePDFGaussian::composePoint(
    const mrpt::math::TPoint2D& l, CPoint2DPDFGaussian& g) const
{
    // Mean:
    double gx, gy;
    mean.composePoint(l.x, l.y, gx, gy);
    g.mean.x(gx);
    g.mean.y(gy);

    // COV:
    CMatrixDouble33 df_dx(UNINITIALIZED_MATRIX), df_du(UNINITIALIZED_MATRIX);
    CPosePDF::jacobiansPoseComposition(
        this->mean,  // x
        this->mean,  // u
        df_dx, df_du,
        true,  // Eval df_dx
        false  // Eval df_du (not needed)
    );

    const auto dp_dx = CMatrixFixed<double, 2, 3>(df_dx.block<2, 3>(0, 0));
    g.cov = dp_dx * this->cov * dp_dx.transpose();
}

bool mrpt::poses::operator==(
    const CPosePDFGaussian& p1, const CPosePDFGaussian& p2)
{
    return p1.mean == p2.mean && p1.cov == p2.cov;
}

CPosePDFGaussian mrpt::poses::operator+(
    const CPosePDFGaussian& a, const CPosePDFGaussian& b)
{
    CPosePDFGaussian res(a);
    res += b;
    return res;
}

CPosePDFGaussian mrpt::poses::operator-(
    const CPosePDFGaussian& a, const CPosePDFGaussian& b)
{
    CPosePDFGaussian res;
    res.inverseComposition(a, b);
    return res;
}