CPosePDFGaussian.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 "base-precomp.h"  // Precompiled headers
 
#include <mrpt/poses/CPosePDFGaussian.h>
#include <mrpt/poses/CPoint2DPDFGaussian.h>
#include <mrpt/poses/CPose3DPDF.h>
#include <mrpt/poses/CPose3D.h>
#include <mrpt/math/CMatrix.h>
#include <mrpt/math/distributions.h>
#include <mrpt/math/wrap2pi.h>
#include <mrpt/system/os.h>
#include <mrpt/utils/CStream.h>
 
#include <mrpt/random.h>
 
using namespace mrpt;
using namespace mrpt::utils;
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.zeros();
}
 
/*---------------------------------------------------------------
                                                writeToStream
  ---------------------------------------------------------------*/
void CPosePDFGaussian::writeToStream(
        mrpt::utils::CStream& out, int* version) const
{
        if (version)
                *version = 2;
        else
        {
                out << mean;
                out << cov(0, 0) << cov(1, 1) << cov(2, 2);
                out << cov(0, 1) << cov(0, 2) << cov(1, 2);
        }
}
 
/*---------------------------------------------------------------
                                                readFromStream
  ---------------------------------------------------------------*/
void CPosePDFGaussian::readFromStream(mrpt::utils::CStream& in, int version)
{
        switch (version)
        {
                case 2:
                {
                        double x;
                        in >> mean;
 
                        in >> x;
                        cov(0, 0) = x;
                        in >> x;
                        cov(1, 1) = x;
                        in >> x;
                        cov(2, 2) = x;
 
                        in >> x;
                        cov(1, 0) = x;
                        cov(0, 1) = x;
                        in >> x;
                        cov(2, 0) = x;
                        cov(0, 2) = x;
                        in >> x;
                        cov(1, 2) = x;
                        cov(2, 1) = x;
                }
                break;
                case 1:
                {
                        float x;
                        in >> mean;
 
                        in >> x;
                        cov(0, 0) = x;
                        in >> x;
                        cov(1, 1) = x;
                        in >> x;
                        cov(2, 2) = x;
 
                        in >> x;
                        cov(1, 0) = x;
                        cov(0, 1) = x;
                        in >> x;
                        cov(2, 0) = x;
                        cov(0, 2) = x;
                        in >> x;
                        cov(1, 2) = x;
                        cov(2, 1) = x;
                }
                break;
                case 0:
                {
                        CMatrix auxCov;
                        in >> mean >> auxCov;
                        cov = auxCov.cast<double>();
                }
                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(0, 0, 3, 3);
}
 
/*---------------------------------------------------------------
 
  ---------------------------------------------------------------*/
void CPosePDFGaussian::saveToTextFile(const std::string& file) const
{
        FILE* f = os::fopen(file.c_str(), "wt");
        if (!f) return;
 
        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);
}
 
/*---------------------------------------------------------------
                                                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(16)
                const double rot_vals[] = {ccos, -ssin, 0., ssin, ccos, 0., 0., 0., 1.};
 
        const CMatrixFixedNumeric<double, 3, 3> rot(rot_vals);
        cov = (rot * cov * rot.adjoint()).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 (unsigned int 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_,
        const double& minMahalanobisDistToDrop)
{
        MRPT_START
 
        MRPT_UNUSED_PARAM(minMahalanobisDistToDrop);  // Not used in this class!
 
        ASSERT_(p1_.GetRuntimeClass() == CLASS_ID(CPosePDFGaussian));
        ASSERT_(p2_.GetRuntimeClass() == CLASS_ID(CPosePDFGaussian));
 
        const CPosePDFGaussian* p1 = static_cast<const CPosePDFGaussian*>(&p1_);
        const CPosePDFGaussian* p2 = static_cast<const CPosePDFGaussian*>(&p2_);
 
        CMatrixDouble33 C1 = p1->cov;
        CMatrixDouble33 C2 = p2->cov;
 
        CMatrixDouble33 C1_inv;
        C1.inv(C1_inv);
 
        CMatrixDouble33 C2_inv;
        C2.inv(C2_inv);
 
        CMatrixDouble31 x1 = CMatrixDouble31(p1->mean);
        CMatrixDouble31 x2 = CMatrixDouble31(p2->mean);
 
        CMatrixDouble33 auxC = C1_inv + C2_inv;
        auxC.inv(this->cov);
        this->assureSymmetry();
 
        CMatrixDouble31 x = this->cov * (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));
        CPosePDFGaussian* out = static_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(16) const double H_values[] = {
                -ccos, -ssin, mean.x() * ssin - mean.y() * ccos,
                ssin,  -ccos, mean.x() * ccos + mean.y() * ssin,
                0,       0,      -1};
        const CMatrixFixedNumeric<double, 3, 3> H(H_values);
 
        out->cov.noalias() =
                (H * cov * H.adjoint()).eval();  // o.cov = H * cov * Ht
}
 
/*---------------------------------------------------------------
                                                        +=
 ---------------------------------------------------------------*/
void CPosePDFGaussian::operator+=(const CPose2D& Ap)
{
        mean = mean + Ap;
        rotateCov(Ap.phi());
}
 
/*---------------------------------------------------------------
                                                evaluatePDF
 ---------------------------------------------------------------*/
double CPosePDFGaussian::evaluatePDF(const CPose2D& x) const
{
        CMatrixDouble31 X = CMatrixDouble31(x);
        CMatrixDouble31 MU = CMatrixDouble31(mean);
 
        return math::normalPDF(X, MU, this->cov);
}
 
/*---------------------------------------------------------------
                                                evaluateNormalizedPDF
 ---------------------------------------------------------------*/
double CPosePDFGaussian::evaluateNormalizedPDF(const CPose2D& x) const
{
        CMatrixDouble31 X = CMatrixDouble31(x);
        CMatrixDouble31 MU = CMatrixDouble31(mean);
 
        return math::normalPDF(X, MU, this->cov) /
                   math::normalPDF(MU, MU, this->cov);
}
 
/*---------------------------------------------------------------
                                                assureSymmetry
 ---------------------------------------------------------------*/
void CPosePDFGaussian::assureSymmetry()
{
        // 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
 
        CArrayDouble<3> MU = CArrayDouble<3>(mean);
        MU -= CArrayDouble<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;
 
        CMatrixDouble33 COV_inv(UNINITIALIZED_MATRIX);
        COV_.inv_fast(COV_inv);
 
        // (~MU) * (!COV_) * MU
        return std::sqrt(mrpt::math::multiply_HCHt_scalar(MU, 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(
        const double& minStdXY, const 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
        dh_xv.multiply_HCHt(xv.cov, this->cov);
        dh_xi.multiply_HCHt(xi.cov, this->cov, true);  // Accum. result
 
        // 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
        dh_x0.multiply_HCHt(x0.cov, this->cov);
        dh_x1.multiply_HCHt(x1.cov, this->cov, true);  // Accum. result
 
        CMatrixDouble33 M;
        M.multiply_ABCt(dh_x0, COV_01, dh_x1);
 
        this->cov.add_AAt(M);
 
        // 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 = H1*this->cov*~H1 + H2*Ap.cov*~H2;
        df_dx.multiply_HCHt(OLD_COV, cov);
        df_du.multiply_HCHt(Ap.cov, cov, true);  // Accumulate result
 
        // 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 CMatrixFixedNumeric<double, 2, 3> dp_dx = 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;
}