CPosePDFGaussianInf.h

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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          |
   +------------------------------------------------------------------------+ */
#pragma once

#include <mrpt/math/CMatrixFixed.h>
#include <mrpt/poses/CPosePDF.h>

namespace mrpt::poses
{
class CPose3DPDF;

// This must be added to any CSerializable derived class:

/** A Probability Density  function (PDF) of a 2D pose \f$ p(\mathbf{x}) = [x ~
 * y ~ \phi ]^t \f$ as a Gaussian with a mean and the inverse of the covariance.
 *
 *   This class implements a PDF as a mono-modal Gaussian distribution in its
 * <b>information form</b>, that is,
 *     keeping the inverse of the covariance matrix instead of the covariance
 * matrix itself.
 *
 *  This class is the dual of CPosePDFGaussian.
 *
 * \sa CPose2D, CPosePDF, CPosePDFParticles
 * \ingroup poses_pdf_grp
 */
class CPosePDFGaussianInf : public CPosePDF
{
    // This must be added to any CSerializable derived class:
    DEFINE_SERIALIZABLE(CPosePDFGaussianInf, mrpt::poses)
    DEFINE_SCHEMA_SERIALIZABLE()
    using self_t = CPosePDFGaussianInf;

   protected:
    /** Assures the symmetry of the covariance matrix (eventually certain
     * operations in the math-coprocessor lead to non-symmetric matrixes!)
     */
    void enforceCovSymmetry();

   public:
    /** @name Data fields
        @{ */

    /** The mean value */
    CPose2D mean;
    /** The inverse of the 3x3 covariance matrix (the "information" matrix) */
    mrpt::math::CMatrixDouble33 cov_inv;

    /** @} */

    inline const CPose2D& getPoseMean() const { return mean; }
    inline CPose2D& getPoseMean() { return mean; }
    /** Default constructor (mean=all zeros, inverse covariance=all zeros -> so
     * be careful!) */
    CPosePDFGaussianInf();

    /** Constructor with a mean value (inverse covariance=all zeros -> so be
     * careful!) */
    explicit CPosePDFGaussianInf(const CPose2D& init_Mean);

    /** Constructor */
    CPosePDFGaussianInf(
        const CPose2D& init_Mean,
        const mrpt::math::CMatrixDouble33& init_CovInv);

    /** Copy constructor, including transformations between other PDFs */
    explicit CPosePDFGaussianInf(const CPosePDF& o) { copyFrom(o); }
    /** Copy constructor, including transformations between other PDFs */
    explicit CPosePDFGaussianInf(const CPose3DPDF& o) { copyFrom(o); }
    /** Returns an estimate of the pose, (the mean, or mathematical expectation
     * of the PDF).
     * \sa getCovariance */
    void getMean(CPose2D& mean_pose) const override { mean_pose = mean; }
    bool isInfType() const override { return true; }

    std::tuple<cov_mat_t, type_value> getCovarianceAndMean() const override
    {
        return {cov_inv.inverse_LLt(), mean};
    }

    /** Returns the information (inverse covariance) matrix (a STATE_LEN x
     * STATE_LEN matrix) \sa getMean, getCovarianceAndMean */
    void getInformationMatrix(mrpt::math::CMatrixDouble33& inf) const override
    {
        inf = cov_inv;
    }

    /** Copy operator, translating if necesary (for example, between particles
     * and gaussian representations) */
    void copyFrom(const CPosePDF& o) override;

    /** Copy operator, translating if necesary (for example, between particles
     * and gaussian representations) */
    void copyFrom(const CPose3DPDF& o);

    /** Save PDF's particles to a text file, containing the 2D pose in the first
     * line, then the covariance matrix in next 3 lines. */
    bool saveToTextFile(const std::string& file) const override;

    /** this = p (+) this. This can be used to convert a PDF from local
     * coordinates to global, providing the point (newReferenceBase) from which
     *   "to project" the current pdf. Result PDF substituted the currently
     * stored one in the object */
    void changeCoordinatesReference(const CPose3D& newReferenceBase) override;

    /** this = p (+) this. This can be used to convert a PDF from local
     * coordinates to global, providing the point (newReferenceBase) from which
     *   "to project" the current pdf. Result PDF substituted the currently
     * stored one in the object. */
    void changeCoordinatesReference(const CPose2D& newReferenceBase);

    /** Rotate the covariance matrix by replacing it by \f$
     * \mathbf{R}~\mathbf{COV}~\mathbf{R}^t \f$, where \f$ \mathbf{R} = \left[
     * \begin{array}{ccc} \cos\alpha & -\sin\alpha & 0 \\ \sin\alpha &
     * \cos\alpha & 0 \\ 0 & 0 & 1 \end{array}\right] \f$. */
    void rotateCov(const double ang);

    /** Set \f$ this = x1 \ominus x0 \f$ , computing the mean using the "-"
     * operator and the covariances through the corresponding Jacobians (For
     * 'x0' and 'x1' being independent variables!).  */
    void inverseComposition(
        const CPosePDFGaussianInf& x, const CPosePDFGaussianInf& ref);

    /** 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 x1). */
    void inverseComposition(
        const CPosePDFGaussianInf& x1, const CPosePDFGaussianInf& x0,
        const mrpt::math::CMatrixDouble33& COV_01);

    /** Draws a single sample from the distribution */
    void drawSingleSample(CPose2D& outPart) const override;

    /** Draws a number of samples from the distribution, and saves as a list of
     * 1x3 vectors, where each row contains a (x,y,phi) datum. */
    void drawManySamples(
        size_t N,
        std::vector<mrpt::math::CVectorDouble>& outSamples) const override;

    /** Bayesian fusion of two points gauss. distributions, then save the result
     *in this object.
     *  The process is as follows:<br>
     *      - (x1,S1): Mean and variance of the p1 distribution.
     *      - (x2,S2): Mean and variance of the p2 distribution.
     *      - (x,S): Mean and variance of the resulting distribution.
     *
     *    S = (S1<sup>-1</sup> + S2<sup>-1</sup>)<sup>-1</sup>;
     *    x = S * ( S1<sup>-1</sup>*x1 + S2<sup>-1</sup>*x2 );
     */
    void bayesianFusion(
        const CPosePDF& p1, const CPosePDF& p2,
        const double minMahalanobisDistToDrop = 0) override;

    /** Returns a new PDF such as: NEW_PDF = (0,0,0) - THIS_PDF */
    void inverse(CPosePDF& o) const override;

    /** Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the
     * mean, and the covariance matrix are updated). */
    void operator+=(const CPose2D& Ap);

    /** Evaluates the PDF at a given point */
    double evaluatePDF(const CPose2D& x) const;

    /** Evaluates the ratio PDF(x) / PDF(MEAN), that is, the normalized PDF in
     * the range [0,1]. */
    double evaluateNormalizedPDF(const CPose2D& x) const;

    /** Computes the Mahalanobis distance between the centers of two Gaussians.
     */
    double mahalanobisDistanceTo(const CPosePDFGaussianInf& theOther);

    /** Makes: thisPDF = thisPDF + Ap, where "+" is pose composition (both the
     * mean, and the covariance matrix are updated) (see formulas in
     * jacobiansPoseComposition ). */
    void operator+=(const CPosePDFGaussianInf& Ap);

    /** Makes: thisPDF = thisPDF - Ap, where "-" is pose inverse composition
     * (both the mean, and the covariance matrix are updated) */
    inline void operator-=(const CPosePDFGaussianInf& ref)
    {
        this->inverseComposition(*this, ref);
    }

};  // End of class def.

bool operator==(const CPosePDFGaussianInf& p1, const CPosePDFGaussianInf& p2);
/** Pose compose operator: RES = A (+) B , computing both the mean and the
 * covariance */
CPosePDFGaussianInf operator+(
    const CPosePDFGaussianInf& a, const CPosePDFGaussianInf& b);
/** Pose inverse compose operator: RES = A (-) B , computing both the mean and
 * the covariance */
CPosePDFGaussianInf operator-(
    const CPosePDFGaussianInf& a, const CPosePDFGaussianInf& b);
/** Returns the Gaussian distribution of \f$ \mathbf{C} \f$, for \f$ \mathbf{C}
 * = \mathbf{A} \oplus \mathbf{B} \f$. */
poses::CPosePDFGaussianInf operator+(
    const mrpt::poses::CPose2D& A, const mrpt::poses::CPosePDFGaussianInf& B);

/** Dumps the mean and covariance matrix to a text stream. */
std::ostream& operator<<(std::ostream& out, const CPosePDFGaussianInf& obj);

}  // namespace mrpt::poses