[mrpt-math]

Overview

Math C++ library: vectors and matrices, probability distributions, statistics, geometry, etc.

Library mrpt-math

This library is part of MRPT and can be installed in Debian-based systems with:

sudo apt install libmrpt-math-dev

The main classes and concepts associated with this library:

mrpt_math_vectors_matrices_grp: Vectors and matrices (compatible with the Eigen library).
mrpt_math_lwgeom_grp: TPose2D, TPose3D, TPoint3D, TLine3D, geometry functions, etc. (See also: [mrpt-poses])

Other important elements:

Eigen integration (MRPT 3.x)

MRPT uses Eigen 3 for all matrix/vector types. Key points for MRPT 3 users:

mrpt::math::CMatrixDynamic<T> and mrpt::math::CMatrixFixed<T,R,C> wrap Eigen matrices and are fully serializable via mrpt::serialization::CArchive.
Use .asEigen() on any MRPT matrix to get the underlying Eigen expression for use with Eigen algorithms (decompositions, solvers, etc.).
mrpt::math::CVectorDynamic<T> is a column-vector equivalent.
Sparse matrices: use Eigen::SparseMatrix<double> directly; MRPT does not wrap sparse types but provides helpers in mrpt::math::CSparseMatrix (CXSparse-backed) for serialization.
Geometric operations (e.g. point clouds): lightweight structs mrpt::math::TPoint2Df, mrpt::math::TPoint3Df (float) and their double variants are used for performance; they convert freely to/from Eigen vectors.

KD-tree nearest-neighbor search

mrpt::math::KDTreeCapable is a CRTP adapter around nanoflann providing:

kdTreeClosestPoint2D() / kdTreeClosestPoint3D() — single NN query.
kdTreeNClosestPoint2D() / kdTreeNClosestPoint3D() — k-NN query.
kdTreeRadiusSearch2D() / kdTreeRadiusSearch3D() — radius search.

Derived classes must implement kdtree_get_point_count() and kdtree_get_pt(idx, dim). The KD-tree index is built lazily on first query and invalidated by calling kdtree_mark_as_outdated().

Library contents

Custom I/O for math containers
Filtering algorithms
Find polynomial roots (<tt>#include
Fourier transform functions
Fresnel integrals (<tt>#include
Gaussian PDF transformation functions
Interpolation, least-squares fit, splines
Lightweight SE(2)/SE(3) types, geometry functions.
RANSAC and other model fitting algorithms
Statistics functions, probability distributions
Vector and matrices mathematical operations
Vectors, matrices, linear Algebra

// typedefs

typedef CLevenbergMarquardtTempl<mrpt::math::CVectorDouble> mrpt::math::CLevenbergMarquardt;

// enums

enum mrpt::math::TMatrixTextFileFormat;
enum mrpt::math::TRobustKernelType;

// structs

template <
    typename Scalar,
    int NROWS,
    int NCOLS,
    typename INFO,
    bool HAS_REMAP,
    typename INDEX_REMAP_MAP_IMPL = mrpt::containers::map_as_vector<size_t, size_t>
    >
struct mrpt::math::MatrixBlockSparseCols;

template <typename T>
struct mrpt::math::RobustKernel<rkPseudoHuber, T>;

template <typename T>
struct mrpt::math::RobustKernel<rkLeastSquares, T>;

template <TRobustKernelType KERNEL_TYPE, typename T = double>
struct mrpt::math::RobustKernel;

struct mrpt::math::matrix_size_t;

// classes

class mrpt::math::CAtan2LookUpTable;
class mrpt::math::CAtan2LookUpTableMultiRes;

template <typename T, typename U, bool UIsObject = false>
class mrpt::math::CBinaryRelation;

class mrpt::math::CHistogram;

template <typename VECTORTYPE = CVectorDouble, class USERPARAM = VECTORTYPE>
class mrpt::math::CLevenbergMarquardtTempl;

class mrpt::math::CMatrixB;
class mrpt::math::CMatrixD;

template <class T>
class mrpt::math::CMatrixDynamic;

class mrpt::math::CMatrixF;

template <typename T, matrix_dim_t ROWS, matrix_dim_t COLS>
class mrpt::math::CMatrixFixed;

template <typename T, typename NUM, typename OTHER>
class mrpt::math::CMonteCarlo;

template <class TDATA, size_t STATE_LEN>
class mrpt::math::CProbabilityDensityFunction;

template <class T>
class mrpt::math::CQuaternion;

template <class T>
class mrpt::math::CSparseMatrixTemplate;

template <class T>
class mrpt::math::CVectorDynamic;

template <
    class Derived,
    typename num_t = float,
    typename metric_t = nanoflann::L2_Simple_Adaptor<num_t, Derived>
    >
class mrpt::math::KDTreeCapable;

template <typename Scalar, class Derived>
class mrpt::math::MatrixBase;

template <typename Scalar, class Derived>
class mrpt::math::MatrixVectorBase;

// global functions

void mrpt::math::setEpsilon(double nE);
double mrpt::math::getEpsilon();

template <class Derived>
const Derived& mrpt::math::mat2eig(const Eigen::EigenBase<Derived>& m);

template <
    class VECTORLIKE,
    class VECTORLIKE2,
    class VECTORLIKE3,
    class MATRIXLIKE,
    class USERPARAM
    >
void mrpt::math::estimateJacobian(
    const VECTORLIKE& x,
    const std::function<void(const VECTORLIKE&x, const USERPARAM&y, VECTORLIKE3&out)>& functor,
    const VECTORLIKE2& increments,
    const USERPARAM& userParam,
    MATRIXLIKE& out_Jacobian
    );

void mrpt::math::registerAllClasses_mrpt_math();

Typedefs

typedef CLevenbergMarquardtTempl<mrpt::math::CVectorDouble> mrpt::math::CLevenbergMarquardt

The default name for the LM class is an instantiation for “double”.

Global Functions

void mrpt::math::setEpsilon(double nE)

Changes the value of the geometric epsilon (default = 1e-5)