Detailed Description

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

Library `mrpt-math`

[New in MRPT 2.0.0]

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

    sudo apt install libmrpt-math-dev

See: Using MRPT from your CMake project

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:

Collaboration diagram for [mrpt-math]:

Classes
class	mrpt::math::CAtan2LookUpTable
	A look-up-table (LUT) of atan values for any (x,y) value in a square/rectangular grid of predefined resolution. More...

class	mrpt::math::CAtan2LookUpTableMultiRes
	Like CAtan2LookUpTable but with a multiresolution grid for increasingly better accuracy in points nearer to the origin. More...

class	mrpt::math::CBinaryRelation< T, U, UIsObject >
	This class models a binary relation through the elements of any given set. More...

class	mrpt::math::CHistogram
	This class provides an easy way of computing histograms for unidimensional real valued variables. More...

class	mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >
	An implementation of the Levenberg-Marquardt algorithm for least-square minimization. More...

class	mrpt::math::CMatrixB
	This class is a "CSerializable" wrapper for "CMatrixBool". More...

class	mrpt::math::CMatrixD
	This class is a "CSerializable" wrapper for "CMatrixDynamic<double>". More...

class	mrpt::math::CMatrixDynamic< T >
	This template class provides the basic functionality for a general 2D any-size, resizable container of numerical or non-numerical elements. More...

class	mrpt::math::CMatrixF
	This class is a "CSerializable" wrapper for "CMatrixFloat". More...

class	mrpt::math::CMatrixFixed< T, ROWS, COLS >
	A compile-time fixed-size numeric matrix container. More...

class	mrpt::math::CMonteCarlo< T, NUM, OTHER >
	Montecarlo simulation for experiments in 1D. More...

class	mrpt::math::CProbabilityDensityFunction< TDATA, STATE_LEN >
	A generic template for probability density distributions (PDFs). More...

class	mrpt::math::CQuaternion< T >
	A quaternion, which can represent a 3D rotation as pair $(r,\mathbf{u}) *$ , with a real part "r" and a 3D vector $\mathbf{u} = (x,y,z)$ , or alternatively, q = r + ix + jy + kz. More...

class	mrpt::math::CSparseMatrix
	A sparse matrix structure, wrapping T. More...

class	mrpt::math::CSparseMatrixTemplate< T >
	A sparse matrix container (with cells of any type), with iterators. More...

class	mrpt::math::CVectorDynamic< T >
	Template for column vectors of dynamic size, compatible with Eigen. More...

class	mrpt::math::KDTreeCapable< Derived, num_t, metric_t >
	A generic adaptor class for providing Nearest Neighbor (NN) lookup via the `nanoflann` library. More...

struct	mrpt::math::matrix_size_t
	Auxiliary class used in CMatrixDynamic:size(), CMatrixDynamic::resize(), CMatrixFixed::size(), CMatrixFixed::resize(), to mimic the behavior of STL-containers. More...

class	mrpt::math::MatrixBase< Scalar, Derived >
	Base CRTP class for all MRPT matrices. More...

struct	mrpt::math::MatrixBlockSparseCols< Scalar, NROWS, NCOLS, INFO, HAS_REMAP, INDEX_REMAP_MAP_IMPL >
	A templated column-indexed efficient storage of block-sparse Jacobian or Hessian matrices, together with other arbitrary information. More...

class	mrpt::math::MatrixVectorBase< Scalar, Derived >
	Base CRTP class for all MRPT vectors and matrices. More...

struct	mrpt::math::RobustKernel< KERNEL_TYPE, T >

struct	mrpt::math::RobustKernel< rkLeastSquares, T >
	No robust kernel, use standard least squares: rho(r) = r^2. More...

struct	mrpt::math::RobustKernel< rkPseudoHuber, T >
	Pseudo-huber robust kernel: rho(r) = 2 * delta^2 * ( -1+sqrt( 1+ r^2/delta^2 ) ) More...

Namespaces
	mrpt::math
	This base provides a set of functions for maths stuff.

Modules
	Lightweight SE(2)/SE(3) types, geometry functions.
	Lightweight SE(2)/SE(3) data types, geometry functions, etc.

	Vectors, matrices, linear Algebra
	Dynamic and fixed-size vectors and matrices, basic linear Algebra.

	Custom I/O for math containers

	Statistics functions, probability distributions

	Filtering algorithms

	Fourier transform functions

	Fresnel integrals (`#include
	<mrpt/math/fresnel.h>`)

	Interpolation, least-squares fit, splines

	KD-Trees

	Vector and matrices mathematical operations
	and other utilities

	Find polynomial roots (`#include
	<mrpt/math/poly_roots.h>`)

	RANSAC and other model fitting algorithms

	Gaussian PDF transformation functions

	Helper functions for MEX & MATLAB

Enumerations
enum	mrpt::math::TMatrixTextFileFormat { mrpt::math::MATRIX_FORMAT_ENG = 0, mrpt::math::MATRIX_FORMAT_FIXED = 1, mrpt::math::MATRIX_FORMAT_INT = 2 }

enum	mrpt::math::TRobustKernelType { mrpt::math::rkLeastSquares = 0, mrpt::math::rkPseudoHuber }
	The different types of kernels for usage within a robustified least-squares estimator. More...

Functions
void	mrpt::math::setEpsilon (double nE)
	Changes the value of the geometric epsilon (default = 1e-5) More...

double	mrpt::math::getEpsilon ()
	Gets the value of the geometric epsilon (default = 1e-5) More...

template<class Derived >
const Derived &	mrpt::math::mat2eig (const Eigen::EigenBase< Derived > &m)
	Returns an Eigen-compatible type, despite its argument already is an Eigen matrix, or an mrpt-math matrix/vector. More...

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)
	Estimate the Jacobian of a multi-dimensional function around a point "x", using finite differences of a given size in each input dimension. More...

Enumeration Type Documentation

◆ TMatrixTextFileFormat

enum mrpt::math::TMatrixTextFileFormat

Selection of the number format in MatrixVectorBase::saveToTextFile()

Enumerator
MATRIX_FORMAT_ENG	engineering format 'e'
MATRIX_FORMAT_FIXED	fixed floating point 'f'
MATRIX_FORMAT_INT	intergers 'i'

Definition at line 34 of file MatrixVectorBase.h.

◆ TRobustKernelType

enum mrpt::math::TRobustKernelType

The different types of kernels for usage within a robustified least-squares estimator.

See also: Use these types as arguments of the template RobustKernel<>

Enumerator
rkLeastSquares	No robust kernel, use standard least squares: rho(r)= 1/2 * r^2.
rkPseudoHuber	Pseudo-huber robust kernel.

Definition at line 23 of file robust_kernels.h.

Function Documentation

◆ estimateJacobian()

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
	)

Estimate the Jacobian of a multi-dimensional function around a point "x", using finite differences of a given size in each input dimension.

The template argument USERPARAM is for the data can be passed to the functor. If it is not required, set to "int" or any other basic type.

This is a generic template which works with: VECTORLIKE: vector_float, CVectorDouble, CVectorFixed<>, double [N], ... MATRIXLIKE: CMatrixDynamic, CMatrixFixed

Definition at line 31 of file num_jacobian.h.

References ASSERT_, MRPT_END, and MRPT_START.

Referenced by Pose3DTests::check_jacob_expe_e_at_0(), Pose3DTests::check_jacob_LnT_T(), mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), mrpt::vision::recompute_errors_and_Jacobians(), mrpt::bayes::CKalmanFilterCapable< 7, 3, 3, 7 >::runOneKalmanIteration(), Pose3DQuatTests::test_composePointJacob(), Pose3DTests::test_composePointJacob(), Pose3DTests::test_composePointJacob_se3(), Pose3DQuatTests::test_invComposePointJacob(), Pose3DTests::test_invComposePointJacob(), Pose3DTests::test_invComposePointJacob_se3(), Pose3DTests::test_Jacob_dAexpeD_de(), Pose3DTests::test_Jacob_dDexpe_de(), Pose3DTests::test_Jacob_dexpeD_de(), SE_traits_tests< POSE_TYPE >::test_jacobs_AB(), SE_traits_tests< POSE_TYPE >::test_jacobs_DinvP1InvP2(), Pose3DQuatTests::test_normalizeJacob(), Pose3DQuatTests::test_sphericalCoords(), Pose3DPDFGaussTests::testCompositionJacobian(), Pose3DQuatPDFGaussTests::testCompositionJacobian(), and mrpt::math::transform_gaussian_linear().