Detailed Description

This base provides a set of functions for maths stuff.

mrpt_math_grp

Namespaces
	detail

Classes
class	CArrayNumeric
	CArrayNumeric is an array for numeric types supporting several mathematical operations (actually, just a wrapper on Eigen::Matrix<T,N,1>) More...

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

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

class	CBinaryRelation
	This class models a binary relation through the elements of any given set. More...

class	CConstMatrixColumnAccessor
	A vector-like wrapper for a const Matrix for accessing the elements of a given column with a [] operator. More...

class	CConstMatrixColumnAccessorExtended
	A vector-like wrapper for a const Matrix for accessing the elements of a given column with a [] operator, with offset and custom spacing. More...

class	CConstMatrixRowAccessor
	A vector-like wrapper for a const Matrix for accessing the elements of a given row with a [] operator. More...

class	CConstMatrixRowAccessorExtended
	A vector-like wrapper for a const Matrix for accessing the elements of a given row with a [] operator, with offset and custom spacing. More...

struct	CExceptionNotDefPos
	Used in mrpt::math::CSparseMatrix. More...

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

class	CLevenbergMarquardtTempl
	An implementation of the Levenberg-Marquardt algorithm for least-square minimization. More...

class	CMatrix
	This class is a "CSerializable" wrapper for "CMatrixFloat". More...

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

class	CMatrixBool
	Declares a matrix of booleans (non serializable). More...

class	CMatrixColumnAccessor
	A vector-like wrapper for a Matrix for accessing the elements of a given column with a [] operator. More...

class	CMatrixColumnAccessorExtended
	A vector-like wrapper for a Matrix for accessing the elements of a given column with a [] operator, with offset and custom spacing. More...

class	CMatrixD
	This class is a "CSerializable" wrapper for "CMatrixTemplateNumeric<double>". More...

class	CMatrixFixedNumeric
	A numeric matrix of compile-time fixed size. More...

class	CMatrixRowAccessor
	A vector-like wrapper for a Matrix for accessing the elements of a given row with a [] operator. More...

class	CMatrixRowAccessorExtended
	A vector-like wrapper for a Matrix for accessing the elements of a given row with a [] operator, with offset and custom spacing. More...

class	CMatrixTemplate
	This template class provides the basic functionality for a general 2D any-size, resizable container of numerical or non-numerical elements. More...

class	CMatrixTemplateNumeric
	A matrix of dynamic size. More...

class	CMatrixTemplateObjects
	This template class extends the class "CMatrixTemplate" for storing "objects" at each matrix entry. More...

struct	CMatrixTemplateSize
	Auxiliary class used in CMatrixTemplate:size(), CMatrixTemplate::resize(), CMatrixFixedNumeric::size(), CMatrixFixedNumeric::resize(), to mimic the behavior of STL-containers. More...

class	CMonteCarlo
	Montecarlo simulation for experiments in 1D. More...

struct	ContainerType
	ContainerType<T>::element_t exposes the value of any STL or Eigen container. More...

struct	ContainerType< Eigen::EigenBase< Derived > >
	Specialization for Eigen containers. More...

class	CPolygon
	A wrapper of a TPolygon2D class, implementing CSerializable. More...

class	CProbabilityDensityFunction
	A generic template for probability density distributions (PDFs). More...

class	CQuaternion
	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	CSparseMatrix
	A sparse matrix structure, wrapping T. More...

class	CSparseMatrixTemplate
	A sparse matrix container (with cells of any type), with iterators. More...

class	CSparseSymmetricalMatrix
	A sparse matrix container for square symmetrical content around the main diagonal. More...

class	CSplineInterpolator1D
	A (persistent) sequence of (x,y) coordinates, allowing queries of intermediate points through spline interpolation, where possible. More...

class	dynamic_vector
	Column vector, like Eigen::MatrixX*, but automatically initialized to zeros since construction. More...

class	FAddPoint

class	KDTreeCapable
	A generic adaptor class for providing Nearest Neighbor (NN) lookup via the `nanoflann` library. More...

struct	LowPassFilter_IIR1
	1-order low-pass IIR filter. More...

struct	MatrixBlockSparseCols
	A templated column-indexed efficient storage of block-sparse Jacobian or Hessian matrices, together with other arbitrary information. More...

class	ModelSearch
	Model search implementations: RANSAC and genetic algorithm. More...

class	RANSAC_Template
	A generic RANSAC implementation with models as matrices. More...

struct	RobustKernel

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

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

struct	TLine2D
	2D line without bounds, represented by its equation . More...

struct	TLine3D
	3D line, represented by a base point and a director vector. More...

struct	TObject2D
	Standard type for storing any lightweight 2D type. More...

struct	TObject3D
	Standard object for storing any 3D lightweight object. More...

struct	TPlane
	3D Plane, represented by its equation More...

struct	TPoint2D
	Lightweight 2D point. More...

struct	TPoint3D
	Lightweight 3D point. More...

struct	TPoint3Df
	Lightweight 3D point (float version). More...

struct	TPointXYZfIu8
	XYZ point (float) + Intensity(u8) More...

struct	TPointXYZfRGBu8
	XYZ point (float) + RGB(u8) More...

struct	TPointXYZIu8
	XYZ point (double) + Intensity(u8) More...

struct	TPointXYZRGBu8
	XYZ point (double) + RGB(u8) More...

class	TPolygon2D
	2D polygon, inheriting from std::vector<TPoint2D>. More...

class	TPolygon3D
	3D polygon, inheriting from std::vector<TPoint3D> More...

class	TPolygonWithPlane
	Slightly heavyweight type to speed-up calculations with polygons in 3D. More...

struct	TPose2D
	Lightweight 2D pose. More...

struct	TPose3D
	Lightweight 3D pose (three spatial coordinates, plus three angular coordinates). More...

struct	TPose3DQuat
	Lightweight 3D pose (three spatial coordinates, plus a quaternion ). More...

struct	TPoseOrPoint
	Base type of all TPoseXX and TPointXX classes in mrpt::math. More...

struct	TSegment2D
	2D segment, consisting of two points. More...

struct	TSegment3D
	3D segment, consisting of two points. More...

struct	TTwist2D
	2D twist: 2D velocity vector (vx,vy) + planar angular velocity (omega) More...

struct	TTwist3D
	3D twist: 3D velocity vector (vx,vy,vz) + angular velocity (wx,wy,wz) More...

Typedefs
template<std::size_t N>
using	CArrayFloat = CArrayNumeric< float, N >
	A partial specialization of CArrayNumeric for float numbers. More...

template<std::size_t N>
using	CArrayDouble = CArrayNumeric< double, N >
	A partial specialization of CArrayNumeric for double numbers. More...

template<std::size_t N>
using	CArrayInt = CArrayNumeric< int, N >
	A partial specialization of CArrayNumeric for int numbers. More...

template<std::size_t N>
using	CArrayUInt = CArrayNumeric< unsigned int, N >
	A partial specialization of CArrayNumeric for unsigned int numbers. More...

using	CLevenbergMarquardt = CLevenbergMarquardtTempl< mrpt::math::CVectorDouble >
	The default name for the LM class is an instantiation for "double". More...

using	CMatrixFloat = CMatrixTemplateNumeric< float >
	Declares a matrix of float numbers (non serializable). More...

using	CMatrixDouble = CMatrixTemplateNumeric< double >
	Declares a matrix of double numbers (non serializable). More...

using	CMatrixUInt = CMatrixTemplateNumeric< unsigned int >
	Declares a matrix of unsigned ints (non serializable). More...

using	CMatrixLongDouble = CMatrixTemplateNumeric< double >
	Declares a matrix of "long doubles" (non serializable), or of "doubles" if the compiler does not support "long double". More...

using	CQuaternionDouble = CQuaternion< double >
	A quaternion of data type "double". More...

using	CQuaternionFloat = CQuaternion< float >
	A quaternion of data type "float". More...

using	CVectorFloat = dynamic_vector< float >
	Column vector, like Eigen::MatrixXf, but automatically initialized to zeros since construction. More...

using	CVectorDouble = dynamic_vector< double >
	Column vector, like Eigen::MatrixXd, but automatically initialized to zeros since construction. More...

using	TPlane3D = TPlane

using	RANSAC = RANSAC_Template< double >
	The default instance of RANSAC, for double type. More...

using	FFT_TYPE = float
	Copyright(C) 1997 Takuya OOURA (email: ooura.nosp@m.@mmm.nosp@m..t.u-.nosp@m.toky.nosp@m.o.ac..nosp@m.jp). More...

Typedefs for common sizes
using	CMatrixDouble22 = CMatrixFixedNumeric< double, 2, 2 >

using	CMatrixDouble23 = CMatrixFixedNumeric< double, 2, 3 >

using	CMatrixDouble32 = CMatrixFixedNumeric< double, 3, 2 >

using	CMatrixDouble33 = CMatrixFixedNumeric< double, 3, 3 >

using	CMatrixDouble44 = CMatrixFixedNumeric< double, 4, 4 >

using	CMatrixDouble66 = CMatrixFixedNumeric< double, 6, 6 >

using	CMatrixDouble77 = CMatrixFixedNumeric< double, 7, 7 >

using	CMatrixDouble13 = CMatrixFixedNumeric< double, 1, 3 >

using	CMatrixDouble31 = CMatrixFixedNumeric< double, 3, 1 >

using	CMatrixDouble12 = CMatrixFixedNumeric< double, 1, 2 >

using	CMatrixDouble21 = CMatrixFixedNumeric< double, 2, 1 >

using	CMatrixDouble61 = CMatrixFixedNumeric< double, 6, 1 >

using	CMatrixDouble16 = CMatrixFixedNumeric< double, 1, 6 >

using	CMatrixDouble71 = CMatrixFixedNumeric< double, 7, 1 >

using	CMatrixDouble17 = CMatrixFixedNumeric< double, 1, 7 >

using	CMatrixDouble51 = CMatrixFixedNumeric< double, 5, 1 >

using	CMatrixDouble15 = CMatrixFixedNumeric< double, 1, 5 >

using	CMatrixDouble41 = CMatrixFixedNumeric< double, 4, 1 >

using	CMatrixFloat22 = CMatrixFixedNumeric< float, 2, 2 >

using	CMatrixFloat23 = CMatrixFixedNumeric< float, 2, 3 >

using	CMatrixFloat32 = CMatrixFixedNumeric< float, 3, 2 >

using	CMatrixFloat33 = CMatrixFixedNumeric< float, 3, 3 >

using	CMatrixFloat44 = CMatrixFixedNumeric< float, 4, 4 >

using	CMatrixFloat66 = CMatrixFixedNumeric< float, 6, 6 >

using	CMatrixFloat77 = CMatrixFixedNumeric< float, 7, 7 >

using	CMatrixFloat13 = CMatrixFixedNumeric< float, 1, 3 >

using	CMatrixFloat31 = CMatrixFixedNumeric< float, 3, 1 >

using	CMatrixFloat12 = CMatrixFixedNumeric< float, 1, 2 >

using	CMatrixFloat21 = CMatrixFixedNumeric< float, 2, 1 >

using	CMatrixFloat61 = CMatrixFixedNumeric< float, 6, 1 >

using	CMatrixFloat16 = CMatrixFixedNumeric< float, 1, 6 >

using	CMatrixFloat71 = CMatrixFixedNumeric< float, 7, 1 >

using	CMatrixFloat17 = CMatrixFixedNumeric< float, 1, 7 >

using	CMatrixFloat51 = CMatrixFixedNumeric< float, 5, 1 >

using	CMatrixFloat15 = CMatrixFixedNumeric< float, 1, 5 >

Enumerations
enum	TConstructorFlags_Quaternions { UNINITIALIZED_QUATERNION = 0 }

enum	TMatrixTextFileFormat { MATRIX_FORMAT_ENG = 0, MATRIX_FORMAT_FIXED = 1, MATRIX_FORMAT_INT = 2 }

enum	TConstructorFlags_Matrices { UNINITIALIZED_MATRIX = 0 }
	For usage in one of the constructors of CMatrixFixedNumeric or CMatrixTemplate (and derived classes), if it's not required to fill it with zeros at the constructor to save time. More...

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

Functions
template<class MATRIXLIKE >
size_t	size (const MATRIXLIKE &m, const int dim)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, CMatrix::Ptr &pObj)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, CMatrixD::Ptr &pObj)

double	normalPDF (double x, double mu, double std)
	Evaluates the univariate normal (Gaussian) distribution at a given point "x". More...

template<class VECTORLIKE1 , class VECTORLIKE2 , class MATRIXLIKE >
MATRIXLIKE::Scalar	normalPDFInf (const VECTORLIKE1 &x, const VECTORLIKE2 &mu, const MATRIXLIKE &cov_inv, const bool scaled_pdf=false)
	Evaluates the multivariate normal (Gaussian) distribution at a given point "x". More...

template<class VECTORLIKE1 , class VECTORLIKE2 , class MATRIXLIKE >
MATRIXLIKE::Scalar	normalPDF (const VECTORLIKE1 &x, const VECTORLIKE2 &mu, const MATRIXLIKE &cov, const bool scaled_pdf=false)
	Evaluates the multivariate normal (Gaussian) distribution at a given point "x". More...

template<typename VECTORLIKE , typename MATRIXLIKE >
MATRIXLIKE::Scalar	normalPDF (const VECTORLIKE &d, const MATRIXLIKE &cov)
	Evaluates the multivariate normal (Gaussian) distribution at a given point given its distance vector "d" from the Gaussian mean. More...

template<typename VECTORLIKE1 , typename MATRIXLIKE1 , typename VECTORLIKE2 , typename MATRIXLIKE2 >
double	KLD_Gaussians (const VECTORLIKE1 &mu0, const MATRIXLIKE1 &cov0, const VECTORLIKE2 &mu1, const MATRIXLIKE2 &cov1)
	Kullback-Leibler divergence (KLD) between two independent multivariate Gaussians. More...

double	normalQuantile (double p)
	Evaluates the Gaussian distribution quantile for the probability value p=[0,1]. More...

double	normalCDF (double p)
	Evaluates the Gaussian cumulative density function. More...

double	chi2inv (double P, unsigned int dim=1)
	The "quantile" of the Chi-Square distribution, for dimension "dim" and probability 0<P<1 (the inverse of chi2CDF) An aproximation from the Wilson-Hilferty transformation is used. More...

double	noncentralChi2CDF (unsigned int degreesOfFreedom, double noncentrality, double arg)

double	chi2CDF (unsigned int degreesOfFreedom, double arg)

double	chi2PDF (unsigned int degreesOfFreedom, double arg, double accuracy=1e-7)

std::pair< double, double >	noncentralChi2PDF_CDF (unsigned int degreesOfFreedom, double noncentrality, double arg, double eps=1e-7)
	Returns the 'exact' PDF (first) and CDF (second) of a Non-central chi-squared probability distribution, using an iterative method. More...

template<typename CONTAINER >
void	confidenceIntervals (const CONTAINER &data, typename mrpt::math::ContainerType< CONTAINER >::element_t &out_mean, typename mrpt::math::ContainerType< CONTAINER >::element_t &out_lower_conf_interval, typename mrpt::math::ContainerType< CONTAINER >::element_t &out_upper_conf_interval, const double confidenceInterval=0.1, const size_t histogramNumBins=1000)
	Return the mean and the 10%-90% confidence points (or with any other confidence value) of a set of samples by building the cummulative CDF of all the elements of the container. More...

void	fft_real (CVectorFloat &in_realData, CVectorFloat &out_FFT_Re, CVectorFloat &out_FFT_Im, CVectorFloat &out_FFT_Mag)
	Computes the FFT of a 2^N-size vector of real numbers, and returns the Re+Im+Magnitude parts. More...

void	dft2_real (const CMatrixFloat &in_data, CMatrixFloat &out_real, CMatrixFloat &out_imag)
	Compute the 2D Discrete Fourier Transform (DFT) of a real matrix, returning the real and imaginary parts separately. More...

void	idft2_real (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_data)
	Compute the 2D inverse Discrete Fourier Transform (DFT) More...

void	dft2_complex (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_real, CMatrixFloat &out_imag)
	Compute the 2D Discrete Fourier Transform (DFT) of a complex matrix, returning the real and imaginary parts separately. More...

void	idft2_complex (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_real, CMatrixFloat &out_imag)
	Compute the 2D inverse Discrete Fourier Transform (DFT). More...

void	cross_correlation_FFT (const CMatrixFloat &A, const CMatrixFloat &B, CMatrixFloat &out_corr)
	Correlation of two matrixes using 2D FFT. More...

double	fresnel_sin_integral (double x) noexcept
	Evaluates the integral from 0 to x of sqrt(2/pi) sin(t^2) dt. More...

double	fresnel_cos_integral (double x) noexcept
	Evaluates the integral from 0 to x of sqrt(2/pi) cos(t^2) dt. More...

long double	lfresnel_sin_integral (long double x) noexcept
	long double version of fresnel_sin_integral More...

long double	lfresnel_cos_integral (long double x) noexcept
	long double version of fresnel_cos_integral More...

template<class MATRIXLIKE1 , class MATRIXLIKE2 >
void	homogeneousMatrixInverse (const MATRIXLIKE1 &M, MATRIXLIKE2 &out_inverse_M)
	Efficiently compute the inverse of a 4x4 homogeneous matrix by only transposing the rotation 3x3 part and solving the translation with dot products. More...

template<class IN_ROTMATRIX , class IN_XYZ , class OUT_ROTMATRIX , class OUT_XYZ >
void	homogeneousMatrixInverse (const IN_ROTMATRIX &in_R, const IN_XYZ &in_xyz, OUT_ROTMATRIX &out_R, OUT_XYZ &out_xyz)

template<class MATRIXLIKE >
void	homogeneousMatrixInverse (MATRIXLIKE &M)

template<class T , class VECTOR >
T	interpolate (const T &x, const VECTOR &ys, const T &x0, const T &x1)
	Interpolate a data sequence "ys" ranging from "x0" to "x1" (equally spaced), to obtain the approximation of the sequence at the point "x". More...

double	interpolate2points (const double x, const double x0, const double y0, const double x1, const double y1, bool wrap2pi=false)
	Linear interpolation/extrapolation: evaluates at "x" the line (x0,y0)-(x1,y1). More...

template<typename NUMTYPE , class VECTORLIKE >
NUMTYPE	spline (const NUMTYPE t, const VECTORLIKE &x, const VECTORLIKE &y, bool wrap2pi=false)
	Interpolates the value of a function in a point "t" given 4 SORTED points where "t" is between the two middle points If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range). More...

template<typename NUMTYPE , class VECTORLIKE , int NUM_POINTS = Eigen::Dynamic>
NUMTYPE	leastSquareLinearFit (const NUMTYPE t, const VECTORLIKE &x, const VECTORLIKE &y, bool wrap2pi=false)
	Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a single point "t". More...

template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 , int NUM_POINTS = Eigen::Dynamic>
void	leastSquareLinearFit (const VECTORLIKE1 &ts, VECTORLIKE2 &outs, const VECTORLIKE3 &x, const VECTORLIKE3 &y, bool wrap2pi=false)
	Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a sequence of points "ts" and returned at "outs". More...

TPose3D	operator- (const TPose3D &p)
	Unary $$ operator: computes inverse SE(3) element. More...

TPose3D	operator- (const TPose3D &b, const TPose3D &a)
	Binary $$ operator: $b a$ computes the relative SE(3) pose of `b` "as seen from" `a` More...

std::ostream &	operator<< (std::ostream &o, const TPoint2D &p)

std::ostream &	operator<< (std::ostream &o, const TPoint3D &p)

std::ostream &	operator<< (std::ostream &o, const TPose2D &p)

std::ostream &	operator<< (std::ostream &o, const TPose3D &p)

std::ostream &	operator<< (std::ostream &o, const TPose3DQuat &p)

constexpr TPoint3D	operator- (const TPoint3D &p1)
	Unary minus operator for 3D points. More...

constexpr bool	operator== (const TPoint2D &p1, const TPoint2D &p2)
	Exact comparison between 2D points. More...

constexpr bool	operator!= (const TPoint2D &p1, const TPoint2D &p2)
	Exact comparison between 2D points. More...

constexpr bool	operator== (const TPoint3D &p1, const TPoint3D &p2)
	Exact comparison between 3D points. More...

constexpr bool	operator!= (const TPoint3D &p1, const TPoint3D &p2)
	Exact comparison between 3D points. More...

bool	operator== (const TPose2D &p1, const TPose2D &p2)
	Exact comparison between 2D poses, taking possible cycles into account. More...

bool	operator!= (const TPose2D &p1, const TPose2D &p2)
	Exact comparison between 2D poses, taking possible cycles into account. More...

bool	operator== (const TPose3D &p1, const TPose3D &p2)
	Exact comparison between 3D poses, taking possible cycles into account. More...

bool	operator!= (const TPose3D &p1, const TPose3D &p2)
	Exact comparison between 3D poses, taking possible cycles into account. More...

bool	operator== (const TSegment2D &s1, const TSegment2D &s2)

bool	operator!= (const TSegment2D &s1, const TSegment2D &s2)

bool	operator== (const TSegment3D &s1, const TSegment3D &s2)

bool	operator!= (const TSegment3D &s1, const TSegment3D &s2)

template<class PoseOrPoint , typename = std::enable_if_t<std::is_base_of< mrpt::math::TPoseOrPoint, PoseOrPoint>::value>>
mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, PoseOrPoint &o)

template<class PoseOrPoint , typename = std::enable_if_t<std::is_base_of< mrpt::math::TPoseOrPoint, PoseOrPoint>::value>>
mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const PoseOrPoint &o)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TSegment2D &s)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TSegment2D &s)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TLine2D &l)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TLine2D &l)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TObject2D &o)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TObject2D &o)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TSegment3D &s)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TSegment3D &s)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TLine3D &l)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TLine3D &l)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TPlane &p)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TPlane &p)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TObject3D &o)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TObject3D &o)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TTwist2D &o)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TTwist2D &o)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::TTwist3D &o)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const mrpt::math::TTwist3D &o)

template<class CONTAINER1 , class CONTAINER2 >
void	cumsum (const CONTAINER1 &in_data, CONTAINER2 &out_cumsum)

template<class CONTAINER >
CONTAINER::Scalar	norm (const CONTAINER &v)

template<class CONTAINER >
CONTAINER::Scalar	norm_inf (const CONTAINER &v)

template<class MAT_A , class SKEW_3VECTOR , class MAT_OUT >
void	multiply_A_skew3 (const MAT_A &A, const SKEW_3VECTOR &v, MAT_OUT &out)
	Only for vectors/arrays "v" of length3, compute out = A * Skew(v), where Skew(v) is the skew symmetric matric generated from v (see mrpt::math::skew_symmetric3) More...

template<class SKEW_3VECTOR , class MAT_A , class MAT_OUT >
void	multiply_skew3_A (const SKEW_3VECTOR &v, const MAT_A &A, MAT_OUT &out)
	Only for vectors/arrays "v" of length3, compute out = Skew(v) * A, where Skew(v) is the skew symmetric matric generated from v (see mrpt::math::skew_symmetric3) More...

template<class T >
T	wrapTo2Pi (T a)
	Modifies the given angle to translate it into the [0,2pi[ range. More...

template<typename MAT >
CMatrixRowAccessor< MAT >	getRowAccessor (MAT &m, size_t rowIdx)

template<typename MAT >
CMatrixRowAccessorExtended< MAT >	getRowAccessor (MAT &m, size_t rowIdx, size_t offset, size_t space=1)

template<typename MAT >
CConstMatrixRowAccessor< MAT >	getRowAccessor (const MAT &m, size_t rowIdx)

template<typename MAT >
CConstMatrixRowAccessorExtended< MAT >	getRowAccessor (const MAT &m, size_t rowIdx, size_t offset, size_t space=1)

template<typename MAT >
CMatrixColumnAccessor< MAT >	getColumnAccessor (MAT &m, size_t colIdx)

template<typename MAT >
CMatrixColumnAccessorExtended< MAT >	getColumnAccessor (MAT &m, size_t colIdx, size_t offset, size_t space=1)

template<typename MAT >
CConstMatrixColumnAccessor< MAT >	getColumnAccessor (const MAT &m, size_t colIdx)

template<typename MAT >
CConstMatrixColumnAccessorExtended< MAT >	getColumnAccessor (const MAT &m, size_t colIdx, size_t offset, size_t space=1)

template<class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 , class MATRIXLIKE , class USERPARAM >
void	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...

template<class CONTAINER >
std::vector< double >	histogram (const CONTAINER &v, double limit_min, double limit_max, size_t number_bins, bool do_normalization=false, std::vector< double > *out_bin_centers=nullptr)
	Computes the normalized or normal histogram of a sequence of numbers given the number of bins and the limits. More...

template<class EIGEN_CONTAINER >
void	resizeLike (EIGEN_CONTAINER &trg, const EIGEN_CONTAINER &src)

template<typename T >
void	resizeLike (std::vector< T > &trg, const std::vector< T > &src)

template<class CONTAINER1 , class CONTAINER2 , typename VALUE >
void	cumsum_tmpl (const CONTAINER1 &in_data, CONTAINER2 &out_cumsum)
	Computes the cumulative sum of all the elements, saving the result in another container. More...

template<class CONTAINER >
CONTAINER	cumsum (const CONTAINER &in_data)
	Computes the cumulative sum of all the elements. More...

template<class CONTAINER >
CONTAINER::Scalar	maximum (const CONTAINER &v)

template<class CONTAINER >
CONTAINER::Scalar	minimum (const CONTAINER &v)

template<typename T >
T	maximum (const std::vector< T > &v)

template<typename T >
T	minimum (const std::vector< T > &v)

template<class Derived >
const Eigen::MatrixBase< Derived >::AdjointReturnType	operator~ (const Eigen::MatrixBase< Derived > &m)
	Transpose operator for matrices. More...

template<class Derived >
Eigen::MatrixBase< Derived >::PlainObject	operator! (const Eigen::MatrixBase< Derived > &m)
	Unary inversion operator. More...

template<typename MAT_H , typename MAT_C , typename MAT_R >
void	multiply_HCHt (const MAT_H &H, const MAT_C &C, MAT_R &R, bool accumResultInOutput)
	R = H * C * H^t (with C symmetric) More...

template<typename VECTOR_H , typename MAT_C >
MAT_C::Scalar	multiply_HCHt_scalar (const VECTOR_H &H, const MAT_C &C)
	r (a scalar) = H * C * H^t (with a vector H and a symmetric matrix C) More...

template<typename MAT_H , typename MAT_C , typename MAT_R >
void	multiply_HtCH (const MAT_H &H, const MAT_C &C, MAT_R &R, bool accumResultInOutput)
	R = H^t * C * H (with C symmetric) More...

template<class MAT_IN , class VECTOR , class MAT_OUT >
void	meanAndCovMat (const MAT_IN &v, VECTOR &out_mean, MAT_OUT &out_cov)
	Computes the mean vector and covariance from a list of samples in an NxM matrix, where each row is a sample, so the covariance is MxM. More...

template<class MATRIX >
Eigen::Matrix< typename MATRIX::Scalar, MATRIX::ColsAtCompileTime, MATRIX::ColsAtCompileTime >	cov (const MATRIX &v)
	Computes the covariance matrix from a list of samples in an NxM matrix, where each row is a sample, so the covariance is MxM. More...

template<class T >
std::ostream &	operator<< (std::ostream &out, const std::vector< T > &d)
	A template function for printing out the contents of a std::vector variable. More...

template<class T >
std::ostream &	operator<< (std::ostream &out, std::vector< T > *d)
	A template function for printing out the contents of a std::vector variable. More...

template<typename T , size_t N>
mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &ostrm, const CArrayNumeric< T, N > &a)
	Binary dump of a CArrayNumeric<T,N> to a stream. More...

template<typename T , size_t N>
mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &istrm, CArrayNumeric< T, N > &a)
	Binary read of a CArrayNumeric<T,N> from a stream. More...

int	solve_poly3 (double *x, double a, double b, double c) noexcept
	Solves cubic equation `x^3 + ax^2 + bx + c = 0`. More...

int	solve_poly4 (double *x, double a, double b, double c, double d) noexcept
	Solves quartic equation `x^4 + ax^3 + bx^2 + c*x + d = 0` by Dekart-Euler method. More...

int	solve_poly5 (double *x, double a, double b, double c, double d, double e) noexcept
	Solves equation `x^5 + ax^4 + bx^3 + cx^2 + dx + e = 0`. More...

int	solve_poly4Bi (double *x, double b, double d) noexcept
	Solve equation x^4 + b*x^2 + d = 0. More...

int	solve_poly4De (double *x, double b, double c, double d) noexcept
	Solve equation x^4 + bx^2 + cx + d = 0. More...

int	solve_poly2 (double a, double b, double c, double &r1, double &r2) noexcept
	Solves equation `ax^2 + bx + c = 0`. More...

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void	transform_gaussian_unscented (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const bool elem_do_wrap2pi=nullptr, const double alpha=1e-3, const double K=0, const double beta=2.0)
	Scaled unscented transformation (SUT) for estimating the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user. More...

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void	transform_gaussian_montecarlo (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const size_t num_samples=1000, mrpt::aligned_std_vector< VECTORLIKE3 > out_samples_y=nullptr)
	Simple Montecarlo-base estimation of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user. More...

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void	transform_gaussian_linear (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(*functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const VECTORLIKE1 &x_increments)
	First order uncertainty propagation estimator of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user. More...

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &s, const mrpt::math::CVectorFloat &a)

mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &s, const mrpt::math::CVectorDouble &a)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::CVectorDouble &a)

mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, mrpt::math::CVectorFloat &a)

template<class T1 , class T2 >
bool	approximatelyEqual (T1 a, T1 b, T2 epsilon)
	Compare 2 floats and determine whether they are equal. More...

template<class T >
bool	approximatelyEqual (T a, T b)
	Compare 2 floats and determine whether they are equal. More...

template<class T >
T	absDiff (const T &lhs, const T &rhs)
	Absolute difference between two numbers. More...

bool	loadVector (std::istream &f, std::vector< int > &d)
	Loads one row of a text file as a numerical std::vector. More...

bool	loadVector (std::istream &f, std::vector< double > &d)
	Loads one row of a text file as a numerical std::vector. More...

void	medianFilter (const std::vector< double > &inV, std::vector< double > &outV, const int &winSize, const int &numberOfSigmas=2)

template<typename T , typename VECTOR >
void	linspace (T first, T last, size_t count, VECTOR &out_vector)
	Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points. More...

template<class T , T STEP>
std::vector< T >	sequenceStdVec (T first, size_t length)
	Generates a sequence of values [first,first+STEP,first+2*STEP,...]. More...

template<class VEC1 , class VEC2 >
void	normalize (const VEC1 &v, VEC2 &out_v)
	Normalize a vector, such as its norm is the unity. More...

template<class VECTOR_OF_VECTORS , class VECTORLIKE >
void	extractColumnFromVectorOfVectors (const size_t colIndex, const VECTOR_OF_VECTORS &data, VECTORLIKE &out_column)
	Extract a column from a vector of vectors, and store it in another vector. More...

uint64_t	factorial64 (unsigned int n)
	Computes the factorial of an integer number and returns it as a 64-bit integer number. More...

double	factorial (unsigned int n)
	Computes the factorial of an integer number and returns it as a double value (internally it uses logarithms for avoiding overflow). More...

std::string	MATLAB_plotCovariance2D (const CMatrixFloat &cov22, const CVectorFloat &mean, const float &stdCount, const std::string &style=std::string("b"), const size_t &nEllipsePoints=30)
	Generates a string with the MATLAB commands required to plot an confidence interval (ellipse) for a 2D Gaussian ('float' version). More...

std::string	MATLAB_plotCovariance2D (const CMatrixDouble &cov22, const CVectorDouble &mean, const float &stdCount, const std::string &style=std::string("b"), const size_t &nEllipsePoints=30)
	Generates a string with the MATLAB commands required to plot an confidence interval (ellipse) for a 2D Gaussian ('double' version). More...

template<typename EIGEN_VECTOR , typename At , size_t N>
EIGEN_VECTOR &	loadVector (EIGEN_VECTOR &v, At(&theArray)[N])
	Assignment operator for initializing a std::vector from a C array (The vector will be automatically set to the correct size). More...

template<typename T , typename At , size_t N>
std::vector< T > &	loadVector (std::vector< T > &v, At(&theArray)[N])

template<class TRIPLET >
bool	saveEigenSparseTripletsToFile (const std::string &sFile, std::vector< TRIPLET > &tri)
	Saves to a plain-text file the nonzero entries of a Eigen sparse matrix, represented as a vector of triplets. More...

template<typename Derived >
mxArray *	convertToMatlab (const Eigen::EigenBase< Derived > &mat)
	Convert vectors, arrays and matrices into Matlab vectors/matrices. More...

template<typename CONTAINER >
mxArray *	convertVectorToMatlab (const CONTAINER &vec)
	Convert std::vector<> or std::deque<> of numeric types into Matlab vectors. More...

template<class T >
void	wrapTo2PiInPlace (T &a)
	Modifies the given angle to translate it into the [0,2pi[ range. More...

template<class T >
T	wrapToPi (T a)
	Modifies the given angle to translate it into the ]-pi,pi] range. More...

template<class T >
void	wrapToPiInPlace (T &a)
	Modifies the given angle to translate it into the ]-pi,pi] range. More...

template<class VECTOR >
void	unwrap2PiSequence (VECTOR &x)
	Modify a sequence of angle values such as no consecutive values have a jump larger than PI in absolute value. More...

template<class T >
T	angDistance (T from, T to)
	Computes the shortest angular increment (or distance) between two planar orientations, such that it is constrained to [-pi,pi] and is correct for any combination of angles (e.g. More...

static void	four1 (float data[], unsigned long nn, int isign)

static void	realft (float data[], unsigned long n)

static void	makewt (int nw, int ip, FFT_TYPE w)

static void	bitrv2 (int n, int ip, FFT_TYPE a)
	Copyright(C) 1997 Takuya OOURA (email: ooura.nosp@m.@mmm.nosp@m..t.u-.nosp@m.toky.nosp@m.o.ac..nosp@m.jp). More...

static void	cftbsub (int n, FFT_TYPE a, FFT_TYPE w)

static void	cftfsub (int n, FFT_TYPE a, FFT_TYPE w)

static void	rftfsub (int n, FFT_TYPE a, int nc, FFT_TYPE c)

static void	rftbsub (int n, FFT_TYPE a, int nc, FFT_TYPE c)

static void	makect (int nc, int ip, FFT_TYPE c)
	Copyright(C) 1997 Takuya OOURA (email: ooura.nosp@m.@mmm.nosp@m..t.u-.nosp@m.toky.nosp@m.o.ac..nosp@m.jp). More...

static void	cdft (int n, int isgn, FFT_TYPE a, int ip, FFT_TYPE *w)
	Copyright(C) 1997 Takuya OOURA (email: ooura.nosp@m.@mmm.nosp@m..t.u-.nosp@m.toky.nosp@m.o.ac..nosp@m.jp). More...

static void	rdft (int n, int isgn, FFT_TYPE a, int ip, FFT_TYPE *w)

static void	rdft2d (int n1, int n2, int isgn, FFT_TYPE *a, FFT_TYPE t, int ip, FFT_TYPE w)
	Copyright(C) 1997 Takuya OOURA (email: ooura.nosp@m.@mmm.nosp@m..t.u-.nosp@m.toky.nosp@m.o.ac..nosp@m.jp). More...

static void	cdft2d (int n1, int n2, int isgn, FFT_TYPE *a, FFT_TYPE t, int ip, FFT_TYPE w)
	Copyright(C) 1997 Takuya OOURA (email: ooura.nosp@m.@mmm.nosp@m..t.u-.nosp@m.toky.nosp@m.o.ac..nosp@m.jp). More...

template<class T >
void	removeUnusedVertices (T &poly)

template<class T >
void	removeRepVertices (T &poly)

double	isLeft (const mrpt::math::TPoint2D &P0, const mrpt::math::TPoint2D &P1, const mrpt::math::TPoint2D &P2)

template<typename T >
void	ransac3Dplane_fit (const CMatrixTemplateNumeric< T > &allData, const std::vector< size_t > &useIndices, vector< CMatrixTemplateNumeric< T >> &fitModels)

template<typename T >
void	ransac3Dplane_distance (const CMatrixTemplateNumeric< T > &allData, const vector< CMatrixTemplateNumeric< T >> &testModels, const T distanceThreshold, unsigned int &out_bestModelIndex, std::vector< size_t > &out_inlierIndices)

template<typename T >
bool	ransac3Dplane_degenerate (const CMatrixTemplateNumeric< T > &allData, const std::vector< size_t > &useIndices)
	Return "true" if the selected points are a degenerate (invalid) case. More...

Probability density distributions (pdf) distance metrics
template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
MAT::Scalar	mahalanobisDistance2 (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV)
	Computes the squared mahalanobis distance of a vector X given the mean MU and the covariance inverse COV_inv $d^2 = (X-MU)^\top \Sigma^{-1} (X-MU)$ . More...

template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
VECTORLIKE1::Scalar	mahalanobisDistance (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV)
	Computes the mahalanobis distance of a vector X given the mean MU and the covariance inverse COV_inv $d = \sqrt{ (X-MU)^\top \Sigma^{-1} (X-MU) }$ . More...

template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
MAT1::Scalar	mahalanobisDistance2 (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12)
	Computes the squared mahalanobis distance between two non-independent Gaussians, given the two covariance matrices and the vector with the difference of their means. More...

template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
VECTORLIKE::Scalar	mahalanobisDistance (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12)
	Computes the mahalanobis distance between two non-independent Gaussians (or independent if CROSS_COV12=nullptr), given the two covariance matrices and the vector with the difference of their means. More...

template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::Scalar	mahalanobisDistance2 (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov)
	Computes the squared mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point. More...

template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::Scalar	mahalanobisDistance (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov)
	Computes the mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point. More...

template<typename T >
T	productIntegralTwoGaussians (const std::vector< T > &mean_diffs, const CMatrixTemplateNumeric< T > &COV1, const CMatrixTemplateNumeric< T > &COV2)
	Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2". More...

template<typename T , size_t DIM>
T	productIntegralTwoGaussians (const std::vector< T > &mean_diffs, const CMatrixFixedNumeric< T, DIM, DIM > &COV1, const CMatrixFixedNumeric< T, DIM, DIM > &COV2)
	Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2". More...

template<typename T , class VECLIKE , class MATLIKE1 , class MATLIKE2 >
void	productIntegralAndMahalanobisTwoGaussians (const VECLIKE &mean_diffs, const MATLIKE1 &COV1, const MATLIKE2 &COV2, T &maha2_out, T &intprod_out, const MATLIKE1 *CROSS_COV12=nullptr)
	Computes both, the integral of the product of two Gaussians and their square Mahalanobis distance. More...

template<typename T , class VECLIKE , class MATRIXLIKE >
void	mahalanobisDistance2AndLogPDF (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &log_pdf_out)
	Computes both, the logarithm of the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian. More...

template<typename T , class VECLIKE , class MATRIXLIKE >
void	mahalanobisDistance2AndPDF (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &pdf_out)
	Computes both, the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian. More...

template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 >
void	covariancesAndMeanWeighted (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const VECTORLIKE2 weights_mean, const VECTORLIKE3 weights_cov, const bool *elem_do_wrap2pi=nullptr)
	Computes covariances and mean of any vector of containers, given optional weights for the different samples. More...

template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE >
void	covariancesAndMean (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const bool *elem_do_wrap2pi=nullptr)
	Computes covariances and mean of any vector of containers. More...

template<class VECTORLIKE1 , class VECTORLIKE2 >
void	weightedHistogram (const VECTORLIKE1 &values, const VECTORLIKE1 &weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues)
	Computes the weighted histogram for a vector of values and their corresponding weights. More...

template<class VECTORLIKE1 , class VECTORLIKE2 >
void	weightedHistogramLog (const VECTORLIKE1 &values, const VECTORLIKE1 &log_weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues)
	Computes the weighted histogram for a vector of values and their corresponding log-weights. More...

double	averageLogLikelihood (const CVectorDouble &logLikelihoods)
	A numerically-stable method to compute average likelihood values with strongly different ranges (unweighted likelihoods: compute the arithmetic mean). More...

double	averageWrap2Pi (const CVectorDouble &angles)
	Computes the average of a sequence of angles in radians taking into account the correct wrapping in the range $]-\pi,\pi [$ , for example, the mean of (2,-2) is $\pi$ , not 0. More...

double	averageLogLikelihood (const CVectorDouble &logWeights, const CVectorDouble &logLikelihoods)
	A numerically-stable method to average likelihood values with strongly different ranges (weighted likelihoods). More...

Simple intersection operations, relying basically on geometrical
operations.
bool	intersect (const TSegment3D &s1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between two 3D segments. More...

bool	intersect (const TSegment3D &s1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D segment and a plane. More...

bool	intersect (const TSegment3D &s1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between a 3D segment and a 3D line. More...

bool	intersect (const TPlane &p1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a plane and a 3D segment. More...

bool	intersect (const TPlane &p1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between two planes. More...

bool	intersect (const TPlane &p1, const TLine3D &p2, TObject3D &obj)
	Gets the intersection between a plane and a 3D line. More...

bool	intersect (const TLine3D &r1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a 3D line and a 3D segment. More...

bool	intersect (const TLine3D &r1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D line and a plane. More...

bool	intersect (const TLine3D &r1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between two 3D lines. More...

bool	intersect (const TLine2D &r1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between two 2D lines. More...

bool	intersect (const TLine2D &r1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D segment. More...

bool	intersect (const TSegment2D &s1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D segment. More...

bool	intersect (const TSegment2D &s1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between two 2D segments. More...

Angle retrieval methods. Methods which use TSegments will
automatically use TLines' implicit constructors.
double	getAngle (const TPlane &p1, const TPlane &p2)
	Computes the angle between two planes. More...

double	getAngle (const TPlane &p1, const TLine3D &r2)
	Computes the angle between a plane and a 3D line or segment (implicit constructor will be used if passing a segment instead of a line). More...

double	getAngle (const TLine3D &r1, const TPlane &p2)
	Computes the angle between a 3D line or segment and a plane (implicit constructor will be used if passing a segment instead of a line). More...

double	getAngle (const TLine3D &r1, const TLine3D &r2)
	Computes the angle between two 3D lines or segments (implicit constructor will be used if passing a segment instead of a line). More...

double	getAngle (const TLine2D &r1, const TLine2D &r2)
	Computes the angle between two 2D lines or segments (implicit constructor will be used if passing a segment instead of a line). More...

Creation of lines from poses.
void	createFromPoseX (const mrpt::math::TPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the X axis in a given pose. More...

void	createFromPoseY (const mrpt::math::TPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Y axis in a given pose. More...

void	createFromPoseZ (const mrpt::math::TPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Z axis in a given pose. More...

void	createFromPoseAndVector (const mrpt::math::TPose3D &p, const double(&vector)[3], TLine3D &r)
	Gets a 3D line corresponding to any arbitrary vector, in the base given by the pose. More...

void	createFromPoseX (const TPose2D &p, TLine2D &r)
	Gets a 2D line corresponding to the X axis in a given pose. More...

void	createFromPoseY (const TPose2D &p, TLine2D &r)
	Gets a 2D line corresponding to the Y axis in a given pose. More...

void	createFromPoseAndVector (const TPose2D &p, const double(&vector)[2], TLine2D &r)
	Gets a 2D line corresponding to any arbitrary vector, in the base given the given pose. More...

Other line or plane related methods.
bool	conformAPlane (const std::vector< TPoint3D > &points)
	Checks whether this polygon or set of points acceptably fits a plane. More...

bool	conformAPlane (const std::vector< TPoint3D > &points, TPlane &p)
	Checks whether this polygon or set of points acceptably fits a plane, and if it's the case returns it in the second argument. More...

bool	areAligned (const std::vector< TPoint2D > &points)
	Checks whether this set of points acceptably fits a 2D line. More...

bool	areAligned (const std::vector< TPoint2D > &points, TLine2D &r)
	Checks whether this set of points acceptably fits a 2D line, and if it's the case returns it in the second argument. More...

bool	areAligned (const std::vector< TPoint3D > &points)
	Checks whether this set of points acceptably fits a 3D line. More...

bool	areAligned (const std::vector< TPoint3D > &points, TLine3D &r)
	Checks whether this set of points acceptably fits a 3D line, and if it's the case returns it in the second argument. More...

Projections
void	project3D (const TPoint3D &point, const mrpt::math::TPose3D &newXYpose, TPoint3D &newPoint)
	Uses the given pose 3D to project a point into a new base. More...

void	project3D (const TSegment3D &segment, const mrpt::math::TPose3D &newXYpose, TSegment3D &newSegment)
	Uses the given pose 3D to project a segment into a new base. More...

void	project3D (const TLine3D &line, const mrpt::math::TPose3D &newXYpose, TLine3D &newLine)
	Uses the given pose 3D to project a line into a new base. More...

void	project3D (const TPlane &plane, const mrpt::math::TPose3D &newXYpose, TPlane &newPlane)
	Uses the given pose 3D to project a plane into a new base. More...

void	project3D (const TPolygon3D &polygon, const mrpt::math::TPose3D &newXYpose, TPolygon3D &newPolygon)
	Uses the given pose 3D to project a polygon into a new base. More...

void	project3D (const TObject3D &object, const mrpt::math::TPose3D &newXYPose, TObject3D &newObject)
	Uses the given pose 3D to project any 3D object into a new base. More...

template<class T >
void	project3D (const T &obj, const TPlane &newXYPlane, T &newObj)
	Projects any 3D object into the plane's base, using its inverse pose. More...

template<class T >
void	project3D (const T &obj, const TPlane &newXYPlane, const TPoint3D &newOrigin, T &newObj)
	Projects any 3D object into the plane's base, using its inverse pose and forcing the position of the new coordinates origin. More...

template<class T >
void	project3D (const std::vector< T > &objs, const mrpt::math::TPose3D &newXYpose, std::vector< T > &newObjs)
	Projects a set of 3D objects into the plane's base. More...

void	project2D (const TPoint2D &point, const TPose2D &newXpose, TPoint2D &newPoint)
	Uses the given pose 2D to project a point into a new base. More...

void	project2D (const TSegment2D &segment, const TPose2D &newXpose, TSegment2D &newSegment)
	Uses the given pose 2D to project a segment into a new base. More...

void	project2D (const TLine2D &line, const TPose2D &newXpose, TLine2D &newLine)
	Uses the given pose 2D to project a line into a new base. More...

void	project2D (const TPolygon2D &polygon, const TPose2D &newXpose, TPolygon2D &newPolygon)
	Uses the given pose 2D to project a polygon into a new base. More...

void	project2D (const TObject2D &object, const TPose2D &newXpose, TObject2D &newObject)
	Uses the given pose 2D to project any 2D object into a new base. More...

template<class T , class CPOSE2D >
void	project2D (const T &obj, const TLine2D &newXLine, T &newObj)
	Projects any 2D object into the line's base, using its inverse pose. More...

template<class T , class CPOSE2D >
void	project2D (const T &obj, const TLine2D &newXLine, const TPoint2D &newOrigin, T &newObj)
	Projects any 2D object into the line's base, using its inverse pose and forcing the position of the new coordinate origin. More...

template<class T >
void	project2D (const std::vector< T > &objs, const TPose2D &newXpose, std::vector< T > &newObjs)
	Projects a set of 2D objects into the line's base. More...

Polygon intersections. These operations rely more on spatial reasoning
than in raw numerical operations.
bool	intersect (const TPolygon2D &p1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between a 2D polygon and a 2D segment. More...

bool	intersect (const TPolygon2D &p1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between a 2D polygon and a 2D line. More...

bool	intersect (const TPolygon2D &p1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between two 2D polygons. More...

bool	intersect (const TSegment2D &s1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between a 2D segment and a 2D polygon. More...

bool	intersect (const TLine2D &r1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D polygon. More...

bool	intersect (const TPolygon3D &p1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a 3D segment. More...

bool	intersect (const TPolygon3D &p1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a 3D line. More...

bool	intersect (const TPolygon3D &p1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a plane. More...

bool	intersect (const TPolygon3D &p1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between two 3D polygons. More...

bool	intersect (const TSegment3D &s1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a 3D segment and a 3D polygon. More...

bool	intersect (const TLine3D &r1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a 3D line and a 3D polygon. More...

bool	intersect (const TPlane &p1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a plane and a 3D polygon. More...

size_t	intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, CSparseMatrixTemplate< TObject3D > &objs)
	Gets the intersection between two sets of 3D polygons. More...

size_t	intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, std::vector< TObject3D > &objs)
	Gets the intersection between two sets of 3D polygons. More...

Other intersections
template<class T , class U , class O >
size_t	intersect (const std::vector< T > &v1, const std::vector< U > &v2, CSparseMatrixTemplate< O > &objs)
	Gets the intersection between vectors of geometric objects and returns it in a sparse matrix of either TObject2D or TObject3D. More...

template<class T , class U , class O >
size_t	intersect (const std::vector< T > &v1, const std::vector< U > &v2, std::vector< O > objs)
	Gets the intersection between vectors of geometric objects and returns it in a vector of either TObject2D or TObject3D. More...

bool	intersect (const TObject2D &o1, const TObject2D &o2, TObject2D &obj)
	Gets the intersection between any pair of 2D objects. More...

bool	intersect (const TObject3D &o1, const TObject3D &o2, TObject3D &obj)
	Gets the intersection between any pair of 3D objects. More...

Distances
double	distance (const TPoint2D &p1, const TPoint2D &p2)
	Gets the distance between two points in a 2D space. More...

double	distance (const TPoint3D &p1, const TPoint3D &p2)
	Gets the distance between two points in a 3D space. More...

double	distance (const TLine2D &r1, const TLine2D &r2)
	Gets the distance between two lines in a 2D space. More...

double	distance (const TLine3D &r1, const TLine3D &r2)
	Gets the distance between two lines in a 3D space. More...

double	distance (const TPlane &p1, const TPlane &p2)
	Gets the distance between two planes. More...

double	distance (const TPolygon2D &p1, const TPolygon2D &p2)
	Gets the distance between two polygons in a 2D space. More...

double	distance (const TPolygon2D &p1, const TSegment2D &s2)
	Gets the distance between a polygon and a segment in a 2D space. More...

double	distance (const TSegment2D &s1, const TPolygon2D &p2)
	Gets the distance between a segment and a polygon in a 2D space. More...

double	distance (const TPolygon2D &p1, const TLine2D &l2)
	Gets the distance between a polygon and a line in a 2D space. More...

double	distance (const TLine2D &l1, const TPolygon2D &p2)

double	distance (const TPolygon3D &p1, const TPolygon3D &p2)
	Gets the distance between two polygons in a 3D space. More...

double	distance (const TPolygon3D &p1, const TSegment3D &s2)
	Gets the distance between a polygon and a segment in a 3D space. More...

double	distance (const TSegment3D &s1, const TPolygon3D &p2)
	Gets the distance between a segment and a polygon in a 3D space. More...

double	distance (const TPolygon3D &p1, const TLine3D &l2)
	Gets the distance between a polygon and a line in a 3D space. More...

double	distance (const TLine3D &l1, const TPolygon3D &p2)
	Gets the distance between a line and a polygon in a 3D space. More...

double	distance (const TPolygon3D &po, const TPlane &pl)
	Gets the distance between a polygon and a plane. More...

double	distance (const TPlane &pl, const TPolygon3D &po)
	Gets the distance between a plane and a polygon. More...

Bound checkers
void	getRectangleBounds (const std::vector< TPoint2D > &poly, TPoint2D &pMin, TPoint2D &pMax)
	Gets the rectangular bounds of a 2D polygon or set of 2D points. More...

void	getPrismBounds (const std::vector< TPoint3D > &poly, TPoint3D &pMin, TPoint3D &pMax)
	Gets the prism bounds of a 3D polygon or set of 3D points. More...

Creation of planes from poses
void	createPlaneFromPoseXY (const mrpt::math::TPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Z vector. More...

void	createPlaneFromPoseXZ (const mrpt::math::TPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Y vector. More...

void	createPlaneFromPoseYZ (const mrpt::math::TPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its X vector. More...

void	createPlaneFromPoseAndNormal (const mrpt::math::TPose3D &pose, const double(&normal)[3], TPlane &plane)
	Given a pose and any vector, creates a plane orthogonal to that vector in the pose's coordinates. More...

void	generateAxisBaseFromDirectionAndAxis (const double(&vec)[3], char coord, CMatrixDouble44 &matrix)
	Creates a homogeneus matrix (4x4) such that the coordinate given (0 for x, 1 for y, 2 for z) corresponds to the provided vector. More...

Linear regression methods
double	getRegressionLine (const std::vector< TPoint2D > &points, TLine2D &line)
	Using eigenvalues, gets the best fitting line for a set of 2D points. More...

double	getRegressionLine (const std::vector< TPoint3D > &points, TLine3D &line)
	Using eigenvalues, gets the best fitting line for a set of 3D points. More...

double	getRegressionPlane (const std::vector< TPoint3D > &points, TPlane &plane)
	Using eigenvalues, gets the best fitting plane for a set of 3D points. More...

Miscellaneous Geometry methods
void	assemblePolygons (const std::vector< TSegment3D > &segms, std::vector< TPolygon3D > &polys)
	Tries to assemble a set of segments into a set of closed polygons. More...

void	assemblePolygons (const std::vector< TSegment3D > &segms, std::vector< TPolygon3D > &polys, std::vector< TSegment3D > &remainder)
	Tries to assemble a set of segments into a set of closed polygons, returning the unused segments as another out parameter. More...

void	assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys)
	Extracts all the polygons, including those formed from segments, from the set of objects. More...

void	assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys, std::vector< TObject3D > &remainder)
	Extracts all the polygons, including those formed from segments, from the set of objects. More...

void	assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys, std::vector< TSegment3D > &remainder1, std::vector< TObject3D > &remainder2)
	Extracts all the polygons, including those formed from segments, from the set of objects. More...

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

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

bool	splitInConvexComponents (const TPolygon2D &poly, std::vector< TPolygon2D > &components)
	Splits a 2D polygon into convex components. More...

bool	splitInConvexComponents (const TPolygon3D &poly, std::vector< TPolygon3D > &components)
	Splits a 3D polygon into convex components. More...

void	getSegmentBisector (const TSegment2D &sgm, TLine2D &bis)
	Gets the bisector of a 2D segment. More...

void	getSegmentBisector (const TSegment3D &sgm, TPlane &bis)
	Gets the bisector of a 3D segment. More...

void	getAngleBisector (const TLine2D &l1, const TLine2D &l2, TLine2D &bis)
	Gets the bisector of two lines or segments (implicit constructor will be used if necessary) More...

void	getAngleBisector (const TLine3D &l1, const TLine3D &l2, TLine3D &bis)
	Gets the bisector of two lines or segments (implicit constructor will be used if necessary) More...

bool	traceRay (const std::vector< TPolygonWithPlane > &vec, const mrpt::math::TPose3D &pose, double &dist)
	Fast ray tracing method using polygons' properties. More...

bool	traceRay (const std::vector< TPolygon3D > &vec, const mrpt::math::TPose3D &pose, double &dist)
	Fast ray tracing method using polygons' properties. More...

template<class T , class U , class V >
void	crossProduct3D (const T &v0, const U &v1, V &vOut)
	Computes the cross product of two 3D vectors, returning a vector normal to both. More...

template<class T >
void	crossProduct3D (const std::vector< T > &v0, const std::vector< T > &v1, std::vector< T > &v_out)

template<class VEC1 , class VEC2 >
Eigen::Matrix< double, 3, 1 >	crossProduct3D (const VEC1 &v0, const VEC2 &v1)
	overload (returning a vector of size 3 by value). More...

template<class VECTOR , class MATRIX >
void	skew_symmetric3 (const VECTOR &v, MATRIX &M)
	Computes the 3x3 skew symmetric matrix from a 3-vector or 3-array: $M([x ~ y ~ z]^\top) = \left( \begin{array}{c c c} 0 & -z & y \\ z & 0 & -x \\ -y & x & 0 \end{array} \right)$ . More...

template<class VECTOR >
mrpt::math::CMatrixDouble33	skew_symmetric3 (const VECTOR &v)

template<class VECTOR , class MATRIX >
void	skew_symmetric3_neg (const VECTOR &v, MATRIX &M)
	Computes the negative version of a 3x3 skew symmetric matrix from a 3-vector or 3-array: $-M([x ~ y ~ z]^\top) = \left( \begin{array}{c c c} 0 & z & -y \\ -z & 0 & x \\ y & -x & 0 \end{array} \right)$ . More...

template<class VECTOR >
mrpt::math::CMatrixDouble33	skew_symmetric3_neg (const VECTOR &v)

template<class T , class U >
bool	vectorsAreParallel2D (const T &v1, const U &v2)
	Returns true if two 2D vectors are parallel. More...

template<class T , class U >
bool	vectorsAreParallel3D (const T &v1, const U &v2)
	Returns true if two 3D vectors are parallel. More...

void	closestFromPointToSegment (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const double &y2, double &out_x, double &out_y)
	Computes the closest point from a given point to a segment. More...

void	closestFromPointToLine (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const double &y2, double &out_x, double &out_y)
	Computes the closest point from a given point to a (infinite) line. More...

double	closestSquareDistanceFromPointToLine (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const double &y2)
	Returns the square distance from a point to a line. More...

template<typename T >
T	distanceBetweenPoints (const T x1, const T y1, const T x2, const T y2)
	Returns the distance between 2 points in 2D. More...

template<typename T >
T	distanceBetweenPoints (const T x1, const T y1, const T z1, const T x2, const T y2, const T z2)
	Returns the distance between 2 points in 3D. More...

template<typename T >
T	distanceSqrBetweenPoints (const T x1, const T y1, const T x2, const T y2)
	Returns the square distance between 2 points in 2D. More...

template<typename T >
T	distanceSqrBetweenPoints (const T x1, const T y1, const T z1, const T x2, const T y2, const T z2)
	Returns the square distance between 2 points in 3D. More...

template<typename T >
double	minimumDistanceFromPointToSegment (const double Px, const double Py, const double x1, const double y1, const double x2, const double y2, T &out_x, T &out_y)
	Computes the closest point from a given point to a segment, and returns that minimum distance. More...

bool	SegmentsIntersection (const double x1, const double y1, const double x2, const double y2, const double x3, const double y3, const double x4, const double y4, double &ix, double &iy)
	Returns the intersection point, and if it exists, between two segments. More...

bool	SegmentsIntersection (const double x1, const double y1, const double x2, const double y2, const double x3, const double y3, const double x4, const double y4, float &ix, float &iy)
	Returns the intersection point, and if it exists, between two segments. More...

bool	pointIntoPolygon2D (const double &px, const double &py, unsigned int polyEdges, const double poly_xs, const double poly_ys)
	Returns true if the 2D point (px,py) falls INTO the given polygon. More...

template<typename T >
bool	pointIntoQuadrangle (T x, T y, T v1x, T v1y, T v2x, T v2y, T v3x, T v3y, T v4x, T v4y)
	Specialized method to check whether a point (x,y) falls into a quadrangle. More...

double	distancePointToPolygon2D (const double &px, const double &py, unsigned int polyEdges, const double poly_xs, const double poly_ys)
	Returns the closest distance of a given 2D point to a polygon, or "0" if the point is INTO the polygon or its perimeter. More...

bool	minDistBetweenLines (const double &p1_x, const double &p1_y, const double &p1_z, const double &p2_x, const double &p2_y, const double &p2_z, const double &p3_x, const double &p3_y, const double &p3_z, const double &p4_x, const double &p4_y, const double &p4_z, double &x, double &y, double &z, double &dist)
	Calculates the minimum distance between a pair of lines. More...

bool	RectanglesIntersection (const double &R1_x_min, const double &R1_x_max, const double &R1_y_min, const double &R1_y_max, const double &R2_x_min, const double &R2_x_max, const double &R2_y_min, const double &R2_y_max, const double &R2_pose_x, const double &R2_pose_y, const double &R2_pose_phi)
	Returns whether two rotated rectangles intersect. More...

template<class T >
CMatrixTemplateNumeric< T >	generateAxisBaseFromDirection (T dx, T dy, T dz)
	Computes an axis base (a set of three 3D normal vectors) with the given vector being the first of them ("X") NOTE: Make sure of passing all floats or doubles and that the template of the receiving matrix is of the same type! More...

k-means algorithms
template<class LIST_OF_VECTORS1 , class LIST_OF_VECTORS2 >
double	kmeans (const size_t k, const LIST_OF_VECTORS1 &points, std::vector< int > &assignments, LIST_OF_VECTORS2 *out_centers=nullptr, const size_t attempts=3)
	k-means algorithm to cluster a list of N points of arbitrary dimensionality into exactly K clusters. More...

template<class LIST_OF_VECTORS1 , class LIST_OF_VECTORS2 >
double	kmeanspp (const size_t k, const LIST_OF_VECTORS1 &points, std::vector< int > &assignments, LIST_OF_VECTORS2 *out_centers=nullptr, const size_t attempts=3)
	k-means++ algorithm to cluster a list of N points of arbitrary dimensionality into exactly K clusters. More...

Container initializer from pose classes
template<class CONTAINER , class POINT_OR_POSE >
CONTAINER &	containerFromPoseOrPoint (CONTAINER &C, const POINT_OR_POSE &p)
	Conversion of poses (TPose2D,TPoint2D,..., mrpt::poses::CPoint2D,CPose3D,...) to MRPT containers (vector/matrix) More...

Operators for binary streaming of MRPT matrices
template<size_t NROWS, size_t NCOLS>
mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, CMatrixFixedNumeric< float, NROWS, NCOLS > &M)
	Read operator from a CStream. More...

template<size_t NROWS, size_t NCOLS>
mrpt::serialization::CArchive &	operator>> (mrpt::serialization::CArchive &in, CMatrixFixedNumeric< double, NROWS, NCOLS > &M)
	Read operator from a CStream. More...

template<size_t NROWS, size_t NCOLS>
mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const CMatrixFixedNumeric< float, NROWS, NCOLS > &M)
	Write operator for writing into a CStream. More...

template<size_t NROWS, size_t NCOLS>
mrpt::serialization::CArchive &	operator<< (mrpt::serialization::CArchive &out, const CMatrixFixedNumeric< double, NROWS, NCOLS > &M)
	Write operator for writing into a CStream. More...

Operators for text streaming of MRPT matrices
template<typename T , size_t NROWS, size_t NCOLS>
std::ostream &	operator<< (std::ostream &s, const CMatrixFixedNumeric< T, NROWS, NCOLS > &m)
	Dumps the matrix to a text ostream, adding a final "\n" to Eigen's default output. More...

template<typename T >
std::ostream &	operator<< (std::ostream &s, const CMatrixTemplateNumeric< T > &m)
	Dumps the matrix to a text ostream, adding a final "\n" to Eigen's default output. More...

template<typename MAT >
void	deserializeSymmetricMatrixFrom (MAT &m, mrpt::serialization::CArchive &in)
	Binary serialization of symmetric matrices, saving the space of duplicated values. More...

template<typename MAT >
void	serializeSymmetricMatrixTo (MAT &m, mrpt::serialization::CArchive &out)
	Binary serialization of symmetric matrices, saving the space of duplicated values. More...

Generic container element-wise operations - Miscelaneous
template<class CONTAINER , typename VALUE >
VALUE	squareNorm_accum (const VALUE total, const CONTAINER &v)
	Accumulate the squared-norm of a vector/array/matrix into "total" (this function is compatible with std::accumulate). More...

template<size_t N, class T , class U >
T	squareNorm (const U &v)
	Compute the square norm of anything implementing []. More...

template<class CONTAINER1 , class CONTAINER2 >
CONTAINER1::Scalar	dotProduct (const CONTAINER1 &v1, const CONTAINER1 &v2)
	v1*v2: The dot product of two containers (vectors/arrays/matrices) More...

template<size_t N, class T , class U , class V >
T	dotProduct (const U &v1, const V &v2)
	v1*v2: The dot product of any two objects supporting [] More...

template<class CONTAINER >
CONTAINER::Scalar	sum (const CONTAINER &v)
	Computes the sum of all the elements. More...

template<typename T >
T	sum (const std::vector< T > &v)

template<class CONTAINER , typename RET >
RET	sumRetType (const CONTAINER &v)
	Computes the sum of all the elements, with a custom return type. More...

template<class CONTAINER >
double	mean (const CONTAINER &v)
	Computes the mean value of a vector. More...

template<typename T >
void	minimum_maximum (const std::vector< T > &V, T &curMin, T &curMax)
	Return the maximum and minimum values of a std::vector. More...

template<class Derived >
void	minimum_maximum (const Eigen::MatrixBase< Derived > &V, typename Eigen::MatrixBase< Derived >::Scalar &curMin, typename Eigen::MatrixBase< Derived >::Scalar &curMax)
	Return the maximum and minimum values of a Eigen-based vector or matrix. More...

template<class CONTAINER1 , class CONTAINER2 >
size_t	countCommonElements (const CONTAINER1 &a, const CONTAINER2 &b)
	Counts the number of elements that appear in both STL-like containers (comparison through the == operator) It is assumed that no repeated elements appear within each of the containers. More...

template<class CONTAINER >
void	adjustRange (CONTAINER &m, const typename CONTAINER::Scalar minVal, const typename CONTAINER::Scalar maxVal)
	Adjusts the range of all the elements such as the minimum and maximum values being those supplied by the user. More...

template<class VECTORLIKE >
void	meanAndStd (const VECTORLIKE &v, double &out_mean, double &out_std, bool unbiased=true)
	Computes the standard deviation of a vector. More...

template<class VECTORLIKE >
double	stddev (const VECTORLIKE &v, bool unbiased=true)
	Computes the standard deviation of a vector. More...

template<class VECTOR_OF_VECTOR , class VECTORLIKE , class MATRIXLIKE >
void	meanAndCovVec (const VECTOR_OF_VECTOR &v, VECTORLIKE &out_mean, MATRIXLIKE &out_cov)
	Computes the mean vector and covariance from a list of values given as a vector of vectors, where each row is a sample. More...

template<class VECTOR_OF_VECTOR , class RETURN_MATRIX >
RETURN_MATRIX	covVector (const VECTOR_OF_VECTOR &v)
	Computes the covariance matrix from a list of values given as a vector of vectors, where each row is a sample. More...

template<class CONT1 , class CONT2 >
double	ncc_vector (const CONT1 &patch1, const CONT2 &patch2)
	Normalised Cross Correlation between two vector patches The Matlab code for this is a = a - mean2(a); b = b - mean2(b); r = sum(sum(a. More...

Generic std::vector element-wise operations
template<typename T1 , typename T2 >
std::vector< T1 > &	operator*= (std::vector< T1 > &a, const std::vector< T2 > &b)
	a*=b (element-wise multiplication) More...

template<typename T1 >
std::vector< T1 > &	operator*= (std::vector< T1 > &a, const T1 b)
	a*=k (multiplication by a constant) More...

template<typename T1 , typename T2 >
std::vector< T1 >	operator* (const std::vector< T1 > &a, const std::vector< T2 > &b)
	a*b (element-wise multiplication) More...

template<typename T1 , typename T2 >
std::vector< T1 > &	operator+= (std::vector< T1 > &a, const std::vector< T2 > &b)
	a+=b (element-wise sum) More...

template<typename T1 >
std::vector< T1 > &	operator+= (std::vector< T1 > &a, const T1 b)
	a+=b (sum a constant) More...

template<typename T1 , typename T2 >
std::vector< T1 >	operator+ (const std::vector< T1 > &a, const std::vector< T2 > &b)
	a+b (element-wise sum) More...

template<typename T1 , typename T2 >
std::vector< T1 >	operator- (const std::vector< T1 > &v1, const std::vector< T2 > &v2)

RANSAC detectors
template<typename NUMTYPE >
void	ransac_detect_3D_planes (const Eigen::Matrix< NUMTYPE, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< NUMTYPE, Eigen::Dynamic, 1 > &y, const Eigen::Matrix< NUMTYPE, Eigen::Dynamic, 1 > &z, std::vector< std::pair< size_t, TPlane >> &out_detected_planes, const double threshold, const size_t min_inliers_for_valid_plane=10)
	Fit a number of 3-D planes to a given point cloud, automatically determining the number of existing planes by means of the provided threshold and minimum number of supporting inliers. More...

template<typename NUMTYPE >
void	ransac_detect_2D_lines (const Eigen::Matrix< NUMTYPE, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< NUMTYPE, Eigen::Dynamic, 1 > &y, std::vector< std::pair< size_t, TLine2D >> &out_detected_lines, const double threshold, const size_t min_inliers_for_valid_line=5)
	Fit a number of 2-D lines to a given point cloud, automatically determining the number of existing lines by means of the provided threshold and minimum number of supporting inliers. More...

template<class POINTSMAP >
void	ransac_detect_3D_planes (const POINTSMAP *points_map, std::vector< std::pair< size_t, TPlane >> &out_detected_planes, const double threshold, const size_t min_inliers_for_valid_plane)
	A stub for ransac_detect_3D_planes() with the points given as a mrpt::maps::CPointsMap. More...

SLERP (Spherical Linear Interpolation) functions
template<typename T >
void	slerp (const CQuaternion< T > &q0, const CQuaternion< T > &q1, const double t, CQuaternion< T > &q)
	SLERP interpolation between two quaternions. More...

void	slerp (const TPose3D &q0, const TPose3D &q1, const double t, TPose3D &p)
	SLERP interpolation between two 6D poses - like mrpt::math::slerp for quaternions, but interpolates the [X,Y,Z] coordinates as well. More...

void	slerp_ypr (const mrpt::math::TPose3D &q0, const mrpt::math::TPose3D &q1, const double t, mrpt::math::TPose3D &p)

Variables
static constexpr unsigned char	GEOMETRIC_TYPE_POINT = 0
	Object type identifier for TPoint2D or TPoint3D. More...

static constexpr unsigned char	GEOMETRIC_TYPE_SEGMENT = 1
	Object type identifier for TSegment2D or TSegment3D. More...

static constexpr unsigned char	GEOMETRIC_TYPE_LINE = 2
	Object type identifier for TLine2D or TLine3D. More...

static constexpr unsigned char	GEOMETRIC_TYPE_POLYGON = 3
	Object type identifier for TPolygon2D or TPolygon3D. More...

static constexpr unsigned char	GEOMETRIC_TYPE_PLANE = 4
	Object type identifier for TPlane. More...

static constexpr unsigned char	GEOMETRIC_TYPE_UNDEFINED = 255
	Object type identifier for empty TObject2D or TObject3D. More...

Typedef Documentation

◆ CArrayDouble

template<std::size_t N>

using mrpt::math::CArrayDouble = typedef CArrayNumeric<double, N>

A partial specialization of CArrayNumeric for double numbers.

See also: CArrayNumeric, CArray

Definition at line 64 of file CArrayNumeric.h.

◆ CArrayFloat

template<std::size_t N>

using mrpt::math::CArrayFloat = typedef CArrayNumeric<float, N>

A partial specialization of CArrayNumeric for float numbers.

See also: CArrayNumeric, CArray

Definition at line 59 of file CArrayNumeric.h.

◆ CArrayInt

template<std::size_t N>

using mrpt::math::CArrayInt = typedef CArrayNumeric<int, N>

A partial specialization of CArrayNumeric for int numbers.

See also: CArrayNumeric, CArray

Definition at line 69 of file CArrayNumeric.h.

◆ CArrayUInt

template<std::size_t N>

using mrpt::math::CArrayUInt = typedef CArrayNumeric<unsigned int, N>

A partial specialization of CArrayNumeric for unsigned int numbers.

See also: CArrayNumeric, CArray

Definition at line 74 of file CArrayNumeric.h.

◆ CLevenbergMarquardt

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

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

Definition at line 258 of file CLevenbergMarquardt.h.

◆ CMatrixDouble

typedef CMatrixTemplateNumeric< double > mrpt::math::CMatrixDouble

Declares a matrix of double numbers (non serializable).

For a serializable version, use math::CMatrixD

See also: CMatrixFloat, CMatrix, CMatrixD

Definition at line 144 of file CMatrixTemplateNumeric.h.

◆ CMatrixDouble12

using mrpt::math::CMatrixDouble12 = typedef CMatrixFixedNumeric<double, 1, 2>

Definition at line 63 of file eigen_frwds.h.

◆ CMatrixDouble13

using mrpt::math::CMatrixDouble13 = typedef CMatrixFixedNumeric<double, 1, 3>

Definition at line 61 of file eigen_frwds.h.

◆ CMatrixDouble15

using mrpt::math::CMatrixDouble15 = typedef CMatrixFixedNumeric<double, 1, 5>

Definition at line 70 of file eigen_frwds.h.

◆ CMatrixDouble16

using mrpt::math::CMatrixDouble16 = typedef CMatrixFixedNumeric<double, 1, 6>

Definition at line 66 of file eigen_frwds.h.

◆ CMatrixDouble17

using mrpt::math::CMatrixDouble17 = typedef CMatrixFixedNumeric<double, 1, 7>

Definition at line 68 of file eigen_frwds.h.

◆ CMatrixDouble21

using mrpt::math::CMatrixDouble21 = typedef CMatrixFixedNumeric<double, 2, 1>

Definition at line 64 of file eigen_frwds.h.

◆ CMatrixDouble22

using mrpt::math::CMatrixDouble22 = typedef CMatrixFixedNumeric<double, 2, 2>

Definition at line 54 of file eigen_frwds.h.

◆ CMatrixDouble23

using mrpt::math::CMatrixDouble23 = typedef CMatrixFixedNumeric<double, 2, 3>

Definition at line 55 of file eigen_frwds.h.

◆ CMatrixDouble31

using mrpt::math::CMatrixDouble31 = typedef CMatrixFixedNumeric<double, 3, 1>

Definition at line 62 of file eigen_frwds.h.

◆ CMatrixDouble32

using mrpt::math::CMatrixDouble32 = typedef CMatrixFixedNumeric<double, 3, 2>

Definition at line 56 of file eigen_frwds.h.

◆ CMatrixDouble33

using mrpt::math::CMatrixDouble33 = typedef CMatrixFixedNumeric<double, 3, 3>

Definition at line 57 of file eigen_frwds.h.

◆ CMatrixDouble41

using mrpt::math::CMatrixDouble41 = typedef CMatrixFixedNumeric<double, 4, 1>

Definition at line 71 of file eigen_frwds.h.

◆ CMatrixDouble44

using mrpt::math::CMatrixDouble44 = typedef CMatrixFixedNumeric<double, 4, 4>

Definition at line 58 of file eigen_frwds.h.

◆ CMatrixDouble51

using mrpt::math::CMatrixDouble51 = typedef CMatrixFixedNumeric<double, 5, 1>

Definition at line 69 of file eigen_frwds.h.

◆ CMatrixDouble61

using mrpt::math::CMatrixDouble61 = typedef CMatrixFixedNumeric<double, 6, 1>

Definition at line 65 of file eigen_frwds.h.

◆ CMatrixDouble66

using mrpt::math::CMatrixDouble66 = typedef CMatrixFixedNumeric<double, 6, 6>

Definition at line 59 of file eigen_frwds.h.

◆ CMatrixDouble71

using mrpt::math::CMatrixDouble71 = typedef CMatrixFixedNumeric<double, 7, 1>

Definition at line 67 of file eigen_frwds.h.

◆ CMatrixDouble77

using mrpt::math::CMatrixDouble77 = typedef CMatrixFixedNumeric<double, 7, 7>

Definition at line 60 of file eigen_frwds.h.

◆ CMatrixFloat

typedef CMatrixTemplateNumeric< float > mrpt::math::CMatrixFloat

Declares a matrix of float numbers (non serializable).

For a serializable version, use math::CMatrix

See also: CMatrixDouble, CMatrix, CMatrixD

Definition at line 138 of file CMatrixTemplateNumeric.h.

◆ CMatrixFloat12

using mrpt::math::CMatrixFloat12 = typedef CMatrixFixedNumeric<float, 1, 2>

Definition at line 82 of file eigen_frwds.h.

◆ CMatrixFloat13

using mrpt::math::CMatrixFloat13 = typedef CMatrixFixedNumeric<float, 1, 3>

Definition at line 80 of file eigen_frwds.h.

◆ CMatrixFloat15

using mrpt::math::CMatrixFloat15 = typedef CMatrixFixedNumeric<float, 1, 5>

Definition at line 89 of file eigen_frwds.h.

◆ CMatrixFloat16

using mrpt::math::CMatrixFloat16 = typedef CMatrixFixedNumeric<float, 1, 6>

Definition at line 85 of file eigen_frwds.h.

◆ CMatrixFloat17

using mrpt::math::CMatrixFloat17 = typedef CMatrixFixedNumeric<float, 1, 7>

Definition at line 87 of file eigen_frwds.h.

◆ CMatrixFloat21

using mrpt::math::CMatrixFloat21 = typedef CMatrixFixedNumeric<float, 2, 1>

Definition at line 83 of file eigen_frwds.h.

◆ CMatrixFloat22

using mrpt::math::CMatrixFloat22 = typedef CMatrixFixedNumeric<float, 2, 2>

Definition at line 73 of file eigen_frwds.h.

◆ CMatrixFloat23

using mrpt::math::CMatrixFloat23 = typedef CMatrixFixedNumeric<float, 2, 3>

Definition at line 74 of file eigen_frwds.h.

◆ CMatrixFloat31

using mrpt::math::CMatrixFloat31 = typedef CMatrixFixedNumeric<float, 3, 1>

Definition at line 81 of file eigen_frwds.h.

◆ CMatrixFloat32

using mrpt::math::CMatrixFloat32 = typedef CMatrixFixedNumeric<float, 3, 2>

Definition at line 75 of file eigen_frwds.h.

◆ CMatrixFloat33

using mrpt::math::CMatrixFloat33 = typedef CMatrixFixedNumeric<float, 3, 3>

Definition at line 76 of file eigen_frwds.h.

◆ CMatrixFloat44

using mrpt::math::CMatrixFloat44 = typedef CMatrixFixedNumeric<float, 4, 4>

Definition at line 77 of file eigen_frwds.h.

◆ CMatrixFloat51

using mrpt::math::CMatrixFloat51 = typedef CMatrixFixedNumeric<float, 5, 1>

Definition at line 88 of file eigen_frwds.h.

◆ CMatrixFloat61

using mrpt::math::CMatrixFloat61 = typedef CMatrixFixedNumeric<float, 6, 1>

Definition at line 84 of file eigen_frwds.h.

◆ CMatrixFloat66

using mrpt::math::CMatrixFloat66 = typedef CMatrixFixedNumeric<float, 6, 6>

Definition at line 78 of file eigen_frwds.h.

◆ CMatrixFloat71

using mrpt::math::CMatrixFloat71 = typedef CMatrixFixedNumeric<float, 7, 1>

Definition at line 86 of file eigen_frwds.h.

◆ CMatrixFloat77

using mrpt::math::CMatrixFloat77 = typedef CMatrixFixedNumeric<float, 7, 7>

Definition at line 79 of file eigen_frwds.h.

◆ CMatrixLongDouble

using mrpt::math::CMatrixLongDouble = typedef CMatrixTemplateNumeric<double>

Declares a matrix of "long doubles" (non serializable), or of "doubles" if the compiler does not support "long double".

See also: CMatrixDouble, CMatrixFloat

Definition at line 162 of file CMatrixTemplateNumeric.h.

◆ CMatrixUInt

using mrpt::math::CMatrixUInt = typedef CMatrixTemplateNumeric<unsigned int>

Declares a matrix of unsigned ints (non serializable).

See also: CMatrixDouble, CMatrixFloat

Definition at line 149 of file CMatrixTemplateNumeric.h.

◆ CQuaternionDouble

using mrpt::math::CQuaternionDouble = typedef CQuaternion<double>

A quaternion of data type "double".

Definition at line 502 of file CQuaternion.h.

◆ CQuaternionFloat

using mrpt::math::CQuaternionFloat = typedef CQuaternion<float>

A quaternion of data type "float".

Definition at line 504 of file CQuaternion.h.

◆ CVectorDouble

typedef dynamic_vector< double > mrpt::math::CVectorDouble

Column vector, like Eigen::MatrixXd, but automatically initialized to zeros since construction.

Definition at line 46 of file eigen_frwds.h.

◆ CVectorFloat

typedef dynamic_vector< float > mrpt::math::CVectorFloat

Column vector, like Eigen::MatrixXf, but automatically initialized to zeros since construction.

Definition at line 45 of file eigen_frwds.h.

◆ FFT_TYPE

using mrpt::math::FFT_TYPE = typedef float

You may use, copy, modify this code for any purpose and without fee. You may distribute this ORIGINAL package.

Definition at line 147 of file fourier.cpp.

Enumeration Type Documentation

◆ TConstructorFlags_Matrices

enum mrpt::math::TConstructorFlags_Matrices

For usage in one of the constructors of CMatrixFixedNumeric or CMatrixTemplate (and derived classes), if it's not required to fill it with zeros at the constructor to save time.

Enumerator
UNINITIALIZED_MATRIX

Definition at line 73 of file math_frwds.h.

◆ TConstructorFlags_Quaternions

enum mrpt::math::TConstructorFlags_Quaternions

Enumerator
UNINITIALIZED_QUATERNION

Definition at line 20 of file CQuaternion.h.

◆ TMatrixTextFileFormat

enum mrpt::math::TMatrixTextFileFormat

Selection of the number format in CMatrixTemplate::saveToTextFile

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

Definition at line 60 of file math_frwds.h.

Function Documentation

◆ absDiff()

template<class T >

T mrpt::math::absDiff	(	const T &	lhs,
		const T &	rhs
	)

Absolute difference between two numbers.

Definition at line 54 of file math/include/mrpt/math/utils.h.

Referenced by mrpt::graphslam::deciders::CICPCriteriaERD< GRAPH_T >::checkRegistrationCondition2D(), mrpt::graphslam::deciders::CICPCriteriaERD< GRAPH_T >::checkRegistrationCondition3D(), mrpt::graphs::CNetworkOfPoses< CPOSE, MAPS_IMPLEMENTATION, NODE_ANNOTATIONS, EDGE_ANNOTATIONS >::extractSubGraph(), mrpt::graphslam::deciders::CLoopCloserERD< GRAPH_T >::registerNewEdge(), and mrpt::graphslam::deciders::CLoopCloserERD< GRAPH_T >::updateState().

◆ adjustRange()

template<class CONTAINER >

void mrpt::math::adjustRange	(	CONTAINER &	m,
		const typename CONTAINER::Scalar	minVal,
		const typename CONTAINER::Scalar	maxVal
	)

Adjusts the range of all the elements such as the minimum and maximum values being those supplied by the user.

Definition at line 283 of file ops_containers.h.

References minimum_maximum().

◆ approximatelyEqual() [1/2]

template<class T1 , class T2 >

bool mrpt::math::approximatelyEqual	(	T1	a,
		T1	b,
		T2	epsilon
	)

Compare 2 floats and determine whether they are equal.

Returns: True if equal, false otherwise

Parameters

a	Fist num
b	Second num
epsilon	Difference below which a, b are considered equal

Definition at line 34 of file math/include/mrpt/math/utils.h.

Referenced by mrpt::graphslam::deciders::CLoopCloserERD< GRAPH_T >::addScanMatchingEdges(), approximatelyEqual(), and mrpt::graphslam::deciders::CLoopCloserERD< GRAPH_T >::computeDominantEigenVector().

◆ approximatelyEqual() [2/2]

template<class T >

bool mrpt::math::approximatelyEqual	(	T	a,
		T	b
	)

Compare 2 floats and determine whether they are equal.

Returns: True if equal, false otherwise

Parameters

a	Fist num
b	Second num

Definition at line 45 of file math/include/mrpt/math/utils.h.

References approximatelyEqual().

◆ bitrv2()

static void mrpt::math::bitrv2	(	int	n,
		int *	ip,
		FFT_TYPE *	a
	)

static

You may use, copy, modify this code for any purpose and without fee. You may distribute this ORIGINAL package.

Definition at line 455 of file fourier.cpp.

Referenced by cdft(), makewt(), and rdft().

◆ cdft()

static void mrpt::math::cdft	(	int	n,
		int	isgn,
		FFT_TYPE *	a,
		int *	ip,
		FFT_TYPE *	w
	)

static

You may use, copy, modify this code for any purpose and without fee. You may distribute this ORIGINAL package.

Definition at line 522 of file fourier.cpp.

References bitrv2(), cftbsub(), cftfsub(), and makewt().

Referenced by cdft2d(), and rdft2d().

◆ cdft2d()

static void mrpt::math::cdft2d	(	int	n1,
		int	n2,
		int	isgn,
		FFT_TYPE **	a,
		FFT_TYPE *	t,
		int *	ip,
		FFT_TYPE *	w
	)

static

You may use, copy, modify this code for any purpose and without fee. You may distribute this ORIGINAL package.

-----— Complex DFT (Discrete Fourier Transform) -----— [definition] <case1> X[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 x[j1][j2] * exp(2*pi*i*j1*k1/n1) * exp(2*pi*i*j2*k2/n2), 0<=k1<n1, 0<=k2<n2 <case2> X[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 x[j1][j2] * exp(-2*pi*i*j1*k1/n1) * exp(-2*pi*i*j2*k2/n2), 0<=k1<n1, 0<=k2<n2 (notes: sum_j=0^n-1 is a summation from j=0 to n-1) [usage] <case1> ip[0] = 0; // first time only cdft2d(n1, 2*n2, 1, a, t, ip, w); <case2> ip[0] = 0; // first time only cdft2d(n1, 2*n2, -1, a, t, ip, w); [parameters] n1 :data length (int) n1 >= 1, n1 = power of 2 2*n2 :data length (int) n2 >= 1, n2 = power of 2 a[0...n1-1][0...2*n2-1] :input/output data (double **) input data a[j1][2*j2] = Re(x[j1][j2]), a[j1][2*j2+1] = Im(x[j1][j2]), 0<=j1<n1, 0<=j2<n2 output data a[k1][2*k2] = Re(X[k1][k2]), a[k1][2*k2+1] = Im(X[k1][k2]), 0<=k1<n1, 0<=k2<n2 t[0...2*n1-1] :work area (double *) ip[0...*] :work area for bit reversal (int *) length of ip >= 2+sqrt(n) ; if n % 4 == 0 2+sqrt(n/2); otherwise (n = max(n1, n2)) ip[0],ip[1] are pointers of the cos/sin table. w[0...*] :cos/sin table (double *) length of w >= max(n1/2, n2/2) w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of cdft2d(n1, 2*n2, -1, a, t, ip, w); is cdft2d(n1, 2*n2, 1, a, t, ip, w); for (j1 = 0; j1 <= n1 - 1; j1++) { for (j2 = 0; j2 <= 2 * n2 - 1; j2++) { a[j1][j2] *= 1.0 / (n1 * n2); } }

Definition at line 886 of file fourier.cpp.

References cdft(), and makewt().

Referenced by dft2_complex(), and idft2_complex().

◆ cftbsub()

static void mrpt::math::cftbsub	(	int	n,
		FFT_TYPE *	a,
		FFT_TYPE *	w
	)

static

Definition at line 156 of file fourier.cpp.

Referenced by cdft(), and rdft().

◆ cftfsub()

static void mrpt::math::cftfsub	(	int	n,
		FFT_TYPE *	a,
		FFT_TYPE *	w
	)

static

Definition at line 276 of file fourier.cpp.

Referenced by cdft(), and rdft().

◆ containerFromPoseOrPoint()

template<class CONTAINER , class POINT_OR_POSE >

CONTAINER & mrpt::math::containerFromPoseOrPoint	(	CONTAINER &	C,
		const POINT_OR_POSE &	p
	)

Conversion of poses (TPose2D,TPoint2D,..., mrpt::poses::CPoint2D,CPose3D,...) to MRPT containers (vector/matrix)

Conversion of poses to MRPT containers (vector/matrix)

Definition at line 21 of file point_poses2vectors.h.

References static_size.

◆ countCommonElements()

template<class CONTAINER1 , class CONTAINER2 >

size_t mrpt::math::countCommonElements	(	const CONTAINER1 &	a,
		const CONTAINER2 &	b
	)

Counts the number of elements that appear in both STL-like containers (comparison through the == operator) It is assumed that no repeated elements appear within each of the containers.

Definition at line 269 of file ops_containers.h.

Referenced by mrpt::slam::CRangeBearingKFSLAM::computeOffDiagonalBlocksApproximationError().

◆ cov()

template<class MATRIX >

Eigen::Matrix<typename MATRIX::Scalar, MATRIX::ColsAtCompileTime, MATRIX::ColsAtCompileTime> mrpt::math::cov ( const MATRIX & v )

inline

Computes the covariance matrix from a list of samples in an NxM matrix, where each row is a sample, so the covariance is MxM.

Parameters

v	The set of data, as a NxM matrix.
out_cov	The output MxM matrix for the estimated covariance matrix.

See also: math::mean,math::stddev, math::cov

Definition at line 148 of file ops_matrices.h.

References meanAndCovMat().

◆ covVector()

template<class VECTOR_OF_VECTOR , class RETURN_MATRIX >

RETURN_MATRIX mrpt::math::covVector ( const VECTOR_OF_VECTOR & v )

inline

Computes the covariance matrix from a list of values given as a vector of vectors, where each row is a sample.

Parameters

v	The set of data, as a vector of N vectors of M elements.
out_cov	The output MxM matrix for the estimated covariance matrix.

Template Parameters

RETURN_MATRIX The type of the returned matrix, e.g. Eigen::MatrixXd

See also: math::mean,math::stddev, math::cov, meanAndCovVec

Definition at line 395 of file ops_containers.h.

References meanAndCovVec().

◆ cumsum() [1/2]

template<class CONTAINER1 , class CONTAINER2 >

void mrpt::math::cumsum	(	const CONTAINER1 &	in_data,
		CONTAINER2 &	out_cumsum
	)

inline

Definition at line 109 of file ops_containers.h.

References cumsum_tmpl().

Referenced by confidenceIntervals(), and cumsum().

◆ cumsum() [2/2]

template<class CONTAINER >

CONTAINER mrpt::math::cumsum ( const CONTAINER & in_data )

inline

Computes the cumulative sum of all the elements.

See also: sum

Definition at line 119 of file ops_containers.h.

References cumsum().

◆ cumsum_tmpl()

template<class CONTAINER1 , class CONTAINER2 , typename VALUE >

void mrpt::math::cumsum_tmpl	(	const CONTAINER1 &	in_data,
		CONTAINER2 &	out_cumsum
	)

inline

Computes the cumulative sum of all the elements, saving the result in another container.

This works for both matrices (even mixing their types) and vectores/arrays (even mixing types), and even to store the cumsum of any matrix into any vector/array, but not in opposite direction.

See also: sum

Definition at line 100 of file ops_containers.h.

References resizeLike().

Referenced by cumsum().

◆ dotProduct() [1/2]

template<class CONTAINER1 , class CONTAINER2 >

CONTAINER1::Scalar mrpt::math::dotProduct	(	const CONTAINER1 &	v1,
		const CONTAINER1 &	v2
	)

inline

v1*v2: The dot product of two containers (vectors/arrays/matrices)

Definition at line 188 of file ops_containers.h.

◆ dotProduct() [2/2]

template<size_t N, class T , class U , class V >

T mrpt::math::dotProduct	(	const U &	v1,
		const V &	v2
	)

inline

v1*v2: The dot product of any two objects supporting []

Definition at line 196 of file ops_containers.h.

◆ 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, CArrayNumeric<>, double [N], ... MATRIXLIKE: CMatrixTemplateNumeric, CMatrixFixedNumeric

Definition at line 29 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_dexpeD_de(), SE_traits_tests< POSE_TYPE >::test_jacobs_P1DP2inv(), Pose3DQuatTests::test_normalizeJacob(), Pose3DQuatTests::test_sphericalCoords(), Pose3DQuatPDFGaussTests::testCompositionJacobian(), Pose3DPDFGaussTests::testCompositionJacobian(), and transform_gaussian_linear().

◆ four1()

static void mrpt::math::four1	(	float	data[],
		unsigned long	nn,
		int	isign
	)

static

Definition at line 31 of file fourier.cpp.

Referenced by realft().

◆ getColumnAccessor() [1/4]

template<typename MAT >

CMatrixColumnAccessor<MAT> mrpt::math::getColumnAccessor	(	MAT &	m,
		size_t	colIdx
	)

inline

Definition at line 548 of file matrix_adaptors.h.

◆ getColumnAccessor() [2/4]

template<typename MAT >

CMatrixColumnAccessorExtended<MAT> mrpt::math::getColumnAccessor	(	MAT &	m,
		size_t	colIdx,
		size_t	offset,
		size_t	space = `1`
	)

inline

Definition at line 623 of file matrix_adaptors.h.

◆ getColumnAccessor() [3/4]

template<typename MAT >

CConstMatrixColumnAccessor<MAT> mrpt::math::getColumnAccessor	(	const MAT &	m,
		size_t	colIdx
	)

inline

Definition at line 679 of file matrix_adaptors.h.

◆ getColumnAccessor() [4/4]

template<typename MAT >

CConstMatrixColumnAccessorExtended<MAT> mrpt::math::getColumnAccessor	(	const MAT &	m,
		size_t	colIdx,
		size_t	offset,
		size_t	space = `1`
	)

inline

Definition at line 740 of file matrix_adaptors.h.

◆ getRowAccessor() [1/4]

template<typename MAT >

CMatrixRowAccessor<MAT> mrpt::math::getRowAccessor	(	MAT &	m,
		size_t	rowIdx
	)

inline

Definition at line 280 of file matrix_adaptors.h.

◆ getRowAccessor() [2/4]

template<typename MAT >

CMatrixRowAccessorExtended<MAT> mrpt::math::getRowAccessor	(	MAT &	m,
		size_t	rowIdx,
		size_t	offset,
		size_t	space = `1`
	)

inline

Definition at line 357 of file matrix_adaptors.h.

◆ getRowAccessor() [3/4]

template<typename MAT >

CConstMatrixRowAccessor<MAT> mrpt::math::getRowAccessor	(	const MAT &	m,
		size_t	rowIdx
	)

inline

Definition at line 415 of file matrix_adaptors.h.

◆ getRowAccessor() [4/4]

template<typename MAT >

CConstMatrixRowAccessorExtended<MAT> mrpt::math::getRowAccessor	(	const MAT &	m,
		size_t	rowIdx,
		size_t	offset,
		size_t	space = `1`
	)

inline

Definition at line 477 of file matrix_adaptors.h.

◆ histogram()

template<class CONTAINER >

std::vector<double> mrpt::math::histogram	(	const CONTAINER &	v,
		double	limit_min,
		double	limit_max,
		size_t	number_bins,
		bool	do_normalization = `false`,
		std::vector< double > *	out_bin_centers = `nullptr`
	)

Computes the normalized or normal histogram of a sequence of numbers given the number of bins and the limits.

In any case this is a "linear" histogram, i.e. for matrices, all the elements are taken as if they were a plain sequence, not taking into account they were in columns or rows. If desired, out_bin_centers can be set to receive the bins centers.

Definition at line 63 of file ops_containers.h.

References mrpt::math::CHistogram::add(), mrpt::math::CHistogram::getHistogram(), and mrpt::math::CHistogram::getHistogramNormalized().

Referenced by confidenceIntervals(), and mrpt::pbmap::getMode().

◆ homogeneousMatrixInverse() [1/3]

template<class MATRIXLIKE1 , class MATRIXLIKE2 >

void mrpt::math::homogeneousMatrixInverse	(	const MATRIXLIKE1 &	M,
		MATRIXLIKE2 &	out_inverse_M
	)

Efficiently compute the inverse of a 4x4 homogeneous matrix by only transposing the rotation 3x3 part and solving the translation with dot products.

This is a generic template which works with: MATRIXLIKE: CMatrixTemplateNumeric, CMatrixFixedNumeric

Definition at line 22 of file homog_matrices.h.

References ASSERT_, MRPT_END, and MRPT_START.

Referenced by mrpt::poses::CPoseOrPoint< CPoint3D >::getInverseHomogeneousMatrix(), mrpt::math::TPose3D::getInverseHomogeneousMatrix(), mrpt::poses::CPose3D::inverse(), mrpt::poses::CPose3D::inverseComposeFrom(), mrpt::poses::CPose3D::inverseComposePoint(), and mrpt::obs::detail::project3DPointsFromDepthImageInto().

◆ homogeneousMatrixInverse() [2/3]

template<class IN_ROTMATRIX , class IN_XYZ , class OUT_ROTMATRIX , class OUT_XYZ >

void mrpt::math::homogeneousMatrixInverse	(	const IN_ROTMATRIX &	in_R,
		const IN_XYZ &	in_xyz,
		OUT_ROTMATRIX &	out_R,
		OUT_XYZ &	out_xyz
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 77 of file homog_matrices.h.

References ASSERT_, MRPT_END, and MRPT_START.

◆ homogeneousMatrixInverse() [3/3]

template<class MATRIXLIKE >

void mrpt::math::homogeneousMatrixInverse ( MATRIXLIKE & M )

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 106 of file homog_matrices.h.

References ASSERTDEB_.

◆ isLeft()

double mrpt::math::isLeft	(	const mrpt::math::TPoint2D &	P0,
		const mrpt::math::TPoint2D &	P1,
		const mrpt::math::TPoint2D &	P2
	)

inline

Definition at line 1024 of file lightweight_geom_data.cpp.

References mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

Referenced by mrpt::math::TPolygon2D::contains().

◆ kmeans()

template<class LIST_OF_VECTORS1 , class LIST_OF_VECTORS2 >

double mrpt::math::kmeans	(	const size_t	k,
		const LIST_OF_VECTORS1 &	points,
		std::vector< int > &	assignments,
		LIST_OF_VECTORS2 *	out_centers = `nullptr`,
		const size_t	attempts = `3`
	)

inline

k-means algorithm to cluster a list of N points of arbitrary dimensionality into exactly K clusters.

The list of input points can be any template CONTAINER<POINT> with:

CONTAINER can be: Any STL container: std::vector,std::list,std::deque,...
POINT can be:
- std::vector<double/float>
- CArrayDouble<N> / CArrayFloat<N>

Parameters

k	[IN] Number of cluster to look for.
points	[IN] The list of N input points. It can be any STL-like containers of std::vector<float/double>, for example a std::vector<mrpt::math::CVectorDouble>, a std::list<CVectorFloat>, etc...
assignments	[OUT] At output it will have a number [0,k-1] for each of the N input points.
out_centers	[OUT] If not nullptr, at output will have the centers of each group. Can be of any of the supported types of "points", but the basic coordinates should be float or double exactly as in "points".
attempts	[IN] Number of attempts.

See also: A more advanced algorithm, see: kmeanspp

Note: Uses the kmeans++ implementation by David Arthur (2009, http://www.stanford.edu/~darthur/kmpp.zip).

Definition at line 124 of file include/mrpt/math/kmeans.h.

References mrpt::math::detail::stub_kmeans().

◆ kmeanspp()

template<class LIST_OF_VECTORS1 , class LIST_OF_VECTORS2 >

double mrpt::math::kmeanspp	(	const size_t	k,
		const LIST_OF_VECTORS1 &	points,
		std::vector< int > &	assignments,
		LIST_OF_VECTORS2 *	out_centers = `nullptr`,
		const size_t	attempts = `3`
	)

inline

k-means++ algorithm to cluster a list of N points of arbitrary dimensionality into exactly K clusters.

The list of input points can be any template CONTAINER<POINT> with:

CONTAINER can be: Any STL container: std::vector,std::list,std::deque,...
POINT can be:
- std::vector<double/float>
- CArrayDouble<N> / CArrayFloat<N>

Parameters

k	[IN] Number of cluster to look for.
points	[IN] The list of N input points. It can be any STL-like containers of std::vector<float/double>, for example a std::vector<mrpt::math::CVectorDouble>, a std::list<CVectorFloat>, etc...
assignments	[OUT] At output it will have a number [0,k-1] for each of the N input points.
out_centers	[OUT] If not nullptr, at output will have the centers of each group. Can be of any of the supported types of "points", but the basic coordinates should be float or double exactly as in "points".
attempts	[IN] Number of attempts.

See also: The standard kmeans algorithm, see: kmeans

Note: Uses the kmeans++ implementation by David Arthur (2009, http://www.stanford.edu/~darthur/kmpp.zip).

Definition at line 159 of file include/mrpt/math/kmeans.h.

References mrpt::math::detail::stub_kmeans().

Referenced by find_chessboard_corners_multiple().

◆ makect()

static void mrpt::math::makect	(	int	nc,
		int *	ip,
		FFT_TYPE *	c
	)

static

You may use, copy, modify this code for any purpose and without fee. You may distribute this ORIGINAL package.

Definition at line 430 of file fourier.cpp.

Referenced by rdft(), and rdft2d().

◆ makewt()

static void mrpt::math::makewt	(	int	nw,
		int *	ip,
		FFT_TYPE *	w
	)

static

Definition at line 396 of file fourier.cpp.

References bitrv2().

Referenced by cdft(), cdft2d(), rdft(), and rdft2d().

◆ maximum() [1/2]

template<class CONTAINER >

CONTAINER::Scalar mrpt::math::maximum ( const CONTAINER & v )

inline

Definition at line 137 of file ops_containers.h.

Referenced by averageLogLikelihood(), mrpt::poses::CPointPDFParticles::computeKurtosis(), mrpt::bayes::CParticleFilterCapable::computeResampling(), confidenceIntervals(), mrpt::hmtslam::CLSLAM_RBPF_2DLASER::particlesEvaluator_AuxPFOptimal(), mrpt::slam::PF_implementation< mrpt::math::TPose3D, CMonteCarloLocalization3D, mrpt::bayes::particle_storage_mode::VALUE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), mrpt::hmtslam::CLSLAM_RBPF_2DLASER::prediction_and_update_pfAuxiliaryPFOptimal(), mrpt::bayes::CParticleFilterCapable::prepareFastDrawSample(), weightedHistogram(), and weightedHistogramLog().

◆ maximum() [2/2]

template<typename T >

T mrpt::math::maximum ( const std::vector< T > & v )

inline

Definition at line 148 of file ops_containers.h.

References ASSERT_, and mrpt::keep_max().

◆ mean()

template<class CONTAINER >

double mrpt::math::mean ( const CONTAINER & v )

inline

Computes the mean value of a vector.

Returns: The mean, as a double number.

See also: math::stddev,math::meanAndStd

Definition at line 232 of file ops_containers.h.

References sum().

Referenced by mrpt::slam::CGridMapAligner::AlignPDF_robustMatch(), confidenceIntervals(), mrpt::maps::CGasConcentrationGridMap2D::internal_insertObservation(), MATLAB_plotCovariance2D(), mrpt::slam::PF_implementation< mrpt::math::TPose3D, CMonteCarloLocalization3D, mrpt::bayes::particle_storage_mode::VALUE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), mrpt::opengl::CSetOfObjects::posePDF2opengl(), and mrpt::hmtslam::CLSLAM_RBPF_2DLASER::prediction_and_update_pfAuxiliaryPFOptimal().

◆ meanAndCovMat()

template<class MAT_IN , class VECTOR , class MAT_OUT >

void mrpt::math::meanAndCovMat	(	const MAT_IN &	v,
		VECTOR &	out_mean,
		MAT_OUT &	out_cov
	)

Computes the mean vector and covariance from a list of samples in an NxM matrix, where each row is a sample, so the covariance is MxM.

Parameters

v	The set of data as a NxM matrix, of types: CMatrixTemplateNumeric or CMatrixFixedNumeric
out_mean	The output M-vector for the estimated mean.
out_cov	The output MxM matrix for the estimated covariance matrix, this can also be either a fixed-size of dynamic size matrix.

See also: mrpt::math::meanAndCovVec, math::mean,math::stddev, math::cov

Definition at line 103 of file ops_matrices.h.

References ASSERTMSG_, and mrpt::square().

Referenced by cov().

◆ meanAndCovVec()

template<class VECTOR_OF_VECTOR , class VECTORLIKE , class MATRIXLIKE >

void mrpt::math::meanAndCovVec	(	const VECTOR_OF_VECTOR &	v,
		VECTORLIKE &	out_mean,
		MATRIXLIKE &	out_cov
	)

Computes the mean vector and covariance from a list of values given as a vector of vectors, where each row is a sample.

Parameters

v	The set of data, as a vector of N vectors of M elements.
out_mean	The output M-vector for the estimated mean.
out_cov	The output MxM matrix for the estimated covariance matrix.

See also: mrpt::math::meanAndCovMat, math::mean,math::stddev, math::cov

Definition at line 349 of file ops_containers.h.

References ASSERTMSG_, and mrpt::square().

Referenced by covVector().

◆ meanAndStd()

template<class VECTORLIKE >

void mrpt::math::meanAndStd	(	const VECTORLIKE &	v,
		double &	out_mean,
		double &	out_std,
		bool	unbiased = `true`
	)

Computes the standard deviation of a vector.

Parameters

v	The set of data
out_mean	The output for the estimated mean
out_std	The output for the estimated standard deviation
unbiased	If set to true or false the std is normalized by "N-1" or "N", respectively.

See also: math::mean,math::stddev

Definition at line 304 of file ops_containers.h.

References mrpt::square(), and sum().

Referenced by mrpt::vision::CFeature::internal_distanceBetweenPolarImages(), stddev(), and mrpt::vision::updateBaseList().

◆ minimum() [1/2]

template<class CONTAINER >

CONTAINER::Scalar mrpt::math::minimum ( const CONTAINER & v )

inline

Definition at line 142 of file ops_containers.h.

Referenced by mrpt::slam::CGridMapAligner::AlignPDF_robustMatch(), mrpt::slam::PF_implementation< mrpt::math::TPose3D, CMonteCarloLocalization3D, mrpt::bayes::particle_storage_mode::VALUE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), mrpt::hmtslam::CLSLAM_RBPF_2DLASER::prediction_and_update_pfAuxiliaryPFOptimal(), weightedHistogram(), and weightedHistogramLog().

◆ minimum() [2/2]

template<typename T >

T mrpt::math::minimum ( const std::vector< T > & v )

inline

Definition at line 156 of file ops_containers.h.

References ASSERT_, and mrpt::keep_min().

◆ minimum_maximum() [1/2]

template<typename T >

void mrpt::math::minimum_maximum	(	const std::vector< T > &	V,
		T &	curMin,
		T &	curMax
	)

inline

Return the maximum and minimum values of a std::vector.

Definition at line 242 of file ops_containers.h.

References ASSERT_, mrpt::keep_max(), and mrpt::keep_min().

Referenced by adjustRange(), confidenceIntervals(), and mrpt::opengl::CPointCloud::render().

◆ minimum_maximum() [2/2]

template<class Derived >

void mrpt::math::minimum_maximum	(	const Eigen::MatrixBase< Derived > &	V,
		typename Eigen::MatrixBase< Derived >::Scalar &	curMin,
		typename Eigen::MatrixBase< Derived >::Scalar &	curMax
	)

inline

Return the maximum and minimum values of a Eigen-based vector or matrix.

Definition at line 256 of file ops_containers.h.

◆ multiply_A_skew3()

template<class MAT_A , class SKEW_3VECTOR , class MAT_OUT >

void mrpt::math::multiply_A_skew3	(	const MAT_A &	A,
		const SKEW_3VECTOR &	v,
		MAT_OUT &	out
	)

Only for vectors/arrays "v" of length3, compute out = A * Skew(v), where Skew(v) is the skew symmetric matric generated from v (see mrpt::math::skew_symmetric3)

Definition at line 166 of file ops_matrices.h.

References ASSERT_EQUAL_, MRPT_END, and MRPT_START.

Referenced by multiply_A_skew3().

◆ multiply_HCHt()

template<typename MAT_H , typename MAT_C , typename MAT_R >

void mrpt::math::multiply_HCHt	(	const MAT_H &	H,
		const MAT_C &	C,
		MAT_R &	R,
		bool	accumResultInOutput
	)

inline

R = H * C * H^t (with C symmetric)

Definition at line 51 of file ops_matrices.h.

References R.

◆ multiply_HCHt_scalar()

template<typename VECTOR_H , typename MAT_C >

MAT_C::Scalar mrpt::math::multiply_HCHt_scalar	(	const VECTOR_H &	H,
		const MAT_C &	C
	)

r (a scalar) = H * C * H^t (with a vector H and a symmetric matrix C)

Definition at line 69 of file ops_matrices.h.

Referenced by mrpt::graphs::detail::graph_ops< graph_t >::auxMaha2Dist(), mrpt::slam::joint_pdf_metric(), KLD_Gaussians(), mahalanobisDistance2(), mahalanobisDistance2AndLogPDF(), mrpt::poses::CPosePDFGaussian::mahalanobisDistanceTo(), mrpt::poses::CPosePDFGaussianInf::mahalanobisDistanceTo(), normalPDF(), and normalPDFInf().

◆ multiply_HtCH()

template<typename MAT_H , typename MAT_C , typename MAT_R >

void mrpt::math::multiply_HtCH	(	const MAT_H &	H,
		const MAT_C &	C,
		MAT_R &	R,
		bool	accumResultInOutput
	)

R = H^t * C * H (with C symmetric)

Definition at line 76 of file ops_matrices.h.

References R.

◆ multiply_skew3_A()

template<class SKEW_3VECTOR , class MAT_A , class MAT_OUT >

void mrpt::math::multiply_skew3_A	(	const SKEW_3VECTOR &	v,
		const MAT_A &	A,
		MAT_OUT &	out
	)

Only for vectors/arrays "v" of length3, compute out = Skew(v) * A, where Skew(v) is the skew symmetric matric generated from v (see mrpt::math::skew_symmetric3)

Definition at line 190 of file ops_matrices.h.

References ASSERT_EQUAL_, MRPT_END, and MRPT_START.

Referenced by multiply_skew3_A().

◆ ncc_vector()

template<class CONT1 , class CONT2 >

double mrpt::math::ncc_vector	(	const CONT1 &	patch1,
		const CONT2 &	patch2
	)

Normalised Cross Correlation between two vector patches The Matlab code for this is a = a - mean2(a); b = b - mean2(b); r = sum(sum(a.

*b))/sqrt(sum(sum(a.*a))*sum(sum(b.*b)));

Definition at line 410 of file ops_containers.h.

References ASSERT_, ASSERTMSG_, and mrpt::square().

◆ norm()

template<class CONTAINER >

CONTAINER::Scalar mrpt::math::norm ( const CONTAINER & v )

inline

Definition at line 132 of file ops_containers.h.

Referenced by mrpt::vision::pnp::rpnp::calcampose(), mrpt::pbmap::Plane::calcConvexHullandParams(), mrpt::nav::collision_free_dist_arc_circ_robot(), mrpt::vision::pnp::ppnp::compute_pose(), mrpt::vision::pnp::rpnp::compute_pose(), mrpt::poses::CPoses2DSequence::computeTraveledDistanceAfter(), mrpt::poses::CPoses3DSequence::computeTraveledDistanceAfter(), mrpt::pbmap::SubgraphMatcher::evalBinaryConstraints(), mrpt::nav::CHolonomicFullEval::evalSingleTarget(), mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), mrpt::pbmap::getMultiDimMeanShift_color(), mrpt::poses::CPoseInterpolatorBase< 3 >::getPreviousPoseWithMinDistance(), mrpt::pbmap::PbMapMaker::mergePlanes(), mrpt::graphslam::optimize_graph_spa_levmarq(), ransac3Dplane_distance(), mrpt::vision::pnp::p3p::solve(), and TEST().

◆ norm_inf()

template<class CONTAINER >

CONTAINER::Scalar mrpt::math::norm_inf ( const CONTAINER & v )

inline

Definition at line 127 of file ops_containers.h.

Referenced by mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), and mrpt::graphslam::optimize_graph_spa_levmarq().

◆ operator<<() [1/2]

CArchive & mrpt::math::operator<<	(	mrpt::serialization::CArchive &	s,
		const mrpt::math::CVectorFloat &	a
	)

Definition at line 625 of file math.cpp.

◆ operator<<() [2/2]

CArchive & mrpt::math::operator<<	(	mrpt::serialization::CArchive &	s,
		const mrpt::math::CVectorDouble &	a
	)

Definition at line 631 of file math.cpp.

◆ operator>>() [1/4]

mrpt::serialization::CArchive& mrpt::math::operator>>	(	mrpt::serialization::CArchive &	in,
		CMatrixD::Ptr &	pObj
	)

◆ operator>>() [2/4]

mrpt::serialization::CArchive& mrpt::math::operator>>	(	mrpt::serialization::CArchive &	in,
		CMatrix::Ptr &	pObj
	)

◆ operator>>() [3/4]

CArchive & mrpt::math::operator>>	(	mrpt::serialization::CArchive &	in,
		mrpt::math::CVectorDouble &	a
	)

Definition at line 619 of file math.cpp.

References mrpt::serialization::CArchive::ReadBufferFixEndianness().

◆ operator>>() [4/4]

CArchive & mrpt::math::operator>>	(	mrpt::serialization::CArchive &	in,
		mrpt::math::CVectorFloat &	a
	)

Definition at line 613 of file math.cpp.

References mrpt::serialization::CArchive::ReadBufferFixEndianness().

◆ ransac3Dplane_degenerate()

template<typename T >

bool mrpt::math::ransac3Dplane_degenerate	(	const CMatrixTemplateNumeric< T > &	allData,
		const std::vector< size_t > &	useIndices
	)

Return "true" if the selected points are a degenerate (invalid) case.

Definition at line 94 of file ransac_applications.cpp.

References MRPT_UNUSED_PARAM.

◆ ransac3Dplane_distance()

template<typename T >

void mrpt::math::ransac3Dplane_distance	(	const CMatrixTemplateNumeric< T > &	allData,
		const vector< CMatrixTemplateNumeric< T >> &	testModels,
		const T	distanceThreshold,
		unsigned int &	out_bestModelIndex,
		std::vector< size_t > &	out_inlierIndices
	)

Definition at line 60 of file ransac_applications.cpp.

References ASSERT_, and mrpt::math::TPlane::coefs.

◆ ransac3Dplane_fit()

template<typename T >

void mrpt::math::ransac3Dplane_fit	(	const CMatrixTemplateNumeric< T > &	allData,
		const std::vector< size_t > &	useIndices,
		vector< CMatrixTemplateNumeric< T >> &	fitModels
	)

Definition at line 26 of file ransac_applications.cpp.

References ASSERT_, and mrpt::math::TPlane::coefs.

◆ rdft()

static void mrpt::math::rdft	(	int	n,
		int	isgn,
		FFT_TYPE *	a,
		int *	ip,
		FFT_TYPE *	w
	)

static

Definition at line 566 of file fourier.cpp.

References bitrv2(), cftbsub(), cftfsub(), makect(), makewt(), rftbsub(), and rftfsub().

Referenced by rdft2d().

◆ rdft2d()

static void mrpt::math::rdft2d	(	int	n1,
		int	n2,
		int	isgn,
		FFT_TYPE **	a,
		FFT_TYPE *	t,
		int *	ip,
		FFT_TYPE *	w
	)

static

You may use, copy, modify this code for any purpose and without fee. You may distribute this ORIGINAL package.

-----— Real DFT / Inverse of Real DFT -----— [definition] <case1> RDFT R[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 a[j1][j2] * cos(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2), 0<=k1<n1, 0<=k2<n2 I[k1][k2] = sum_j1=0^n1-1 sum_j2=0^n2-1 a[j1][j2] * sin(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2), 0<=k1<n1, 0<=k2<n2 <case2> IRDFT (excluding scale) a[k1][k2] = (1/2) * sum_j1=0^n1-1 sum_j2=0^n2-1 (R[j1][j2] * cos(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2) + I[j1][j2] * sin(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2)), 0<=k1<n1, 0<=k2<n2 (notes: R[n1-k1][n2-k2] = R[k1][k2], I[n1-k1][n2-k2] = -I[k1][k2], R[n1-k1][0] = R[k1][0], I[n1-k1][0] = -I[k1][0], R[0][n2-k2] = R[0][k2], I[0][n2-k2] = -I[0][k2], 0<k1<n1, 0<k2<n2) [usage] <case1> ip[0] = 0; // first time only rdft2d(n1, n2, 1, a, t, ip, w); <case2> ip[0] = 0; // first time only rdft2d(n1, n2, -1, a, t, ip, w); [parameters] n1 :data length (int) n1 >= 2, n1 = power of 2 n2 :data length (int) n2 >= 2, n2 = power of 2 a[0...n1-1][0...n2-1] :input/output data (FFT_TYPE **) <case1> output data a[k1][2*k2] = R[k1][k2] = R[n1-k1][n2-k2], a[k1][2*k2+1] = I[k1][k2] = -I[n1-k1][n2-k2], 0<k1<n1, 0<k2<n2/2, a[0][2*k2] = R[0][k2] = R[0][n2-k2], a[0][2*k2+1] = I[0][k2] = -I[0][n2-k2], 0<k2<n2/2, a[k1][0] = R[k1][0] = R[n1-k1][0], a[k1][1] = I[k1][0] = -I[n1-k1][0], a[n1-k1][1] = R[k1][n2/2] = R[n1-k1][n2/2], a[n1-k1][0] = -I[k1][n2/2] = I[n1-k1][n2/2], 0<k1<n1/2, a[0][0] = R[0][0], a[0][1] = R[0][n2/2], a[n1/2][0] = R[n1/2][0], a[n1/2][1] = R[n1/2][n2/2] <case2> input data a[j1][2*j2] = R[j1][j2] = R[n1-j1][n2-j2], a[j1][2*j2+1] = I[j1][j2] = -I[n1-j1][n2-j2], 0<j1<n1, 0<j2<n2/2, a[0][2*j2] = R[0][j2] = R[0][n2-j2], a[0][2*j2+1] = I[0][j2] = -I[0][n2-j2], 0<j2<n2/2, a[j1][0] = R[j1][0] = R[n1-j1][0], a[j1][1] = I[j1][0] = -I[n1-j1][0], a[n1-j1][1] = R[j1][n2/2] = R[n1-j1][n2/2], a[n1-j1][0] = -I[j1][n2/2] = I[n1-j1][n2/2], 0<j1<n1/2, a[0][0] = R[0][0], a[0][1] = R[0][n2/2], a[n1/2][0] = R[n1/2][0], a[n1/2][1] = R[n1/2][n2/2] t[0...2*n1-1] :work area (FFT_TYPE *) ip[0...*] :work area for bit reversal (int *) length of ip >= 2+sqrt(n) ; if n % 4 == 0 2+sqrt(n/2); otherwise (n = max(n1, n2/2)) ip[0],ip[1] are pointers of the cos/sin table. w[0...*] :cos/sin table (FFT_TYPE *) length of w >= max(n1/2, n2/4) + n2/4 w[],ip[] are initialized if ip[0] == 0. [remark] Inverse of rdft2d(n1, n2, 1, a, t, ip, w); is rdft2d(n1, n2, -1, a, t, ip, w); for (j1 = 0; j1 <= n1 - 1; j1++) { for (j2 = 0; j2 <= n2 - 1; j2++) { a[j1][j2] *= 2.0 / (n1 * n2); } }

Definition at line 734 of file fourier.cpp.

References cdft(), makect(), makewt(), and rdft().

Referenced by dft2_real(), and idft2_real().

◆ realft()

static void mrpt::math::realft	(	float	data[],
		unsigned long	n
	)

static

Definition at line 100 of file fourier.cpp.

References four1().

Referenced by fft_real().

◆ removeRepVertices()

template<class T >

void mrpt::math::removeRepVertices ( T & poly )

inline

Definition at line 962 of file lightweight_geom_data.cpp.

References distance(), and getEpsilon().

Referenced by mrpt::math::TPolygon2D::removeRepeatedVertices(), and mrpt::math::TPolygon3D::removeRepeatedVertices().

◆ removeUnusedVertices()

template<class T >

void mrpt::math::removeUnusedVertices ( T & poly )

inline

Definition at line 930 of file lightweight_geom_data.cpp.

References distance(), and getEpsilon().

Referenced by mrpt::math::TPolygon2D::removeRedundantVertices(), and mrpt::math::TPolygon3D::removeRedundantVertices().

◆ resizeLike() [1/2]

template<class EIGEN_CONTAINER >

void mrpt::math::resizeLike	(	EIGEN_CONTAINER &	trg,
		const EIGEN_CONTAINER &	src
	)

Definition at line 82 of file ops_containers.h.

Referenced by cumsum_tmpl().

◆ resizeLike() [2/2]

template<typename T >

void mrpt::math::resizeLike	(	std::vector< T > &	trg,
		const std::vector< T > &	src
	)

Definition at line 87 of file ops_containers.h.

◆ rftbsub()

static void mrpt::math::rftbsub	(	int	n,
		FFT_TYPE *	a,
		int	nc,
		FFT_TYPE *	c
	)

static

Definition at line 611 of file fourier.cpp.

Referenced by rdft().

◆ rftfsub()

static void mrpt::math::rftfsub	(	int	n,
		FFT_TYPE *	a,
		int	nc,
		FFT_TYPE *	c
	)

static

Definition at line 542 of file fourier.cpp.

Referenced by rdft().

◆ size()

template<class MATRIXLIKE >

size_t mrpt::math::size	(	const MATRIXLIKE &	m,
		const int	dim
	)

inline

Returns the size of the matrix in the i'th dimension: 1=rows, 2=columns (MATLAB-compatible function)

Note: Template argument MATRIXLIKE can be: mrpt::math::CMatrixTemplate, mrpt::math::CMatrixTemplateNumeric, mrpt::math::CMatrixFixedNumeric

Definition at line 21 of file math/include/mrpt/math/bits_math.h.

References THROW_EXCEPTION_FMT.

Referenced by mrpt::math::TPolygon2D::contains(), mrpt::math::TPolygon2D::getAsSegmentList(), mrpt::math::TPolygon3D::getAsSegmentList(), mrpt::math::TPolygon2D::getBoundingBox(), mrpt::math::TPolygon2D::getCenter(), mrpt::math::TPolygon3D::getCenter(), mrpt::math::TPolygon2D::getPlotData(), mrpt::math::TPolygon2D::isConvex(), mrpt::tfest::TMatchingPairList::overallSquareError(), mrpt::tfest::TMatchingPairList::overallSquareErrorAndPoints(), and mrpt::tfest::TMatchingPairList::squareErrorVector().

◆ squareNorm()

template<size_t N, class T , class U >

T mrpt::math::squareNorm ( const U & v )

inline

Compute the square norm of anything implementing [].

See also: norm

Definition at line 179 of file ops_containers.h.

References mrpt::square().

◆ squareNorm_accum()

template<class CONTAINER , typename VALUE >

VALUE mrpt::math::squareNorm_accum	(	const VALUE	total,
		const CONTAINER &	v
	)

Accumulate the squared-norm of a vector/array/matrix into "total" (this function is compatible with std::accumulate).

Definition at line 171 of file ops_containers.h.

◆ stddev()

template<class VECTORLIKE >

double mrpt::math::stddev	(	const VECTORLIKE &	v,
		bool	unbiased = `true`
	)

inline

Computes the standard deviation of a vector.

Parameters

v	The set of data
unbiased	If set to true or false the std is normalized by "N-1" or "N", respectively.

See also: math::mean,math::meanAndStd

Definition at line 334 of file ops_containers.h.

References meanAndStd().

Referenced by mrpt::pbmap::getHistogramMeanShift().

◆ sum() [1/2]

template<class CONTAINER >

CONTAINER::Scalar mrpt::math::sum ( const CONTAINER & v )

inline

Computes the sum of all the elements.

Note: If used with containers of integer types (uint8_t, int, etc...) this could overflow. In those cases, use sumRetType the second argument RET to specify a larger type to hold the sum.

See also: cumsum

Definition at line 209 of file ops_containers.h.

Referenced by mrpt::vision::CDifodo::buildCoordinatesPyramid(), mrpt::vision::CDifodo::buildCoordinatesPyramidFast(), Pose3DTests::check_jacob_LnT_T(), mrpt::detectors::CFaceDetection::checkIfFaceRegions(), mrpt::vision::computeHistogramOfOrientations(), mrpt::slam::CRangeBearingKFSLAM::computeOffDiagonalBlocksApproximationError(), mrpt::nav::CHolonomicND::evaluateGaps(), mrpt::detectors::CFaceDetection::experimental_viewFacePointsAndEigenVects(), mrpt::pbmap::getHistogramMeanShift(), mrpt::pbmap::getMultiDimMeanShift_color(), mrpt::graphslam::detail::CEdgeCounter::getTotalNumOfEdges(), mrpt::slam::CICP::ICP_Method_LM(), mrpt::vision::pnp::p3p::jacobi_4x4(), mean(), meanAndStd(), meanAndStd(), meanAndStdAll(), noncentralChi2PDF_CDF(), mrpt::vision::reprojectionResiduals(), reprojectionResidualsElement(), run_test_so3_avrg(), mrpt::bayes::CKalmanFilterCapable< 7, 3, 3, 7 >::runOneKalmanIteration(), TEST(), Pose3DQuatTests::test_composePointJacob(), Pose3DTests::test_composePointJacob(), Pose3DTests::test_composePointJacob_se3(), QuaternionTests::test_ExpAndLnMatches(), TEST_F(), QuaternionTests::test_gimbalLock(), Pose3DQuatTests::test_invComposePointJacob(), Pose3DTests::test_invComposePointJacob(), Pose3DTests::test_invComposePointJacob_se3(), Pose3DTests::test_inverse(), SE_traits_tests< POSE_TYPE >::test_jacobs_P1DP2inv(), QuaternionTests::test_lnAndExpMatches(), Pose3DQuatTests::test_normalizeJacob(), Pose3DQuatTests::test_sphericalCoords(), Pose3DQuatPDFGaussTests::testCompositionJacobian(), Pose3DPDFGaussTests::testCompositionJacobian(), and mrpt::graphs::ScalarFactorGraph::updateEstimation().

◆ sum() [2/2]

template<typename T >

T mrpt::math::sum ( const std::vector< T > & v )

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 216 of file ops_containers.h.

◆ sumRetType()

template<class CONTAINER , typename RET >

RET mrpt::math::sumRetType ( const CONTAINER & v )

inline

Computes the sum of all the elements, with a custom return type.

See also: sum, cumsum

Definition at line 224 of file ops_containers.h.

Detailed Description

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ CArrayDouble

◆ CArrayFloat

◆ CArrayInt

◆ CArrayUInt

◆ CLevenbergMarquardt

◆ CMatrixDouble

◆ CMatrixDouble12

◆ CMatrixDouble13

◆ CMatrixDouble15

◆ CMatrixDouble16

◆ CMatrixDouble17

◆ CMatrixDouble21

◆ CMatrixDouble22

◆ CMatrixDouble23

◆ CMatrixDouble31

◆ CMatrixDouble32

◆ CMatrixDouble33

◆ CMatrixDouble41

◆ CMatrixDouble44

◆ CMatrixDouble51

◆ CMatrixDouble61

◆ CMatrixDouble66

◆ CMatrixDouble71

◆ CMatrixDouble77

◆ CMatrixFloat

◆ CMatrixFloat12

◆ CMatrixFloat13

◆ CMatrixFloat15

◆ CMatrixFloat16

◆ CMatrixFloat17

◆ CMatrixFloat21

◆ CMatrixFloat22

◆ CMatrixFloat23

◆ CMatrixFloat31

◆ CMatrixFloat32

◆ CMatrixFloat33

◆ CMatrixFloat44

◆ CMatrixFloat51

◆ CMatrixFloat61

◆ CMatrixFloat66

◆ CMatrixFloat71

◆ CMatrixFloat77

◆ CMatrixLongDouble

◆ CMatrixUInt

◆ CQuaternionDouble

◆ CQuaternionFloat

◆ CVectorDouble

◆ CVectorFloat

◆ FFT_TYPE

Enumeration Type Documentation

◆ TConstructorFlags_Matrices

◆ TConstructorFlags_Quaternions

◆ TMatrixTextFileFormat

Function Documentation

◆ absDiff()

◆ adjustRange()

◆ approximatelyEqual() [1/2]

◆ approximatelyEqual() [2/2]

◆ bitrv2()

◆ cdft()

◆ cdft2d()

◆ cftbsub()

◆ cftfsub()

◆ containerFromPoseOrPoint()

◆ countCommonElements()

◆ cov()

◆ covVector()

◆ cumsum() [1/2]

◆ cumsum() [2/2]

◆ cumsum_tmpl()

◆ dotProduct() [1/2]

◆ dotProduct() [2/2]