Detailed Description

This base provides a set of functions for maths stuff.

Namespaces
	detail

	jacobians
	A collection of functions to compute jacobians of diverse transformations, etc (some functions are redirections to existing methods elsewhere, so this namespace is actually used with grouping purposes).

Classes
class	CArrayDouble
	A partial specialization of CArrayNumeric for double numbers. More...

class	CArrayFloat
	A partial specialization of CArrayNumeric for float numbers. More...

class	CArrayInt
	A partial specialization of CArrayNumeric for int numbers. More...

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	CArrayUInt
	A partial specialization of CArrayNumeric for unsigned int numbers. 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...

class	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	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	CRuntimeCompiledExpression
	A wrapper of `exprtk` runtime expression compiler: it takes a string representing an expression (from a simple mathematical formula to a complete program), compiles it and evaluates its result as many times as required. 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	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
typedef CLevenbergMarquardtTempl< mrpt::math::CVectorDouble >	CLevenbergMarquardt
	The default name for the LM class is an instantiation for "double". More...

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

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

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

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

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

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

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

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

typedef TPlane	TPlane3D

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

typedef float	FFT_TYPE
	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
typedef CMatrixFixedNumeric< double, 2, 2 >	CMatrixDouble22

typedef CMatrixFixedNumeric< double, 2, 3 >	CMatrixDouble23

typedef CMatrixFixedNumeric< double, 3, 2 >	CMatrixDouble32

typedef CMatrixFixedNumeric< double, 3, 3 >	CMatrixDouble33

typedef CMatrixFixedNumeric< double, 4, 4 >	CMatrixDouble44

typedef CMatrixFixedNumeric< double, 6, 6 >	CMatrixDouble66

typedef CMatrixFixedNumeric< double, 7, 7 >	CMatrixDouble77

typedef CMatrixFixedNumeric< double, 1, 3 >	CMatrixDouble13

typedef CMatrixFixedNumeric< double, 3, 1 >	CMatrixDouble31

typedef CMatrixFixedNumeric< double, 1, 2 >	CMatrixDouble12

typedef CMatrixFixedNumeric< double, 2, 1 >	CMatrixDouble21

typedef CMatrixFixedNumeric< double, 6, 1 >	CMatrixDouble61

typedef CMatrixFixedNumeric< double, 1, 6 >	CMatrixDouble16

typedef CMatrixFixedNumeric< double, 7, 1 >	CMatrixDouble71

typedef CMatrixFixedNumeric< double, 1, 7 >	CMatrixDouble17

typedef CMatrixFixedNumeric< double, 5, 1 >	CMatrixDouble51

typedef CMatrixFixedNumeric< double, 1, 5 >	CMatrixDouble15

typedef CMatrixFixedNumeric< double, 4, 1 >	CMatrixDouble41

typedef CMatrixFixedNumeric< float, 2, 2 >	CMatrixFloat22

typedef CMatrixFixedNumeric< float, 2, 3 >	CMatrixFloat23

typedef CMatrixFixedNumeric< float, 3, 2 >	CMatrixFloat32

typedef CMatrixFixedNumeric< float, 3, 3 >	CMatrixFloat33

typedef CMatrixFixedNumeric< float, 4, 4 >	CMatrixFloat44

typedef CMatrixFixedNumeric< float, 6, 6 >	CMatrixFloat66

typedef CMatrixFixedNumeric< float, 7, 7 >	CMatrixFloat77

typedef CMatrixFixedNumeric< float, 1, 3 >	CMatrixFloat13

typedef CMatrixFixedNumeric< float, 3, 1 >	CMatrixFloat31

typedef CMatrixFixedNumeric< float, 1, 2 >	CMatrixFloat12

typedef CMatrixFixedNumeric< float, 2, 1 >	CMatrixFloat21

typedef CMatrixFixedNumeric< float, 6, 1 >	CMatrixFloat61

typedef CMatrixFixedNumeric< float, 1, 6 >	CMatrixFloat16

typedef CMatrixFixedNumeric< float, 7, 1 >	CMatrixFloat71

typedef CMatrixFixedNumeric< float, 1, 7 >	CMatrixFloat17

typedef CMatrixFixedNumeric< float, 5, 1 >	CMatrixFloat51

typedef CMatrixFixedNumeric< float, 1, 5 >	CMatrixFloat15

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
BASE_IMPEXP ::mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, CMatrixPtr &pObj)

::mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, CMatrixBPtr &pObj)

BASE_IMPEXP ::mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, CMatrixDPtr &pObj)

::mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, CPolygonPtr &pObj)

::mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, CSplineInterpolator1DPtr &pObj)

double BASE_IMPEXP	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 BASE_IMPEXP	erfc (const double x)
	The complementary error function of a Normal distribution. More...

double BASE_IMPEXP	erf (const double x)
	The error function of a Normal distribution. More...

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

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

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

double BASE_IMPEXP	chi2CDF (unsigned int degreesOfFreedom, double arg)

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

std::pair< double, double > BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	idft2_real (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_data)
	Compute the 2D inverse Discrete Fourier Transform (DFT) More...

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

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

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

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

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

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

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

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

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

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

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

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

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)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint3D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint3D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPose2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPose3D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose3D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment2D &s)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment2D &s)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TLine2D &l)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine2D &l)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TObject2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment3D &s)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment3D &s)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TLine3D &l)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine3D &l)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPlane &p)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPlane &p)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TObject3D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject3D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TTwist2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TTwist2D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TTwist3D &o)

BASE_IMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &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, void(*functor)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out), 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=NULL)
	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::utils::CStream &	operator<< (mrpt::utils::CStream &ostrm, const CArrayNumeric< T, N > &a)
	Binary dump of a CArrayNumeric<T,N> to a stream. More...

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

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

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

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

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

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

int BASE_IMPEXP	solve_poly2 (double a, double b, double c, double &r1, double &r2) MRPT_NO_THROWS
	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=NULL, 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, typename mrpt::aligned_containers< VECTORLIKE3 >::vector_t out_samples_y=NULL)
	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...

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

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

bool BASE_IMPEXP	isNaN (float f) MRPT_NO_THROWS
	Returns true if the number is NaN. More...

bool BASE_IMPEXP	isNaN (double f) MRPT_NO_THROWS
	Returns true if the number is NaN. More...

bool BASE_IMPEXP	isFinite (float f) MRPT_NO_THROWS
	Returns true if the number is non infinity. More...

bool BASE_IMPEXP	isFinite (double f) MRPT_NO_THROWS
	Returns true if the number is non infinity. More...

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

double BASE_IMPEXP	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...

template<class T >
T	round2up (T val)
	Round up to the nearest power of two of a given number. More...

std::string BASE_IMPEXP	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 BASE_IMPEXP	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<size_t N, typename T >
std::vector< T >	make_vector (const T val1,...)
	A versatile template to build vectors on-the-fly in a style close to MATLAB's v=[a b c d ...] The first argument of the template is the vector length, and the second the type of the numbers. More...

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...

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

template<class T >
T	square (const T x)
	Inline function for the square of a number. More...

template<class T >
T	hypot_fast (const T x, const T y)
	Faster version of std::hypot(), to use when overflow is not an issue and we prefer fast code. 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)

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

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

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

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...

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

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

void	dctsub (int n, FFT_TYPE a, int nc, FFT_TYPE c)

void	dstsub (int n, FFT_TYPE a, int nc, FFT_TYPE c)

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

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

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...

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...

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

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...

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<typename T >
void	ransac3Dplane_fit (const CMatrixTemplateNumeric< T > &allData, const 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, vector_size_t &out_inlierIndices)

template<typename T >
bool	ransac3Dplane_degenerate (const CMatrixTemplateNumeric< T > &allData, const mrpt::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=NULL), 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=NULL)
	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=NULL)
	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=NULL)
	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	intersect (const TSegment3D &s1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between two 3D segments. More...

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

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

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

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

bool BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	getAngle (const TPlane &p1, const TPlane &p2)
	Computes the angle between two planes. More...

double BASE_IMPEXP	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 BASE_IMPEXP	getAngle (const TLine3D &r1, const TLine3D &r2)
	Computes the accute relative angle (range: [-PI/2,PI/2]) between two lines. More...

double BASE_IMPEXP	getAngle (const TLine2D &r1, const TLine2D &r2)
	Computes the relative angle (range: [-PI,PI]) of line 2 wrt line 1. More...

Creation of lines from poses.
void BASE_IMPEXP	createFromPoseX (const mrpt::poses::CPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the X axis in a given pose. More...

void BASE_IMPEXP	createFromPoseY (const mrpt::poses::CPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Y axis in a given pose. More...

void BASE_IMPEXP	createFromPoseZ (const mrpt::poses::CPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Z axis in a given pose. More...

void BASE_IMPEXP	createFromPoseAndVector (const mrpt::poses::CPose3D &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 BASE_IMPEXP	createFromPoseX (const TPose2D &p, TLine2D &r)
	Gets a 2D line corresponding to the X axis in a given pose. More...

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

void BASE_IMPEXP	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 BASE_IMPEXP	conformAPlane (const std::vector< TPoint3D > &points)
	Checks whether this polygon or set of points acceptably fits a plane. More...

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

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

bool BASE_IMPEXP	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::poses::CPose3D &newXYpose, TPoint3D &newPoint)
	Uses the given pose 3D to project a point into a new base. More...

void	project3D (const TSegment3D &segment, const mrpt::poses::CPose3D &newXYpose, TSegment3D &newSegment)
	Uses the given pose 3D to project a segment into a new base. More...

void BASE_IMPEXP	project3D (const TLine3D &line, const mrpt::poses::CPose3D &newXYpose, TLine3D &newLine)
	Uses the given pose 3D to project a line into a new base. More...

void BASE_IMPEXP	project3D (const TPlane &plane, const mrpt::poses::CPose3D &newXYpose, TPlane &newPlane)
	Uses the given pose 3D to project a plane into a new base. More...

void BASE_IMPEXP	project3D (const TPolygon3D &polygon, const mrpt::poses::CPose3D &newXYpose, TPolygon3D &newPolygon)
	Uses the given pose 3D to project a polygon into a new base. More...

void BASE_IMPEXP	project3D (const TObject3D &object, const mrpt::poses::CPose3D &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::poses::CPose3D &newXYpose, std::vector< T > &newObjs)
	Projects a set of 3D objects into the plane's base. More...

void BASE_IMPEXP	project2D (const TPoint2D &point, const mrpt::poses::CPose2D &newXpose, TPoint2D &newPoint)
	Uses the given pose 2D to project a point into a new base. More...

void	project2D (const TSegment2D &segment, const mrpt::poses::CPose2D &newXpose, TSegment2D &newSegment)
	Uses the given pose 2D to project a segment into a new base. More...

void BASE_IMPEXP	project2D (const TLine2D &line, const mrpt::poses::CPose2D &newXpose, TLine2D &newLine)
	Uses the given pose 2D to project a line into a new base. More...

void BASE_IMPEXP	project2D (const TPolygon2D &polygon, const mrpt::poses::CPose2D &newXpose, TPolygon2D &newPolygon)
	Uses the given pose 2D to project a polygon into a new base. More...

void BASE_IMPEXP	project2D (const TObject2D &object, const mrpt::poses::CPose2D &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 mrpt::poses::CPose2D &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 BASE_IMPEXP	intersect (const TPolygon2D &p1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between a 2D polygon and a 2D segment. More...

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

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

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

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

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

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

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

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

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

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

double BASE_IMPEXP	distance (const TPlane &p1, const TPlane &p2)
	Gets the distance between two planes. It will be zero if the planes are not parallel. More...

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

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

double BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	createPlaneFromPoseXY (const mrpt::poses::CPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Z vector. More...

void BASE_IMPEXP	createPlaneFromPoseXZ (const mrpt::poses::CPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Y vector. More...

void BASE_IMPEXP	createPlaneFromPoseYZ (const mrpt::poses::CPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its X vector. More...

void BASE_IMPEXP	createPlaneFromPoseAndNormal (const mrpt::poses::CPose3D &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 BASE_IMPEXP	generateAxisBaseFromDirectionAndAxis (const double(&vec)[3], char coord, CMatrixDouble &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 BASE_IMPEXP	getRegressionLine (const std::vector< TPoint2D > &points, TLine2D &line)
	Using eigenvalues, gets the best fitting line for a set of 2D points. More...

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

double BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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. More...

double	getEpsilon ()
	Gets the value of the geometric epsilon. More...

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

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

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

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

void BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	traceRay (const std::vector< TPolygonWithPlane > &vec, const mrpt::poses::CPose3D &pose, double &dist)
	Fast ray tracing method using polygons' properties. More...

bool	traceRay (const std::vector< TPolygon3D > &vec, const mrpt::poses::CPose3D &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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	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=NULL, 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=NULL, 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::utils::CStream &	operator>> (mrpt::utils::CStream &in, CMatrixFixedNumeric< float, NROWS, NCOLS > &M)
	Read operator from a CStream. More...

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

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

template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &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...

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 BASE_IMPEXP	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 BASE_IMPEXP	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 BASE_IMPEXP	slerp (const mrpt::poses::CPose3D &q0, const mrpt::poses::CPose3D &q1, const double t, mrpt::poses::CPose3D &p)
	SLERP interpolation between two 6D poses - like mrpt::math::slerp for quaternions, but interpolates the [X,Y,Z] coordinates as well. More...

void BASE_IMPEXP	slerp (const mrpt::poses::CPose3DQuat &q0, const mrpt::poses::CPose3DQuat &q1, const double t, mrpt::poses::CPose3DQuat &p)

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

Variables
double BASE_IMPEXP	geometryEpsilon =1e-5
	Global epsilon to overcome small precision errors (Default=1e-5) More...

struct BASE_IMPEXP	TSegment3D

struct BASE_IMPEXP	TLine3D

class BASE_IMPEXP	TPolygon3D

struct BASE_IMPEXP	TObject3D

const unsigned char	GEOMETRIC_TYPE_POINT =0
	Object type identifier for TPoint2D or TPoint3D. More...

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

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

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

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

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

Typedef Documentation

◆ CLevenbergMarquardt

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

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

Definition at line 232 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 130 of file CMatrixTemplateNumeric.h.

◆ CMatrixDouble12

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

Definition at line 54 of file eigen_frwds.h.

◆ CMatrixDouble13

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

Definition at line 52 of file eigen_frwds.h.

◆ CMatrixDouble15

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

Definition at line 61 of file eigen_frwds.h.

◆ CMatrixDouble16

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

Definition at line 57 of file eigen_frwds.h.

◆ CMatrixDouble17

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

Definition at line 59 of file eigen_frwds.h.

◆ CMatrixDouble21

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

Definition at line 55 of file eigen_frwds.h.

◆ CMatrixDouble22

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

Definition at line 45 of file eigen_frwds.h.

◆ CMatrixDouble23

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

Definition at line 46 of file eigen_frwds.h.

◆ CMatrixDouble31

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

Definition at line 53 of file eigen_frwds.h.

◆ CMatrixDouble32

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

Definition at line 47 of file eigen_frwds.h.

◆ CMatrixDouble33

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

Definition at line 48 of file eigen_frwds.h.

◆ CMatrixDouble41

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

Definition at line 62 of file eigen_frwds.h.

◆ CMatrixDouble44

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

Definition at line 49 of file eigen_frwds.h.

◆ CMatrixDouble51

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

Definition at line 60 of file eigen_frwds.h.

◆ CMatrixDouble61

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

Definition at line 56 of file eigen_frwds.h.

◆ CMatrixDouble66

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

Definition at line 50 of file eigen_frwds.h.

◆ CMatrixDouble71

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

Definition at line 58 of file eigen_frwds.h.

◆ CMatrixDouble77

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

Definition at line 51 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 124 of file CMatrixTemplateNumeric.h.

◆ CMatrixFloat12

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

Definition at line 73 of file eigen_frwds.h.

◆ CMatrixFloat13

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

Definition at line 71 of file eigen_frwds.h.

◆ CMatrixFloat15

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

Definition at line 80 of file eigen_frwds.h.

◆ CMatrixFloat16

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

Definition at line 76 of file eigen_frwds.h.

◆ CMatrixFloat17

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

Definition at line 78 of file eigen_frwds.h.

◆ CMatrixFloat21

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

Definition at line 74 of file eigen_frwds.h.

◆ CMatrixFloat22

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

Definition at line 64 of file eigen_frwds.h.

◆ CMatrixFloat23

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

Definition at line 65 of file eigen_frwds.h.

◆ CMatrixFloat31

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

Definition at line 72 of file eigen_frwds.h.

◆ CMatrixFloat32

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

Definition at line 66 of file eigen_frwds.h.

◆ CMatrixFloat33

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

Definition at line 67 of file eigen_frwds.h.

◆ CMatrixFloat44

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

Definition at line 68 of file eigen_frwds.h.

◆ CMatrixFloat51

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

Definition at line 79 of file eigen_frwds.h.

◆ CMatrixFloat61

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

Definition at line 75 of file eigen_frwds.h.

◆ CMatrixFloat66

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

Definition at line 69 of file eigen_frwds.h.

◆ CMatrixFloat71

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

Definition at line 77 of file eigen_frwds.h.

◆ CMatrixFloat77

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

Definition at line 70 of file eigen_frwds.h.

◆ CMatrixLongDouble

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

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 146 of file CMatrixTemplateNumeric.h.

◆ CMatrixUInt

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

Declares a matrix of unsigned ints (non serializable).

See also: CMatrixDouble, CMatrixFloat

Definition at line 135 of file CMatrixTemplateNumeric.h.

◆ CQuaternionDouble

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

A quaternion of data type "double".

Definition at line 408 of file CQuaternion.h.

◆ CQuaternionFloat

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

A quaternion of data type "float".

Definition at line 409 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 37 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 35 of file eigen_frwds.h.

◆ FFT_TYPE

typedef float mrpt::math::FFT_TYPE

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

Definition at line 143 of file math.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 72 of file math_frwds.h.

◆ TConstructorFlags_Quaternions

enum mrpt::math::TConstructorFlags_Quaternions

Enumerator
UNINITIALIZED_QUATERNION

Definition at line 22 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 63 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 50 of file base/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 225 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 32 of file base/include/mrpt/math/utils.h.

Referenced by 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 42 of file base/include/mrpt/math/utils.h.

References approximatelyEqual().

◆ bitrv2()

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

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

Definition at line 437 of file math.cpp.

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

◆ cdft()

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

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

Definition at line 495 of file math.cpp.

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

Referenced by cdft2d(), and rdft2d().

◆ cdft2d()

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

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 869 of file math.cpp.

References cdft(), and makewt().

Referenced by dft2_complex(), and idft2_complex().

◆ cftbsub()

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

Definition at line 156 of file math.cpp.

Referenced by cdft(), and rdft().

◆ cftfsub()

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

Definition at line 268 of file math.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 23 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 213 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 135 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 334 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 97 of file ops_containers.h.

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 102 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 87 of file ops_containers.h.

References resizeLike().

◆ dctsub()

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

Definition at line 533 of file math.cpp.

◆ 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 151 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 158 of file ops_containers.h.

◆ dstsub()

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

Definition at line 553 of file math.cpp.

◆ estimateJacobian()

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

void mrpt::math::estimateJacobian	(	const VECTORLIKE &	x,
		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 26 of file num_jacobian.h.

References ASSERT_, MRPT_END, and MRPT_START.

Referenced by mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), mrpt::math::jacobians::jacob_numeric_estimate(), and mrpt::bayes::CKalmanFilterCapable< 7, 3, 3, 7 >::runOneKalmanIteration().

◆ four1()

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

Definition at line 41 of file math.cpp.

Referenced by realft().

◆ getColumnAccessor() [1/4]

template<typename MAT >

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

inline

Definition at line 449 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 513 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 556 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 603 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 238 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 303 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 347 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 395 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 = `NULL`
	)

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 55 of file ops_containers.h.

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

Referenced by compute_color(), confidenceIntervals(), fill_inverse_cmap(), mrpt::pbmap::getMode(), pass2_fs_dither(), pass2_no_dither(), prescan_quantize(), start_pass_2_quant(), and update_box().

◆ 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 27 of file homog_matrices.h.

References ASSERT_, MRPT_END, MRPT_START, and size().

Referenced by mrpt::poses::CPoseOrPoint< CPoint3D >::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 79 of file homog_matrices.h.

References ASSERT_, MRPT_END, MRPT_START, and size().

◆ 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 108 of file homog_matrices.h.

References ASSERTDEB_, and size().

◆ hypot_fast()

template<class T >

T mrpt::math::hypot_fast	(	const T	x,
		const T	y
	)

inline

Faster version of std::hypot(), to use when overflow is not an issue and we prefer fast code.

Definition at line 56 of file bits.h.

◆ isLeft()

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

inline

Definition at line 680 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 = `NULL`,
		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 NULL, 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 118 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 = `NULL`,
		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 NULL, 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 146 of file include/mrpt/math/kmeans.h.

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

Referenced by find_chessboard_corners_multiple().

◆ makect()

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

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

Definition at line 414 of file math.cpp.

Referenced by rdft(), and rdft2d().

◆ makewt()

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

Definition at line 382 of file math.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 111 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::poses::CPose3D, CMonteCarloLocalization3D >::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 114 of file ops_containers.h.

References ASSERT_, and mrpt::mrpt::utils::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 179 of file ops_containers.h.

References sum().

Referenced by mrpt::slam::CGridMapAligner::AlignPDF_robustMatch(), confidenceIntervals(), mrpt::maps::CGasConcentrationGridMap2D::internal_insertObservation(), mrpt::slam::PF_implementation< mrpt::poses::CPose3D, CMonteCarloLocalization3D >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), 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 89 of file ops_matrices.h.

References ASSERTMSG_, and 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 288 of file ops_containers.h.

References ASSERTMSG_, and 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 244 of file ops_containers.h.

References 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 112 of file ops_containers.h.

Referenced by mrpt::slam::CGridMapAligner::AlignPDF_robustMatch(), mrpt::slam::PF_implementation< mrpt::poses::CPose3D, CMonteCarloLocalization3D >::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 121 of file ops_containers.h.

References ASSERT_, and mrpt::mrpt::utils::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 188 of file ops_containers.h.

References ASSERT_, mrpt::mrpt::utils::keep_max(), and mrpt::mrpt::utils::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 202 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 150 of file ops_matrices.h.

References ASSERT_EQUAL_, MRPT_END, MRPT_START, and size().

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 47 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 62 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::CPosePDFGaussianInf::mahalanobisDistanceTo(), mrpt::poses::CPosePDFGaussian::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 69 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 169 of file ops_matrices.h.

References ASSERT_EQUAL_, MRPT_END, MRPT_START, and size().

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 350 of file ops_containers.h.

References ASSERT_, ASSERTMSG_, and square().

◆ norm()

template<class CONTAINER >

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

inline

Definition at line 110 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(), TEST(), and mrpt::pbmap::PbMapMaker::watchProperties().

◆ norm_inf()

template<class CONTAINER >

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

inline

Definition at line 109 of file ops_containers.h.

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

◆ operator>>() [1/5]

::mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		CPolygonPtr &	pObj
	)

◆ operator>>() [2/5]

::mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		CMatrixBPtr &	pObj
	)

◆ operator>>() [3/5]

::mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		CSplineInterpolator1DPtr &	pObj
	)

◆ operator>>() [4/5]

BASE_IMPEXP ::mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		CMatrixDPtr &	pObj
	)

◆ operator>>() [5/5]

BASE_IMPEXP ::mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		CMatrixPtr &	pObj
	)

◆ ransac3Dplane_degenerate()

template<typename T >

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

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

Definition at line 92 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,
		vector_size_t &	out_inlierIndices
	)

Definition at line 59 of file ransac_applications.cpp.

References ASSERT_, mrpt::math::TPlane::coefs, and mrpt::math::TPlane::distance().

◆ ransac3Dplane_fit()

template<typename T >

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

Definition at line 29 of file ransac_applications.cpp.

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

◆ rdft()

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

Definition at line 574 of file math.cpp.

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

Referenced by rdft2d().

◆ rdft2d()

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

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 math.cpp.

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

Referenced by dft2_real(), and idft2_real().

◆ realft()

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

Definition at line 102 of file math.cpp.

References four1().

Referenced by fft_real().

◆ removeRepVertices()

template<class T >

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

inline

Definition at line 625 of file lightweight_geom_data.cpp.

References distance(), and geometryEpsilon.

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 609 of file lightweight_geom_data.cpp.

References distance(), and geometryEpsilon.

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 74 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 78 of file ops_containers.h.

◆ rftbsub()

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

Definition at line 611 of file math.cpp.

Referenced by rdft().

◆ rftfsub()

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

Definition at line 510 of file math.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 43 of file bits.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(), homogeneousMatrixInverse(), mrpt::math::TPolygon2D::isConvex(), KLD_Gaussians(), mahalanobisDistance2(), multiply_A_skew3(), multiply_skew3_A(), and normalPDFInf().

◆ square()

template<class T >

T mrpt::math::square ( const T x )

inline

Inline function for the square of a number.

Definition at line 52 of file bits.h.

◆ 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 142 of file ops_containers.h.

References 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 135 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 274 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 167 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::utils::TMatchingPairList::overallSquareError(), mrpt::utils::TMatchingPairList::overallSquareErrorAndPoints(), 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 170 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 174 of file ops_containers.h.

Detailed Description

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ 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()

◆ dctsub()

◆ dotProduct() [1/2]

◆ dotProduct() [2/2]

◆ dstsub()

◆ estimateJacobian()

◆ four1()