This base provides a set of functions for maths stuff. More...

Namespaces
namespace	detail
Classes
class	CArray
	A STL container (as wrapper) for arrays of constant size defined at compile time - Users will most likely prefer to use CArrayPOD and its derived classes instead. More...
class	CArray< T, 0 >
class	CArrayPOD
	A CArray for Plain Old Datatypes (POD), that is, int's, double's, etc or struct's with only PODs. More...
class	CArrayNumeric
	A CArrayPOD for numeric types, supporting several mathematical operations. More...
class	CArrayFloat
	A partial specialization of CArrayNumeric for float numbers. More...
class	CArrayDouble
	A partial specialization of CArrayNumeric for double numbers. More...
class	CArrayInt
	A partial specialization of CArrayNumeric for int numbers. More...
class	CArrayUInt
	A partial specialization of CArrayNumeric for unsigned int numbers. More...
struct	CMatrixTemplateSize
	Auxiliary class used in CMatrixTemplate:size(), CMatrixTemplate::resize(), CMatrixFixedNumeric::size(), CMatrixFixedNumeric::resize(), to mimic the behavior of STL-containers. More...
class	CAStarAlgorithm
	This class is intended to efficiently solve graph-search problems using heuristics to determine the best path. More...
class	CBinaryRelation
	This class models a binary relation through the elements of any given set. More...
class	CGraphPartitioner
	Algorithms for finding the min-normalized-cut of a weighted undirected graph. 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	CMatrixD
	This class is a "CSerializable" wrapper for "CMatrixTemplateNumeric<double>". More...
class	CMatrixFixedNumeric
	A numeric matrix of compile-time fixed size. 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
	This template class extends the class "CMatrixTemplate" with many common operations with numerical matrixes. More...
class	CMatrixTemplateObjects
	This template class extends the class "CMatrixTemplate" for storing "objects" at each matrix entry. More...
class	CMatrixView
	The base for all matrix views. More...
class	CMatrixViewTranspose
	A wrapper around an existing matrix (of any kind) that allows operating on the transposed matrix. More...
class	CConstMatrixViewTranspose
	A wrapper around an existing const matrix (of any kind) that allows operating on the transposed matrix. More...
class	CSubmatrixView
	A wrapper around an existing matrix (of any kind) that allows operating on a subrange of the elements. More...
class	CArbitrarySubmatrixView
	A wrapper around an existing matrix (of any kind) that allows operating on a subrange of the elements. More...
class	CConstArbitrarySubmatrixView
class	CDiagonalMatrixView
	View the diagonal of an existing NxN matrix as a 1xN matrix (or equivalently for many MRPT methods, an N-vector). 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	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	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	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	CVectorRowWrapper
class	CConstVectorRowWrapper
class	CVectorColumnWrapper
class	CConstVectorColumnWrapper
class	JointHorizontalAccessor
	Access to two matrices joint horizontally [A\|B]. More...
class	JointVerticalAccessor
	Access to two matrices joint vertically [A;B]. More...
class	JointAccessor
	For usage with JointVerticalAccessor and JointHorizontalAccessor. More...
class	IndirectAccessWrapper
class	CMonteCarlo
class	CPolygon
	A wrapper of a TPolygon2D class, implementing CSerializable. More...
class	CQuaternion
	General functions for quaternion. 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	CVectorTemplate
	This template class provides the basic functionality for a general 1D any-size, resizable container of numerical or non-numerical elements. More...
class	CDijkstra
	The Dijkstra algorithm for finding the shortest path between a given source node in a (weighted) directed graph and all other nodes. More...
class	TPolygonWithPlane
	Slightly heavyweight type to speed-up calculations with polygons in 3D. More...
class	CDirectedGraph
	A directed graph with the argument of the template specifying the type of the annotations in the edges. More...
struct	TPoint2D
	Lightweight 2D point. More...
struct	TPose2D
	Lightweight 2D pose. More...
struct	TPoint3D
	Lightweight 3D point. More...
struct	TPose3D
	Lightweight 3D pose (three spatial coordinates, plus three angular coordinates). More...
struct	TSegment2D
	2D segment, consisting of two points. More...
struct	TSegment3D
	3D segment, consisting of two points. 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	TPlane
	3D Plane, represented by its equation More...
class	TPolygon2D
	2D polygon, inheriting from std::vector<TPoint2D>. More...
class	TPolygon3D
	3D polygon, inheriting from std::vector<TPoint3D> More...
struct	TObject2D
	Standard type for storing any lightweight 2D type. More...
struct	TObject3D
	Standard object for storing any 3D lightweight object. More...
class	RANSAC_Template
Typedefs
typedef CLevenbergMarquardtTempl < vector_double >	CLevenbergMarquardt
	The default name for the LM class is an instantiation for "double".
typedef CMatrixTemplateNumeric < float >	CMatrixFloat
	Declares a matrix of float numbers (non serializable).
typedef CMatrixTemplateNumeric < double >	CMatrixDouble
	Declares a matrix of double numbers (non serializable).
typedef CMatrixTemplateNumeric < unsigned int >	CMatrixUInt
	Declares a matrix of unsigned ints (non serializable).
typedef CMatrixTemplate< bool >	CMatrixBool
	Declares a matrix of booleans (non serializable).
typedef CMatrixTemplateNumeric < double >	CMatrixLongDouble
	Declares a matrix of "long doubles" (non serializable), or of "doubles" if the compiler does not support "long double".
typedef CQuaternion< double >	CQuaternionDouble
	A quaternion of data type "double".
typedef CQuaternion< float >	CQuaternionFloat
	A quaternion of data type "float".
typedef CVectorTemplate< float >	CVectorFloat
	Declares a vector of float elements.
typedef CVectorTemplate< double >	CVectorDouble
	Declares a vector of double elements.
typedef TPlane	TPlane3D
typedef RANSAC_Template< double >	RANSAC
	The default instance of RANSAC, for double type.
Typedefs for common sizes

typedef CMatrixFixedNumeric < double, 2, 2 >	CMatrixDouble22
typedef CMatrixFixedNumeric < double, 3, 3 >	CMatrixDouble33
typedef CMatrixFixedNumeric < double, 4, 4 >	CMatrixDouble44
typedef CMatrixFixedNumeric < double, 6, 6 >	CMatrixDouble66
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 < float, 2, 2 >	CMatrixFloat22
typedef CMatrixFixedNumeric < float, 3, 3 >	CMatrixFloat33
typedef CMatrixFixedNumeric < float, 4, 4 >	CMatrixFloat44
typedef CMatrixFixedNumeric < float, 6, 6 >	CMatrixFloat66
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
Enumerations
enum	TMatrixTextFileFormat { MATRIX_FORMAT_ENG = 0, MATRIX_FORMAT_FIXED = 1, MATRIX_FORMAT_INT = 2 }
Functions
bool MRPTDLLIMPEXP	isNaN (float f) MRPT_NO_THROWS
	Returns true if the number is NaN.
bool MRPTDLLIMPEXP	isNaN (double f) MRPT_NO_THROWS
	Returns true if the number is NaN.
bool MRPTDLLIMPEXP	isFinite (float f) MRPT_NO_THROWS
	Returns true if the number is non infinity.
bool MRPTDLLIMPEXP	isFinite (double f) MRPT_NO_THROWS
	Returns true if the number is non infinity.
template<class MATRIXLIKE >
size_t	size (const MATRIXLIKE &m, int dim)
template<class T , std::size_t N>
bool	operator== (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool	operator< (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool	operator!= (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool	operator> (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool	operator<= (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool	operator>= (const CArray< T, N > &x, const CArray< T, N > &y)
template<typename U >
U	myStaticCast (double val)
template<>
bool	myStaticCast (double val)
template<typename MAT >
CMatrixViewTranspose< MAT >	getTransposed (MAT &m)
template<typename MAT >
CConstMatrixViewTranspose< MAT >	getTransposed (const MAT &m)
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<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 VEC >
CVectorRowWrapper< VEC >	getAsRow (VEC &v)
template<typename VEC >
CConstVectorRowWrapper< VEC >	getAsRow (const VEC &v)
bool MRPTDLLIMPEXP	traceRay (const vector< TPolygonWithPlane > &vec, const mrpt::poses::CPose3D &pose, double &dist)
	Fast ray tracing method using polygons' properties.
bool	traceRay (const vector< TPolygon3D > &vec, const mrpt::poses::CPose3D &pose, double &dist)
	Fast ray tracing method using polygons' properties.
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.
template<class T >
void	crossProduct3D (const std::vector< T > &v0, const std::vector< T > &v1, std::vector< T > &v_out)
	Computes the cross product of two 3D vectors, returning a vector normal to both.
template<class T , class U >
bool	vectorsAreParallel2D (const T &v1, const U &v2)
	Returns true if two 2D vectors are parallel.
template<class T , class U >
bool	vectorsAreParallel3D (const T &v1, const U &v2)
	Returns true if two 3D vectors are parallel.
double MRPTDLLIMPEXP	minimumDistanceFromPointToSegment (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, and returns that minimum distance.
double MRPTDLLIMPEXP	minimumDistanceFromPointToSegment (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const double &y2, float &out_x, float &out_y)
	Computes the closest point from a given point to a segment, and returns that minimum distance.
void MRPTDLLIMPEXP	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.
void MRPTDLLIMPEXP	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.
double MRPTDLLIMPEXP	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.
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.
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.
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.
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.
bool MRPTDLLIMPEXP	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.
bool MRPTDLLIMPEXP	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.
bool MRPTDLLIMPEXP	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.
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.
double MRPTDLLIMPEXP	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.
bool MRPTDLLIMPEXP	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.
bool MRPTDLLIMPEXP	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 wether two rotated rectangles intersect.
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.
TPoint3D	operator- (const TPoint3D &p1)
	Unary minus operator for 3D points.
bool	operator== (const TPoint2D &p1, const TPoint2D &p2)
	Exact comparison between 2D points.
bool	operator!= (const TPoint2D &p1, const TPoint2D &p2)
	Exact comparison between 2D points.
bool	operator== (const TPoint3D &p1, const TPoint3D &p2)
	Exact comparison between 3D points.
bool	operator!= (const TPoint3D &p1, const TPoint3D &p2)
	Exact comparison between 3D points.
bool	operator== (const TPose2D &p1, const TPose2D &p2)
	Exact comparison between 2D poses, taking possible cycles into account.
bool	operator!= (const TPose2D &p1, const TPose2D &p2)
	Exact comparison between 2D poses, taking possible cycles into account.
bool	operator== (const TPose3D &p1, const TPose3D &p2)
	Exact comparison between 3D poses, taking possible cycles into account.
bool	operator!= (const TPose3D &p1, const TPose3D &p2)
	Exact comparison between 3D poses, taking possible cycles into account.
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)
MRPTDLLIMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint2D &o)
	TPoint2D binary input.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint2D &o)
	TPoint2D binary output.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint3D &o)
	TPoint3D binary input.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint3D &o)
	TPoint3D binary output.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPose2D &o)
	TPose2D binary input.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose2D &o)
	TPose2D binary output.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPose3D &o)
	TPose3D binary input.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose3D &o)
	TPose3D binary output.
mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment2D &s)
	TSegment2D binary input.
mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment2D &s)
	TSegment2D binary output.
mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TLine2D &l)
	TLine2D binary input.
mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine2D &l)
	TLine2D binary output.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TObject2D &o)
	TObject2D binary input.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject2D &o)
	TObject2D binary input.
mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment3D &s)
	TSegment3D binary input.
mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment3D &s)
	TSegment3D binary output.
mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TLine3D &l)
	TLine3D binary input.
mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine3D &l)
	TLine3D binary output.
mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TPlane &p)
	TPlane binary input.
mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TPlane &p)
	TPlane binary output.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator>> (mrpt::utils::CStream &in, mrpt::math::TObject3D &o)
	TObject3D binary input.
MRPTDLLIMPEXP mrpt::utils::CStream &	operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject3D &o)
	TObject3D binary output.
template<class CONTAINER >
size_t	countNonZero (const CONTAINER &a)
template<class CONTAINER >
CONTAINER::value_type	maximum (const CONTAINER &v, size_t *maxIndex=NULL)
template<class CONTAINER >
CONTAINER::value_type	minimum (const CONTAINER &v, size_t *minIndex=NULL)
template<class CONTAINER >
void	minimum_maximum (const CONTAINER &v, typename CONTAINER::mrpt_autotype::value_type &out_min, typename CONTAINER::mrpt_autotype::value_type &out_max, size_t minIndex=static_cast< size_t >(NULL), size_t maxIndex=static_cast< size_t >(NULL))
template<class CONTAINER >
CONTAINER::value_type	norm_inf (const CONTAINER &v, size_t *maxIndex=NULL)
template<class CONTAINER >
CONTAINER::value_type	squareNorm (const CONTAINER &v)
template<class CONTAINER >
CONTAINER::value_type	norm (const CONTAINER &v)
template<class CONTAINER >
double	mean (const CONTAINER &v)
template<class CONTAINER >
CONTAINER::value_type	sum (const CONTAINER &v)
template<class CONTAINER >
void	adjustRange (CONTAINER &m, const typename CONTAINER::value_type minVal, const typename CONTAINER::value_type maxVal)
template<class CONTAINER1 , class CONTAINER2 >
void	cumsum (const CONTAINER1 &in_data, CONTAINER2 &out_cumsum)
template<class CONTAINER1 , class CONTAINER2 >
size_t	countCommonElements (const CONTAINER1 &a, const CONTAINER2 &b)
template<class CONTAINER >
std::vector< double >	histogram (const CONTAINER &v, double limit_min, double limit_max, size_t number_bins, bool do_normalization=false)
template<class VECTORLIKE >
double	stddev (const VECTORLIKE &v, bool unbiased=true)
template<class VECTORLIKE >
void	meanAndStd (const VECTORLIKE &v, double &out_mean, double &out_std, bool unbiased=true)
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.
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.
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.
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.
template<class T , size_t NROWS, size_t NCOLS>
bool	operator== (const CMatrixFixedNumeric< T, NROWS, NCOLS > &M1, const CMatrixFixedNumeric< T, NROWS, NCOLS > &M2)
	Equal comparison (==).
template<class MATRIX >
	RET_TYPE_ASSERT_MRPTMATRIX (MATRIX, std::ostream)&operator<< (std
	Textual output stream function.
template<class MAT1 , class MAT2 >
MAT1::value_type	multiply_HCHt_scalar (const MAT1 &H, const MAT2 &C)
	Just like s=H.multiply_HCHt_scalar(C), but defined in mrpt::math for backward compatibility.
template<class T >
CMatrixTemplateNumeric< T >	operator/ (const CMatrixTemplateNumeric< T > &m1, const CMatrixTemplateNumeric< T > &m2)
	Binary matrix division operator A/B = A*inv(B).
template<class T >
CMatrixTemplateNumeric< T >	operator^ (const CMatrixTemplateNumeric< T > &m, const unsigned int pow)
	binary power operator
template<class MAT >
	MAT_TYPE_TRANSPOSE_OF (MAT) operator~(const MAT &m)
	unary transpose operator ~
template<class MATRIX >
	RET_MAT_ASSERT_MRPTMATRIX (MATRIX) operator!(const MATRIX &m)
	Unary inversion operator.
template<class MAT1 , class MAT2 >
	MAT_TYPE_PRODUCT_OF (MAT1, MAT2) operator*(const MAT1 &A
	Matrix multiplication operator: A * B -> RES The meaning of the lengthy macros in the declaration is: MAT_TYPE_PRODUCT_OF: Return type is the correct one for A*B, e.g.
class MAT_OUT void	meanAndCov (const MAT_IN &v, vector_double &out_mean, MAT_OUT &out_cov)
template<class MATRIX >
	MAT_TYPE_COVARIANCE_OF (MATRIX) 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.
bool MRPTDLLIMPEXP	loadVector (utils::CFileStream &f, std::vector< int > &d)
	Loads one row of a text file as a numerical std::vector.
bool MRPTDLLIMPEXP	loadVector (utils::CFileStream &f, std::vector< double > &d)
	Loads one row of a text file as a numerical std::vector.
template<typename T , typename K >
void	linspace (T first, T last, size_t count, std::vector< K > &out_vector)
	Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.
template<class T >
std::vector< T >	linspace (T first, T last, size_t count)
	Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.
template<class T , T STEP>
std::vector< T >	sequence (T first, size_t length)
	Generates a sequence of values [first,first+STEP,first+2*STEP,...].
template<class T >
std::vector< T >	ones (size_t count)
	Generates a vector of all ones of the given length.
template<class T >
std::vector< T >	zeros (size_t count)
	Generates a vector of all zeros of the given length.
template<class T >
void	normalize (const std::vector< T > &v, std::vector< T > &out_v)
	Normalize a vector, such as its norm is the unity.
template<class VECTOR_OF_VECTOR , class VECTORLIKE , class MATRIXLIKE >
void	meanAndCovVector (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.
template<class VECTOR_OF_VECTOR >
CMatrixDouble	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.
template<typename T , size_t N, typename U >
void	covariancesAndMean (const std::vector< T > &elements, CMatrixTemplateNumeric< U > &covariances, U(&means)[N])
	Computes covariances and mean of any vector of containers.
template<typename T , size_t N, typename U >
void	covariancesAndMean (const std::vector< T > &elements, CMatrixFixedNumeric< U, N, N > &covariances, U(&means)[N])
	Computes covariances and mean of any vector of containers.
template<typename T , size_t N, typename U >
void	covariancesAndMean (const std::vector< T > &elements, CMatrixFixedNumeric< U, N, N > &covariances, std::vector< U > &means)
	Computes covariances and mean of any vector of containers.
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.
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.
uint64_t MRPTDLLIMPEXP	factorial64 (unsigned int n)
	Computes the factorial of an integer number and returns it as a 64-bit integer number.
double MRPTDLLIMPEXP	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).
template<class T >
void	wrapTo2PiInPlace (T &a)
	Modifies the given angle to translate it into the [0,2pi[ range.
template<class T >
T	wrapTo2Pi (T a)
	Modifies the given angle to translate it into the [0,2pi[ range.
template<class T >
T	wrapToPi (T a)
	Modifies the given angle to translate it into the ]-pi,pi] range.
template<class T >
void	wrapToPiInPlace (T &a)
	Modifies the given angle to translate it into the ]-pi,pi] range.
template<class T >
T	round2up (T val)
	Round up to the nearest power of two of a given number.
template<class T >
T	round_10power (T val, int power10)
	Round a decimal number up to the given 10'th power (eg, to 1000,100,10, and also fractions) power10 means round up to: 1 -> 10, 2 -> 100, 3 -> 1000, ...
template<class T >
double	correlate_matrix (const CMatrixTemplateNumeric< T > &a1, const CMatrixTemplateNumeric< T > &a2)
	Calculate the correlation between two matrices (by AJOGD @ JAN-2007).
template<class T >
void MRPTDLLIMPEXP	qr_decomposition (CMatrixTemplateNumeric< T > &A, CMatrixTemplateNumeric< T > &R, CMatrixTemplateNumeric< T > &Q, CVectorTemplate< T > &c, int &sing)
	Matrix QR decomposition.
template<class T >
void MRPTDLLIMPEXP	UpdateCholesky (CMatrixTemplateNumeric< T > &chol, CVectorTemplate< T > &r1Modification)
	If R = CHOL(A) is the original Cholesky factorization of A, then R1 = CHOLUPDATE(R,X) returns the upper triangular Cholesky factor of A + X*X', where X is a column vector of appropriate length.
void MRPTDLLIMPEXP	computeEigenValues2x2 (const CMatrixFloat &in_matrix, float &min_eigenvalue, float &max_eigenvalue)
	Compute the two eigenvalues of a 2x2 matrix.
double MRPTDLLIMPEXP	averageLogLikelihood (const vector_double &logLikelihoods)
	A numerically-stable method to compute average likelihood values with strongly different ranges (unweighted likelihoods: compute the arithmetic mean).
double MRPTDLLIMPEXP	averageWrap2Pi (const vector_double &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.
double MRPTDLLIMPEXP	averageLogLikelihood (const vector_double &logWeights, const vector_double &logLikelihoods)
	A numerically-stable method to average likelihood values with strongly different ranges (weighted likelihoods).
std::string MRPTDLLIMPEXP	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).
template<class MATRIXLIKE1 , class MATRIXLIKE2 >
	RET_VOID_ASSERT_MRPTMATRICES (MATRIXLIKE1, MATRIXLIKE2) homogeneousMatrixInverse(const MATRIXLIKE1 &M
	Efficiently compute the inverse of a 4x4 homogeneous matrix by only transposing the rotation 3x3 part and solving the translation with dot products.
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)
template<typename T , typename At , size_t N>
std::vector< T > &	loadVector (std::vector< T > &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).
void	unwrap2PiSequence (vector_double &x)
	Modify a sequence of angle values such as no consecutive values have a jump larger than PI in absolute value.
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.
Array operators

template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric< T, N >	operator+ (const CArrayNumeric< T, N > &A, const VECTORLIKE &B)
	Operator ARRAY <- ARRAY + VECTORorARRAY.
template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric< T, N >	operator- (const CArrayNumeric< T, N > &A, const VECTORLIKE &B)
	Operator ARRAY <- ARRAY - VECTORorARRAY.
template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric< T, N >	operator* (const CArrayNumeric< T, N > &A, const VECTORLIKE &B)
	Dot product: ARRAY <- ARRAY .
template<typename T , size_t N>
std::ostream &	operator<< (std::ostream &ostrm, const CArray< T, N > &a)
	Textual output stream function.
Conversions from point & poses to matrices
Used from the "operator =" from poses/points to CMatrixFixedNumeric
template<typename T , size_t NROWS, size_t NCOLS>
CMatrixFixedNumeric< T, NROWS, NCOLS > &	matrixFromPoseOrPoint (CMatrixFixedNumeric< T, NROWS, NCOLS > &M, const CPoint2D &p)
template<typename T , size_t NROWS, size_t NCOLS>
CMatrixFixedNumeric< T, NROWS, NCOLS > &	matrixFromPoseOrPoint (CMatrixFixedNumeric< T, NROWS, NCOLS > &M, const CPoint3D &p)
template<typename T , size_t NROWS, size_t NCOLS>
CMatrixFixedNumeric< T, NROWS, NCOLS > &	matrixFromPoseOrPoint (CMatrixFixedNumeric< T, NROWS, NCOLS > &M, const CPose2D &p)
template<typename T , size_t NROWS, size_t NCOLS>
CMatrixFixedNumeric< T, NROWS, NCOLS > &	matrixFromPoseOrPoint (CMatrixFixedNumeric< T, NROWS, NCOLS > &M, const CPose3D &p)
template<>
CMatrixDouble21 &	matrixFromPoseOrPoint (CMatrixDouble21 &M, const CPoint2D &p)
template<>
CMatrixDouble31 &	matrixFromPoseOrPoint (CMatrixDouble31 &M, const CPoint3D &p)
template<>
CMatrixDouble31 &	matrixFromPoseOrPoint (CMatrixDouble31 &M, const CPose2D &p)
template<>
CMatrixDouble61 &	matrixFromPoseOrPoint (CMatrixDouble61 &M, const CPose3D &p)
Statistics functions

double MRPTDLLIMPEXP	normalPDF (double x, double mu, double std)
	Evaluates the univariate normal (Gaussian) distribution at a given point "x".
template<typename T >
T	normalPDF (const CMatrixTemplateNumeric< T > &x, const CMatrixTemplateNumeric< T > &mu, const CMatrixTemplateNumeric< T > &cov)
	Evaluates the multivariate normal (Gaussian) distribution at a given point "x" ("x" and "mu" can be 1xN or Nx1 matrixes).
template<typename T , size_t N>
T	normalPDF (const CMatrixFixedNumeric< T, N, 1 > &x, const CMatrixFixedNumeric< T, N, 1 > &mu, const CMatrixFixedNumeric< T, N, N > &cov)
	Evaluates the multivariate normal (Gaussian) distribution at a given point "x" ("x" and "mu" can be 1xN or Nx1 matrixes).
template<typename VECTORLIKE , typename MATRIXLIKE >
MATRIXLIKE::value_type	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.
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.
double MRPTDLLIMPEXP	erfc (double x)
	The complementary error function of a Normal distribution.
double MRPTDLLIMPEXP	erf (double x)
	The error function of a Normal distribution.
double MRPTDLLIMPEXP	normalQuantile (double p)
	Evaluates the Gaussian distribution quantile for the probability value p=[0,1].
double MRPTDLLIMPEXP	normalCDF (double p)
	Evaluates the Gaussian cumulative density function.
double MRPTDLLIMPEXP	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.
template<class T >
double	noncentralChi2CDF (unsigned int degreesOfFreedom, T noncentrality, T arg)
double	chi2CDF (unsigned int degreesOfFreedom, double arg)
double	chi2PDF (unsigned int degreesOfFreedom, double arg, double accuracy=1e-7)
template<typename CONTAINER >
void	condidenceIntervals (const CONTAINER &data, typename CONTAINER::value_type &out_mean, typename CONTAINER::value_type &out_lower_conf_interval, typename CONTAINER::value_type &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.
Fourier functions

void MRPTDLLIMPEXP	fft_real (vector_float &in_realData, vector_float &out_FFT_Re, vector_float &out_FFT_Im, vector_float &out_FFT_Mag)
	Computes the FFT of a 2^N-size vector of real numbers, and returns the Re+Im+Magnitude parts.
void MRPTDLLIMPEXP	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.
void MRPTDLLIMPEXP	idft2_real (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_data)
	Compute the 2D inverse Discrete Fourier Transform (DFT).
void MRPTDLLIMPEXP	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.
void MRPTDLLIMPEXP	idft2_complex (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_real, CMatrixFloat &out_imag)
	Compute the 2D inverse Discrete Fourier Transform (DFT).
void MRPTDLLIMPEXP	cross_correlation_FFT (const CMatrixFloat &A, const CMatrixFloat &B, CMatrixFloat &out_corr)
	Correlation of two matrixes using 2D FFT.
Simple intersection operations, relying basically on geometrical operations.

bool MRPTDLLIMPEXP	intersect (const TSegment3D &s1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between two 3D segments.
bool MRPTDLLIMPEXP	intersect (const TSegment3D &s1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D segment and a plane.
bool MRPTDLLIMPEXP	intersect (const TSegment3D &s1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between a 3D segment and a 3D line.
bool	intersect (const TPlane &p1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a plane and a 3D segment.
bool MRPTDLLIMPEXP	intersect (const TPlane &p1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between two planes.
bool MRPTDLLIMPEXP	intersect (const TPlane &p1, const TLine3D &p2, TObject3D &obj)
	Gets the intersection between a plane and a 3D line.
bool	intersect (const TLine3D &r1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a 3D line and a 3D segment.
bool	intersect (const TLine3D &r1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D line and a plane.
bool MRPTDLLIMPEXP	intersect (const TLine3D &r1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between two 3D lines.
bool MRPTDLLIMPEXP	intersect (const TLine2D &r1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between two 2D lines.
bool MRPTDLLIMPEXP	intersect (const TLine2D &r1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D segment.
bool	intersect (const TSegment2D &s1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D segment.
bool MRPTDLLIMPEXP	intersect (const TSegment2D &s1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between two 2D segments.
Angle retrieval methods. Methods which use TSegments will automatically use TLines' implicit constructors.

double MRPTDLLIMPEXP	getAngle (const TPlane &p1, const TPlane &p2)
	Computes the angle between two planes.
double MRPTDLLIMPEXP	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).
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).
double MRPTDLLIMPEXP	getAngle (const TLine3D &r1, const TLine3D &r2)
	Computes the angle between two 3D lines or segments (implicit constructor will be used if passing a segment instead of a line).
double MRPTDLLIMPEXP	getAngle (const TLine2D &r1, const TLine2D &r2)
	Computes the angle between two 2D lines or segments (implicit constructor will be used if passing a segment instead of a line).
Creation of lines from poses.

void MRPTDLLIMPEXP	createFromPoseX (const CPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the X axis in a given pose.
void MRPTDLLIMPEXP	createFromPoseY (const CPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Y axis in a given pose.
void MRPTDLLIMPEXP	createFromPoseZ (const CPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Z axis in a given pose.
void MRPTDLLIMPEXP	createFromPoseAndVector (const CPose3D &p, const double(&vector)[3], TLine3D &r)
	Gets a 3D line corresponding to any arbitrary vector, in the base given by the pose.
void MRPTDLLIMPEXP	createFromPoseX (const TPose2D &p, TLine2D &r)
	Gets a 2D line corresponding to the X axis in a given pose.
void MRPTDLLIMPEXP	createFromPoseY (const TPose2D &p, TLine2D &r)
	Gets a 2D line corresponding to the Y axis in a given pose.
void MRPTDLLIMPEXP	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.
Other line or plane related methods.

bool MRPTDLLIMPEXP	conformAPlane (const std::vector< TPoint3D > &points)
	Checks whether this polygon or set of points acceptably fits a plane.
bool MRPTDLLIMPEXP	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.
bool MRPTDLLIMPEXP	areAligned (const std::vector< TPoint2D > &points)
	Checks whether this set of points acceptably fits a 2D line.
bool MRPTDLLIMPEXP	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.
bool MRPTDLLIMPEXP	areAligned (const std::vector< TPoint3D > &points)
	Checks whether this set of points acceptably fits a 3D line.
bool MRPTDLLIMPEXP	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.
Projections

void	project3D (const TPoint3D &point, const CPose3D &newXYpose, TPoint3D &newPoint)
	Uses the given pose 3D to project a point into a new base.
void	project3D (const TSegment3D &segment, const CPose3D &newXYpose, TSegment3D &newSegment)
	Uses the given pose 3D to project a segment into a new base.
void MRPTDLLIMPEXP	project3D (const TLine3D &line, const CPose3D &newXYpose, TLine3D &newLine)
	Uses the given pose 3D to project a line into a new base.
void MRPTDLLIMPEXP	project3D (const TPlane &plane, const CPose3D &newXYpose, TPlane &newPlane)
	Uses the given pose 3D to project a plane into a new base.
void MRPTDLLIMPEXP	project3D (const TPolygon3D &polygon, const CPose3D &newXYpose, TPolygon3D &newPolygon)
	Uses the given pose 3D to project a polygon into a new base.
void MRPTDLLIMPEXP	project3D (const TObject3D &object, const CPose3D &newXYPose, TObject3D &newObject)
	Uses the given pose 3D to project any 3D object into a new base.
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.
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.
template<class T >
void	project3D (const std::vector< T > &objs, const CPose3D &newXYpose, std::vector< T > &newObjs)
	Projects a set of 3D objects into the plane's base.
void	project2D (const TPoint2D &point, const CPose2D &newXpose, TPoint2D &newPoint)
	Uses the given pose 2D to project a point into a new base.
void	project2D (const TSegment2D &segment, const CPose2D &newXpose, TSegment2D &newSegment)
	Uses the given pose 2D to project a segment into a new base.
void MRPTDLLIMPEXP	project2D (const TLine2D &line, const CPose2D &newXpose, TLine2D &newLine)
	Uses the given pose 2D to project a line into a new base.
void MRPTDLLIMPEXP	project2D (const TPolygon2D &polygon, const CPose2D &newXpose, TPolygon2D &newPolygon)
	Uses the given pose 2D to project a polygon into a new base.
void MRPTDLLIMPEXP	project2D (const TObject2D &object, const CPose2D &newXpose, TObject2D &newObject)
	Uses the given pose 2D to project any 2D object into a new base.
template<class T >
void	project2D (const T &obj, const TLine2D &newXLine, T &newObj)
	Projects any 2D object into the line's base, using its inverse pose.
template<class T >
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.
template<class T >
void	project2D (const std::vector< T > &objs, const CPose2D &newXpose, std::vector< T > &newObjs)
	Projects a set of 2D objects into the line's base.
Polygon intersections. These operations rely more on spatial reasoning than in raw numerical operations.

bool MRPTDLLIMPEXP	intersect (const TPolygon2D &p1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between a 2D polygon and a 2D segment.
bool MRPTDLLIMPEXP	intersect (const TPolygon2D &p1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between a 2D polygon and a 2D line.
bool MRPTDLLIMPEXP	intersect (const TPolygon2D &p1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between two 2D polygons.
bool	intersect (const TSegment2D &s1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between a 2D segment and a 2D polygon.
bool	intersect (const TLine2D &r1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D polygon.
bool MRPTDLLIMPEXP	intersect (const TPolygon3D &p1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a 3D segment.
bool MRPTDLLIMPEXP	intersect (const TPolygon3D &p1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a 3D line.
bool MRPTDLLIMPEXP	intersect (const TPolygon3D &p1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a plane.
bool MRPTDLLIMPEXP	intersect (const TPolygon3D &p1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between two 3D polygons.
bool	intersect (const TSegment3D &s1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a 3D segment and a 3D polygon.
bool	intersect (const TLine3D &r1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a 3D line and a 3D polygon.
bool	intersect (const TPlane &p1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a plane and a 3D polygon.
size_t MRPTDLLIMPEXP	intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, CSparseMatrixTemplate< TObject3D > &objs)
	Gets the intersection between two sets of 3D polygons.
size_t MRPTDLLIMPEXP	intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, std::vector< TObject3D > &objs)
	Gets the intersection between two sets of 3D polygons.
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.
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.
bool MRPTDLLIMPEXP	intersect (const TObject2D &o1, const TObject2D &o2, TObject2D &obj)
	Gets the intersection between any pair of 2D objects.
bool MRPTDLLIMPEXP	intersect (const TObject3D &o1, const TObject3D &o2, TObject3D &obj)
	Gets the intersection between any pair of 3D objects.
Distances

double MRPTDLLIMPEXP	distance (const TPoint2D &p1, const TPoint2D &p2)
	Gets the distance between two points in a 2D space.
double MRPTDLLIMPEXP	distance (const TPoint3D &p1, const TPoint3D &p2)
	Gets the distance between two points in a 3D space.
double MRPTDLLIMPEXP	distance (const TLine2D &r1, const TLine2D &r2)
	Gets the distance between two lines in a 2D space.
double MRPTDLLIMPEXP	distance (const TLine3D &r1, const TLine3D &r2)
	Gets the distance between two lines in a 3D space.
double MRPTDLLIMPEXP	distance (const TPlane &p1, const TPlane &p2)
	Gets the distance between two planes.
double MRPTDLLIMPEXP	distance (const TPolygon2D &p1, const TPolygon2D &p2)
	Gets the distance between two polygons in a 2D space.
double MRPTDLLIMPEXP	distance (const TPolygon2D &p1, const TSegment2D &s2)
	Gets the distance between a polygon and a segment in a 2D space.
double	distance (const TSegment2D &s1, const TPolygon2D &p2)
	Gets the distance between a segment and a polygon in a 2D space.
double MRPTDLLIMPEXP	distance (const TPolygon2D &p1, const TLine2D &l2)
	Gets the distance between a polygon and a line in a 2D space.
double	distance (const TLine2D &l1, const TPolygon2D &p2)
double MRPTDLLIMPEXP	distance (const TPolygon3D &p1, const TPolygon3D &p2)
	Gets the distance between two polygons in a 3D space.
double MRPTDLLIMPEXP	distance (const TPolygon3D &p1, const TSegment3D &s2)
	Gets the distance between a polygon and a segment in a 3D space.
double	distance (const TSegment3D &s1, const TPolygon3D &p2)
	Gets the distance between a segment and a polygon in a 3D space.
double MRPTDLLIMPEXP	distance (const TPolygon3D &p1, const TLine3D &l2)
	Gets the distance between a polygon and a line in a 3D space.
double	distance (const TLine3D &l1, const TPolygon3D &p2)
	Gets the distance between a line and a polygon in a 3D space.
double MRPTDLLIMPEXP	distance (const TPolygon3D &po, const TPlane &pl)
	Gets the distance between a polygon and a plane.
double	distance (const TPlane &pl, const TPolygon3D &po)
	Gets the distance between a plane and a polygon.
Bound checkers

void MRPTDLLIMPEXP	getRectangleBounds (const std::vector< TPoint2D > &poly, TPoint2D &pMin, TPoint2D &pMax)
	Gets the rectangular bounds of a 2D polygon or set of 2D points.
void MRPTDLLIMPEXP	getPrismBounds (const std::vector< TPoint3D > &poly, TPoint3D &pMin, TPoint3D &pMax)
	Gets the prism bounds of a 3D polygon or set of 3D points.
Creation of planes from poses

void MRPTDLLIMPEXP	createPlaneFromPoseXY (const CPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Z vector.
void MRPTDLLIMPEXP	createPlaneFromPoseXZ (const CPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Y vector.
void MRPTDLLIMPEXP	createPlaneFromPoseYZ (const CPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its X vector.
void MRPTDLLIMPEXP	createPlaneFromPoseAndNormal (const 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.
void MRPTDLLIMPEXP	generateAxisBaseFromDirectionAndAxis (const double(&vec)[3], char coord, CMatrixDouble &matrix)
	Creates a rotation matrix so that the coordinate given (0 for x, 1 for y, 2 for z) corresponds to the vector.
Linear regression methods

double MRPTDLLIMPEXP	getRegressionLine (const std::vector< TPoint2D > &points, TLine2D &line)
	Using eigenvalues, gets the best fitting line for a set of 2D points.
double MRPTDLLIMPEXP	getRegressionLine (const std::vector< TPoint3D > &points, TLine3D &line)
	Using eigenvalues, gets the best fitting line for a set of 3D points.
double MRPTDLLIMPEXP	getRegressionPlane (const std::vector< TPoint3D > &points, TPlane &plane)
	Using eigenvalues, gets the best fitting plane for a set of 3D points.
Miscellaneous methods

void MRPTDLLIMPEXP	assemblePolygons (const std::vector< TSegment3D > &segms, std::vector< TPolygon3D > &polys)
	Tries to assemble a set of segments into a set of closed polygons.
void MRPTDLLIMPEXP	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.
void MRPTDLLIMPEXP	assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys)
	Extracts all the polygons, including those formed from segments, from the set of objects.
void MRPTDLLIMPEXP	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.
void MRPTDLLIMPEXP	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.
void	setEpsilon (double nE)
	Changes the value of the geometric epsilon.
double	getEpsilon ()
	Gets the value of the geometric epsilon.
bool MRPTDLLIMPEXP	splitInConvexComponents (const TPolygon2D &poly, vector< TPolygon2D > &components)
	Splits a 2D polygon into convex components.
bool MRPTDLLIMPEXP	splitInConvexComponents (const TPolygon3D &poly, vector< TPolygon3D > &components)
	Splits a 3D polygon into convex components.
void MRPTDLLIMPEXP	getSegmentBisector (const TSegment2D &sgm, TLine2D &bis)
	Gets the bisector of a 2D segment.
void MRPTDLLIMPEXP	getSegmentBisector (const TSegment3D &sgm, TPlane &bis)
	Gets the bisector of a 3D segment.
void MRPTDLLIMPEXP	getAngleBisector (const TLine2D &l1, const TLine2D &l2, TLine2D &bis)
	Gets the bisector of two lines or segments (implicit constructor will be used if necessary).
void MRPTDLLIMPEXP	getAngleBisector (const TLine3D &l1, const TLine3D &l2, TLine3D &bis)
	Gets the bisector of two lines or segments (implicit constructor will be used if necessary).
RANSAC detectors

template<typename NUMTYPE >
void MRPTDLLIMPEXP	ransac_detect_3D_planes (const std::vector< NUMTYPE > &x, const std::vector< NUMTYPE > &y, const std::vector< NUMTYPE > &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.
void MRPTDLLIMPEXP	ransac_detect_3D_planes (const mrpt::slam::CPointsMap *points_map, 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.
template<typename NUMTYPE >
void MRPTDLLIMPEXP	ransac_detect_2D_lines (const std::vector< NUMTYPE > &x, const std::vector< NUMTYPE > &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.
Interpolation functions

template<class T >
T	interpolate (const T &x, const std::vector< T > &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".
double MRPTDLLIMPEXP	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).
double MRPTDLLIMPEXP	spline (const double t, const std::vector< double > &x, const std::vector< double > &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).
template<typename NUMTYPE , class VECTORLIKE >
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".
template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 >
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".
Probability density distributions (pdf) distance metrics

template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
VECTORLIKE1::value_type	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 $d^2 = (X-MU)^\top \Sigma^{-1} (X-MU)$ .
template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
VECTORLIKE1::value_type	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 $d = \sqrt{ (X-MU)^\top \Sigma^{-1} (X-MU) }$ .
template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
VECTORLIKE::value_type	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.
template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
VECTORLIKE::value_type	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.
template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::value_type	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.
template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::value_type	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.
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".
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".
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.
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.
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.
Variables
double	geometryEpsilon
	Global epsilon to overcome small precision errors.
struct MRPTDLLIMPEXP	TSegment3D
struct MRPTDLLIMPEXP	TLine3D
class MRPTDLLIMPEXP	TPolygon3D
struct MRPTDLLIMPEXP	TObject3D
const unsigned char	GEOMETRIC_TYPE_POINT = 0
	Object type identifier for TPoint2D or TPoint3D.
const unsigned char	GEOMETRIC_TYPE_SEGMENT = 1
	Object type identifier for TSegment2D or TSegment3D.
const unsigned char	GEOMETRIC_TYPE_LINE = 2
	Object type identifier for TLine2D or TLine3D.
const unsigned char	GEOMETRIC_TYPE_POLYGON = 3
	Object type identifier for TPolygon2D or TPolygon3D.
const unsigned char	GEOMETRIC_TYPE_PLANE = 4
	Object type identifier for TPlane.
const unsigned char	GEOMETRIC_TYPE_UNDEFINED = 255
	Object type identifier for empty TObject2D or TObject3D.
class MRPTDLLIMPEXP	CMatrixTemplateNumeric
class MRPTDLLIMPEXP	CMatrix
class MRPTDLLIMPEXP	CMatrixD

Detailed Description

This base provides a set of functions for maths stuff.

Typedef Documentation

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

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

Definition at line 234 of file CLevenbergMarquardt.h.

typedef CMatrixTemplate<bool> mrpt::math::CMatrixBool

Declares a matrix of booleans (non serializable).

See also:: CMatrixDouble, CMatrixFloat, CMatrixB

Definition at line 475 of file CMatrixTemplateNumeric.h.

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 465 of file CMatrixTemplateNumeric.h.

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

Definition at line 502 of file CMatrixFixedNumeric.h.

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

Definition at line 500 of file CMatrixFixedNumeric.h.

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

Definition at line 505 of file CMatrixFixedNumeric.h.

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

Definition at line 503 of file CMatrixFixedNumeric.h.

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

Definition at line 496 of file CMatrixFixedNumeric.h.

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

Definition at line 501 of file CMatrixFixedNumeric.h.

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

Definition at line 497 of file CMatrixFixedNumeric.h.

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

Definition at line 498 of file CMatrixFixedNumeric.h.

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

Definition at line 504 of file CMatrixFixedNumeric.h.

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

Definition at line 499 of file CMatrixFixedNumeric.h.

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 459 of file CMatrixTemplateNumeric.h.

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

Definition at line 513 of file CMatrixFixedNumeric.h.

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

Definition at line 511 of file CMatrixFixedNumeric.h.

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

Definition at line 516 of file CMatrixFixedNumeric.h.

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

Definition at line 514 of file CMatrixFixedNumeric.h.

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

Definition at line 507 of file CMatrixFixedNumeric.h.

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

Definition at line 512 of file CMatrixFixedNumeric.h.

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

Definition at line 508 of file CMatrixFixedNumeric.h.

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

Definition at line 509 of file CMatrixFixedNumeric.h.

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

Definition at line 515 of file CMatrixFixedNumeric.h.

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

Definition at line 510 of file CMatrixFixedNumeric.h.

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 486 of file CMatrixTemplateNumeric.h.

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

Declares a matrix of unsigned ints (non serializable).

See also:: CMatrixDouble, CMatrixFloat

Definition at line 470 of file CMatrixTemplateNumeric.h.

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

A quaternion of data type "double".

Definition at line 227 of file CQuaternion.h.

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

A quaternion of data type "float".

Definition at line 228 of file CQuaternion.h.

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

Declares a vector of double elements.

See also:: CVectorFloat

Definition at line 473 of file CVectorTemplate.h.

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

Declares a vector of float elements.

See also:: CVectorDouble

Definition at line 468 of file CVectorTemplate.h.

typedef RANSAC_Template<double> mrpt::math::RANSAC

The default instance of RANSAC, for double type.

Definition at line 90 of file ransac.h.

typedef TPlane mrpt::math::TPlane3D

Definition at line 936 of file lightweight_geom_data.h.

Enumeration Type Documentation

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 61 of file math_frwds.h.

Function Documentation

template<class CONTAINER >

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

bool MRPTDLLIMPEXP mrpt::math::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.

See also:: geometryEpsilon

bool MRPTDLLIMPEXP mrpt::math::areAligned ( const std::vector< TPoint3D > & points )

Checks whether this set of points acceptably fits a 3D line.

See also:: geometryEpsilon

bool MRPTDLLIMPEXP mrpt::math::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.

bool MRPTDLLIMPEXP mrpt::math::areAligned ( const std::vector< TPoint2D > & points )

Checks whether this set of points acceptably fits a 2D line.

See also:: geometryEpsilon

void MRPTDLLIMPEXP mrpt::math::assemblePolygons	(	const std::vector< TSegment3D > &	segms,
		std::vector< TPolygon3D > &	polys
	)

Tries to assemble a set of segments into a set of closed polygons.

void MRPTDLLIMPEXP mrpt::math::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.

void MRPTDLLIMPEXP mrpt::math::assemblePolygons	(	const std::vector< TObject3D > &	objs,
		std::vector< TPolygon3D > &	polys
	)

Extracts all the polygons, including those formed from segments, from the set of objects.

void MRPTDLLIMPEXP mrpt::math::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.

void MRPTDLLIMPEXP mrpt::math::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.

double MRPTDLLIMPEXP mrpt::math::averageLogLikelihood ( const vector_double & logLikelihoods )

A numerically-stable method to compute average likelihood values with strongly different ranges (unweighted likelihoods: compute the arithmetic mean).

This method implements this equation:

$return = - \log N + \log \sum_{i=1}^N e^{ll_i-ll_{max}} + ll_{max}$

See also the tutorial page.

double MRPTDLLIMPEXP mrpt::math::averageWrap2Pi ( const vector_double & 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.

double mrpt::math::chi2CDF	(	unsigned int	degreesOfFreedom,
		double	arg
	)			`[inline]`

Cumulative chi square distribution.

Computes the cumulative density of a chi square distribution with degreesOfFreedom and tolerance accuracy at the given argument arg, i.e. the probability that a random number drawn from the distribution is below arg by calling noncentralChi2CDF(degreesOfFreedom, 0.0, arg, accuracy).

Note:: Function code from the Vigra project (http://hci.iwr.uni-heidelberg.de/vigra/); code under "MIT X11 License", GNU GPL-compatible.

Definition at line 205 of file distributions.h.

References noncentralChi2CDF().

double MRPTDLLIMPEXP mrpt::math::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.

Referenced by mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), and mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfStandardProposal().

double mrpt::math::chi2PDF	(	unsigned int	degreesOfFreedom,
		double	arg,
		double	accuracy = `1e-7`
	)			`[inline]`

Chi square distribution.

Computes the density of a chi square distribution with degreesOfFreedom and tolerance accuracy at the given argument arg by calling noncentralChi2(degreesOfFreedom, 0.0, arg, accuracy).

Note:: Function code from the Vigra project (http://hci.iwr.uni-heidelberg.de/vigra/); code under "MIT X11 License", GNU GPL-compatible.

Definition at line 307 of file distributions.h.

References mrpt::math::detail::noncentralChi2CDF_exact().

void MRPTDLLIMPEXP mrpt::math::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.

See also:: closestFromPointToSegment

void MRPTDLLIMPEXP mrpt::math::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.

See also:: closestFromPointToLine

double MRPTDLLIMPEXP mrpt::math::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.

void MRPTDLLIMPEXP mrpt::math::computeEigenValues2x2	(	const CMatrixFloat &	in_matrix,
		float &	min_eigenvalue,
		float &	max_eigenvalue
	)

Compute the two eigenvalues of a 2x2 matrix.

Parameters:

	in_matrx	The 2x2 input matrix.
	min_eigenvalue	(out) The minimum eigenvalue of the matrix.
	max_eigenvalue	(out) The maximum eigenvalue of the matrix. by FAMD, MAR-2007

template<typename CONTAINER >

void mrpt::math::condidenceIntervals	(	const CONTAINER &	data,
		typename CONTAINER::value_type &	out_mean,
		typename CONTAINER::value_type &	out_lower_conf_interval,
		typename CONTAINER::value_type &	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.

The container can be any MRPT container (CArray, matrices, vectors).

Parameters:

confidenceInterval

A number in the range (0,1) such as the confidence interval will be [100*confidenceInterval, 100*(1-confidenceInterval)].

Definition at line 317 of file distributions.h.

References ASSERT_, cumsum(), distance(), histogram(), maximum(), mean(), minimum_maximum(), MRPT_END, and MRPT_START.

bool MRPTDLLIMPEXP mrpt::math::conformAPlane ( const std::vector< TPoint3D > & points )

Checks whether this polygon or set of points acceptably fits a plane.

See also:: TPolygon3D,geometryEpsilon

bool MRPTDLLIMPEXP mrpt::math::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.

See also:: TPolygon3D,geometryEpsilon

template<class T >

double mrpt::math::correlate_matrix	(	const CMatrixTemplateNumeric< T > &	a1,
		const CMatrixTemplateNumeric< T > &	a2
	)

Calculate the correlation between two matrices (by AJOGD @ JAN-2007).

Definition at line 482 of file math/utils.h.

References mrpt::math::CMatrixTemplate< T >::getColCount(), mrpt::math::CMatrixTemplate< T >::getRowCount(), and THROW_EXCEPTION.

template<class CONTAINER1 , class CONTAINER2 >

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

template<class CONTAINER >

size_t mrpt::math::countNonZero ( const CONTAINER & a )

template<typename T , size_t N, typename U >

void mrpt::math::covariancesAndMean	(	const std::vector< T > &	elements,
		CMatrixFixedNumeric< U, N, N > &	covariances,
		U(&)	means[N]
	)

Computes covariances and mean of any vector of containers.

T is some container of U which allows operator[]. N is the size of the containers, and thus the size of the resulting matrix and array. This method may adopt additional interfaces in the future.

Definition at line 251 of file math/utils.h.

References mrpt::math::CMatrixFixedNumeric< T, NROWS, NCOLS >::get_unsafe().

template<typename T , size_t N, typename U >

void mrpt::math::covariancesAndMean	(	const std::vector< T > &	elements,
		CMatrixFixedNumeric< U, N, N > &	covariances,
		std::vector< U > &	means
	)

Computes covariances and mean of any vector of containers.

T is some container of U which allows operator[]. N is the size of the containers, and thus the size of the resulting matrix and array. This method may adopt additional interfaces in the future.

Definition at line 272 of file math/utils.h.

References mrpt::math::CMatrixFixedNumeric< T, NROWS, NCOLS >::get_unsafe().

template<typename T , size_t N, typename U >

void mrpt::math::covariancesAndMean	(	const std::vector< T > &	elements,
		CMatrixTemplateNumeric< U > &	covariances,
		U(&)	means[N]
	)

Computes covariances and mean of any vector of containers.

T is some container of U which allows operator[]. N is the size of the containers, and thus the size of the resulting matrix and array. This method may adopt additional interfaces in the future.

Definition at line 229 of file math/utils.h.

References mrpt::math::CMatrixTemplate< T >::get_unsafe(), and mrpt::math::CMatrixTemplateNumeric< T >::resize().

template<class VECTOR_OF_VECTOR >

CMatrixDouble 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.

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

Definition at line 215 of file math/utils.h.

References meanAndCovVector().

void MRPTDLLIMPEXP mrpt::math::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.

An implicit constructor is used if a CPose2D is given.

See also:: createFromPoseY,createFromPoseAndVector

void MRPTDLLIMPEXP mrpt::math::createFromPoseAndVector	(	const CPose3D &	p,
		const double(&)	vector[3],
		TLine3D &	r
	)

Gets a 3D line corresponding to any arbitrary vector, in the base given by the pose.

An implicit constructor is used if a TPose3D is given.

See also:: createFromPoseX,createFromPoseY,createFromPoseZ

void MRPTDLLIMPEXP mrpt::math::createFromPoseX	(	const CPose3D &	p,
		TLine3D &	r
	)

Gets a 3D line corresponding to the X axis in a given pose.

An implicit constructor is used if a TPose3D is given.

See also:: createFromPoseY,createFromPoseZ,createFromPoseAndVector

void MRPTDLLIMPEXP mrpt::math::createFromPoseX	(	const TPose2D &	p,
		TLine2D &	r
	)

Gets a 2D line corresponding to the X axis in a given pose.

An implicit constructor is used if a CPose2D is given.

See also:: createFromPoseY,createFromPoseAndVector

void MRPTDLLIMPEXP mrpt::math::createFromPoseY	(	const CPose3D &	p,
		TLine3D &	r
	)

Gets a 3D line corresponding to the Y axis in a given pose.

An implicit constructor is used if a TPose3D is given.

See also:: createFromPoseX,createFromPoseZ,createFromPoseAndVector

void MRPTDLLIMPEXP mrpt::math::createFromPoseY	(	const TPose2D &	p,
		TLine2D &	r
	)

Gets a 2D line corresponding to the Y axis in a given pose.

An implicit constructor is used if a CPose2D is given.

See also:: createFromPoseX,createFromPoseAndVector

void MRPTDLLIMPEXP mrpt::math::createFromPoseZ	(	const CPose3D &	p,
		TLine3D &	r
	)

Gets a 3D line corresponding to the Z axis in a given pose.

An implicit constructor is used if a TPose3D is given.

See also:: createFromPoseX,createFromPoseY,createFromPoseAndVector

void MRPTDLLIMPEXP mrpt::math::createPlaneFromPoseAndNormal	(	const 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.

See also:: createPlaneFromPoseXY,createPlaneFromPoseXZ,createPlaneFromPoseYZ

void MRPTDLLIMPEXP mrpt::math::createPlaneFromPoseXY	(	const CPose3D &	pose,
		TPlane &	plane
	)

Given a pose, creates a plane orthogonal to its Z vector.

See also:: createPlaneFromPoseXZ,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal

void MRPTDLLIMPEXP mrpt::math::createPlaneFromPoseXZ	(	const CPose3D &	pose,
		TPlane &	plane
	)

Given a pose, creates a plane orthogonal to its Y vector.

See also:: createPlaneFromPoseXY,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal

void MRPTDLLIMPEXP mrpt::math::createPlaneFromPoseYZ	(	const CPose3D &	pose,
		TPlane &	plane
	)

Given a pose, creates a plane orthogonal to its X vector.

See also:: createPlaneFromPoseXY,createPlaneFromPoseXZ,createPlaneFromPoseAndNormal

void MRPTDLLIMPEXP mrpt::math::cross_correlation_FFT	(	const CMatrixFloat &	A,
		const CMatrixFloat &	B,
		CMatrixFloat &	out_corr
	)

Correlation of two matrixes using 2D FFT.

template<class T , class U , class V >

void mrpt::math::crossProduct3D	(	const T &	v0,
		const U &	v1,
		V &	vOut
	)			`[inline]`

Computes the cross product of two 3D vectors, returning a vector normal to both.

It uses the simple implementation:

$v_out = \left( \begin{array}{c c c} \hat{i} ~ \hat{j} ~ \hat{k} \\ x0 ~ y0 ~ z0 \\ x1 ~ y1 ~ z1 \\ \end{array} \right)$

Definition at line 768 of file geometry.h.

Referenced by generateAxisBaseFromDirection().

template<class T >

void mrpt::math::crossProduct3D	(	const std::vector< T > &	v0,
		const std::vector< T > &	v1,
		std::vector< T > &	v_out
	)			`[inline]`

Computes the cross product of two 3D vectors, returning a vector normal to both.

It uses the simple implementation:

$v_out = \left( \begin{array}{c c c} \hat{i} ~ \hat{j} ~ \hat{k} \\ x0 ~ y0 ~ z0 \\ x1 ~ y1 ~ z1 \\ \end{array} \right)$

Definition at line 786 of file geometry.h.

References ASSERT_.

template<class CONTAINER1 , class CONTAINER2 >

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

Referenced by condidenceIntervals().

void MRPTDLLIMPEXP mrpt::math::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.

Parameters:

	in_real	The N_1xN_2 matrix with the real part.
	in_imag	The N_1xN_2 matrix with the imaginary part.
	out_real	The N_1xN_2 output matrix which will store the real values (user has not to initialize the size of this matrix).
	out_imag	The N_1xN_2 output matrix which will store the imaginary values (user has not to initialize the size of this matrix). If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.

See also:: fft_real, idft2_complex,dft2_real

void MRPTDLLIMPEXP mrpt::math::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.

Parameters:

	in_data	The N_1xN_2 matrix.
	out_real	The N_1xN_2 output matrix which will store the real values (user has not to initialize the size of this matrix).
	out_imag	The N_1xN_2 output matrix which will store the imaginary values (user has not to initialize the size of this matrix).

See also:: fft_real, ifft2_read, fft2_complex If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPolygon2D &	p1,
		const TPolygon2D &	p2
	)

Gets the distance between two polygons in a 2D space.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPolygon2D &	p1,
		const TSegment2D &	s2
	)

Gets the distance between a polygon and a segment in a 2D space.

double mrpt::math::distance	(	const TSegment2D &	s1,
		const TPolygon2D &	p2
	)			`[inline]`

Gets the distance between a segment and a polygon in a 2D space.

Definition at line 560 of file geometry.h.

References distance().

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPolygon2D &	p1,
		const TLine2D &	l2
	)

Gets the distance between a polygon and a line in a 2D space.

double mrpt::math::distance	(	const TLine2D &	l1,
		const TPolygon2D &	p2
	)			`[inline]`

Definition at line 567 of file geometry.h.

References distance().

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPolygon3D &	p1,
		const TPolygon3D &	p2
	)

Gets the distance between two polygons in a 3D space.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPolygon3D &	p1,
		const TSegment3D &	s2
	)

Gets the distance between a polygon and a segment in a 3D space.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPlane &	p1,
		const TPlane &	p2
	)

Gets the distance between two planes.

It will be zero if the planes are not parallel.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPolygon3D &	p1,
		const TLine3D &	l2
	)

Gets the distance between a polygon and a line in a 3D space.

double mrpt::math::distance	(	const TLine3D &	l1,
		const TPolygon3D &	p2
	)			`[inline]`

Gets the distance between a line and a polygon in a 3D space.

Definition at line 591 of file geometry.h.

References distance().

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPolygon3D &	po,
		const TPlane &	pl
	)

Gets the distance between a polygon and a plane.

double mrpt::math::distance	(	const TSegment3D &	s1,
		const TPolygon3D &	p2
	)			`[inline]`

Gets the distance between a segment and a polygon in a 3D space.

Definition at line 581 of file geometry.h.

References distance().

double mrpt::math::distance	(	const TPlane &	pl,
		const TPolygon3D &	po
	)			`[inline]`

Gets the distance between a plane and a polygon.

Definition at line 601 of file geometry.h.

References distance().

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPoint2D &	p1,
		const TPoint2D &	p2
	)

Gets the distance between two points in a 2D space.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TPoint3D &	p1,
		const TPoint3D &	p2
	)

Gets the distance between two points in a 3D space.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TLine2D &	r1,
		const TLine2D &	r2
	)

Gets the distance between two lines in a 2D space.

double MRPTDLLIMPEXP mrpt::math::distance	(	const TLine3D &	r1,
		const TLine3D &	r2
	)

Gets the distance between two lines in a 3D space.

template<typename T >

T mrpt::math::distanceBetweenPoints	(	const T	x1,
		const T	y1,
		const T	x2,
		const T	y2
	)

Returns the distance between 2 points in 2D.

Definition at line 880 of file geometry.h.

References mrpt::utils::square().

template<typename T >

T mrpt::math::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.

Definition at line 886 of file geometry.h.

References mrpt::utils::square().

double MRPTDLLIMPEXP mrpt::math::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.

template<typename T >

T mrpt::math::distanceSqrBetweenPoints	(	const T	x1,
		const T	y1,
		const T	x2,
		const T	y2
	)

Returns the square distance between 2 points in 2D.

Definition at line 892 of file geometry.h.

References mrpt::utils::square().

template<typename T >

T mrpt::math::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.

Definition at line 898 of file geometry.h.

References mrpt::utils::square().

double MRPTDLLIMPEXP mrpt::math::erf ( double x )

The error function of a Normal distribution.

Referenced by noncentralChi2CDF(), and mrpt::math::detail::noncentralChi2CDF_exact().

double MRPTDLLIMPEXP mrpt::math::erfc ( double x )

The complementary error function of a Normal distribution.

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
	)

Definition at line 674 of file math/utils.h.

References ASSERT_, MRPT_END, and MRPT_START.

Referenced by mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), and mrpt::bayes::CKalmanFilterCapable< 6, 3, 3, 6 >::runOneKalmanIteration().

double MRPTDLLIMPEXP mrpt::math::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).

uint64_t MRPTDLLIMPEXP mrpt::math::factorial64 ( unsigned int n )

Computes the factorial of an integer number and returns it as a 64-bit integer number.

void MRPTDLLIMPEXP mrpt::math::fft_real	(	vector_float &	in_realData,
		vector_float &	out_FFT_Re,
		vector_float &	out_FFT_Im,
		vector_float &	out_FFT_Mag
	)

Computes the FFT of a 2^N-size vector of real numbers, and returns the Re+Im+Magnitude parts.

See also:: fft2_real

template<class T >

CMatrixTemplateNumeric<T> mrpt::math::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.

NOTE: Make sure of passing all floats or doubles and that the template of the receiving matrix is of the same type!

If $ d = [ dx ~ dy ~ dz ] $ is the input vector, then this function returns a matrix $ M $ such as:

$M = \left( \begin{array}{c c c} v^1_x ~ v^2_x ~ v^3_x \\ v^1_y ~ v^2_y ~ v^3_y \\ v^1_z ~ v^2_z ~ v^3_z \end{array} \right)$

And the three normal vectors are computed as:

$v^1 = \frac{d}{|d|}$

If (dx!=0 or dy!=0):

$v^2 = \frac{[-dy ~ dx ~ 0 ]}{\sqrt{dx^2+dy^2}}$

otherwise (the direction vector is vertical):

$v^2 = [1 ~ 0 ~ 0]$

And finally, the third vector is the cross product of the others:

$v^3 = v^1 \times v^2$

Returns:: The 3x3 matrix (CMatrixTemplateNumeric<T>), containing one vector per column. Throws an std::exception on invalid input (i.e. null direction vector)

(JLB @ 18-SEP-2007)

Definition at line 1022 of file geometry.h.

References crossProduct3D(), getColumnAccessor(), mrpt::utils::square(), and THROW_EXCEPTION.

void MRPTDLLIMPEXP mrpt::math::generateAxisBaseFromDirectionAndAxis	(	const double(&)	vec[3],
		char	coord,
		CMatrixDouble &	matrix
	)

Creates a rotation matrix so that the coordinate given (0 for x, 1 for y, 2 for z) corresponds to the vector.

double mrpt::math::getAngle	(	const TLine3D &	r1,
		const TPlane &	p2
	)			`[inline]`

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).

Definition at line 190 of file geometry.h.

References getAngle().

double MRPTDLLIMPEXP mrpt::math::getAngle	(	const TLine3D &	r1,
		const TLine3D &	r2
	)

Computes the angle between two 3D lines or segments (implicit constructor will be used if passing a segment instead of a line).

double MRPTDLLIMPEXP mrpt::math::getAngle	(	const TLine2D &	r1,
		const TLine2D &	r2
	)

Computes the angle between two 2D lines or segments (implicit constructor will be used if passing a segment instead of a line).

double MRPTDLLIMPEXP mrpt::math::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).

double MRPTDLLIMPEXP mrpt::math::getAngle	(	const TPlane &	p1,
		const TPlane &	p2
	)

Computes the angle between two planes.

Referenced by getAngle().

void MRPTDLLIMPEXP mrpt::math::getAngleBisector	(	const TLine2D &	l1,
		const TLine2D &	l2,
		TLine2D &	bis
	)

Gets the bisector of two lines or segments (implicit constructor will be used if necessary).

void MRPTDLLIMPEXP mrpt::math::getAngleBisector	(	const TLine3D &	l1,
		const TLine3D &	l2,
		TLine3D &	bis
	)

Gets the bisector of two lines or segments (implicit constructor will be used if necessary).

Exceptions:

std::logic_error

if the lines do not fit in a single plane.

template<typename VEC >

CConstVectorColumnWrapper< VEC > mrpt::math::getAsRow ( VEC & v ) [inline]

Definition at line 1203 of file CMatrixViews.h.

template<typename VEC >

CConstVectorRowWrapper<VEC> mrpt::math::getAsRow ( const VEC & v ) [inline]

Definition at line 1121 of file CMatrixViews.h.

template<typename MAT >

CMatrixColumnAccessor<MAT> mrpt::math::getColumnAccessor	(	MAT &	m,
		size_t	colIdx
	)			`[inline]`

Definition at line 655 of file CMatrixViews.h.

Referenced by generateAxisBaseFromDirection().

template<typename MAT >

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

Definition at line 722 of file CMatrixViews.h.

template<typename MAT >

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

Definition at line 768 of file CMatrixViews.h.

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 818 of file CMatrixViews.h.

double mrpt::math::getEpsilon ( ) [inline]

Gets the value of the geometric epsilon.

See also:: geometryEpsilon,setEpsilon

Definition at line 707 of file geometry.h.

References geometryEpsilon.

void MRPTDLLIMPEXP mrpt::math::getPrismBounds	(	const std::vector< TPoint3D > &	poly,
		TPoint3D &	pMin,
		TPoint3D &	pMax
	)

Gets the prism bounds of a 3D polygon or set of 3D points.

void MRPTDLLIMPEXP mrpt::math::getRectangleBounds	(	const std::vector< TPoint2D > &	poly,
		TPoint2D &	pMin,
		TPoint2D &	pMax
	)

Gets the rectangular bounds of a 2D polygon or set of 2D points.

double MRPTDLLIMPEXP mrpt::math::getRegressionLine	(	const std::vector< TPoint2D > &	points,
		TLine2D &	line
	)

Using eigenvalues, gets the best fitting line for a set of 2D points.

Returns an estimation of the error.

See also:: spline, leastSquareLinearFit

double MRPTDLLIMPEXP mrpt::math::getRegressionLine	(	const std::vector< TPoint3D > &	points,
		TLine3D &	line
	)

Using eigenvalues, gets the best fitting line for a set of 3D points.

Returns an estimation of the error.

See also:: spline, leastSquareLinearFit

double MRPTDLLIMPEXP mrpt::math::getRegressionPlane	(	const std::vector< TPoint3D > &	points,
		TPlane &	plane
	)

Using eigenvalues, gets the best fitting plane for a set of 3D points.

Returns an estimation of the error.

See also:: spline, leastSquareLinearFit

template<typename MAT >

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

Definition at line 989 of file CMatrixViews.h.

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 1039 of file CMatrixViews.h.

template<typename MAT >

CMatrixRowAccessor<MAT> mrpt::math::getRowAccessor	(	MAT &	m,
		size_t	rowIdx
	)			`[inline]`

Definition at line 876 of file CMatrixViews.h.

template<typename MAT >

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

Definition at line 943 of file CMatrixViews.h.

void MRPTDLLIMPEXP mrpt::math::getSegmentBisector	(	const TSegment3D &	sgm,
		TPlane &	bis
	)

Gets the bisector of a 3D segment.

void MRPTDLLIMPEXP mrpt::math::getSegmentBisector	(	const TSegment2D &	sgm,
		TLine2D &	bis
	)

Gets the bisector of a 2D segment.

template<typename MAT >

CConstMatrixViewTranspose<MAT> mrpt::math::getTransposed ( const MAT & m )

Definition at line 156 of file CMatrixViews.h.

template<typename MAT >

CMatrixViewTranspose<MAT> mrpt::math::getTransposed ( MAT & m )

Definition at line 109 of file CMatrixViews.h.

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`
	)

Referenced by condidenceIntervals().

void MRPTDLLIMPEXP mrpt::math::idft2_complex	(	const CMatrixFloat &	in_real,
		const CMatrixFloat &	in_imag,
		CMatrixFloat &	out_real,
		CMatrixFloat &	out_imag
	)

Compute the 2D inverse Discrete Fourier Transform (DFT).

Parameters:

	in_real	The N_1xN_2 input matrix with real values, where both dimensions MUST BE powers of 2.
	in_imag	The N_1xN_2 input matrix with imaginary values, where both dimensions MUST BE powers of 2.
	out_real	The N_1xN_2 output matrix for real part (user has not to initialize the size of this matrix).
	out_imag	The N_1xN_2 output matrix for imaginary part (user has not to initialize the size of this matrix).

See also:: fft_real, dft2_real,dft2_complex If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.

void MRPTDLLIMPEXP mrpt::math::idft2_real	(	const CMatrixFloat &	in_real,
		const CMatrixFloat &	in_imag,
		CMatrixFloat &	out_data
	)

Compute the 2D inverse Discrete Fourier Transform (DFT).

Parameters:

	in_real	The N_1xN_2 input matrix with real values.
	in_imag	The N_1xN_2 input matrix with imaginary values.
	out_data	The N_1xN_2 output matrix (user has not to initialize the size of this matrix). Note that the real and imaginary parts of the FFT will NOT be checked to assure that they represent the transformation of purely real data. If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.

See also:: fft_real, fft2_real

template<class T >

T mrpt::math::interpolate	(	const T &	x,
		const std::vector< T > &	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".

If the point "x" is out of the range [x0,x1], the closest extreme "ys" value is returned.

See also:: spline, interpolate2points

Definition at line 728 of file math/utils.h.

References ASSERT_, MRPT_END, and MRPT_START.

double MRPTDLLIMPEXP mrpt::math::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).

If wrap2pi is true, output is wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also:: spline, interpolate, leastSquareLinearFit

bool mrpt::math::intersect	(	const TLine3D &	r1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)			`[inline]`

Gets the intersection between a 3D line and a 3D segment.

See also:: TObject3D

Definition at line 136 of file geometry.h.

References intersect().

bool mrpt::math::intersect	(	const TLine3D &	r1,
		const TPlane &	p2,
		TObject3D &	obj
	)			`[inline]`

Gets the intersection between a 3D line and a plane.

See also:: TObject3D

Definition at line 143 of file geometry.h.

References intersect().

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TLine3D &	r1,
		const TLine3D &	r2,
		TObject3D &	obj
	)

Gets the intersection between two 3D lines.

See also:: TObject3D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TLine2D &	r1,
		const TSegment2D &	s2,
		TObject2D &	obj
	)

Gets the intersection between a 2D line and a 2D segment.

See also:: TObject2D

bool mrpt::math::intersect	(	const TSegment2D &	s1,
		const TLine2D &	r2,
		TObject2D &	obj
	)			`[inline]`

Gets the intersection between a 2D line and a 2D segment.

See also:: TObject2D

Definition at line 165 of file geometry.h.

References intersect().

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TSegment2D &	s1,
		const TSegment2D &	s2,
		TObject2D &	obj
	)

Gets the intersection between two 2D segments.

See also:: TObject2D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TLine2D &	r1,
		const TLine2D &	r2,
		TObject2D &	obj
	)

Gets the intersection between two 2D lines.

See also:: TObject2D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPolygon2D &	p1,
		const TSegment2D &	s2,
		TObject2D &	obj
	)

Gets the intersection between a 2D polygon and a 2D segment.

See also:: TObject2D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPolygon2D &	p1,
		const TLine2D &	r2,
		TObject2D &	obj
	)

Gets the intersection between a 2D polygon and a 2D line.

See also:: TObject2D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPolygon2D &	p1,
		const TPolygon2D &	p2,
		TObject2D &	obj
	)

Gets the intersection between two 2D polygons.

See also:: TObject2D

bool mrpt::math::intersect	(	const TSegment2D &	s1,
		const TPolygon2D &	p2,
		TObject2D &	obj
	)			`[inline]`

Gets the intersection between a 2D segment and a 2D polygon.

See also:: TObject2D

Definition at line 419 of file geometry.h.

References intersect().

bool mrpt::math::intersect	(	const TLine2D &	r1,
		const TPolygon2D &	p2,
		TObject2D &	obj
	)			`[inline]`

Gets the intersection between a 2D line and a 2D polygon.

See also:: TObject2D

Definition at line 426 of file geometry.h.

References intersect().

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)

Gets the intersection between a 3D polygon and a 3D segment.

See also:: TObject3D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TLine3D &	r2,
		TObject3D &	obj
	)

Gets the intersection between a 3D polygon and a 3D line.

See also:: TObject3D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TPlane &	p2,
		TObject3D &	obj
	)

Gets the intersection between a 3D polygon and a plane.

See also:: TObject3D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)

Gets the intersection between two 3D polygons.

See also:: TObject3D

bool mrpt::math::intersect	(	const TSegment3D &	s1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)			`[inline]`

Gets the intersection between a 3D segment and a 3D polygon.

See also:: TObject3D

Definition at line 453 of file geometry.h.

References intersect().

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TSegment3D &	s1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)

Gets the intersection between two 3D segments.

See also:: TObject3D

Referenced by mrpt::opengl::CPolyhedron::getIntersection(), and intersect().

bool mrpt::math::intersect	(	const TLine3D &	r1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)			`[inline]`

Gets the intersection between a 3D line and a 3D polygon.

See also:: TObject3D

Definition at line 460 of file geometry.h.

References intersect().

bool mrpt::math::intersect	(	const TPlane &	p1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)			`[inline]`

Gets the intersection between a plane and a 3D polygon.

See also:: TObject3D

Definition at line 467 of file geometry.h.

References intersect().

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TSegment3D &	s1,
		const TPlane &	p2,
		TObject3D &	obj
	)

Gets the intersection between a 3D segment and a plane.

See also:: TObject3D

size_t MRPTDLLIMPEXP mrpt::math::intersect	(	const std::vector< TPolygon3D > &	v1,
		const std::vector< TPolygon3D > &	v2,
		CSparseMatrixTemplate< TObject3D > &	objs
	)

Gets the intersection between two sets of 3D polygons.

The intersection is returned as an sparse matrix with each pair of polygons' intersections, and the return value is the amount of intersections found.

See also:: TObject3D,CSparseMatrixTemplate

size_t MRPTDLLIMPEXP mrpt::math::intersect	(	const std::vector< TPolygon3D > &	v1,
		const std::vector< TPolygon3D > &	v2,
		std::vector< TObject3D > &	objs
	)

Gets the intersection between two sets of 3D polygons.

The intersection is returned as a vector with every intersection found, and the return value is the amount of intersections found.

See also:: TObject3D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TSegment3D &	s1,
		const TLine3D &	r2,
		TObject3D &	obj
	)

Gets the intersection between a 3D segment and a 3D line.

See also:: TObject3D

template<class T , class U , class O >

size_t mrpt::math::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.

See also:: TObject2D,TObject3D,CSparseMatrix

Definition at line 491 of file geometry.h.

References mrpt::math::CSparseMatrixTemplate< T >::clear(), mrpt::math::CSparseMatrixTemplate< T >::getNonNullElements(), intersect(), and mrpt::math::CSparseMatrixTemplate< T >::resize().

template<class T , class U , class O >

size_t mrpt::math::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.

See also:: TObject2D,TObject3D

Definition at line 504 of file geometry.h.

References intersect().

bool mrpt::math::intersect	(	const TPlane &	p1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)			`[inline]`

Gets the intersection between a plane and a 3D segment.

See also:: TObject3D

Definition at line 119 of file geometry.h.

References intersect().

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TObject2D &	o1,
		const TObject2D &	o2,
		TObject2D &	obj
	)

Gets the intersection between any pair of 2D objects.

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TObject3D &	o1,
		const TObject3D &	o2,
		TObject3D &	obj
	)

Gets the intersection between any pair of 3D objects.

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPlane &	p1,
		const TPlane &	p2,
		TObject3D &	obj
	)

Gets the intersection between two planes.

See also:: TObject3D

bool MRPTDLLIMPEXP mrpt::math::intersect	(	const TPlane &	p1,
		const TLine3D &	p2,
		TObject3D &	obj
	)

Gets the intersection between a plane and a 3D line.

See also:: TObject3D

bool MRPTDLLIMPEXP mrpt::math::isFinite ( double f )

Returns true if the number is non infinity.

bool MRPTDLLIMPEXP mrpt::math::isFinite ( float f )

Returns true if the number is non infinity.

bool MRPTDLLIMPEXP mrpt::math::isNaN ( double f )

Returns true if the number is NaN.

bool MRPTDLLIMPEXP mrpt::math::isNaN ( float f )

Returns true if the number is NaN.

template<typename VECTORLIKE1 , typename MATRIXLIKE1 , typename VECTORLIKE2 , typename MATRIXLIKE2 >

double mrpt::math::KLD_Gaussians	(	const VECTORLIKE1 &	mu0,
		const MATRIXLIKE1 &	cov0,
		const VECTORLIKE2 &	mu1,
		const MATRIXLIKE2 &	cov1
	)

Kullback-Leibler divergence (KLD) between two independent multivariate Gaussians.

$D_\mathrm{KL}(\mathcal{N}_0 \| \mathcal{N}_1) = { 1 \over 2 } ( \log_e ( { \det \Sigma_1 \over \det \Sigma_0 } ) + \mathrm{tr} ( \Sigma_1^{-1} \Sigma_0 ) + ( \mu_1 - \mu_0 )^\top \Sigma_1^{-1} ( \mu_1 - \mu_0 ) - N )$

Definition at line 128 of file distributions.h.

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

template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 >

void mrpt::math::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".

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).

See also:: spline, getRegressionLine, getRegressionPlane

Definition at line 816 of file math/utils.h.

References ASSERT_, mrpt::math::CMatrixTemplateNumeric< T >::inv_fast(), minimum(), MRPT_END, MRPT_START, mrpt::math::CMatrixTemplateNumeric< T >::multiply(), mrpt::math::CMatrixTemplateNumeric< T >::multiply_AAt(), mrpt::math::CMatrixTemplateNumeric< T >::multiply_Ab(), mrpt::math::CMatrixTemplate< T >::set_unsafe(), and wrapToPi().

template<typename NUMTYPE , class VECTORLIKE >

NUMTYPE mrpt::math::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".

The vectors x and y must have size >=2, and all values of "x" must be different. 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).

See also:: spline; getRegressionLine, getRegressionPlane

Definition at line 766 of file math/utils.h.

References ASSERT_, mrpt::math::CMatrixTemplateNumeric< T >::inv_fast(), minimum(), MRPT_END, MRPT_START, mrpt::math::CMatrixTemplateNumeric< T >::multiply(), mrpt::math::CMatrixTemplateNumeric< T >::multiply_AAt(), mrpt::math::CMatrixTemplateNumeric< T >::multiply_Ab(), mrpt::math::CMatrixTemplate< T >::set_unsafe(), and wrapToPi().

template<typename T , typename K >

void mrpt::math::linspace	(	T	first,
		T	last,
		size_t	count,
		std::vector< K > &	out_vector
	)

Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.

See also:: sequence

Definition at line 90 of file math/utils.h.

Referenced by linspace().

template<class T >

std::vector<T> mrpt::math::linspace	(	T	first,
		T	last,
		size_t	count
	)			`[inline]`

Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.

See also:: sequence

Definition at line 110 of file math/utils.h.

References linspace().

bool MRPTDLLIMPEXP mrpt::math::loadVector	(	utils::CFileStream &	f,
		std::vector< double > &	d
	)

Loads one row of a text file as a numerical std::vector.

Returns:: false on EOF or invalid format. The body of the function is implemented in MATH.cpp

template<typename T , typename At , size_t N>

std::vector<T>& mrpt::math::loadVector	(	std::vector< T > &	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).

         vector_double  v;
  const double numbers[] = { 1,2,3,5,6,7,8,9,10 };
  loadVector( v, numbers );

Note:: This operator performs the appropiate type castings, if required.

Definition at line 878 of file math/utils.h.

References MRPT_COMPILE_TIME_ASSERT.

bool MRPTDLLIMPEXP mrpt::math::loadVector	(	utils::CFileStream &	f,
		std::vector< int > &	d
	)

Loads one row of a text file as a numerical std::vector.

Returns:: false on EOF or invalid format. The body of the function is implemented in MATH.cpp

template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >

VECTORLIKE1::value_type mrpt::math::mahalanobisDistance	(	const VECTORLIKE1 &	X,
		const VECTORLIKE2 &	MU,
		const MAT &	COV
	)			`[inline]`

Computes the mahalanobis distance of a vector X given the mean MU and the covariance *inverse* COV_inv

$d = \sqrt{ (X-MU)^\top \Sigma^{-1} (X-MU) }$

.

Definition at line 923 of file math/utils.h.

References mahalanobisDistance2().

Referenced by mahalanobisDistance().

template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >

VECTORLIKE::value_type mrpt::math::mahalanobisDistance	(	const VECTORLIKE &	mean_diffs,
		const MAT1 &	COV1,
		const MAT2 &	COV2,
		const MAT3 &	CROSS_COV12
	)			`[inline]`

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.

$d = \sqrt{ \Delta_\mu^\top (\Sigma_1 + \Sigma_2 - 2 \Sigma_12 )^{-1} \Delta_\mu }$

Definition at line 964 of file math/utils.h.

References mahalanobisDistance().

template<class VECTORLIKE , class MATRIXLIKE >

MATRIXLIKE::value_type mrpt::math::mahalanobisDistance	(	const VECTORLIKE &	delta_mu,
		const MATRIXLIKE &	cov
	)			`[inline]`

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.

$d^2 = \sqrt( \Delta_\mu^\top \Sigma^{-1} \Delta_\mu )$

Definition at line 992 of file math/utils.h.

References mahalanobisDistance2().

template<class VECTORLIKE , class MATRIXLIKE >

MATRIXLIKE::value_type mrpt::math::mahalanobisDistance2	(	const VECTORLIKE &	delta_mu,
		const MATRIXLIKE &	cov
	)			`[inline]`

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.

$d^2 = \Delta_\mu^\top \Sigma^{-1} \Delta_\mu$

Definition at line 978 of file math/utils.h.

References ASSERTDEB_, and multiply_HCHt_scalar().

template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >

VECTORLIKE1::value_type mrpt::math::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

$d^2 = (X-MU)^\top \Sigma^{-1} (X-MU)$

.

Definition at line 900 of file math/utils.h.

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

Referenced by mahalanobisDistance().

template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >

VECTORLIKE::value_type mrpt::math::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.

$d^2 = \Delta_\mu^\top (\Sigma_1 + \Sigma_2 - 2 \Sigma_12 )^{-1} \Delta_\mu$

Definition at line 937 of file math/utils.h.

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

template<typename T , class VECLIKE , class MATRIXLIKE >

void mrpt::math::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.

See also:: productIntegralTwoGaussians, mahalanobisDistance2, normalPDF, mahalanobisDistance2AndPDF

Definition at line 1073 of file math/utils.h.

References ASSERTDEB_, M_2PI, MRPT_END, MRPT_START, and multiply_HCHt_scalar().

Referenced by mahalanobisDistance2AndPDF().

template<typename T , class VECLIKE , class MATRIXLIKE >

void mrpt::math::mahalanobisDistance2AndPDF	(	const VECLIKE &	diff_mean,
		const MATRIXLIKE &	cov,
		T &	maha2_out,
		T &	pdf_out
	)			`[inline]`

Computes both, the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian.

See also:: productIntegralTwoGaussians, mahalanobisDistance2, normalPDF

Definition at line 1097 of file math/utils.h.

References mahalanobisDistance2AndLogPDF().

template<size_t N, typename T >

std::vector<T> mrpt::math::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.

Some examples:

    vector_double  = make_vector<4,double>(1.0,3.0,4.0,5.0);
    vector_float   = make_vector<2,float>(-8.12, 3e4);

Definition at line 1119 of file math/utils.h.

References MRPT_COMPILE_TIME_ASSERT.

template<class MATRIX >

mrpt::math::MAT_TYPE_COVARIANCE_OF ( MATRIX ) const [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 1105 of file ops_matrices.h.

References meanAndCov().

template<class MAT1 , class MAT2 >

mrpt::math::MAT_TYPE_PRODUCT_OF	(	MAT1	,
		MAT2
	)			const `[inline]`

Matrix multiplication operator: A * B -> RES The meaning of the lengthy macros in the declaration is:

MAT_TYPE_PRODUCT_OF: Return type is the correct one for A*B, e.g.

NxM * MxK -> NxK, DYN*DYN -> DYN.

RET_MAT_ASSERT_MRPTMATRIX: Assure that the compiler will use this "operator*" only with MRPT matrices.

Referenced by mrpt::math::detail::multiply_HCHt().

template<class MAT >

mrpt::math::MAT_TYPE_TRANSPOSE_OF ( MAT ) const [inline]

unary transpose operator ~

Definition at line 1010 of file ops_matrices.h.

std::string MRPTDLLIMPEXP mrpt::math::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).

Generates a string with the MATLAB commands required to plot an confidence interval (ellipse) for a 2D Gaussian ('double' version).

Parameters:

	cov22	The 2x2 covariance matrix
	mean	The 2-length vector with the mean
	stdCount	How many "quantiles" to get into the area of the ellipse: 2: 95%, 3:99.97%,...
	style	A matlab style string, for colors, line styles,...
	nEllipsePoints	The number of points in the ellipse to generate
	cov22	The 2x2 covariance matrix
	mean	The 2-length vector with the mean
	stdCount	How many "quantiles" to get into the area of the ellipse: 2: 95%, 3:99.97%,...
	style	A matlab style string, for colors, line styles,...
	nEllipsePoints	The number of points in the ellipse to generate

template<typename T , size_t NROWS, size_t NCOLS>

CMatrixFixedNumeric<T,NROWS,NCOLS>& mrpt::math::matrixFromPoseOrPoint	(	CMatrixFixedNumeric< T, NROWS, NCOLS > &	M,
		const CPoint3D &	p
	)

Definition at line 525 of file CMatrixFixedNumeric.h.

References THROW_EXCEPTION.

template<typename T , size_t NROWS, size_t NCOLS>

CMatrixFixedNumeric<T,NROWS,NCOLS>& mrpt::math::matrixFromPoseOrPoint	(	CMatrixFixedNumeric< T, NROWS, NCOLS > &	M,
		const CPose2D &	p
	)

Definition at line 526 of file CMatrixFixedNumeric.h.

References THROW_EXCEPTION.

template<typename T , size_t NROWS, size_t NCOLS>

CMatrixFixedNumeric<T,NROWS,NCOLS>& mrpt::math::matrixFromPoseOrPoint	(	CMatrixFixedNumeric< T, NROWS, NCOLS > &	M,
		const CPose3D &	p
	)

Definition at line 527 of file CMatrixFixedNumeric.h.

References THROW_EXCEPTION.

template<typename T , size_t NROWS, size_t NCOLS>

CMatrixFixedNumeric<T,NROWS,NCOLS>& mrpt::math::matrixFromPoseOrPoint	(	CMatrixFixedNumeric< T, NROWS, NCOLS > &	M,
		const CPoint2D &	p
	)

Definition at line 524 of file CMatrixFixedNumeric.h.

References THROW_EXCEPTION.

Referenced by mrpt::math::CMatrixFixedNumeric< float, 4, 4 >::CMatrixFixedNumeric(), and mrpt::math::CMatrixFixedNumeric< float, 4, 4 >::operator=().

template<>

CMatrixDouble12 & mrpt::math::matrixFromPoseOrPoint	(	CMatrixDouble21 &	M,
		const CPoint2D &	p
	)

template<>

CMatrixDouble13 & mrpt::math::matrixFromPoseOrPoint	(	CMatrixDouble31 &	M,
		const CPoint3D &	p
	)

template<>

CMatrixDouble13 & mrpt::math::matrixFromPoseOrPoint	(	CMatrixDouble31 &	M,
		const CPose2D &	p
	)

template<>

CMatrixDouble16 & mrpt::math::matrixFromPoseOrPoint	(	CMatrixDouble61 &	M,
		const CPose3D &	p
	)

template<class CONTAINER >

CONTAINER::value_type mrpt::math::maximum	(	const CONTAINER &	v,
		size_t *	maxIndex = `NULL`
	)

Referenced by condidenceIntervals(), mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), weightedHistogram(), and weightedHistogramLog().

template<class CONTAINER >

double mrpt::math::mean ( const CONTAINER & v ) [inline]

Referenced by condidenceIntervals(), mrpt::random::CRandomGenerator::drawGaussian1DMatrix(), mrpt::random::CRandomGenerator::drawGaussian1DVector(), mrpt::random::CRandomGenerator::drawGaussianMultivariate(), mrpt::random::CRandomGenerator::drawGaussianMultivariateMany(), mrpt::random::matrixRandomNormal(), mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), and mrpt::random::vectorRandomNormal().

class MAT_OUT void mrpt::math::meanAndCov	(	const MAT_IN &	v,
		vector_double &	out_mean,
		MAT_OUT &	out_cov
	)

Definition at line 1060 of file ops_matrices.h.

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

Referenced by MAT_TYPE_COVARIANCE_OF().

template<class VECTOR_OF_VECTOR , class VECTORLIKE , class MATRIXLIKE >

void mrpt::math::meanAndCovVector	(	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:: math::mean,math::stddev, math::cov

Definition at line 170 of file math/utils.h.

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

Referenced by covVector().

template<class VECTORLIKE >

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

bool MRPTDLLIMPEXP mrpt::math::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.

The lines are given by:

Line 1 = P1 + f (P2-P1)
Line 2 = P3 + f (P4-P3) The Euclidean distance is returned in "dist", and the mid point between the lines in (x,y,z)
Returns:
It returns false if there is no solution, i.e. lines are (almost, up to EPS) parallel.

template<class CONTAINER >

CONTAINER::value_type mrpt::math::minimum	(	const CONTAINER &	v,
		size_t *	minIndex = `NULL`
	)

Referenced by leastSquareLinearFit(), mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), weightedHistogram(), and weightedHistogramLog().

template<class CONTAINER >

void mrpt::math::minimum_maximum	(	const CONTAINER &	v,
		typename CONTAINER::mrpt_autotype::value_type &	out_min,
		typename CONTAINER::mrpt_autotype::value_type &	out_max,
		size_t *	minIndex = `static_cast< size_t * >(NULL)`,
		size_t *	maxIndex = `static_cast< size_t * >(NULL)`
	)

Referenced by condidenceIntervals().

double MRPTDLLIMPEXP mrpt::math::minimumDistanceFromPointToSegment	(	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, and returns that minimum distance.

double MRPTDLLIMPEXP mrpt::math::minimumDistanceFromPointToSegment	(	const double &	Px,
		const double &	Py,
		const double &	x1,
		const double &	y1,
		const double &	x2,
		const double &	y2,
		float &	out_x,
		float &	out_y
	)

Computes the closest point from a given point to a segment, and returns that minimum distance.

template<class MAT1 , class MAT2 >

MAT1::value_type mrpt::math::multiply_HCHt_scalar	(	const MAT1 &	H,
		const MAT2 &	C
	)			`[inline]`

Just like s=H.multiply_HCHt_scalar(C), but defined in mrpt::math for backward compatibility.

Definition at line 988 of file ops_matrices.h.

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

Referenced by KLD_Gaussians(), mahalanobisDistance2(), mahalanobisDistance2AndLogPDF(), and normalPDF().

template<>

bool mrpt::math::myStaticCast ( double val )

Definition at line 43 of file CMatrixTemplate.h.

template<typename U >

U mrpt::math::myStaticCast ( double val )

Definition at line 43 of file CMatrixTemplate.h.

template<class T >

double mrpt::math::noncentralChi2CDF	(	unsigned int	degreesOfFreedom,
		T	noncentrality,
		T	arg
	)

Cumulative non-central chi square distribution (approximate).

Computes approximate values of the cumulative density of a chi square distribution with degreesOfFreedom, and noncentrality parameter noncentrality at the given argument arg, i.e. the probability that a random number drawn from the distribution is below arg It uses the approximate transform into a normal distribution due to Wilson and Hilferty (see Abramovitz, Stegun: "Handbook of Mathematical Functions", formula 26.3.32). The algorithm's running time is independent of the inputs. The accuracy is only about 0.1 for few degrees of freedom, but reaches about 0.001 above dof = 5.

Note:: Function code from the Vigra project (http://hci.iwr.uni-heidelberg.de/vigra/); code under "MIT X11 License", GNU GPL-compatible.

Definition at line 188 of file distributions.h.

References erf(), and mrpt::utils::square().

Referenced by chi2CDF().

template<class CONTAINER >

CONTAINER::value_type mrpt::math::norm ( const CONTAINER & v ) [inline]

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

template<class CONTAINER >

CONTAINER::value_type mrpt::math::norm_inf	(	const CONTAINER &	v,
		size_t *	maxIndex = `NULL`
	)

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

double MRPTDLLIMPEXP mrpt::math::normalCDF ( double p )

Evaluates the Gaussian cumulative density function.

The employed approximation is that from W. J. Cody freely available in http://www.netlib.org/specfun/erf

template<class T >

void mrpt::math::normalize	(	const std::vector< T > &	v,
		std::vector< T > &	out_v
	)

Normalize a vector, such as its norm is the unity.

If the vector has a null norm, the output is a null vector.

Definition at line 146 of file math/utils.h.

References mrpt::utils::square().

template<typename T >

T mrpt::math::normalPDF	(	const CMatrixTemplateNumeric< T > &	x,
		const CMatrixTemplateNumeric< T > &	mu,
		const CMatrixTemplateNumeric< T > &	cov
	)

Evaluates the multivariate normal (Gaussian) distribution at a given point "x" ("x" and "mu" can be 1xN or Nx1 matrixes).

Definition at line 57 of file distributions.h.

References mrpt::math::CMatrixTemplateNumeric< T >::det(), mrpt::math::CMatrixTemplate< T >::getRowCount(), and mrpt::math::CMatrixTemplateNumeric< T >::inv().

template<typename T , size_t N>

T mrpt::math::normalPDF	(	const CMatrixFixedNumeric< T, N, 1 > &	x,
		const CMatrixFixedNumeric< T, N, 1 > &	mu,
		const CMatrixFixedNumeric< T, N, N > &	cov
	)

Evaluates the multivariate normal (Gaussian) distribution at a given point "x" ("x" and "mu" can be 1xN or Nx1 matrixes).

Definition at line 86 of file distributions.h.

References mrpt::math::CMatrixFixedNumeric< T, NROWS, NCOLS >::det(), and mrpt::math::CMatrixFixedNumeric< T, NROWS, NCOLS >::inv().

template<typename VECTORLIKE , typename MATRIXLIKE >

MATRIXLIKE::value_type mrpt::math::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.

Definition at line 108 of file distributions.h.

References ASSERTDEB_, MRPT_END, MRPT_START, and multiply_HCHt_scalar().

double MRPTDLLIMPEXP mrpt::math::normalPDF	(	double	x,
		double	mu,
		double	std
	)

Evaluates the univariate normal (Gaussian) distribution at a given point "x".

double MRPTDLLIMPEXP mrpt::math::normalQuantile ( double p )

Evaluates the Gaussian distribution quantile for the probability value p=[0,1].

The employed approximation is that from Peter J. Acklam (pjacklam@online.no), freely available in http://home.online.no/~pjacklam.

template<class T >

std::vector<T> mrpt::math::ones ( size_t count )

Generates a vector of all ones of the given length.

Definition at line 130 of file math/utils.h.

template<class T , std::size_t N>

bool mrpt::math::operator!=	(	const CArray< T, N > &	x,
		const CArray< T, N > &	y
	)

Definition at line 294 of file CArray.h.

bool mrpt::math::operator!=	(	const TPoint2D &	p1,
		const TPoint2D &	p2
	)			`[inline]`

Exact comparison between 2D points.

Definition at line 473 of file lightweight_geom_data.h.

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

bool mrpt::math::operator!=	(	const TPoint3D &	p1,
		const TPoint3D &	p2
	)			`[inline]`

Exact comparison between 3D points.

Definition at line 485 of file lightweight_geom_data.h.

References mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

bool mrpt::math::operator!=	(	const TPose2D &	p1,
		const TPose2D &	p2
	)			`[inline]`

Exact comparison between 2D poses, taking possible cycles into account.

Definition at line 497 of file lightweight_geom_data.h.

References mrpt::math::TPose2D::phi, wrapTo2Pi(), mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

bool mrpt::math::operator!=	(	const TPose3D &	p1,
		const TPose3D &	p2
	)			`[inline]`

Exact comparison between 3D poses, taking possible cycles into account.

Definition at line 509 of file lightweight_geom_data.h.

References mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, wrapTo2Pi(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::z.

bool mrpt::math::operator!=	(	const TSegment2D &	s1,
		const TSegment2D &	s2
	)			`[inline]`

Definition at line 657 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

bool mrpt::math::operator!=	(	const TSegment3D &	s1,
		const TSegment3D &	s2
	)			`[inline]`

Definition at line 665 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

template<typename T , std::size_t N, class VECTORLIKE >

CArrayNumeric<T,N> mrpt::math::operator*	(	const CArrayNumeric< T, N > &	A,
		const VECTORLIKE &	B
	)

Dot product: ARRAY <- ARRAY .

* VECTORorARRAY

Definition at line 461 of file CArray.h.

References ASSERT_, and mrpt::math::CArray< T, N >::size().

template<typename T , std::size_t N, class VECTORLIKE >

CArrayNumeric<T,N> mrpt::math::operator+	(	const CArrayNumeric< T, N > &	A,
		const VECTORLIKE &	B
	)

Operator ARRAY <- ARRAY + VECTORorARRAY.

Definition at line 443 of file CArray.h.

References ASSERT_, and mrpt::math::CArray< T, N >::size().

TPoint3D mrpt::math::operator- ( const TPoint3D & p1 ) [inline]

Unary minus operator for 3D points.

Definition at line 461 of file lightweight_geom_data.h.

References mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

template<typename T , std::size_t N, class VECTORLIKE >

CArrayNumeric<T,N> mrpt::math::operator-	(	const CArrayNumeric< T, N > &	A,
		const VECTORLIKE &	B
	)

Operator ARRAY <- ARRAY - VECTORorARRAY.

Definition at line 452 of file CArray.h.

References ASSERT_, and mrpt::math::CArray< T, N >::size().

template<class T >

CMatrixTemplateNumeric<T> mrpt::math::operator/	(	const CMatrixTemplateNumeric< T > &	m1,
		const CMatrixTemplateNumeric< T > &	m2
	)			`[inline]`

Binary matrix division operator A/B = A*inv(B).

Definition at line 994 of file ops_matrices.h.

template<class T , std::size_t N>

bool mrpt::math::operator<	(	const CArray< T, N > &	x,
		const CArray< T, N > &	y
	)

Definition at line 290 of file CArray.h.

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

TObject2D binary input.

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

TObject3D binary output.

template<size_t NROWS, size_t NCOLS>

mrpt::utils::CStream& mrpt::math::operator<<	(	mrpt::utils::CStream &	out,
		const CMatrixFixedNumeric< float, NROWS, NCOLS > &	M
	)

Write operator for writing into a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 73 of file ops_matrices.h.

mrpt::utils::CStream& mrpt::math::operator<<	(	mrpt::utils::CStream &	out,
		const mrpt::math::TSegment3D &	s
	)			`[inline]`

TSegment3D binary output.

Definition at line 2259 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

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

TPose3D binary output.

mrpt::utils::CStream& mrpt::math::operator<<	(	mrpt::utils::CStream &	out,
		const mrpt::math::TLine2D &	l
	)			`[inline]`

TLine2D binary output.

Definition at line 2237 of file lightweight_geom_data.h.

References mrpt::math::TLine2D::coefs.

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

TPoint2D binary output.

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

TPose2D binary output.

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

TPoint3D binary output.

mrpt::utils::CStream& mrpt::math::operator<<	(	mrpt::utils::CStream &	out,
		const mrpt::math::TSegment2D &	s
	)			`[inline]`

TSegment2D binary output.

Definition at line 2224 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

template<size_t NROWS, size_t NCOLS>

mrpt::utils::CStream& mrpt::math::operator<<	(	mrpt::utils::CStream &	out,
		const CMatrixFixedNumeric< double, NROWS, NCOLS > &	M
	)

Write operator for writing into a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 80 of file ops_matrices.h.

mrpt::utils::CStream& mrpt::math::operator<<	(	mrpt::utils::CStream &	out,
		const mrpt::math::TLine3D &	l
	)			`[inline]`

TLine3D binary output.

Definition at line 2272 of file lightweight_geom_data.h.

References mrpt::math::TLine3D::director, and mrpt::math::TLine3D::pBase.

template<typename T , size_t N>

std::ostream& mrpt::math::operator<<	(	std::ostream &	ostrm,
		const CArray< T, N > &	a
	)

Textual output stream function.

Use only for text output, for example: "std::cout << mat;"

Definition at line 472 of file CArray.h.

mrpt::utils::CStream& mrpt::math::operator<<	(	mrpt::utils::CStream &	out,
		const mrpt::math::TPlane &	p
	)			`[inline]`

TPlane binary output.

Definition at line 2285 of file lightweight_geom_data.h.

References mrpt::math::TPlane::coefs.

template<class T , std::size_t N>

bool mrpt::math::operator<=	(	const CArray< T, N > &	x,
		const CArray< T, N > &	y
	)

Definition at line 302 of file CArray.h.

bool mrpt::math::operator==	(	const TPoint3D &	p1,
		const TPoint3D &	p2
	)			`[inline]`

Exact comparison between 3D points.

Definition at line 479 of file lightweight_geom_data.h.

References mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

bool mrpt::math::operator==	(	const TSegment3D &	s1,
		const TSegment3D &	s2
	)			`[inline]`

Definition at line 661 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

bool mrpt::math::operator==	(	const TSegment2D &	s1,
		const TSegment2D &	s2
	)			`[inline]`

Definition at line 653 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

bool mrpt::math::operator==	(	const TPose3D &	p1,
		const TPose3D &	p2
	)			`[inline]`

Exact comparison between 3D poses, taking possible cycles into account.

Definition at line 503 of file lightweight_geom_data.h.

References mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, wrapTo2Pi(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::z.

bool mrpt::math::operator==	(	const TPose2D &	p1,
		const TPose2D &	p2
	)			`[inline]`

Exact comparison between 2D poses, taking possible cycles into account.

Definition at line 491 of file lightweight_geom_data.h.

References mrpt::math::TPose2D::phi, wrapTo2Pi(), mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

template<class T , size_t NROWS, size_t NCOLS>

bool mrpt::math::operator==	(	const CMatrixFixedNumeric< T, NROWS, NCOLS > &	M1,
		const CMatrixFixedNumeric< T, NROWS, NCOLS > &	M2
	)

Equal comparison (==).

Definition at line 88 of file ops_matrices.h.

References mrpt::math::CMatrixFixedNumeric< T, NROWS, NCOLS >::get_unsafe().

template<class T , std::size_t N>

bool mrpt::math::operator==	(	const CArray< T, N > &	x,
		const CArray< T, N > &	y
	)

Definition at line 286 of file CArray.h.

References mrpt::math::CArray< T, N >::begin(), and mrpt::math::CArray< T, N >::end().

bool mrpt::math::operator==	(	const TPoint2D &	p1,
		const TPoint2D &	p2
	)			`[inline]`

Exact comparison between 2D points.

Definition at line 467 of file lightweight_geom_data.h.

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

template<class T , std::size_t N>

bool mrpt::math::operator>	(	const CArray< T, N > &	x,
		const CArray< T, N > &	y
	)

Definition at line 298 of file CArray.h.

template<class T , std::size_t N>

bool mrpt::math::operator>=	(	const CArray< T, N > &	x,
		const CArray< T, N > &	y
	)

Definition at line 306 of file CArray.h.

mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		mrpt::math::TLine2D &	l
	)			`[inline]`

TLine2D binary input.

Definition at line 2231 of file lightweight_geom_data.h.

References mrpt::math::TLine2D::coefs.

template<size_t NROWS, size_t NCOLS>

mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		CMatrixFixedNumeric< double, NROWS, NCOLS > &	M
	)

Read operator from a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 64 of file ops_matrices.h.

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

TObject2D binary input.

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

TObject3D binary input.

mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		mrpt::math::TSegment2D &	s
	)			`[inline]`

TSegment2D binary input.

Definition at line 2218 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		mrpt::math::TSegment3D &	s
	)			`[inline]`

TSegment3D binary input.

Definition at line 2253 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		mrpt::math::TLine3D &	l
	)			`[inline]`

TLine3D binary input.

Definition at line 2266 of file lightweight_geom_data.h.

References mrpt::math::TLine3D::director, and mrpt::math::TLine3D::pBase.

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

TPose2D binary input.

template<size_t NROWS, size_t NCOLS>

mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		CMatrixFixedNumeric< float, NROWS, NCOLS > &	M
	)

Read operator from a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 56 of file ops_matrices.h.

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

TPoint2D binary input.

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

TPose3D binary input.

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

TPoint3D binary input.

mrpt::utils::CStream& mrpt::math::operator>>	(	mrpt::utils::CStream &	in,
		mrpt::math::TPlane &	p
	)			`[inline]`

TPlane binary input.

Definition at line 2279 of file lightweight_geom_data.h.

References mrpt::math::TPlane::coefs.

template<class T >

CMatrixTemplateNumeric<T> mrpt::math::operator^	(	const CMatrixTemplateNumeric< T > &	m,
		const unsigned int	pow
	)			`[inline]`

binary power operator

Definition at line 1001 of file ops_matrices.h.

bool MRPTDLLIMPEXP mrpt::math::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.

See also:: pointIntoQuadrangle

template<typename T >

bool mrpt::math::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.

See also:: pointIntoPolygon2D

Definition at line 929 of file geometry.h.

References mrpt::utils::sign(), and wrapToPi().

template<typename T , class VECLIKE , class MATLIKE1 , class MATLIKE2 >

void mrpt::math::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.

See also:: productIntegralTwoGaussians, mahalanobisDistance2

Definition at line 1046 of file math/utils.h.

References ASSERT_, and M_2PI.

template<typename T >

T mrpt::math::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".

$D = \frac{1}{(2 \pi)^{0.5 N} \sqrt{} } \exp( \Delta_\mu^\top (\Sigma_1 + \Sigma_2 - 2 \Sigma_12)^{-1} \Delta_\mu)$

Definition at line 1001 of file math/utils.h.

References ASSERT_, mrpt::math::CMatrixTemplateNumeric< T >::det(), mrpt::math::CMatrixTemplateNumeric< T >::inv_fast(), and M_2PI.

template<typename T , size_t DIM>

T mrpt::math::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".

$D = \frac{1}{(2 \pi)^{0.5 N} \sqrt{} } \exp( \Delta_\mu^\top (\Sigma_1 + \Sigma_2)^{-1} \Delta_\mu)$

Definition at line 1024 of file math/utils.h.

References ASSERT_, mrpt::math::CMatrixFixedNumeric< T, NROWS, NCOLS >::det(), M_2PI, and UNINITIALIZED_MATRIX.

void mrpt::math::project2D	(	const TSegment2D &	segment,
		const CPose2D &	newXpose,
		TSegment2D &	newSegment
	)			`[inline]`

Uses the given pose 2D to project a segment into a new base.

Definition at line 350 of file geometry.h.

References mrpt::math::TSegment2D::point1, mrpt::math::TSegment2D::point2, and project2D().

void mrpt::math::project2D	(	const TPoint2D &	point,
		const CPose2D &	newXpose,
		TPoint2D &	newPoint
	)			`[inline]`

Uses the given pose 2D to project a point into a new base.

Definition at line 344 of file geometry.h.

References mrpt::poses::CPoint2D.

Referenced by project2D().

template<class T >

void mrpt::math::project2D	(	const std::vector< T > &	objs,
		const CPose2D &	newXpose,
		std::vector< T > &	newObjs
	)

Projects a set of 2D objects into the line's base.

Definition at line 389 of file geometry.h.

References project2D().

template<class T >

void mrpt::math::project2D	(	const T &	obj,
		const TLine2D &	newXLine,
		T &	newObj
	)

Projects any 2D object into the line's base, using its inverse pose.

If the object is exactly inside the line, this projection will zero its Y coordinate.

Definition at line 371 of file geometry.h.

References mrpt::poses::CPose2D, mrpt::math::TLine2D::getAsPose2D(), and project2D().

void MRPTDLLIMPEXP mrpt::math::project2D	(	const TLine2D &	line,
		const CPose2D &	newXpose,
		TLine2D &	newLine
	)

Uses the given pose 2D to project a line into a new base.

void MRPTDLLIMPEXP mrpt::math::project2D	(	const TObject2D &	object,
		const CPose2D &	newXpose,
		TObject2D &	newObject
	)

Uses the given pose 2D to project any 2D object into a new base.

void MRPTDLLIMPEXP mrpt::math::project2D	(	const TPolygon2D &	polygon,
		const CPose2D &	newXpose,
		TPolygon2D &	newPolygon
	)

Uses the given pose 2D to project a polygon into a new base.

template<class T >

void mrpt::math::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.

If the object is exactly inside the line, this projection will zero its Y coordinate.

Definition at line 380 of file geometry.h.

References mrpt::poses::CPose2D, mrpt::math::TLine2D::getAsPose2DForcingOrigin(), and project2D().

template<class T >

void mrpt::math::project3D	(	const T &	obj,
		const TPlane &	newXYPlane,
		T &	newObj
	)

Projects any 3D object into the plane's base, using its inverse pose.

If the object is exactly inside the plane, this projection will zero its Z coordinates.

Definition at line 316 of file geometry.h.

References project3D().

void MRPTDLLIMPEXP mrpt::math::project3D	(	const TObject3D &	object,
		const CPose3D &	newXYPose,
		TObject3D &	newObject
	)

Uses the given pose 3D to project any 3D object into a new base.

template<class T >

void mrpt::math::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.

If the object is exactly inside the plane, this projection will zero its Z coordinates.

Definition at line 325 of file geometry.h.

References project3D().

template<class T >

void mrpt::math::project3D	(	const std::vector< T > &	objs,
		const CPose3D &	newXYpose,
		std::vector< T > &	newObjs
	)

Projects a set of 3D objects into the plane's base.

Definition at line 335 of file geometry.h.

References project3D().

void mrpt::math::project3D	(	const TPoint3D &	point,
		const CPose3D &	newXYpose,
		TPoint3D &	newPoint
	)			`[inline]`

Uses the given pose 3D to project a point into a new base.

Definition at line 286 of file geometry.h.

References mrpt::poses::CPose3D::composePoint(), mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

Referenced by project3D().

void MRPTDLLIMPEXP mrpt::math::project3D	(	const TPlane &	plane,
		const CPose3D &	newXYpose,
		TPlane &	newPlane
	)

Uses the given pose 3D to project a plane into a new base.

void MRPTDLLIMPEXP mrpt::math::project3D	(	const TLine3D &	line,
		const CPose3D &	newXYpose,
		TLine3D &	newLine
	)

Uses the given pose 3D to project a line into a new base.

void MRPTDLLIMPEXP mrpt::math::project3D	(	const TPolygon3D &	polygon,
		const CPose3D &	newXYpose,
		TPolygon3D &	newPolygon
	)

Uses the given pose 3D to project a polygon into a new base.

void mrpt::math::project3D	(	const TSegment3D &	segment,
		const CPose3D &	newXYpose,
		TSegment3D &	newSegment
	)			`[inline]`

Uses the given pose 3D to project a segment into a new base.

Definition at line 292 of file geometry.h.

References mrpt::math::TSegment3D::point1, mrpt::math::TSegment3D::point2, and project3D().

template<class T >

void MRPTDLLIMPEXP mrpt::math::qr_decomposition	(	CMatrixTemplateNumeric< T > &	A,
		CMatrixTemplateNumeric< T > &	R,
		CMatrixTemplateNumeric< T > &	Q,
		CVectorTemplate< T > &	c,
		int &	sing
	)

Matrix QR decomposition.

A = QR, where R is upper triangular and Q is orthogonal, that is, ~QQ = 1 If A is a LxM dimension matrix, this function only return the LxL upper triangular matrix R instead of LxM pseudo-upper triangular matrix (been L<=M) This function has been extracted from "Numerical Recipes in C". /param A is the original matrix to decompose /param c,Q. The orthogonal matrix Q is represented as a product of n-1 Householder matrices Q1,...Qn-1, where Qj = 1 - u[j] x u[j]/c[j] The i'th component of u[j] is zero for i = 1,...,j-1 while the nonzero components are returned in Q(i,j) for i=j,...,n /param R is the upper triangular matrix /param sign returns as true (1) is singularity is encountered during the decomposition, but the decomposition is still complete in this case; otherwise it returns false (0)

template<typename NUMTYPE >

void MRPTDLLIMPEXP mrpt::math::ransac_detect_2D_lines	(	const std::vector< NUMTYPE > &	x,
		const std::vector< NUMTYPE > &	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.

Parameters:

	out_detected_lines	The output list of pairs: number of supporting inliers, detected line.
	threshold	The maximum distance between a point and a temptative line such as the point is considered an inlier.
	min_inliers_for_valid_line	The minimum number of supporting inliers to consider a line as valid.

template<typename NUMTYPE >

void MRPTDLLIMPEXP mrpt::math::ransac_detect_3D_planes	(	const std::vector< NUMTYPE > &	x,
		const std::vector< NUMTYPE > &	y,
		const std::vector< NUMTYPE > &	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.

Parameters:

	out_detected_planes	The output list of pairs: number of supporting inliers, detected plane.
	threshold	The maximum distance between a point and a temptative plane such as the point is considered an inlier.
	min_inliers_for_valid_plane	The minimum number of supporting inliers to consider a plane as valid.

void MRPTDLLIMPEXP mrpt::math::ransac_detect_3D_planes	(	const mrpt::slam::CPointsMap *	points_map,
		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.

Parameters:

	out_detected_planes	The output list of pairs: number of supporting inliers, detected plane.
	threshold	The maximum distance between a point and a temptative plane such as the point is considered an inlier.
	min_inliers_for_valid_plane	The minimum number of supporting inliers to consider a plane as valid.

bool MRPTDLLIMPEXP mrpt::math::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 wether two rotated rectangles intersect.

The first rectangle is not rotated and given by (R1_x_min,R1_x_max)-(R1_y_min,R1_y_max). The second rectangle is given is a similar way, but it is internally rotated according to the given coordinates translation (R2_pose_x,R2_pose_y,R2_pose_phi(radians)), relative to the coordinates system of rectangle 1.

template<class MATRIX >

mrpt::math::RET_MAT_ASSERT_MRPTMATRIX ( MATRIX ) const [inline]

Unary inversion operator.

Definition at line 1024 of file ops_matrices.h.

References UNINITIALIZED_MATRIX.

template<class MATRIX >

mrpt::math::RET_TYPE_ASSERT_MRPTMATRIX	(	MATRIX	,
		std::ostream
	)

Textual output stream function.

Use only for text output, for example: "std::cout << mat;"

Definition at line 101 of file ops_matrices.h.

template<class MATRIXLIKE1 , class MATRIXLIKE2 >

mrpt::math::RET_VOID_ASSERT_MRPTMATRICES	(	MATRIXLIKE1	,
		MATRIXLIKE2
	)			const

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

template<class T >

T mrpt::math::round2up ( T val )

Round up to the nearest power of two of a given number.

Definition at line 455 of file math/utils.h.

References THROW_EXCEPTION.

template<class T >

T mrpt::math::round_10power	(	T	val,
		int	power10
	)

Round a decimal number up to the given 10'th power (eg, to 1000,100,10, and also fractions) power10 means round up to: 1 -> 10, 2 -> 100, 3 -> 1000, ...

-1 -> 0.1, -2 -> 0.01, ...

Definition at line 471 of file math/utils.h.

References mrpt::utils::round_long().

bool MRPTDLLIMPEXP mrpt::math::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.

bool MRPTDLLIMPEXP mrpt::math::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.

template<class T , T STEP>

std::vector<T> mrpt::math::sequence	(	T	first,
		size_t	length
	)			`[inline]`

Generates a sequence of values [first,first+STEP,first+2*STEP,...].

See also:: linspace

Definition at line 119 of file math/utils.h.

void mrpt::math::setEpsilon ( double nE ) [inline]

Changes the value of the geometric epsilon.

See also:: geometryEpsilon,getEpsilon

Definition at line 700 of file geometry.h.

References geometryEpsilon.

template<class MATRIXLIKE >

size_t mrpt::math::size	(	const MATRIXLIKE &	m,
		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: CMatrixTemplate, CMatrixTemplateNumeric, CMatrixFixedNumeric

Definition at line 570 of file utils_defs.h.

References THROW_EXCEPTION_CUSTOM_MSG1.

double MRPTDLLIMPEXP mrpt::math::spline	(	const double	t,
		const std::vector< double > &	x,
		const std::vector< double > &	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).

See also:: leastSquareLinearFit

bool MRPTDLLIMPEXP mrpt::math::splitInConvexComponents	(	const TPolygon3D &	poly,
		vector< TPolygon3D > &	components
	)

Splits a 3D polygon into convex components.

Exceptions:

std::logic_error

if the polygon can't be fit into a plane.

bool MRPTDLLIMPEXP mrpt::math::splitInConvexComponents	(	const TPolygon2D &	poly,
		vector< TPolygon2D > &	components
	)

Splits a 2D polygon into convex components.

template<class CONTAINER >

CONTAINER::value_type mrpt::math::squareNorm ( const CONTAINER & v )

template<class VECTORLIKE >

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

template<class CONTAINER >

CONTAINER::value_type mrpt::math::sum ( const CONTAINER & v ) [inline]

Referenced by mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), and mrpt::math::CVectorTemplate< KFTYPE >::mean().

bool MRPTDLLIMPEXP mrpt::math::traceRay	(	const vector< TPolygonWithPlane > &	vec,
		const mrpt::poses::CPose3D &	pose,
		double &	dist
	)

Fast ray tracing method using polygons' properties.

See also:: CRenderizable::rayTrace

Referenced by traceRay().

bool mrpt::math::traceRay	(	const vector< TPolygon3D > &	vec,
		const mrpt::poses::CPose3D &	pose,
		double &	dist
	)			`[inline]`

Fast ray tracing method using polygons' properties.

See also:: CRenderizable::rayTrace

Definition at line 750 of file geometry.h.

References mrpt::math::TPolygonWithPlane::getPlanes(), and traceRay().

void mrpt::math::unwrap2PiSequence ( vector_double & x )

Modify a sequence of angle values such as no consecutive values have a jump larger than PI in absolute value.

See also:: wrapToPi

template<class T >

void MRPTDLLIMPEXP mrpt::math::UpdateCholesky	(	CMatrixTemplateNumeric< T > &	chol,
		CVectorTemplate< T > &	r1Modification
	)

If R = CHOL(A) is the original Cholesky factorization of A, then R1 = CHOLUPDATE(R,X) returns the upper triangular Cholesky factor of A + X*X', where X is a column vector of appropriate length.

template<class T , class U >

bool mrpt::math::vectorsAreParallel2D	(	const T &	v1,
		const U &	v2
	)			`[inline]`

Returns true if two 2D vectors are parallel.

The arguments may be points, arrays, etc.

Definition at line 802 of file geometry.h.

References geometryEpsilon.

template<class T , class U >

bool mrpt::math::vectorsAreParallel3D	(	const T &	v1,
		const U &	v2
	)			`[inline]`

Returns true if two 3D vectors are parallel.

The arguments may be points, arrays, etc.

Definition at line 810 of file geometry.h.

References geometryEpsilon.

template<class VECTORLIKE1 , class VECTORLIKE2 >

void mrpt::math::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.

Parameters:

	values	[IN] The N values
	weights	[IN] The weights for the corresponding N values (don't need to be normalized)
	binWidth	[IN] The desired width of the bins
	out_binCenters	[OUT] The centers of the M bins generated to cover from the minimum to the maximum value of "values" with the given "binWidth"
	out_binValues	[OUT] The ratio of values at each given bin, such as the whole vector sums up the unity.

See also:: weightedHistogramLog

Definition at line 299 of file math/utils.h.

References ASSERT_, ASSERTDEB_, maximum(), minimum(), and mrpt::utils::round().

template<class VECTORLIKE1 , class VECTORLIKE2 >

void mrpt::math::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.

Parameters:

	values	[IN] The N values
	weights	[IN] The log-weights for the corresponding N values (don't need to be normalized)
	binWidth	[IN] The desired width of the bins
	out_binCenters	[OUT] The centers of the M bins generated to cover from the minimum to the maximum value of "values" with the given "binWidth"
	out_binValues	[OUT] The ratio of values at each given bin, such as the whole vector sums up the unity.