math_frwds.h File Reference

#include <mrpt/config.h>
#include <mrpt/base/link_pragmas.h>
#include <mrpt/utils/types.h>
#include <cmath>
#include <cstdlib>
#include <algorithm>

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Namespaces
namespace	mrpt
	This is the global namespace for all Mobile Robot Programming Toolkit (MRPT) libraries.
namespace	mrpt::utils
	Classes for serialization, sockets, ini-file manipulation, streams, list of properties-values, timewatch, extensions to STL.
namespace	mrpt::poses
	Classes for 2D/3D geometry representation, both of single values and probability density distributions (PDFs) in many forms.
namespace	mrpt::math
	This base provides a set of functions for maths stuff.
namespace	mrpt::math::detail
Defines
#define	UNINITIALIZED_MATRIX   false,false,false
	For usage in one of the constructors of CMatrixFixedNumeric or CMatrixTemplate (and derived classes), if it's not required to fill it with zeros at the constructor to save time.
#define	DECLARE_COMMON_CONTAINERS_MEMBERS(NUMTYPE)
#define	DECLARE_COMMON_MATRIX_MEMBERS(NUMTYPE)
	Counts the number of elements that appear in both containers (comparison through the == operator).
Enumerations
enum	mrpt::math::TMatrixTextFileFormat { mrpt::math::MATRIX_FORMAT_ENG = 0, mrpt::math::MATRIX_FORMAT_FIXED = 1, mrpt::math::MATRIX_FORMAT_INT = 2 }
Functions
template<class T >
T	mrpt::utils::square (const T &x)
	Inline function for the square of a number.
template<class MATRIX1 , class MATRIX2 >
bool	mrpt::math::detail::chol (const MATRIX1 &in, MATRIX2 &out)
	Cholesky factorization: in = out' · out (Upper triangular version: M=U'*U ) Given a positive-definite symmetric matrix, this routine constructs its Cholesky decomposition.
template<class MATRIX1 >
MATRIX1::value_type	mrpt::math::detail::trace (const MATRIX1 &m)
	The trace of a matrix (the sum of its diagonal).
template<class MATRIX1 , class MATRIX2 , class MATRIXRES >
void	mrpt::math::detail::multiply_AB (const MATRIX1 &m1, const MATRIX2 &m2, MATRIXRES &RESULT)
	Multiply 2 matrices: RESULT = A * B.
template<class MATRIX1 , class OTHERVECTOR1 , class OTHERVECTOR2 >
void	mrpt::math::detail::multiply_Ab (const MATRIX1 &m, const OTHERVECTOR1 &vIn, OTHERVECTOR2 &vOut, bool accumToOutput)
	Computes the vector v = A * a, where "a" is a column vector of the appropriate length.
template<class MATRIX1 , class OTHERVECTOR1 , class OTHERVECTOR2 >
void	mrpt::math::detail::multiply_Atb (const MATRIX1 &m, const OTHERVECTOR1 &vIn, OTHERVECTOR2 &vOut, bool accumToOutput)
	Computes the vector v = AT * a, where "a" is a column vector of the appropriate length.
template<class MATRIX1 , class MATRIX2 >
void	mrpt::math::detail::multiply_AAt (const MATRIX1 &m1, MATRIX2 &RESULT)
	RESULT = A * A^t.
template<class MATRIX1 , class MATRIX2 >
void	mrpt::math::detail::multiply_AtA (const MATRIX1 &m1, MATRIX2 &RESULT)
	RESULT = A^t * A.
template<typename MAT_H , typename MAT_C , typename MAT_R >
void	mrpt::math::detail::multiply_HCHt (const MAT_H &H, const MAT_C &C, MAT_R &R, bool accumResultInOutput, bool allow_submatrix_mult)
	R = H * C * H^t (with C symmetric).
template<typename MAT_H , typename MAT_C , typename MAT_R >
void	mrpt::math::detail::multiply_HtCH (const MAT_H &H, const MAT_C &C, MAT_R &R, bool accumResultInOutput, bool allow_submatrix_mult)
	R = H^t * C * H (with C symmetric).
template<typename VECTOR_H , typename MAT_C >
MAT_C::value_type	mrpt::math::detail::multiply_HCHt_scalar (const VECTOR_H &H, const MAT_C &C)
	r (a scalar) = H * C * H^t (with a vector H and a symmetric matrix C)
template<class MAT_X , class MAT_A , class MAT_OUT >
void	mrpt::math::detail::multiply_subMatrix (const MAT_X &X, const MAT_A &A, MAT_OUT &outResult, const size_t A_cols_offset, const size_t A_rows_offset, const size_t A_col_count)
	Matrix multiplication of this matrix with a submatrix of 'A', saving the result in a third matrix.
template<class MAT_A , class MAT_B , class MAT_C , class MAT_OUT >
void	mrpt::math::detail::multiply_ABC (const MAT_A &A, const MAT_B &B, const MAT_C &C, MAT_OUT &RES)
	RES = A*B*C.
template<class MAT_A , class MAT_B , class MAT_C , class MAT_OUT >
void	mrpt::math::detail::multiply_ABCt (const MAT_A &A, const MAT_B &B, const MAT_C &C, MAT_OUT &RES)
	RES = A*B*(C^t).
template<class MAT_A , class MAT_B , class MAT_OUT >
void	mrpt::math::detail::multiply_ABt (const MAT_A &A, const MAT_B &B, MAT_OUT &out)
template<class MAT_A , class MAT_OUT >
void	mrpt::math::detail::multiply_AAt (const MAT_A &A, MAT_OUT &out)
template<class MAT_A , class MAT_B , class MAT_OUT >
void	mrpt::math::detail::multiply_result_is_symmetric (const MAT_A &A, const MAT_B &B, MAT_OUT &out)
template<typename MatrixType >
size_t	mrpt::math::detail::rank (const MatrixType &m, typename MatrixType::value_type eps=1e-7)
template<>
void	mrpt::math::detail::eigenVectorsMatrix< CMatrixFixedNumeric< float, 2, 2 >, CMatrixFixedNumeric< float, 2, 2 >, CArrayNumeric< float, 2 > > (const CMatrixFixedNumeric< float, 2, 2 > &M, CMatrixFixedNumeric< float, 2, 2 > *eVecs, CArrayNumeric< float, 2 > &eVals)
template<>
void	mrpt::math::detail::eigenVectorsMatrix< CMatrixFixedNumeric< double, 2, 2 >, CMatrixFixedNumeric< double, 2, 2 >, CArrayNumeric< double, 2 > > (const CMatrixFixedNumeric< double, 2, 2 > &M, CMatrixFixedNumeric< double, 2, 2 > *eVecs, CArrayNumeric< double, 2 > &eVals)
template<class MAT >
void	mrpt::math::detail::saveMatrixToTextFile (const MAT &theMatrix, const std::string &file, TMatrixTextFileFormat fileFormat, bool appendMRPTHeader, const std::string &userHeader)
	Save matrix to a text file, compatible with MATLAB text format (see also the methods of matrix classes themselves).
template<class MATRIX >
std::string	mrpt::math::detail::matrix_inMatlabFormat (const MATRIX &m, const size_t decimal_digits)
	Dump matrix in matlab format.
template<typename T , size_t NROWS, size_t NCOLS>
void	mrpt::math::detail::fixedToDynMatrix (const CMatrixFixedNumeric< T, NROWS, NCOLS > &SRC, CMatrixTemplateNumeric< T > &DST)
template<class MAT1 , class MAT2 >
void	mrpt::math::detail::insertMatrixInto (MAT1 &M, const size_t nRow, const size_t nCol, const MAT2 &in)
template<class MAT1 , class MAT2 >
void	mrpt::math::detail::insertMatrixTransposeInto (MAT1 &M, const size_t nRow, const size_t nCol, const MAT2 &in)
template<class MATORG , class MATDEST >
void	mrpt::math::detail::extractMatrix (const MATORG &M, const size_t first_row, const size_t first_col, MATDEST &outMat)
	Extract a submatrix - The output matrix must be set to the required size before call.
template<class MAT , class VEC >
void	mrpt::math::detail::extractRowFromMatrix (const MAT &m, size_t nRow, VEC &out, const size_t startingCol)
template<class MAT , class VEC >
void	mrpt::math::detail::extractColFromMatrix (const MAT &m, size_t nCol, VEC &out, const size_t startingRow)
template<class MAT , class VEC >
void	mrpt::math::detail::insertRowToMatrix (MAT &m, size_t nRow, const VEC &in, const size_t startingCol)
template<class MAT , class VEC >
void	mrpt::math::detail::insertColToMatrix (MAT &m, size_t nCol, const VEC &in, const size_t startingRow)
template<class MATRIX >
int	mrpt::math::detail::matrix_pivot (MATRIX &M, const size_t row)
	Matrix pivoting - used for detMatrix, etc.
template<typename MAT1 , typename MAT2 , typename MAT3 >
void	mrpt::math::detail::leftDivideSquare (const MAT1 &C, const MAT2 &A, MAT3 &RES)
template<typename MAT1 , typename MAT2 , typename MAT3 >
void	mrpt::math::detail::rightDivideSquare (const MAT1 &C, const MAT2 &B, MAT3 &RES)
template<typename MAT1 , typename MAT2 >
void	mrpt::math::detail::fastLeftDivideSquare (MAT1 &inout_CB, MAT2 &willBeDestroyed_A)
template<typename MAT1 , typename MAT2 >
void	mrpt::math::detail::fastRightDivideSquare (MAT1 &inout_CA, MAT2 &willBeDestroyed_B)
template<class MATRIX >
bool	mrpt::math::detail::isMatrixTypeResizable (const MATRIX &)
TPoint2D BASE_IMPEXP	mrpt::math::detail::lightFromPose (const mrpt::poses::CPoint2D &p)
	Convert a pose into a light-weight structure (functional form, needed for forward declarations).
TPoint3D BASE_IMPEXP	mrpt::math::detail::lightFromPose (const mrpt::poses::CPoint3D &p)
	Convert a pose into a light-weight structure (functional form, needed for forward declarations).
TPose2D BASE_IMPEXP	mrpt::math::detail::lightFromPose (const mrpt::poses::CPose2D &p)
	Convert a pose into a light-weight structure (functional form, needed for forward declarations).
TPose3D BASE_IMPEXP	mrpt::math::detail::lightFromPose (const mrpt::poses::CPose3D &p)
	Convert a pose into a light-weight structure (functional form, needed for forward declarations).
TPose3DQuat BASE_IMPEXP	mrpt::math::detail::lightFromPose (const mrpt::poses::CPose3DQuat &p)
	Convert a pose into a light-weight structure (functional form, needed for forward declarations).
template<class CONTAINER >
size_t	mrpt::math::countNonZero (const CONTAINER &a)
template<class CONTAINER >
CONTAINER::value_type	mrpt::math::maximum (const CONTAINER &v, size_t *maxIndex=NULL)
template<class CONTAINER >
CONTAINER::value_type	mrpt::math::minimum (const CONTAINER &v, size_t *minIndex=NULL)
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))
template<class CONTAINER >
CONTAINER::value_type	mrpt::math::norm_inf (const CONTAINER &v, size_t *maxIndex=NULL)
template<class CONTAINER >
CONTAINER::value_type	mrpt::math::squareNorm (const CONTAINER &v)
template<class CONTAINER >
CONTAINER::value_type	mrpt::math::norm (const CONTAINER &v)
template<class CONTAINER >
double	mrpt::math::mean (const CONTAINER &v)
template<class CONTAINER >
CONTAINER::value_type	mrpt::math::sum (const CONTAINER &v)
template<class CONTAINER , typename RET >
RET	mrpt::math::sumRetType (const CONTAINER &v)
template<class CONTAINER >
void	mrpt::math::adjustRange (CONTAINER &m, const typename CONTAINER::value_type minVal, const typename CONTAINER::value_type maxVal)
template<class CONTAINER1 , class CONTAINER2 >
void	mrpt::math::cumsum (const CONTAINER1 &in_data, CONTAINER2 &out_cumsum)
template<class CONTAINER1 , class CONTAINER2 >
size_t	mrpt::math::countCommonElements (const CONTAINER1 &a, const CONTAINER2 &b)
template<class CONTAINER >
std::vector< double >	mrpt::math::histogram (const CONTAINER &v, double limit_min, double limit_max, size_t number_bins, bool do_normalization=false, std::vector< double > *out_bin_centers=NULL)
template<class VECTORLIKE >
double	mrpt::math::stddev (const VECTORLIKE &v, bool unbiased=true)
template<class VECTORLIKE >
void	mrpt::math::meanAndStd (const VECTORLIKE &v, double &out_mean, double &out_std, bool unbiased=true)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const TPoint2D &p)
	Conversion of poses to MRPT containers (vector/matrix).
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const TPoint3D &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const TPose2D &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const TPose3D &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const TPose3DQuat &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPoint2D &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPoint3D &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPose2D &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPose3D &p)
template<class CONTAINER >
CONTAINER &	mrpt::math::containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPose3DQuat &p)
template<class T >
T	mrpt::math::wrapTo2Pi (T a)
	Modifies the given angle to translate it into the [0,2pi[ range.
Matrix inverses - Implementation
template<class MATRIXIN , class MATRIXOUT >
void	mrpt::math::detail::invMatrix (const MATRIXIN &M, MATRIXOUT &out_inv)
template<class MATRIXIN , class MATRIXOUT >
void	mrpt::math::detail::invMatrix_destroySrc (MATRIXIN &M, MATRIXOUT &out_inv)
template<class MATRIXIN , class MATRIXOUT >
void	mrpt::math::detail::invMatrix_special_2x2 (const MATRIXIN &M, MATRIXOUT &out_inv)
template<class MATRIXIN , class MATRIXOUT >
void	mrpt::math::detail::invMatrix_special_3x3 (const MATRIXIN &M, MATRIXOUT &out_inv)
Matrix determinants - implementation
template<class MATRIX >
	mrpt::math::detail::RET_ELEMENT_ASSERT_MRPTCONTAINER (MATRIX) detMatrix(const MATRIX &M)
template<class MATRIX >
MATRIX::value_type	mrpt::math::detail::detMatrix_special_2x2 (const MATRIX &M)
template<class MATRIX >
MATRIX::value_type	mrpt::math::detail::detMatrix_special_3x3 (const MATRIX &M)
template<class MATRIX >
MATRIX::value_type	mrpt::math::detail::detMatrix_special_4x4 (const MATRIX &M)
Matrix eigenvectors
template<class MATRIX1 , class MATRIX2 , class VECTOR1 >
void	mrpt::math::detail::eigenVectorsMatrix (const MATRIX1 &M, MATRIX2 *eVecs, VECTOR1 &eVals)
	eigenVectorsMatrix
template<class MATRIX1 , class MATRIX2 , class VECTOR1 >
void	mrpt::math::detail::eigenVectorsMatrix_special_2x2 (const MATRIX1 &M, MATRIX2 *eVecs, VECTOR1 &eVals)
Variables
class BASE_IMPEXP	mrpt::utils::CStream
class BASE_IMPEXP	mrpt::math::CMatrixTemplateNumeric
class BASE_IMPEXP	mrpt::math::CMatrix
class BASE_IMPEXP	mrpt::math::CMatrixD

---

Detailed Description

Forward declarations of all mrpt::math classes related to vectors, arrays and matrices. Many of the function implementations are in ops_matrices.h, others in ops_containers.h

Definition in file math_frwds.h.

---

Define Documentation

#define DECLARE_COMMON_CONTAINERS_MEMBERS

(

NUMTYPE

)

Definition at line 101 of file math_frwds.h.

#define DECLARE_COMMON_MATRIX_MEMBERS

(

NUMTYPE

)

Counts the number of elements that appear in both containers (comparison through the == operator).

It is assumed that no repeated elements appear within each of the containers. Computes the normalized or normal histogram of a sequence of numbers given the number of bins and the limits. In any case this is a "linear" histogram, i.e. for matrices, all the elements are taken as if they were a plain sequence, not taking into account they were in columns or rows.

Definition at line 154 of file math_frwds.h.

#define UNINITIALIZED_MATRIX   false,false,false

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

Definition at line 79 of file math_frwds.h.

Referenced by mrpt::poses::CPoseOrPoint::getHomogeneousMatrixVal(), mrpt::math::normalPDF(), mrpt::math::productIntegralTwoGaussians(), mrpt::math::RET_MAT_ASSERT_MRPTMATRIX(), mrpt::bayes::CKalmanFilterCapable< 7, 3, 3, 7 >::runOneKalmanIteration(), and mrpt::bayes::detail::runOneKalmanIteration_addNewLandmarks().