ops_matrices.h File Reference

This file implements miscelaneous matrix and matrix/vector operations, plus internal functions in mrpt::math::detail. More...

#include <mrpt/math/math_frwds.h>
#include <mrpt/math/CMatrix.h>
#include <mrpt/math/CMatrixD.h>
#include <mrpt/utils/CStream.h>
#include <mrpt/math/CMatrixTemplateNumeric.h>
#include <mrpt/math/CMatrixFixedNumeric.h>
#include <mrpt/math/CVectorTemplate.h>
#include <mrpt/math/ops_containers.h>
#include <mrpt/math/ops_matrices_eigen.h>
#include <mrpt/math/matrices_metaprogramming.h>

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Classes
class	mrpt::math::detail::VicinityTraits< CMatrixTemplate< T > >
	Vicinity traits class specialization for matrices. More...
class	mrpt::math::detail::VicinityTraits< std::vector< T > >
	Vicinity traits class specialization for vectors. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 4 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 5 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 8 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 9 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 12 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 13 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 20 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 21 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 24 >
	Template specialization for getVicinity. More...
struct	mrpt::math::detail::getVicinity< MatrixType, T, ReturnType, 25 >
	Template specialization for getVicinity. More...
Namespaces
namespace	mrpt
	This is the global namespace for all Mobile Robot Programming Toolkit (MRPT) libraries.
namespace	mrpt::math
	This base provides a set of functions for maths stuff.
namespace	mrpt::math::detail
Defines
#define	SAVE_MATRIX(M)   M.saveToTextFile(mrpt::format("%s.txt",#M));
	A useful macro for saving matrixes to a file while debugging.
Functions
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.
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.
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.
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.
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 (==).
template<class MATRIX >
	mrpt::math::RET_TYPE_ASSERT_MRPTMATRIX (MATRIX, std::ostream)&operator<< (std
	Textual output stream function.
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 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<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 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<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<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 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<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<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_B , class MAT_OUT >
void	mrpt::math::detail::multiply_result_is_symmetric (const MAT_A &A, const MAT_B &B, MAT_OUT &out)
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 MAT1 , class MAT2 >
void	mrpt::math::detail::insertMatrixInto (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 MATRIX >
int	mrpt::math::detail::matrix_pivot (MATRIX &M, const size_t row)
	Matrix pivoting - used for detMatrix, etc.
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 MAT1 , class MAT2 >
MAT1::value_type	mrpt::math::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 >	mrpt::math::operator/ (const CMatrixTemplateNumeric< T > &m1, const CMatrixTemplateNumeric< T > &m2)
	Binary matrix division operator A/B = A*inv(B).
template<class T >
CMatrixTemplateNumeric< T >	mrpt::math::operator^ (const CMatrixTemplateNumeric< T > &m, const unsigned int pow)
	binary power operator
template<class MAT >
	mrpt::math::MAT_TYPE_TRANSPOSE_OF (MAT) operator~(const MAT &m)
	unary transpose operator ~
template<class MATRIX >
	mrpt::math::RET_MAT_ASSERT_MRPTMATRIX (MATRIX) operator!(const MATRIX &m)
	Unary inversion operator.
template<class MAT1 , class MAT2 >
	mrpt::math::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	mrpt::math::meanAndCov (const MAT_IN &v, vector_double &out_mean, MAT_OUT &out_cov)
template<class MATRIX >
	mrpt::math::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.
template<typename MatrixType >
size_t	mrpt::math::detail::rank (const MatrixType &m, typename MatrixType::value_type eps=1e-7)
template<typename JA >
void	mrpt::math::detail::pivotUntilIdentity (JointAccessor< JA > &joint)
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)
Matrix inverses - Implementation
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)
template<>
void	mrpt::math::detail::invMatrix< CMatrixFixedNumeric< float, 2, 2 >, CMatrixFixedNumeric< float, 2, 2 > > (const CMatrixFixedNumeric< float, 2, 2 > &M, CMatrixFixedNumeric< float, 2, 2 > &out_inv)
template<>
void	mrpt::math::detail::invMatrix_destroySrc< CMatrixFixedNumeric< float, 2, 2 >, CMatrixFixedNumeric< float, 2, 2 > > (CMatrixFixedNumeric< float, 2, 2 > &M, CMatrixFixedNumeric< float, 2, 2 > &out_inv)
template<>
void	mrpt::math::detail::invMatrix< CMatrixFixedNumeric< double, 2, 2 >, CMatrixFixedNumeric< double, 2, 2 > > (const CMatrixFixedNumeric< double, 2, 2 > &M, CMatrixFixedNumeric< double, 2, 2 > &out_inv)
template<>
void	mrpt::math::detail::invMatrix_destroySrc< CMatrixFixedNumeric< double, 2, 2 >, CMatrixFixedNumeric< double, 2, 2 > > (CMatrixFixedNumeric< double, 2, 2 > &M, CMatrixFixedNumeric< double, 2, 2 > &out_inv)
template<>
void	mrpt::math::detail::invMatrix< CMatrixFixedNumeric< float, 3, 3 >, CMatrixFixedNumeric< float, 3, 3 > > (const CMatrixFixedNumeric< float, 3, 3 > &M, CMatrixFixedNumeric< float, 3, 3 > &out_inv)
template<>
void	mrpt::math::detail::invMatrix_destroySrc< CMatrixFixedNumeric< float, 3, 3 >, CMatrixFixedNumeric< float, 3, 3 > > (CMatrixFixedNumeric< float, 3, 3 > &M, CMatrixFixedNumeric< float, 3, 3 > &out_inv)
template<>
void	mrpt::math::detail::invMatrix< CMatrixFixedNumeric< double, 3, 3 >, CMatrixFixedNumeric< double, 3, 3 > > (const CMatrixFixedNumeric< double, 3, 3 > &M, CMatrixFixedNumeric< double, 3, 3 > &out_inv)
template<>
void	mrpt::math::detail::invMatrix_destroySrc< CMatrixFixedNumeric< double, 3, 3 >, CMatrixFixedNumeric< double, 3, 3 > > (CMatrixFixedNumeric< double, 3, 3 > &M, CMatrixFixedNumeric< double, 3, 3 > &out_inv)
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)
Matrix determinants - implementation
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)
template<>
float	mrpt::math::detail::detMatrix< CMatrixFixedNumeric< float, 2, 2 > > (const CMatrixFixedNumeric< float, 2, 2 > &M)
template<>
double	mrpt::math::detail::detMatrix< CMatrixFixedNumeric< double, 2, 2 > > (const CMatrixFixedNumeric< double, 2, 2 > &M)
template<>
float	mrpt::math::detail::detMatrix< CMatrixFixedNumeric< float, 3, 3 > > (const CMatrixFixedNumeric< float, 3, 3 > &M)
template<>
double	mrpt::math::detail::detMatrix< CMatrixFixedNumeric< double, 3, 3 > > (const CMatrixFixedNumeric< double, 3, 3 > &M)
template<>
float	mrpt::math::detail::detMatrix< CMatrixFixedNumeric< float, 4, 4 > > (const CMatrixFixedNumeric< float, 4, 4 > &M)
template<>
double	mrpt::math::detail::detMatrix< CMatrixFixedNumeric< double, 4, 4 > > (const CMatrixFixedNumeric< double, 4, 4 > &M)
template<class MATRIX >
	mrpt::math::detail::RET_ELEMENT_ASSERT_MRPTCONTAINER (MATRIX) detMatrix(const MATRIX &M)

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Detailed Description

This file implements miscelaneous matrix and matrix/vector operations, plus internal functions in mrpt::math::detail.

Definition in file ops_matrices.h.

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Define Documentation

#define SAVE_MATRIX

(

M

)

M.saveToTextFile(mrpt::format("%s.txt",#M));

A useful macro for saving matrixes to a file while debugging.

Definition at line 1174 of file ops_matrices.h.