/usr/include/x86_64-linux-gnu/visp3/core/vpMatrix.h is in libvisp-core-dev 3.0.0-4.
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*
* This file is part of the ViSP software.
* Copyright (C) 2005 - 2015 by Inria. All rights reserved.
*
* This software is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* ("GPL") version 2 as published by the Free Software Foundation.
* See the file LICENSE.txt at the root directory of this source
* distribution for additional information about the GNU GPL.
*
* For using ViSP with software that can not be combined with the GNU
* GPL, please contact Inria about acquiring a ViSP Professional
* Edition License.
*
* See http://visp.inria.fr for more information.
*
* This software was developed at:
* Inria Rennes - Bretagne Atlantique
* Campus Universitaire de Beaulieu
* 35042 Rennes Cedex
* France
*
* If you have questions regarding the use of this file, please contact
* Inria at visp@inria.fr
*
* This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
* WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* Description:
* Matrix manipulation.
*
* Authors:
* Eric Marchand
*
*****************************************************************************/
#ifndef vpMatrix_H
#define vpMatrix_H
#include <visp3/core/vpConfig.h>
#include <visp3/core/vpException.h>
#include <visp3/core/vpTime.h>
#include <visp3/core/vpArray2D.h>
#include <visp3/core/vpRotationMatrix.h>
#include <visp3/core/vpHomogeneousMatrix.h>
#include <visp3/core/vpVelocityTwistMatrix.h>
#include <visp3/core/vpForceTwistMatrix.h>
#ifdef VISP_HAVE_GSL
# include <gsl/gsl_math.h>
# include <gsl/gsl_eigen.h>
#endif
#include <iostream>
#include <math.h>
class vpRowVector;
class vpColVector;
class vpTranslationVector;
class vpHomogeneousMatrix;
class vpVelocityTwistMatrix;
class vpForceTwistMatrix;
/*!
\file vpMatrix.h
\brief Definition of matrix class as well as a set of operations on
these matrices.
*/
/*!
\class vpMatrix
\ingroup group_core_matrices
\brief Implementation of a matrix and operations on matrices.
vpMatrix class provides a data structure for the matrices as well
as a set of operations on these matrices.
The vpMatrix class is derived from vpArray2D<double>.
\warning Note the matrix in the class (*this) will be noted A in the comment
\ingroup libmath
\sa vpRowVector, vpColVector, vpHomogeneousMatrix, vpRotationMatrix,
vpTwistMatrix, vpHomography
*/
class VISP_EXPORT vpMatrix : public vpArray2D<double>
{
public:
/*!
Method used to compute the determinant of a square matrix.
\sa det()
*/
typedef enum {
LU_DECOMPOSITION /*!< LU decomposition method. */
} vpDetMethod;
public:
/*!
Basic constructor of a matrix of double. Number of columns and rows are zero.
*/
vpMatrix() : vpArray2D<double>(0, 0) {};
/*!
Constructor that initialize a matrix of double with 0.
\param r : Matrix number of rows.
\param c : Matrix number of columns.
*/
vpMatrix(unsigned int r, unsigned int c) : vpArray2D<double>(r, c) {};
/*!
Constructor that initialize a matrix of double with \e val.
\param r : Matrix number of rows.
\param c : Matrix number of columns.
\param val : Each element of the matrix is set to \e val.
*/
vpMatrix(unsigned int r, unsigned int c, double val) : vpArray2D<double>(r, c, val) {};
vpMatrix(const vpMatrix &M, unsigned int r, unsigned int c,
unsigned int nrows, unsigned int ncols) ;
/*!
Create a matrix from a 2D array that could be one of the following container that
inherit from vpArray2D such as vpMatrix, vpRotationMatrix, vpHomogeneousMatrix,
vpPoseVector, vpColVector, vpRowVector...
The following example shows how to create a matrix from an homogeneous matrix:
\code
vpRotationMatrix R;
vpMatrix M(R);
\endcode
*/
vpMatrix(const vpArray2D<double>& A) : vpArray2D<double>(A) {};
//! Destructor (Memory de-allocation)
virtual ~vpMatrix() {};
/*!
Removes all elements from the matrix (which are destroyed),
leaving the container with a size of 0.
*/
void clear()
{
if (data != NULL ) {
free(data);
data=NULL;
}
if (rowPtrs!=NULL) {
free(rowPtrs);
rowPtrs=NULL ;
}
rowNum = colNum = dsize = 0;
}
//-------------------------------------------------
// Setting a diagonal matrix
//-------------------------------------------------
/** @name Setting a diagonal matrix */
//@{
void diag(const double &val = 1.0);
void diag(const vpColVector &A);
// Initialize an identity matrix n-by-n
void eye();
void eye(unsigned int n) ;
// Initialize an identity matrix m-by-n
void eye(unsigned int m, unsigned int n) ;
//@}
//---------------------------------
// Assignment
//---------------------------------
/** @name Assignment operators */
//@{
vpMatrix &operator<<(double*);
vpMatrix &operator=(const vpArray2D<double> &A);
vpMatrix &operator=(const double x);
//@}
//-------------------------------------------------
// Stacking
//-------------------------------------------------
/** @name Stacking */
//@{
// Stack the matrix A below the current one, copy if not initialized this = [ this A ]^T
void stack(const vpMatrix &A);
void stack(const vpRowVector &r);
// Stacks columns of a matrix in a vector
void stackColumns(vpColVector &out );
// Stacks columns of a matrix in a vector
vpColVector stackColumns();
// Stacks columns of a matrix in a vector
void stackRows(vpRowVector &out );
// Stacks columns of a matrix in a vector
vpRowVector stackRows();
//@}
//---------------------------------
// Matrix insertion with Static Public Member Functions
//---------------------------------
/** @name Matrix insertion */
//@{
// Insert matrix A in the current matrix at the given position (r, c).
void insert(const vpMatrix&A, const unsigned int r, const unsigned int c);
//@}
//-------------------------------------------------
// Columns, Rows extraction, SubMatrix
//-------------------------------------------------
/** @name Columns, rows, sub-matrices extraction */
//@{
vpRowVector getRow(const unsigned int i) const;
vpRowVector getRow(const unsigned int i, const unsigned int j_begin, const unsigned int size) const;
vpColVector getCol(const unsigned int j) const;
vpColVector getCol(const unsigned int j, const unsigned int i_begin, const unsigned int size) const;
void init(const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols);
//@}
//---------------------------------
// Matrix operations.
//---------------------------------
/** @name Matrix operations */
//@{
// operation A = A + B
vpMatrix &operator+=(const vpMatrix &B);
// operation A = A - B
vpMatrix &operator-=(const vpMatrix &B);
vpMatrix operator*(const vpMatrix &B) const;
vpMatrix operator*(const vpRotationMatrix &R) const;
vpMatrix operator*(const vpVelocityTwistMatrix &V) const;
vpMatrix operator*(const vpForceTwistMatrix &V) const;
// operation t_out = A * t (A is unchanged, t and t_out are translation vectors)
vpTranslationVector operator*(const vpTranslationVector &tv) const;
vpColVector operator*(const vpColVector &v) const;
vpMatrix operator+(const vpMatrix &B) const;
vpMatrix operator-(const vpMatrix &B) const;
vpMatrix operator-() const;
//! Add x to all the element of the matrix : Aij = Aij + x
vpMatrix &operator+=(const double x);
//! Substract x to all the element of the matrix : Aij = Aij - x
vpMatrix &operator-=(const double x);
//! Multiply all the element of the matrix by x : Aij = Aij * x
vpMatrix &operator*=(const double x);
//! Divide all the element of the matrix by x : Aij = Aij / x
vpMatrix &operator/=(double x);
// Cij = Aij * x (A is unchanged)
vpMatrix operator*(const double x) const;
// Cij = Aij / x (A is unchanged)
vpMatrix operator/(const double x) const;
/*!
Return the sum of all the \f$a_{ij}\f$ elements of the matrix.
\return \f$\sum a_{ij}\f$
*/
double sum() const;
double sumSquare() const;
// return the determinant of the matrix.
double det(vpDetMethod method = LU_DECOMPOSITION) const;
//Compute the exponential matrix of a square matrix
vpMatrix expm() const;
//-------------------------------------------------
// Kronecker product
//-------------------------------------------------
/** @name Kronecker product */
//@{
// Compute Kronecker product matrix
void kron(const vpMatrix &m1, vpMatrix &out) const;
// Compute Kronecker product matrix
vpMatrix kron(const vpMatrix &m1) const;
//@}
//-------------------------------------------------
// Transpose
//-------------------------------------------------
/** @name Transpose */
//@{
// Compute the transpose C = A^T
vpMatrix t() const;
// Compute the transpose C = A^T
vpMatrix transpose()const;
void transpose(vpMatrix & C )const;
vpMatrix AAt() const;
void AAt(vpMatrix &B) const;
vpMatrix AtA() const;
void AtA(vpMatrix &B) const;
//@}
//-------------------------------------------------
// Matrix inversion
//-------------------------------------------------
/** @name Matrix inversion */
//@{
#ifndef DOXYGEN_SHOULD_SKIP_THIS
//! LU Decomposition
void LUDcmp(unsigned int* perm, int& d);
//! solve AX = B using the LU Decomposition
void LUBksb(unsigned int* perm, vpColVector& b);
#endif // doxygen should skip this
// inverse matrix A using the LU decomposition
vpMatrix inverseByLU() const;
#if defined(VISP_HAVE_LAPACK_C)
// inverse matrix A using the Cholesky decomposition (only for real symmetric matrices)
vpMatrix inverseByCholesky() const;
//lapack implementation of inverse by Cholesky
vpMatrix inverseByCholeskyLapack() const;
// inverse matrix A using the QR decomposition
vpMatrix inverseByQR() const;
//lapack implementation of inverse by QR
vpMatrix inverseByQRLapack() const;
#endif
//! Compute the pseudo inverse of the matrix using the SVD.
vpMatrix pseudoInverse(double svThreshold=1e-6) const;
//! Compute the pseudo inverse of the matrix using the SVD.
//! return the rank
unsigned int pseudoInverse(vpMatrix &Ap, double svThreshold=1e-6) const;
//! Compute the pseudo inverse of the matrix using the SVD.
//! return the rank and the singular value
unsigned int pseudoInverse(vpMatrix &Ap, vpColVector &sv, double svThreshold=1e-6) const ;
//! Compute the pseudo inverse of the matrix using the SVD.
//! return the rank and the singular value, image
unsigned int pseudoInverse(vpMatrix &Ap,
vpColVector &sv, double svThreshold,
vpMatrix &ImA,
vpMatrix &ImAt) const ;
//! Compute the pseudo inverse of the matrix using the SVD.
//! return the rank and the singular value, image, kernel.
unsigned int pseudoInverse(vpMatrix &Ap,
vpColVector &sv, double svThreshold,
vpMatrix &ImA,
vpMatrix &ImAt,
vpMatrix &kerA) const ;
//@}
//-------------------------------------------------
// SVD decomposition
//-------------------------------------------------
#ifndef DOXYGEN_SHOULD_SKIP_THIS
void svdFlake(vpColVector& w, vpMatrix& v);
void svdNr(vpColVector& w, vpMatrix& v);
#ifdef VISP_HAVE_GSL
void svdGsl(vpColVector& w, vpMatrix& v);
#endif
#if (VISP_HAVE_OPENCV_VERSION >= 0x020101) // Require opencv >= 2.1.1
void svdOpenCV(vpColVector& w, vpMatrix& v);
#endif
#ifdef VISP_HAVE_LAPACK_C
void svdLapack(vpColVector& W, vpMatrix& V);
#endif
//! solve AX=B using the SVD decomposition
void SVBksb(const vpColVector& w,
const vpMatrix& v,
const vpColVector& b, vpColVector& x);
#endif
/** @name SVD decomposition */
//@{
// singular value decomposition SVD
void svd(vpColVector& w, vpMatrix& v);
// solve Ax=B using the SVD decomposition (usage A = solveBySVD(B,x) )
void solveBySVD(const vpColVector &B, vpColVector &x) const ;
// solve Ax=B using the SVD decomposition (usage x=A.solveBySVD(B))
vpColVector solveBySVD(const vpColVector &B) const ;
unsigned int kernel(vpMatrix &KerA, double svThreshold=1e-6) const;
double cond() const;
//@}
//-------------------------------------------------
// Eigen values and vectors
//-------------------------------------------------
/** @name Eigen values */
//@{
// compute the eigen values using the Gnu Scientific library
vpColVector eigenValues() const;
void eigenValues(vpColVector &evalue, vpMatrix &evector) const;
//@}
//-------------------------------------------------
// Norms
//-------------------------------------------------
/** @name Norms */
//@{
double euclideanNorm() const;
double infinityNorm() const;
//@}
//---------------------------------
// Printing
//---------------------------------
/** @name Printing */
//@{
int print(std::ostream& s, unsigned int length, char const* intro=0) const;
std::ostream & matlabPrint(std::ostream & os) const;
std::ostream & maplePrint(std::ostream & os) const;
std::ostream & csvPrint(std::ostream & os) const;
std::ostream & cppPrint(std::ostream & os, const char * matrixName = NULL, bool octet = false) const;
void printSize() const { std::cout << getRows() <<" x " << getCols() <<" " ; }
//@}
//------------------------------------------------------------------
// Static functionalities
//------------------------------------------------------------------
//---------------------------------
// Setting a diagonal matrix with Static Public Member Functions
//---------------------------------
/** @name Setting a diagonal matrix with Static Public Member Functions */
//@{
// Create a diagonal matrix with the element of a vector DAii = Ai
static void createDiagonalMatrix(const vpColVector &A, vpMatrix &DA) ;
//@}
//---------------------------------
// Matrix insertion with Static Public Member Functions
//---------------------------------
/** @name Matrix insertion with Static Public Member Functions */
//@{
// Insert matrix B in matrix A at the given position (r, c).
static vpMatrix insert(const vpMatrix &A,const vpMatrix &B, const unsigned int r, const unsigned int c) ;
// Insert matrix B in matrix A (not modified) at the given position (r, c), the result is given in matrix C.
static void insert(const vpMatrix &A, const vpMatrix &B, vpMatrix &C, const unsigned int r, const unsigned int c) ;
//---------------------------------
// Stacking with Static Public Member Functions
//---------------------------------
/** @name Stacking with Static Public Member Functions */
//@{
// Juxtapose to matrices C = [ A B ]
static vpMatrix juxtaposeMatrices(const vpMatrix &A,const vpMatrix &B) ;
// Juxtapose to matrices C = [ A B ]
static void juxtaposeMatrices(const vpMatrix &A,const vpMatrix &B, vpMatrix &C) ;
// Stack two matrices C = [ A B ]^T
static vpMatrix stack(const vpMatrix &A, const vpMatrix &B) ;
static vpMatrix stack(const vpMatrix &A, const vpRowVector &r) ;
// Stack two matrices C = [ A B ]^T
static void stack(const vpMatrix &A, const vpMatrix &B, vpMatrix &C);
static void stack(const vpMatrix &A, const vpRowVector &r, vpMatrix &C);
//@}
//---------------------------------
// Matrix operations Static Public Member Functions
//---------------------------------
/** @name Matrix operations with Static Public Member Functions */
//@{
static void add2Matrices(const vpMatrix &A, const vpMatrix &B, vpMatrix &C);
static void add2Matrices(const vpColVector &A, const vpColVector &B, vpColVector &C);
static void add2WeightedMatrices(const vpMatrix &A, const double &wA, const vpMatrix &B,const double &wB, vpMatrix &C);
static void computeHLM(const vpMatrix &H, const double &alpha, vpMatrix &HLM);
static void mult2Matrices(const vpMatrix &A, const vpMatrix &B, vpMatrix &C);
static void mult2Matrices(const vpMatrix &A, const vpMatrix &B, vpRotationMatrix &C);
static void mult2Matrices(const vpMatrix &A, const vpMatrix &B, vpHomogeneousMatrix &C);
static void mult2Matrices(const vpMatrix &A, const vpColVector &B, vpColVector &C);
static void multMatrixVector(const vpMatrix &A, const vpColVector &v, vpColVector &w);
static void negateMatrix(const vpMatrix &A, vpMatrix &C);
static void sub2Matrices(const vpMatrix &A, const vpMatrix &B, vpMatrix &C);
static void sub2Matrices(const vpColVector &A, const vpColVector &B, vpColVector &C);
//@}
//---------------------------------
// Kronecker product Static Public Member Functions
//---------------------------------
/** @name Kronecker product with Static Public Member Functions */
//@{
// Compute Kronecker product matrix
static void kron(const vpMatrix &m1, const vpMatrix &m2 , vpMatrix &out);
// Compute Kronecker product matrix
static vpMatrix kron(const vpMatrix &m1, const vpMatrix &m2 );
//@}
//---------------------------------
// Covariance computation Static Public Member Functions
//---------------------------------
/** @name Covariance computation with Static Public Member Functions */
//@{
static vpMatrix computeCovarianceMatrix(const vpMatrix &A, const vpColVector &x, const vpColVector &b);
static vpMatrix computeCovarianceMatrix(const vpMatrix &A, const vpColVector &x, const vpColVector &b, const vpMatrix &w);
static vpMatrix computeCovarianceMatrixVVS(const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls, const vpMatrix &W);
static vpMatrix computeCovarianceMatrixVVS(const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls);
//@}
//---------------------------------
// Matrix I/O Static Public Member Functions
//---------------------------------
/** @name Matrix I/O with Static Public Member Functions */
//@{
/*!
Load a matrix from a file. This function overloads vpArray2D::load().
\param filename : absolute file name.
\param M : matrix to be loaded.
\param binary :If true the matrix is loaded from a binary file, else from a text file.
\param header : Header of the file is loaded in this parameter
\return Returns true if no problem appends.
*/
static inline bool loadMatrix(const std::string &filename, vpArray2D<double> &M,
const bool binary = false, char *header = NULL)
{
return vpArray2D<double>::load(filename, M, binary, header);
}
/*!
Load a matrix from a YAML-formatted file. This function overloads vpArray2D::loadYAML().
\param filename : absolute file name.
\param M : matrix to be loaded from the file.
\param header : Header of the file is loaded in this parameter.
\return Returns true if no problem appends.
*/
static inline bool loadMatrixYAML(const std::string &filename, vpArray2D<double> &M, char *header = NULL)
{
return vpArray2D<double>::loadYAML(filename, M, header);
}
/*!
Save a matrix to a file. This function overloads vpArray2D::load().
\param filename : absolute file name.
\param M : matrix to be saved.
\param binary : If true the matrix is save in a binary file, else a text file.
\param header : optional line that will be saved at the beginning of the file.
\return Returns true if no problem appends.
Warning : If you save the matrix as in a text file the precision is less than if you save it in a binary file.
*/
static inline bool saveMatrix(const std::string &filename, const vpArray2D<double> &M,
const bool binary = false,
const char *header = "")
{
return vpArray2D<double>::save(filename, M, binary, header);
}
/*!
Save a matrix in a YAML-formatted file. This function overloads vpArray2D::saveYAML().
\param filename : absolute file name.
\param M : matrix to be saved in the file.
\param header : optional lines that will be saved at the beginning of the file. Should be YAML-formatted and will adapt to the indentation if any.
\return Returns true if success.
*/
static inline bool saveMatrixYAML(const std::string &filename, const vpArray2D<double> &M, const char *header = "")
{
return vpArray2D<double>::saveYAML(filename, M, header);
}
//@}
#if defined(VISP_BUILD_DEPRECATED_FUNCTIONS)
/*!
@name Deprecated functions
*/
//@{
/*!
\deprecated Only provided for compatibilty with ViSP previous releases. This function does nothing.
*/
vp_deprecated void init() { };
/*!
\deprecated You should rather use stack(const vpMatrix &A)
*/
vp_deprecated void stackMatrices(const vpMatrix &A) { stack(A); };
/*!
\deprecated You should rather use stack(const vpMatrix &A, const vpMatrix &B)
*/
vp_deprecated static vpMatrix stackMatrices(const vpMatrix &A, const vpMatrix &B) { return vpMatrix::stack(A, B); };
/*!
\deprecated You should rather use stack(const vpMatrix &A, const vpMatrix &B, vpMatrix &C)
*/
vp_deprecated static void stackMatrices(const vpMatrix &A, const vpMatrix &B, vpMatrix &C) { vpMatrix::stack(A, B, C); };
/*!
\deprecated You should rather use stack(const vpMatrix &A, const vpMatrix &B)
*/
vp_deprecated static vpMatrix stackMatrices(const vpMatrix &A, const vpRowVector &B);
/*!
\deprecated You should rather use stack(const vpMatrix &A, const vpRowVector &B, vpMatrix &C)
*/
vp_deprecated static void stackMatrices(const vpMatrix &A, const vpRowVector &B, vpMatrix &C);
/*!
\deprecated You should rather use vpColVector::stack(const vpColVector &A, const vpColVector &B)
*/
vp_deprecated static vpMatrix stackMatrices(const vpColVector &A, const vpColVector &B);
/*!
\deprecated You should rather use vpColVector::stack(const vpColVector &A, const vpColVector &B, vpColVector &C)
*/
vp_deprecated static void stackMatrices(const vpColVector &A, const vpColVector &B, vpColVector &C);
/*!
\deprecated You should rather use diag(const double &)
*/
vp_deprecated void setIdentity(const double & val=1.0) ;
//@}
#endif
private:
double detByLU() const;
static void computeCovarianceMatrixVVS(const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls, vpMatrix &Js, vpColVector &deltaP);
};
//////////////////////////////////////////////////////////////////////////
#ifndef DOXYGEN_SHOULD_SKIP_THIS
VISP_EXPORT
#endif
vpMatrix operator*(const double &x, const vpMatrix &A) ;
#endif
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