vpMatrix.h

/*
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2023 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 as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * 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 https://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.
 */
 
#ifndef vpMatrix_H
#define vpMatrix_H
 
#include <visp3/core/vpArray2D.h>
#include <visp3/core/vpConfig.h>
#include <visp3/core/vpException.h>
#include <visp3/core/vpForceTwistMatrix.h>
#include <visp3/core/vpHomogeneousMatrix.h>
#include <visp3/core/vpRotationMatrix.h>
#include <visp3/core/vpTime.h>
#include <visp3/core/vpVelocityTwistMatrix.h>
 
#include <iostream>
#include <math.h>
 
class vpRowVector;
class vpColVector;
class vpTranslationVector;
class vpHomogeneousMatrix;
class vpVelocityTwistMatrix;
class vpForceTwistMatrix;
 
class VISP_EXPORT vpMatrix : public vpArray2D<double>
{
public:
  typedef enum
  {
    LU_DECOMPOSITION 
  } vpDetMethod;
 
public:
  vpMatrix() : vpArray2D<double>(0, 0) { }
 
  vpMatrix(unsigned int r, unsigned int c) : vpArray2D<double>(r, c) { }
 
  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);
 
  vpMatrix(const vpArray2D<double> &A) : vpArray2D<double>(A) { }
 
  vpMatrix(const vpMatrix &A) : vpArray2D<double>(A) { }
 
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
  vpMatrix(vpMatrix &&A);
  explicit vpMatrix(const std::initializer_list<double> &list);
  explicit vpMatrix(unsigned int nrows, unsigned int ncols, const std::initializer_list<double> &list);
  explicit vpMatrix(const std::initializer_list<std::initializer_list<double> > &lists);
#endif
 
  void clear()
  {
    if (data != nullptr) {
      free(data);
      data = nullptr;
    }
 
    if (rowPtrs != nullptr) {
      free(rowPtrs);
      rowPtrs = nullptr;
    }
    rowNum = colNum = dsize = 0;
  }
 
  //-------------------------------------------------
  // Setting a diagonal matrix
  //-------------------------------------------------
  static unsigned int getLapackMatrixMinSize() { return m_lapack_min_size; }
 
  static void setLapackMatrixMinSize(unsigned int min_size) { m_lapack_min_size = min_size; }
 
  //-------------------------------------------------
  // 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
  //---------------------------------
  vpMatrix &operator<<(double *);
  vpMatrix &operator<<(double val);
  vpMatrix &operator,(double val);
  vpMatrix &operator=(const vpArray2D<double> &A);
  vpMatrix &operator=(const vpMatrix &A);
 
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
  vpMatrix &operator=(vpMatrix &&A);
 
  vpMatrix &operator=(const std::initializer_list<double> &list);
  vpMatrix &operator=(const std::initializer_list<std::initializer_list<double> > &lists);
#endif
  vpMatrix &operator=(double x);
 
  //-------------------------------------------------
  // 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);
  void stack(const vpColVector &c);
  // 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
  //---------------------------------
  // Insert matrix A in the current matrix at the given position (r, c).
  void insert(const vpMatrix &A, unsigned int r, unsigned int c);
 
  //-------------------------------------------------
  // Columns, Rows, Diag extraction, SubMatrix
  //-------------------------------------------------
  vpMatrix extract(unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols) const;
  vpColVector getCol(unsigned int j) const;
  vpColVector getCol(unsigned int j, unsigned int i_begin, unsigned int size) const;
  vpRowVector getRow(unsigned int i) const;
  vpRowVector getRow(unsigned int i, unsigned int j_begin, unsigned int size) const;
  vpColVector getDiag() const;
  void init(const vpMatrix &M, unsigned int r, unsigned int c, unsigned int nrows, unsigned int ncols);
 
  //---------------------------------
  // Matrix operations.
  //---------------------------------
  // return the determinant of the matrix.
  double det(vpDetMethod method = LU_DECOMPOSITION) const;
  double detByLU() const;
#if defined(VISP_HAVE_EIGEN3)
  double detByLUEigen3() const;
#endif
#if defined(VISP_HAVE_LAPACK)
  double detByLULapack() const;
#endif
#if defined(VISP_HAVE_OPENCV)
  double detByLUOpenCV() const;
#endif
 
  // Compute the exponential matrix of a square matrix
  vpMatrix expm() const;
 
  // 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 vpHomogeneousMatrix &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;
 
  vpMatrix &operator+=(double x);
  vpMatrix &operator-=(double x);
  vpMatrix &operator*=(double x);
  vpMatrix &operator/=(double x);
 
  // Cij = Aij * x (A is unchanged)
  vpMatrix operator*(double x) const;
  // Cij = Aij / x (A is unchanged)
  vpMatrix operator/(double x) const;
 
  double sum() const;
  double sumSquare() const;
 
  //-------------------------------------------------
  // Hadamard product
  //-------------------------------------------------
  vpMatrix hadamard(const vpMatrix &m) const;
 
  //-------------------------------------------------
  // 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
  //-------------------------------------------------
  // Compute the transpose C = A^T
  vpMatrix t() const;
 
  // Compute the transpose C = A^T
  vpMatrix transpose() const;
  void transpose(vpMatrix &At) const;
 
  vpMatrix AAt() const;
  void AAt(vpMatrix &B) const;
 
  vpMatrix AtA() const;
  void AtA(vpMatrix &B) const;
 
  //-------------------------------------------------
  // Matrix inversion
  //-------------------------------------------------
  // inverse matrix A using the LU decomposition
  vpMatrix inverseByLU() const;
 
#if defined(VISP_HAVE_EIGEN3)
  vpMatrix inverseByLUEigen3() const;
#endif
#if defined(VISP_HAVE_LAPACK)
  vpMatrix inverseByLULapack() const;
#endif
#if defined(VISP_HAVE_OPENCV)
  vpMatrix inverseByLUOpenCV() const;
#endif
 
  // inverse matrix A using the Cholesky decomposition (only for real
  // symmetric matrices)
  vpMatrix inverseByCholesky() const;
 
#if defined(VISP_HAVE_LAPACK)
  vpMatrix inverseByCholeskyLapack() const;
#endif
#if defined(VISP_HAVE_OPENCV)
  vpMatrix inverseByCholeskyOpenCV() const;
#endif
 
  // inverse matrix A using the QR decomposition
  vpMatrix inverseByQR() const;
#if defined(VISP_HAVE_LAPACK)
  vpMatrix inverseByQRLapack() const;
#endif
 
  // inverse triangular matrix
  vpMatrix inverseTriangular(bool upper = true) const;
 
  vpMatrix pseudoInverse(double svThreshold = 1e-6) const;
  unsigned int pseudoInverse(vpMatrix &Ap, double svThreshold = 1e-6) const;
  unsigned int pseudoInverse(vpMatrix &Ap, vpColVector &sv, double svThreshold = 1e-6) const;
  unsigned int pseudoInverse(vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt) const;
  unsigned int pseudoInverse(vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
  vpMatrix pseudoInverse(int rank_in) const;
  int pseudoInverse(vpMatrix &Ap, int rank_in) const;
  int pseudoInverse(vpMatrix &Ap, vpColVector &sv, int rank_in) const;
  int pseudoInverse(vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt) const;
  int pseudoInverse(vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
 
#if defined(VISP_HAVE_LAPACK)
  vpMatrix pseudoInverseLapack(double svThreshold = 1e-6) const;
  unsigned int pseudoInverseLapack(vpMatrix &Ap, double svThreshold = 1e-6) const;
  unsigned int pseudoInverseLapack(vpMatrix &Ap, vpColVector &sv, double svThreshold = 1e-6) const;
  unsigned int pseudoInverseLapack(vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
  vpMatrix pseudoInverseLapack(int rank_in) const;
  int pseudoInverseLapack(vpMatrix &Ap, int rank_in) const;
  int pseudoInverseLapack(vpMatrix &Ap, vpColVector &sv, int rank_in) const;
  int pseudoInverseLapack(vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
#endif
#if defined(VISP_HAVE_EIGEN3)
  vpMatrix pseudoInverseEigen3(double svThreshold = 1e-6) const;
  unsigned int pseudoInverseEigen3(vpMatrix &Ap, double svThreshold = 1e-6) const;
  unsigned int pseudoInverseEigen3(vpMatrix &Ap, vpColVector &sv, double svThreshold = 1e-6) const;
  unsigned int pseudoInverseEigen3(vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
  vpMatrix pseudoInverseEigen3(int rank_in) const;
  int pseudoInverseEigen3(vpMatrix &Ap, int rank_in) const;
  int pseudoInverseEigen3(vpMatrix &Ap, vpColVector &sv, int rank_in) const;
  int pseudoInverseEigen3(vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
#endif
#if defined(VISP_HAVE_OPENCV)
  vpMatrix pseudoInverseOpenCV(double svThreshold = 1e-6) const;
  unsigned int pseudoInverseOpenCV(vpMatrix &Ap, double svThreshold = 1e-6) const;
  unsigned int pseudoInverseOpenCV(vpMatrix &Ap, vpColVector &sv, double svThreshold = 1e-6) const;
  unsigned int pseudoInverseOpenCV(vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
  vpMatrix pseudoInverseOpenCV(int rank_in) const;
  int pseudoInverseOpenCV(vpMatrix &Ap, int rank_in) const;
  int pseudoInverseOpenCV(vpMatrix &Ap, vpColVector &sv, int rank_in) const;
  int pseudoInverseOpenCV(vpMatrix &Ap, vpColVector &sv, int rank_in, vpMatrix &imA, vpMatrix &imAt, vpMatrix &kerAt) const;
#endif
 
  //-------------------------------------------------
  // SVD decomposition
  //-------------------------------------------------
 
  double cond(double svThreshold = 1e-6) const;
  unsigned int kernel(vpMatrix &kerAt, double svThreshold = 1e-6) const;
  unsigned int nullSpace(vpMatrix &kerA, double svThreshold = 1e-6) const;
  unsigned int nullSpace(vpMatrix &kerA, int dim) const;
 
  // 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;
 
  // singular value decomposition SVD
  void svd(vpColVector &w, vpMatrix &V);
#ifdef VISP_HAVE_EIGEN3
  void svdEigen3(vpColVector &w, vpMatrix &V);
#endif
#if defined(VISP_HAVE_LAPACK)
  void svdLapack(vpColVector &w, vpMatrix &V);
#endif
#if defined(VISP_HAVE_OPENCV) // Require opencv >= 2.1.1
  void svdOpenCV(vpColVector &w, vpMatrix &V);
#endif
 
  //-------------------------------------------------
  // QR decomposition
  //-------------------------------------------------
 
  unsigned int qr(vpMatrix &Q, vpMatrix &R, bool full = false, bool squareR = false, double tol = 1e-6) const;
  unsigned int qrPivot(vpMatrix &Q, vpMatrix &R, vpMatrix &P, bool full = false, bool squareR = false,
                       double tol = 1e-6) const;
  void solveByQR(const vpColVector &b, vpColVector &x) const;
  vpColVector solveByQR(const vpColVector &b) const;
 
  //-------------------------------------------------
  // Eigen values and vectors
  //-------------------------------------------------
  // Compute the eigen values using Lapack.
  vpColVector eigenValues() const;
  void eigenValues(vpColVector &evalue, vpMatrix &evector) const;
 
  //-------------------------------------------------
  // Norms
  //-------------------------------------------------
  double frobeniusNorm() const;
  double inducedL2Norm() const;
  double infinityNorm() const;
 
  //---------------------------------
  // Printing
  //---------------------------------
  std::ostream &cppPrint(std::ostream &os, const std::string &matrixName = "A", bool octet = false) const;
  std::ostream &csvPrint(std::ostream &os) const;
  std::ostream &maplePrint(std::ostream &os) const;
  std::ostream &matlabPrint(std::ostream &os) const;
  int print(std::ostream &s, unsigned int length, const std::string &intro = "") const;
  void printSize() const { std::cout << getRows() << " x " << getCols() << "  "; }
 
  //------------------------------------------------------------------
  // Static functionalities
  //------------------------------------------------------------------
 
  //---------------------------------
  // 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
  //---------------------------------
  // Insert matrix B in matrix A at the given position (r, c).
  static vpMatrix insert(const vpMatrix &A, const vpMatrix &B, unsigned int r, 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, unsigned int r, unsigned int c);
 
  //---------------------------------
  // 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);
  static vpMatrix stack(const vpMatrix &A, const vpColVector &c);
 
  // 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);
  static void stack(const vpMatrix &A, const vpColVector &c, vpMatrix &C);
 
  //---------------------------------
  // Matrix operations 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
  //---------------------------------
  // 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
  //---------------------------------
  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
  //---------------------------------
  static inline bool loadMatrix(const std::string &filename, vpArray2D<double> &M, bool binary = false,
                                char *header = nullptr)
  {
    return vpArray2D<double>::load(filename, M, binary, header);
  }
 
  static inline bool loadMatrixYAML(const std::string &filename, vpArray2D<double> &M, char *header = nullptr)
  {
    return vpArray2D<double>::loadYAML(filename, M, header);
  }
 
  static inline bool saveMatrix(const std::string &filename, const vpArray2D<double> &M, bool binary = false,
                                const char *header = "")
  {
    return vpArray2D<double>::save(filename, M, binary, header);
  }
 
  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)
  vp_deprecated double euclideanNorm() const;
 
  vp_deprecated void init() { }
 
  vp_deprecated void stackMatrices(const vpMatrix &A) { stack(A); }
  vp_deprecated static vpMatrix stackMatrices(const vpMatrix &A, const vpMatrix &B) { return stack(A, B); }
  vp_deprecated static void stackMatrices(const vpMatrix &A, const vpMatrix &B, vpMatrix &C) { stack(A, B, C); }
  vp_deprecated static vpMatrix stackMatrices(const vpMatrix &A, const vpRowVector &B);
  vp_deprecated static void stackMatrices(const vpMatrix &A, const vpRowVector &B, vpMatrix &C);
  vp_deprecated static vpMatrix stackMatrices(const vpColVector &A, const vpColVector &B);
  vp_deprecated static void stackMatrices(const vpColVector &A, const vpColVector &B, vpColVector &C);
 
  vp_deprecated void setIdentity(const double &val = 1.0);
 
  vp_deprecated vpRowVector row(unsigned int i);
  vp_deprecated vpColVector column(unsigned int j);
 
  // Deprecated functions using GSL
#ifndef DOXYGEN_SHOULD_SKIP_THIS
  vp_deprecated double detByLUGsl() const
  {
#if defined(VISP_HAVE_LAPACK)
    return detByLULapack();
#else
    throw(vpException(vpException::fatalError, "Undefined detByLULapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated vpMatrix inverseByLUGsl() const
  {
#if defined(VISP_HAVE_LAPACK)
    return inverseByLULapack();
#else
    throw(vpException(vpException::fatalError, "Undefined inverseByLULapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated vpMatrix inverseByCholeskyGsl() const
  {
#if defined(VISP_HAVE_LAPACK)
    return inverseByCholeskyLapack();
#else
    throw(vpException(vpException::fatalError, "Undefined inverseByCholeskyLapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated vpMatrix inverseByQRGsl() const
  {
#if defined(VISP_HAVE_LAPACK)
    return inverseByQRLapack();
#else
    throw(vpException(vpException::fatalError, "Undefined inverseByQRLapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated vpMatrix pseudoInverseGsl(double svThreshold = 1e-6) const
  {
#if defined(VISP_HAVE_LAPACK)
    return pseudoInverseLapack(svThreshold);
#else
    (void)svThreshold;
    throw(vpException(vpException::fatalError, "Undefined pseudoInverseLapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated unsigned int pseudoInverseGsl(vpMatrix &Ap, double svThreshold = 1e-6) const
  {
#if defined(VISP_HAVE_LAPACK)
    return pseudoInverseLapack(Ap, svThreshold);
#else
    (void)Ap;
    (void)svThreshold;
    throw(vpException(vpException::fatalError, "Undefined pseudoInverseLapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated unsigned int pseudoInverseGsl(vpMatrix &Ap, vpColVector &sv, double svThreshold = 1e-6) const
  {
#if defined(VISP_HAVE_LAPACK)
    return pseudoInverseLapack(Ap, sv, svThreshold);
#else
    (void)Ap;
    (void)sv;
    (void)svThreshold;
    throw(vpException(vpException::fatalError, "Undefined pseudoInverseLapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated unsigned int pseudoInverseGsl(vpMatrix &Ap, vpColVector &sv, double svThreshold, vpMatrix &imA, vpMatrix &imAt,
                                vpMatrix &kerAt) const
  {
#if defined(VISP_HAVE_LAPACK)
    return pseudoInverseLapack(Ap, sv, svThreshold, imA, imAt, kerAt);
#else
    (void)Ap;
    (void)sv;
    (void)svThreshold;
    (void)imA;
    (void)imAt;
    (void)kerAt;
    throw(vpException(vpException::fatalError, "Undefined pseudoInverseLapack(). Install Lapack 3rd party"));
#endif
  }
 
  vp_deprecated void svdGsl(vpColVector &w, vpMatrix &V)
  {
#if defined(VISP_HAVE_LAPACK)
    svdLapack(w, V);
#else
    (void)w;
    (void)V;
    throw(vpException(vpException::fatalError, "Undefined svdLapack(). Install Lapack 3rd party"));
#endif
  }
 
#endif // ifndef DOXYGEN_SHOULD_SKIP_THIS
#endif
 
private:
  static unsigned int m_lapack_min_size;
  static const unsigned int m_lapack_min_size_default;
 
#if defined(VISP_HAVE_LAPACK)
  static void blas_dgemm(char trans_a, char trans_b, unsigned int M_, unsigned int N_, unsigned int K_, double alpha,
                         double *a_data, unsigned int lda_, double *b_data, unsigned int ldb_, double beta,
                         double *c_data, unsigned int ldc_);
  static void blas_dgemv(char trans, unsigned int M_, unsigned int N_, double alpha, double *a_data, unsigned int lda_,
                         double *x_data, int incx_, double beta, double *y_data, int incy_);
  static void blas_dsyev(char jobz, char uplo, unsigned int n_, double *a_data, unsigned int lda_, double *w_data,
                         double *work_data, int lwork_, int &info_);
#endif
 
  static void computeCovarianceMatrixVVS(const vpHomogeneousMatrix &cMo, const vpColVector &deltaS, const vpMatrix &Ls,
                                         vpMatrix &Js, vpColVector &deltaP);
};
 
#if defined(VISP_USE_MSVC) && defined(visp_EXPORTS)
const __declspec(selectany) unsigned int vpMatrix::m_lapack_min_size_default = 0;
__declspec(selectany) unsigned int vpMatrix::m_lapack_min_size = vpMatrix::m_lapack_min_size_default;
#endif
 
#ifndef DOXYGEN_SHOULD_SKIP_THIS
VISP_EXPORT
#endif
vpMatrix operator*(const double &x, const vpMatrix &A);
#endif