vpMatrix_svd.cpp

/*
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2024 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 SVD decomposition.
 */
 
#include <visp3/core/vpColVector.h>
#include <visp3/core/vpConfig.h>
#include <visp3/core/vpException.h>
#include <visp3/core/vpMath.h>
#include <visp3/core/vpMatrix.h>
#include <visp3/core/vpMatrixException.h>
 
#include <cmath> // std::fabs
#include <iostream>
 
#ifdef VISP_HAVE_EIGEN3
#include <Eigen/SVD>
#endif
 
#if defined(VISP_HAVE_OPENCV) // Require opencv >= 2.1.1
#include <opencv2/core/core.hpp>
#endif
 
#ifdef VISP_HAVE_LAPACK
#ifdef VISP_HAVE_GSL
#include <gsl/gsl_linalg.h>
#endif
#ifdef VISP_HAVE_MKL
#include <mkl.h>
typedef MKL_INT integer;
#else
#if defined(VISP_HAVE_LAPACK_BUILT_IN)
typedef long int integer;
#else
typedef int integer;
#endif
extern "C" int dgesdd_(char *jobz, integer *m, integer *n, double *a, integer *lda, double *s, double *u, integer *ldu,
                       double *vt, integer *ldvt, double *work, integer *lwork, integer *iwork, integer *info);
 
#include <stdio.h>
#include <string.h>
#endif
#endif
 
BEGIN_VISP_NAMESPACE

void vpMatrix::solveBySVD(const vpColVector &b, vpColVector &x) const { x = pseudoInverse(1e-6) * b; }

vpColVector vpMatrix::solveBySVD(const vpColVector &B) const
{
  vpColVector X(colNum);
 
  solveBySVD(B, X);
  return X;
}

void vpMatrix::svd(vpColVector &w, vpMatrix &V)
{
#if defined(VISP_HAVE_LAPACK)
  svdLapack(w, V);
#elif defined(VISP_HAVE_EIGEN3)
  svdEigen3(w, V);
#elif defined(VISP_HAVE_OPENCV) // Require opencv >= 2.1.1
  svdOpenCV(w, V);
#else
  (void)w;
  (void)V;
  throw(vpException(vpException::fatalError, "Cannot compute SVD. Install Lapack, Eigen3 or OpenCV 3rd party"));
#endif
}
 
#if defined(VISP_HAVE_OPENCV) // Require opencv >= 2.1.1

void vpMatrix::svdOpenCV(vpColVector &w, vpMatrix &V)
{
  int rows = static_cast<int>(this->getRows());
  int cols = static_cast<int>(this->getCols());
  cv::Mat m(rows, cols, CV_64F, this->data);
  cv::SVD opencvSVD(m);
  cv::Mat opencvV = opencvSVD.vt;
  cv::Mat opencvW = opencvSVD.w;
  V.resize(static_cast<unsigned int>(opencvV.rows), static_cast<unsigned int>(opencvV.cols));
  w.resize(static_cast<unsigned int>(opencvW.rows * opencvW.cols));
 
  memcpy(V.data, opencvV.data, static_cast<size_t>(8 * opencvV.rows * opencvV.cols));
  V = V.transpose();
  memcpy(w.data, opencvW.data, static_cast<size_t>(8 * opencvW.rows * opencvW.cols));
  this->resize(static_cast<unsigned int>(opencvSVD.u.rows), static_cast<unsigned int>(opencvSVD.u.cols));
  memcpy(this->data, opencvSVD.u.data, static_cast<size_t>(8 * opencvSVD.u.rows * opencvSVD.u.cols));
}
 
#endif
 
#if defined(VISP_HAVE_LAPACK)
void vpMatrix::svdLapack(vpColVector &w, vpMatrix &V)
{
#ifdef VISP_HAVE_GSL
  {
    // GSL cannot consider M < N. In that case we transpose input matrix
    vpMatrix U;
    unsigned int nc = getCols();
    unsigned int nr = getRows();
 
    if (rowNum < colNum) {
      U = this->transpose();
      nc = getRows();
      nr = getCols();
    }
    else {
      nc = getCols();
      nr = getRows();
    }
 
    w.resize(nc);
    V.resize(nc, nc);
 
    gsl_vector *work = gsl_vector_alloc(nc);
 
    gsl_matrix A;
    A.size1 = nr;
    A.size2 = nc;
    A.tda = A.size2;
    if (rowNum < colNum) {
      A.data = U.data;
    }
    else {
      A.data = this->data;
    }
    A.owner = 0;
    A.block = 0;
 
    gsl_matrix V_;
    V_.size1 = nc;
    V_.size2 = nc;
    V_.tda = V_.size2;
    V_.data = V.data;
    V_.owner = 0;
    V_.block = 0;
 
    gsl_vector S;
    S.size = nc;
    S.stride = 1;
    S.data = w.data;
    S.owner = 0;
    S.block = 0;
 
    gsl_linalg_SV_decomp(&A, &V_, &S, work);
 
    if (rowNum < colNum) {
      (*this) = V;
      V = U;
    }
 
    gsl_vector_free(work);
  }
#else
  {
    vpMatrix U;
    unsigned int nc = getCols();
    unsigned int nr = getRows();
 
    if (rowNum < colNum) {
      U = this->transpose();
      nc = getRows();
      nr = getCols();
    }
    else {
      nc = getCols();
      nr = getRows();
    }
 
    w.resize(nc);
    V.resize(nc, nc);
 
    double *a = new double[static_cast<unsigned int>(nr * nc)];
    if (rowNum < colNum) {
      memcpy(a, U.data, this->getRows() * this->getCols() * sizeof(double));
    }
    else {
      memcpy(a, this->data, this->getRows() * this->getCols() * sizeof(double));
    }
 
    integer m = (integer)(nc);
    integer n = (integer)(nr);
    integer lda = nc;
    integer ldu = nc;
    integer ldvt = std::min<integer>(nr, nc);
    integer info, lwork;
 
    double wkopt;
    double *work;
 
    integer *iwork = new integer[8 * static_cast<integer>(std::min<integer>(nr, nc))];
 
    double *s = w.data;
    double *u = V.data;
    double *vt;
    if (rowNum < colNum) {
      vt = U.data;
    }
    else {
      vt = this->data;
    }
 
    lwork = -1;
    dgesdd_((char *)"S", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, &wkopt, &lwork, iwork, &info);
    lwork = static_cast<int>(wkopt);
    work = new double[static_cast<unsigned int>(lwork)];
 
    dgesdd_((char *)"S", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, &info);
 
    if (info > 0) {
      throw(vpMatrixException(vpMatrixException::fatalError, "The algorithm computing SVD failed to converge."));
    }
 
    if (rowNum < colNum) {
      (*this) = V.transpose();
      V = U;
    }
    else {
      V = V.transpose();
    }
    delete[] work;
    delete[] iwork;
    delete[] a;
  }
#endif
}
#endif
 
#ifdef VISP_HAVE_EIGEN3
void vpMatrix::svdEigen3(vpColVector &w, vpMatrix &V)
{
  if (rowNum < colNum) {
    w.resize(rowNum);
    V.resize(colNum, rowNum);
  }
  else {
    w.resize(colNum);
    V.resize(colNum, colNum);
  }
 
  Eigen::Map<Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> > M(this->data, this->getRows(),
                                                                                        this->getCols());
  Eigen::JacobiSVD<Eigen::MatrixXd> svd(M, Eigen::ComputeThinU | Eigen::ComputeThinV);
 
  Eigen::Map<Eigen::VectorXd> w_(w.data, w.size());
 
  if (rowNum < colNum) {
    this->resize(rowNum, rowNum);
  }
  else {
    this->resize(rowNum, colNum);
  }
  Eigen::Map<Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> > V_(V.data, V.getRows(), V.getCols());
  Eigen::Map<Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> > U_(this->data, rowNum, colNum);
  w_ = svd.singularValues();
  V_ = svd.matrixV();
  U_ = svd.matrixU();
}
#endif
END_VISP_NAMESPACE