svd.hh

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// Copyright (c) 2015 CNRS
// Author: Joseph Mirabel
//
//
 
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// modification, are permitted provided that the following conditions are
// met:
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// 1. Redistributions of source code must retain the above copyright
//    notice, this list of conditions and the following disclaimer.
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// 2. Redistributions in binary form must reproduce the above copyright
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// DAMAGE.
 
#ifndef HPP_CONSTRAINTS_SVD_HH
#define HPP_CONSTRAINTS_SVD_HH
 
#include <Eigen/SVD>
#include <hpp/constraints/fwd.hh>
 
namespace hpp {
namespace constraints {
template <typename SVD>
static Eigen::Ref<const typename SVD::MatrixUType> getU1(
    const SVD& svd, const size_type& rank) {
  return svd.matrixU().leftCols(rank);
}
 
template <typename SVD>
static Eigen::Ref<const typename SVD::MatrixUType> getU2(
    const SVD& svd, const size_type& rank) {
  return svd.matrixU().rightCols(svd.matrixU().cols() - rank);
}
 
template <typename SVD>
static Eigen::Ref<const typename SVD::MatrixUType> getV1(
    const SVD& svd, const size_type& rank) {
  return svd.matrixV().leftCols(rank);
}
 
template <typename SVD>
static Eigen::Ref<const typename SVD::MatrixUType> getV2(
    const SVD& svd, const size_type& rank) {
  return svd.matrixV().rightCols(svd.matrixV().cols() - rank);
}
 
template <typename SVD>
static void pseudoInverse(const SVD& svd,
                          Eigen::Ref<typename SVD::MatrixType> pinvmat) {
  eigen_assert(
      svd.computeU() && svd.computeV() &&
      "Eigen::JacobiSVD "
      "computation flags must be at least: ComputeThinU | ComputeThinV");
 
  size_type rank = svd.rank();
  typename SVD::SingularValuesType singularValues_inv =
      svd.singularValues().segment(0, rank).cwiseInverse();
 
  pinvmat.noalias() = getV1<SVD>(svd, rank) * singularValues_inv.asDiagonal() *
                      getU1<SVD>(svd, rank).adjoint();
}
 
template <typename SVD>
void projectorOnSpan(const SVD& svd,
                     Eigen::Ref<typename SVD::MatrixType> projector) {
  eigen_assert(
      svd.computeU() && svd.computeV() &&
      "Eigen::JacobiSVD "
      "computation flags must be at least: ComputeThinU | ComputeThinV");
 
  size_type rank = svd.rank();
  projector.noalias() = getV1<SVD>(svd, rank) * getV1<SVD>(svd, rank).adjoint();
}
 
template <typename SVD>
void projectorOnSpanOfInv(const SVD& svd,
                          Eigen::Ref<typename SVD::MatrixType> projector) {
  eigen_assert(
      svd.computeU() && svd.computeV() &&
      "Eigen::JacobiSVD "
      "computation flags must be at least: ComputeThinU | ComputeThinV");
 
  size_type rank = svd.rank();
  projector.noalias() = getU1<SVD>(svd, rank) * getU1<SVD>(svd, rank).adjoint();
}
 
template <typename SVD>
void projectorOnKernel(const SVD& svd,
                       Eigen::Ref<typename SVD::MatrixType> projector,
                       const bool& computeFullV = false) {
  eigen_assert(svd.computeV() &&
               "Eigen::JacobiSVD "
               "computation flags must be at least: ComputeThinV");
 
  size_type rank = svd.rank();
  if (computeFullV)
    projector.noalias() =
        getV2<SVD>(svd, rank) * getV2<SVD>(svd, rank).adjoint();
  else {
    projector.noalias() =
        -getV1<SVD>(svd, rank) * getV1<SVD>(svd, rank).adjoint();
    projector.diagonal().noalias() += vector_t::Ones(svd.matrixV().rows());
  }
}
 
template <typename SVD>
void projectorOnKernelOfInv(const SVD& svd,
                            Eigen::Ref<typename SVD::MatrixType> projector,
                            const bool& computeFullU = false) {
  eigen_assert(svd.computeU() &&
               "Eigen::JacobiSVD "
               "computation flags must be at least: ComputeThinU");
 
  size_type rank = svd.rank();
  if (computeFullU) {
    // U2 * U2*
    projector.noalias() =
        getU2<SVD>(svd, rank) * getU2<SVD>(svd, rank).adjoint();
  } else {
    // I - U1 * U1*
    projector.noalias() =
        -getU1<SVD>(svd, rank) * getU1<SVD>(svd, rank).adjoint();
    projector.diagonal().noalias() += vector_t::Ones(svd.matrixU().rows());
  }
}
}  // namespace constraints
}  // namespace hpp
 
#endif  // HPP_CONSTRAINTS_SVD_HH