SVDBase.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
#ifndef EIGEN_SVDBASE_H
#define EIGEN_SVDBASE_H
 
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
enum OptionsMasks {
  QRPreconditionerBits = NoQRPreconditioner | HouseholderQRPreconditioner | ColPivHouseholderQRPreconditioner |
                         FullPivHouseholderQRPreconditioner,
  ComputationOptionsBits = ComputeThinU | ComputeFullU | ComputeThinV | ComputeFullV
};
 
constexpr int get_qr_preconditioner(int options) { return options & QRPreconditionerBits; }
 
constexpr int get_computation_options(int options) { return options & ComputationOptionsBits; }
 
constexpr bool should_svd_compute_thin_u(int options) { return (options & ComputeThinU) != 0; }
constexpr bool should_svd_compute_full_u(int options) { return (options & ComputeFullU) != 0; }
constexpr bool should_svd_compute_thin_v(int options) { return (options & ComputeThinV) != 0; }
constexpr bool should_svd_compute_full_v(int options) { return (options & ComputeFullV) != 0; }
 
template<typename MatrixType, int Options>
void check_svd_options_assertions(unsigned int computationOptions, Index rows, Index cols) {
  EIGEN_STATIC_ASSERT((Options & ComputationOptionsBits) == 0,
                      "SVDBase: Cannot request U or V using both static and runtime options, even if they match. "
                      "Requesting unitaries at runtime is DEPRECATED: "
                      "Prefer requesting unitaries statically, using the Options template parameter.");
  eigen_assert(!(should_svd_compute_thin_u(computationOptions) && cols < rows && MatrixType::RowsAtCompileTime != Dynamic) &&
               !(should_svd_compute_thin_v(computationOptions) && rows < cols && MatrixType::ColsAtCompileTime != Dynamic) &&
               "SVDBase: If thin U is requested at runtime, your matrix must have more rows than columns or a dynamic number of rows."
               "Similarly, if thin V is requested at runtime, you matrix must have more columns than rows or a dynamic number of columns.");
  (void)computationOptions;
  (void)rows;
  (void)cols;
}
 
template<typename Derived> struct traits<SVDBase<Derived> >
 : traits<Derived>
{
  typedef MatrixXpr XprKind;
  typedef SolverStorage StorageKind;
  typedef int StorageIndex;
  enum { Flags = 0 };
};
 
template <typename MatrixType, int Options_>
struct svd_traits : traits<MatrixType> {
  static constexpr int Options = Options_;
  static constexpr bool ShouldComputeFullU = internal::should_svd_compute_full_u(Options);
  static constexpr bool ShouldComputeThinU = internal::should_svd_compute_thin_u(Options);
  static constexpr bool ShouldComputeFullV = internal::should_svd_compute_full_v(Options);
  static constexpr bool ShouldComputeThinV = internal::should_svd_compute_thin_v(Options);
  enum {
    DiagSizeAtCompileTime =
        internal::min_size_prefer_dynamic(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime),
    MaxDiagSizeAtCompileTime =
        internal::min_size_prefer_dynamic(MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime),
    MatrixUColsAtCompileTime = ShouldComputeThinU ? DiagSizeAtCompileTime
                                                  : MatrixType::RowsAtCompileTime,
    MatrixVColsAtCompileTime = ShouldComputeThinV ? DiagSizeAtCompileTime
                                                  : MatrixType::ColsAtCompileTime,
    MatrixUMaxColsAtCompileTime = ShouldComputeThinU ? MaxDiagSizeAtCompileTime
                                                     : MatrixType::MaxRowsAtCompileTime,
    MatrixVMaxColsAtCompileTime = ShouldComputeThinV ? MaxDiagSizeAtCompileTime
                                                     : MatrixType::MaxColsAtCompileTime
  };
};
}
 
template<typename Derived> class SVDBase
 : public SolverBase<SVDBase<Derived> >
{
public: 
   
  template<typename Derived_>
  friend struct internal::solve_assertion;
 
  typedef typename internal::traits<Derived>::MatrixType MatrixType;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
  typedef typename Eigen::internal::traits<SVDBase>::StorageIndex StorageIndex;
  typedef Eigen::Index Index; 
 
  static constexpr bool ShouldComputeFullU = internal::traits<Derived>::ShouldComputeFullU;
  static constexpr bool ShouldComputeThinU = internal::traits<Derived>::ShouldComputeThinU;
  static constexpr bool ShouldComputeFullV = internal::traits<Derived>::ShouldComputeFullV;
  static constexpr bool ShouldComputeThinV = internal::traits<Derived>::ShouldComputeThinV;
 
  enum {
    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
    DiagSizeAtCompileTime = internal::min_size_prefer_dynamic(RowsAtCompileTime, ColsAtCompileTime),
    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
    MaxDiagSizeAtCompileTime = internal::min_size_prefer_fixed(MaxRowsAtCompileTime, MaxColsAtCompileTime),
    MatrixOptions = MatrixType::Options,
    MatrixUColsAtCompileTime = internal::traits<Derived>::MatrixUColsAtCompileTime,
    MatrixVColsAtCompileTime = internal::traits<Derived>::MatrixVColsAtCompileTime,
    MatrixUMaxColsAtCompileTime = internal::traits<Derived>::MatrixUMaxColsAtCompileTime,
    MatrixVMaxColsAtCompileTime = internal::traits<Derived>::MatrixVMaxColsAtCompileTime
  };
 
  EIGEN_STATIC_ASSERT(!(ShouldComputeFullU && ShouldComputeThinU), "SVDBase: Cannot request both full and thin U")
  EIGEN_STATIC_ASSERT(!(ShouldComputeFullV && ShouldComputeThinV), "SVDBase: Cannot request both full and thin V")
 
  typedef
      typename internal::make_proper_matrix_type<Scalar, RowsAtCompileTime, MatrixUColsAtCompileTime, MatrixOptions,
                                                 MaxRowsAtCompileTime, MatrixUMaxColsAtCompileTime>::type MatrixUType;
  typedef
      typename internal::make_proper_matrix_type<Scalar, ColsAtCompileTime, MatrixVColsAtCompileTime, MatrixOptions,
                                                 MaxColsAtCompileTime, MatrixVMaxColsAtCompileTime>::type MatrixVType;
 
  typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
 
  Derived& derived() { return *static_cast<Derived*>(this); }
  const Derived& derived() const { return *static_cast<const Derived*>(this); }
 
  const MatrixUType& matrixU() const
  {
    _check_compute_assertions();
    eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
    return m_matrixU;
  }
 
  const MatrixVType& matrixV() const
  {
    _check_compute_assertions();
    eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
    return m_matrixV;
  }
 
  const SingularValuesType& singularValues() const
  {
    _check_compute_assertions();
    return m_singularValues;
  }
 
  Index nonzeroSingularValues() const
  {
    _check_compute_assertions();
    return m_nonzeroSingularValues;
  }
  
  inline Index rank() const
  {
    using std::abs;
    _check_compute_assertions();
    if(m_singularValues.size()==0) return 0;
    RealScalar premultiplied_threshold = numext::maxi<RealScalar>(m_singularValues.coeff(0) * threshold(), (std::numeric_limits<RealScalar>::min)());
    Index i = m_nonzeroSingularValues-1;
    while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
    return i+1;
  }
  
  Derived& setThreshold(const RealScalar& threshold)
  {
    m_usePrescribedThreshold = true;
    m_prescribedThreshold = threshold;
    return derived();
  }
 
  Derived& setThreshold(Default_t)
  {
    m_usePrescribedThreshold = false;
    return derived();
  }
 
  RealScalar threshold() const
  {
    eigen_assert(m_isInitialized || m_usePrescribedThreshold);
    // this temporary is needed to workaround a MSVC issue
    Index diagSize = (std::max<Index>)(1,m_diagSize);
    return m_usePrescribedThreshold ? m_prescribedThreshold
                                    : RealScalar(diagSize)*NumTraits<Scalar>::epsilon();
  }
 
  inline bool computeU() const { return m_computeFullU || m_computeThinU; }
  inline bool computeV() const { return m_computeFullV || m_computeThinV; }
 
  inline Index rows() const { return m_rows; }
  inline Index cols() const { return m_cols; }
  
  #ifdef EIGEN_PARSED_BY_DOXYGEN
  template<typename Rhs>
  inline const Solve<Derived, Rhs>
  solve(const MatrixBase<Rhs>& b) const;
  #endif
 
 
  EIGEN_DEVICE_FUNC
  ComputationInfo info() const
  {
    eigen_assert(m_isInitialized && "SVD is not initialized.");
    return m_info;
  }
 
  #ifndef EIGEN_PARSED_BY_DOXYGEN
  template<typename RhsType, typename DstType>
  void _solve_impl(const RhsType &rhs, DstType &dst) const;
 
  template<bool Conjugate, typename RhsType, typename DstType>
  void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const;
  #endif
 
protected:
 
  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
 
  void _check_compute_assertions() const {
    eigen_assert(m_isInitialized && "SVD is not initialized.");
  }
 
  template<bool Transpose_, typename Rhs>
  void _check_solve_assertion(const Rhs& b) const {
      EIGEN_ONLY_USED_FOR_DEBUG(b);
      _check_compute_assertions();
      eigen_assert(computeU() && computeV() && "SVDBase::solve(): Both unitaries U and V are required to be computed (thin unitaries suffice).");
      eigen_assert((Transpose_?cols():rows())==b.rows() && "SVDBase::solve(): invalid number of rows of the right hand side matrix b");
  }
 
  // return true if already allocated
  bool allocate(Index rows, Index cols, unsigned int computationOptions);
 
  MatrixUType m_matrixU;
  MatrixVType m_matrixV;
  SingularValuesType m_singularValues;
  ComputationInfo m_info;
  bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
  bool m_computeFullU, m_computeThinU;
  bool m_computeFullV, m_computeThinV;
  unsigned int m_computationOptions;
  Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
  RealScalar m_prescribedThreshold;
 
  SVDBase()
      : m_matrixU(MatrixUType()),
        m_matrixV(MatrixVType()),
        m_singularValues(SingularValuesType()),
        m_info(Success),
        m_isInitialized(false),
        m_isAllocated(false),
        m_usePrescribedThreshold(false),
        m_computeFullU(false),
        m_computeThinU(false),
        m_computeFullV(false),
        m_computeThinV(false),
        m_computationOptions(0),
        m_nonzeroSingularValues(0),
        m_rows(-1),
        m_cols(-1),
        m_diagSize(0),
        m_prescribedThreshold(0) {}
};
 
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename Derived>
template<typename RhsType, typename DstType>
void SVDBase<Derived>::_solve_impl(const RhsType &rhs, DstType &dst) const
{
  // A = U S V^*
  // So A^{-1} = V S^{-1} U^*
 
  Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
  Index l_rank = rank();
  tmp.noalias() =  m_matrixU.leftCols(l_rank).adjoint() * rhs;
  tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
  dst = m_matrixV.leftCols(l_rank) * tmp;
}
 
template<typename Derived>
template<bool Conjugate, typename RhsType, typename DstType>
void SVDBase<Derived>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const
{
  // A = U S V^*
  // So  A^{-*} = U S^{-1} V^*
  // And A^{-T} = U_conj S^{-1} V^T
  Matrix<typename RhsType::Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
  Index l_rank = rank();
 
  tmp.noalias() =  m_matrixV.leftCols(l_rank).transpose().template conjugateIf<Conjugate>() * rhs;
  tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
  dst = m_matrixU.template conjugateIf<!Conjugate>().leftCols(l_rank) * tmp;
}
#endif
 
template <typename Derived>
bool SVDBase<Derived>::allocate(Index rows, Index cols, unsigned int computationOptions) {
  eigen_assert(rows >= 0 && cols >= 0);
 
  if (m_isAllocated &&
      rows == m_rows &&
      cols == m_cols &&
      computationOptions == m_computationOptions)
  {
    return true;
  }
 
  m_rows = rows;
  m_cols = cols;
  m_info = Success;
  m_isInitialized = false;
  m_isAllocated = true;
  m_computationOptions = computationOptions;
  m_computeFullU = ShouldComputeFullU || internal::should_svd_compute_full_u(computationOptions);
  m_computeThinU = ShouldComputeThinU || internal::should_svd_compute_thin_u(computationOptions);
  m_computeFullV = ShouldComputeFullV || internal::should_svd_compute_full_v(computationOptions);
  m_computeThinV = ShouldComputeThinV || internal::should_svd_compute_thin_v(computationOptions);
 
  eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
  eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
 
  m_diagSize = (std::min)(m_rows, m_cols);
  m_singularValues.resize(m_diagSize);
  if(RowsAtCompileTime==Dynamic)
    m_matrixU.resize(m_rows, m_computeFullU ? m_rows : m_computeThinU ? m_diagSize : 0);
  if(ColsAtCompileTime==Dynamic)
    m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);
 
  return false;
}
 
}// end namespace
 
#endif // EIGEN_SVDBASE_H