eigen_analysis.h

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/**
 *  \file IMP/algebra/eigen_analysis.h
 *  \brief Principal component analysis of a set of points
 *
 *  Copyright 2007-2021 IMP Inventors. All rights reserved.
 */

#ifndef IMPALGEBRA_EIGEN_ANALYSIS_H
#define IMPALGEBRA_EIGEN_ANALYSIS_H

#include "VectorD.h"
#include "Transformation3D.h"
#include "GeometricPrimitiveD.h"
#include "IMP/algebra/internal/utility.h"
#include "IMP/algebra/ReferenceFrame3D.h"
#include <IMP/log.h>
#include <IMP/log_macros.h>

IMPALGEBRA_BEGIN_NAMESPACE

//! Represent an eigen analysis of some data.
template <int D>
class PrincipalComponentAnalysisD : public GeometricPrimitiveD<D> {
 public:
  PrincipalComponentAnalysisD() {}
  PrincipalComponentAnalysisD(const Vector<VectorD<D> > &pcs,
                              VectorD<D> values, VectorD<D> centroid)
      : eigen_vecs_(pcs), eigen_values_(values), centroid_(centroid) {}
  Vector<VectorD<D> > get_principal_components() const {
    IMP_USAGE_CHECK(!eigen_vecs_.empty(), "The PCA was not initialized");
    return eigen_vecs_;
  }
  VectorD<D> get_principal_component(unsigned int i) const {
    IMP_USAGE_CHECK(!eigen_vecs_.empty(), "The PCA was not initialized");
    return eigen_vecs_[i];
  }
  VectorD<D> get_principal_values() const {
    IMP_USAGE_CHECK(!eigen_vecs_.empty(), "The PCA was not initialized");
    return eigen_values_;
  }
  double get_principal_value(unsigned int i) const {
    IMP_USAGE_CHECK(!eigen_vecs_.empty(), "The PCA was not initialized");
    return eigen_values_[i];
  }
  inline VectorD<D> get_centroid() const { return centroid_; }
  void set_centroid(VectorD<D> cntr) {
    IMP_USAGE_CHECK(!eigen_vecs_.empty(), "The PCA was not initialized");
    centroid_ = cntr;
  }
  IMP_SHOWABLE(PrincipalComponentAnalysisD);
  IMP_COMPARISONS(PrincipalComponentAnalysisD);

 private:
  int compare(const PrincipalComponentAnalysisD &o) const {
    IMP_USAGE_CHECK(eigen_vecs_.empty() || o.eigen_vecs_.empty(),
                    "Cannot compare against anything other than the default"
                    " PrincipalComponentAnalysis");
    if (eigen_vecs_.empty() && o.eigen_vecs_.empty()) {
      return 0;
    } else {
      return -1;
    }
  }
  Vector<VectorD<D> > eigen_vecs_;
  VectorD<D> eigen_values_;
  VectorD<D> centroid_;
};

#ifndef IMP_DOXYGEN
typedef PrincipalComponentAnalysisD<1> PrincipalComponentAnalysis1D;
typedef PrincipalComponentAnalysisD<2> PrincipalComponentAnalysis2D;
typedef PrincipalComponentAnalysisD<3> PrincipalComponentAnalysis3D;
typedef PrincipalComponentAnalysisD<4> PrincipalComponentAnalysis4D;
typedef PrincipalComponentAnalysisD<5> PrincipalComponentAnalysis5D;
typedef PrincipalComponentAnalysisD<6> PrincipalComponentAnalysis6D;
typedef PrincipalComponentAnalysisD<-1> PrincipalComponentAnalysisKD;
typedef Vector<PrincipalComponentAnalysisD<1> >
    PrincipalComponentAnalysis1Ds;
typedef Vector<PrincipalComponentAnalysisD<2> >
    PrincipalComponentAnalysis2Ds;
typedef Vector<PrincipalComponentAnalysisD<3> >
    PrincipalComponentAnalysis3Ds;
typedef Vector<PrincipalComponentAnalysisD<4> >
    PrincipalComponentAnalysis4Ds;
typedef Vector<PrincipalComponentAnalysisD<5> >
    PrincipalComponentAnalysis5Ds;
typedef Vector<PrincipalComponentAnalysisD<6> >
    PrincipalComponentAnalysis6Ds;
typedef Vector<PrincipalComponentAnalysisD<-1> >
    PrincipalComponentAnalysisKDs;

template <int D>
inline void PrincipalComponentAnalysisD<D>::show(std::ostream &out) const {
  if (eigen_vecs_.empty()) {
    out << "invalid";
    return;
  }
  out << "vectors: " << eigen_vecs_ << " weights: " << eigen_values_
      << " centroid: " << centroid_ << std::endl;
}

#endif

//! Perform principal components analysis on a set of vectors
/** \see PrincipalComponentAnalysis
 */
template <int D>
PrincipalComponentAnalysisD<D> get_principal_components(
    const Vector<VectorD<D> > &ps) {
  IMP_USAGE_CHECK(!ps.empty(), "Need some vectors to get components.");
  unsigned int dim = ps[0].get_dimension();
  VectorD<D> m =
      std::accumulate(ps.begin(), ps.end(), get_zero_vector_kd(dim)) /
      ps.size();
  Eigen::MatrixXd cov = internal::get_covariance_matrix(ps, m);
  IMP_LOG_VERBOSE("The covariance matrix is " << cov << std::endl);

  Eigen::JacobiSVD<Eigen::MatrixXd> svd = cov.jacobiSvd(Eigen::ComputeFullV);
  Eigen::MatrixXd V = svd.matrixV();
  Eigen::VectorXd SV = svd.singularValues();

  IMP_LOG_VERBOSE("V is " << V << std::endl);
  VectorD<D> values = ps[0];
  Vector<VectorD<D> > vectors(dim, values);
  for (unsigned int i = 0; i < dim; ++i) {
    values[i] = SV[i];
    for (unsigned int j = 0; j < dim; ++j) {
      vectors[i][j] = V(j, i);
    }
  }
  // the principal components are the columns of V
  // pc1(pc3) is the vector of the largest(smallest) eigenvalue
  return PrincipalComponentAnalysisD<D>(vectors, values, m);
}

//! Get all alignments of the first principal component system to the second one
IMPALGEBRAEXPORT Transformation3Ds get_alignments_from_first_to_second(
    const PrincipalComponentAnalysisD<3> &pca1,
    const PrincipalComponentAnalysisD<3> &pca2);

#ifndef IMP_DOXYGEN
typedef PrincipalComponentAnalysisD<3> PrincipalComponentAnalysis;
#endif

IMPALGEBRA_END_NAMESPACE

#endif /* IMPALGEBRA_EIGEN_ANALYSIS_H */