bivariate_functions.h

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/**
 *  \file IMP/isd/bivariate_functions.h
 *  \brief Classes for general functions
 *
 *  Copyright 2007-2019 IMP Inventors. All rights reserved.
 */

#ifndef IMPISD_BIVARIATE_FUNCTIONS_H
#define IMPISD_BIVARIATE_FUNCTIONS_H

#include <IMP/isd/isd_config.h>
#include <IMP/Particle.h>
#include <IMP/isd/Nuisance.h>
#include <IMP/isd/Scale.h>
#include <IMP/isd/Switching.h>
#include <IMP/Object.h>
#include <Eigen/Dense>

#define IMP_ISD_BIVARIATE_FUNCTIONS_MINIMUM 1e-7

IMPISD_BEGIN_NAMESPACE

//! Base class for functions of two variables
class IMPISDEXPORT BivariateFunction : public Object {
 public:
  BivariateFunction(std::string str) : Object(str) {}

  //! evaluate the function at a certain point
  virtual Floats operator()(const Floats& x1, const Floats& x2) const = 0;

  //! evaluate the function at a list of points
  /* returns a NxN matrix of entries where N=xlist.rows()
   * and entry ij of the matrix is f(xlist(i),xlist(j))
   */
  virtual Eigen::MatrixXd operator()(const IMP::FloatsList& xlist)
      const = 0;

  //! used for testing only
  virtual FloatsList operator()(const IMP::FloatsList& xlist,
                                bool stupid) const = 0;

  //! return true if internal parameters have changed.
  virtual bool has_changed() const = 0;

  //! update internal parameters
  virtual void update() = 0;

  //! update derivatives of particles
  virtual void add_to_derivatives(const Floats& x1, const Floats& x2,
                                  DerivativeAccumulator& accum) const = 0;

  //! update derivatives of particles
  /* add to the given particle the specified derivative
   * guarantees that the particle_no (starting at 0) matches with
   * the columns of get_derivative_matrix.
   */
  virtual void add_to_particle_derivative(unsigned particle_no, double value,
                                          DerivativeAccumulator& accum)
      const = 0;

  //! return derivative matrix
  /* m_ij = d(func(xlist[i],xlist[j]))/dparticle_no
   * the matrix is NxN where N = xlist.size()
   */
  virtual Eigen::MatrixXd get_derivative_matrix(
      unsigned particle_no, const FloatsList& xlist) const = 0;

  // for testing purposes
  virtual FloatsList get_derivative_matrix(unsigned particle_no,
                                           const FloatsList& xlist,
                                           bool stupid) const = 0;

  //! return second derivative matrix
  virtual Eigen::MatrixXd get_second_derivative_matrix(
      unsigned particle_a, unsigned particle_b,
      const FloatsList& xlist) const = 0;

  // for testing purposes
  virtual FloatsList get_second_derivative_matrix(unsigned particle_a,
                                                  unsigned particle_b,
                                                  const FloatsList& xlist,
                                                  bool stupid) const = 0;

  //! returns the number of input dimensions
  virtual unsigned get_ndims_x1() const = 0;
  virtual unsigned get_ndims_x2() const = 0;

  //! returns the number of output dimensions
  virtual unsigned get_ndims_y() const = 0;

  //! returns the number of particles that this function uses
  virtual unsigned get_number_of_particles() const = 0;

  //! returns true if the particle whose index is provided is optimized
  virtual bool get_particle_is_optimized(unsigned particle_no) const = 0;

  //! returns the number of particles that are optimized
  virtual unsigned get_number_of_optimized_particles() const = 0;

  //! particle manipulation
  virtual ModelObjectsTemp get_inputs() const = 0;

  IMP_REF_COUNTED_DESTRUCTOR(BivariateFunction);
};
//
//! Covariance function
/* \f[w(x,x') = \tau^2 \exp\left(-\frac{|x-x'|^\alpha}{2\lambda^\alpha} +
 * \delta_{ij} J\f]
 * \param[in] \f$\tau\f$ ISD Scale
 * \param[in] \f$\lambda\f$ ISD Scale
 * \param[in] \f$\alpha\f$ positive double, usually greater than 1.
 *             Default is 2.
 * \param[in] J is some jitter. Try J=0.01 if you get NANs.
 * \param[in] cutoff is a positive double indicating when to consider that
 * values are zero (to avoid computing exponentials). cutoff is relative to the
 * value when x=x', and affects only the call get_derivative_matrix.
 */
class IMPISDEXPORT Covariance1DFunction : public BivariateFunction {
 public:
  Covariance1DFunction(Particle* tau, Particle* ilambda,
                       double alpha = 2.0, double jitter = 0.0,
                       double cutoff = 1e-7)
      : BivariateFunction("Covariance1DFunction %1%"),
        alpha_(alpha),
        tau_(tau),
        lambda_(ilambda),
        J_(jitter),
        cutoff_(cutoff) {
    IMP_LOG_TERSE("Covariance1DFunction: constructor" << std::endl);
    lambda_val_ = Scale(ilambda).get_nuisance();
    tau_val_ = Scale(tau).get_nuisance();
    do_jitter = (jitter > IMP_ISD_BIVARIATE_FUNCTIONS_MINIMUM);
    alpha_square_ = (std::abs(alpha - 2) < IMP_ISD_BIVARIATE_FUNCTIONS_MINIMUM);
    update();
  }

  bool has_changed() const {
    double tmpt = Scale(tau_).get_nuisance();
    double tmpl = Scale(lambda_).get_nuisance();
    IMP_LOG_VERBOSE("Covariance1DFunction: has_changed(): ");
    IMP_LOG_VERBOSE(tmpt << " " << tau_val_ << " ");
    IMP_LOG_VERBOSE(tmpl << " " << lambda_val_ << " ");
    if ((std::abs(tmpt - tau_val_) > IMP_ISD_BIVARIATE_FUNCTIONS_MINIMUM) ||
        (std::abs(tmpl - lambda_val_) > IMP_ISD_BIVARIATE_FUNCTIONS_MINIMUM)) {
      IMP_LOG_VERBOSE("true" << std::endl);
      return true;
    } else {
      IMP_LOG_VERBOSE("false" << std::endl);
      return false;
    }
  }

  void update() {
    lambda_val_ = Scale(lambda_).get_nuisance();
    tau_val_ = Scale(tau_).get_nuisance();
    IMP_LOG_TERSE("Covariance1DFunction: update()  tau:= "
                  << tau_val_ << " lambda:=" << lambda_val_ << std::endl);
    IMP_INTERNAL_CHECK(!IMP::isnan(tau_val_), "tau is nan.");
    IMP_INTERNAL_CHECK(!IMP::isnan(lambda_val_), "lambda is nan.");
    IMP_INTERNAL_CHECK(tau_val_ >= 0, "tau is negative.");
    IMP_INTERNAL_CHECK(lambda_val_ >= 0, "lambda is negative.");
    IMP_INTERNAL_CHECK(lambda_val_ != 0, "lambda is zero.");
  }

  Floats operator()(const Floats& x1, const Floats& x2) const {
    IMP_USAGE_CHECK(x1.size() == 1, "expecting a 1-D vector");
    IMP_USAGE_CHECK(x2.size() == 1, "expecting a 1-D vector");
    Floats ret(1, get_value(x1[0], x2[0]));
    return ret;
  }

  Eigen::MatrixXd operator()(const IMP::FloatsList& xlist) const {
    const unsigned M = xlist.size();
    Eigen::MatrixXd Mret(M, M);
    for (unsigned i = 0; i < M; i++) {
      for (unsigned j = i; j < M; j++) {
        IMP_USAGE_CHECK(xlist[i].size() == 1, "expecting a 1-D vector");
        IMP_USAGE_CHECK(xlist[j].size() == 1, "expecting a 1-D vector");
        double x1 = xlist[i][0];
        double x2 = xlist[j][0];
        double ret = get_value(x1, x2);
        Mret(i, j) = ret;
        if (i != j) Mret(j, i) = ret;
      }
    }
    return Mret;
  }

  FloatsList operator()(const IMP::FloatsList& xlist, bool) const {
    Eigen::MatrixXd mat((*this)(xlist));
    FloatsList ret;
    for (unsigned i = 0; i < xlist.size(); i++)
      for (unsigned j = 0; j < xlist.size(); j++)
        ret.push_back(Floats(1, mat(i, j)));
    return ret;
  }

  void add_to_derivatives(const Floats& x1, const Floats& x2,
                          DerivativeAccumulator& accum) const {
    // d[w(x1,x2)]/dtau = 2/tau*(w(x1,x2))
    double val = get_value(x1[0], x2[0]);
    double tauderiv = 2. / tau_val_ * val;
    IMP_INTERNAL_CHECK(!IMP::isnan(tauderiv), "tau derivative is nan.");
    Scale(tau_).add_to_nuisance_derivative(tauderiv, accum);
    // d[w(x,x')]/dlambda
    // = w(x,x') ( alpha |x'-x|^alpha/(2 lambda^{alpha+1}))
    double lambdaderiv =
        val *
        (alpha_ * std::pow((std::abs(x1[0] - x2[0]) / lambda_val_), alpha_) /
         (2. * lambda_val_));
    IMP_INTERNAL_CHECK(!IMP::isnan(lambdaderiv), "lambda derivative is nan.");
    Scale(lambda_).add_to_nuisance_derivative(lambdaderiv, accum);
  }

  void add_to_particle_derivative(unsigned particle_no, double value,
                                  DerivativeAccumulator& accum) const {
    switch (particle_no) {
      case 0:  // tau
        IMP_INTERNAL_CHECK(!IMP::isnan(value), "tau derivative is nan.");
        Scale(tau_).add_to_nuisance_derivative(value, accum);
        break;
      case 1:  // lambda
        IMP_INTERNAL_CHECK(!IMP::isnan(value), "lambda derivative is nan.");
        Scale(lambda_).add_to_nuisance_derivative(value, accum);
        break;
      default:
        IMP_THROW("Invalid particle number", ModelException);
    }
  }

  Eigen::MatrixXd get_derivative_matrix(unsigned particle_no,
                                        const FloatsList& xlist) const {
    // Strategy: fill in the main diagonal, then fill with zeros
    // if the value of the function falls below cutoff.
    // assumes data points are ordered!
    unsigned N = xlist.size();
    Eigen::MatrixXd ret(N, N);
    double diag;
    switch (particle_no) {
      case 0:  // tau
               // d[w(x1,x1)]/dtau
        //  = 2/tau*w(x1,x1)
        diag = get_value(xlist[0][0], xlist[0][0]);
        diag *= 2. / tau_val_;
        break;
      case 1:  // lambda
               // d[w(x,x)]/dlambda
               //= w(x,x)
        //  *( alpha /(2 lambda^{alpha+1}))
        diag = 0;
        break;
      default:
        IMP_THROW("Invalid particle number", ModelException);
    }
    IMP_INTERNAL_CHECK(!IMP::isnan(diag),
                       "derivative matrix is nan on the diagonal.");
    for (unsigned i = 0; i < N; i++) ret(i, i) = diag;
    //
    bool initial_loop = true;
    double abs_cutoff = cutoff_ * diag;
    double dmax = -1;
    for (unsigned i = 0; i < N; i++) {
      for (unsigned j = i + 1; j < N; j++) {
        double x1(xlist[i][0]), x2(xlist[j][0]);
        double val;
        double dist(std::abs(x1 - x2));
        // compute all entries as long as the cutoff distance was
        // not recorded (initial_loop) or as long as the distance is
        // smaller than the cutoff distance
        if (initial_loop || dist <= dmax) {
          switch (particle_no) {
            case 0:  // tau
                     // d[w(x1,x2)]/dtau
              //  = 2/tau*w(x1,x2)
              val = get_value(xlist[i][0], xlist[j][0]);
              val *= 2. / tau_val_;
              break;
            case 1:  // lambda
                     // d[w(x,x')]/dlambda
                     //= w(x,x')
              //  *( alpha |x'-x|^alpha/(2 lambda^{alpha+1}))
              if (dist < IMP_ISD_BIVARIATE_FUNCTIONS_MINIMUM) {
                val = 0;
              } else {
                val = get_value(xlist[i][0], xlist[j][0]);
                val *= alpha_ * std::pow((dist / lambda_val_), alpha_) /
                       (2. * lambda_val_);
              }
              break;
            default:
              IMP_THROW("Invalid particle number", ModelException);
          }
          // the value has been computed and is in val
          // now check if it is smaller than the cutoff.
          // If true change the flag and update the distance
          if (std::abs(val) <= abs_cutoff) {
            if (initial_loop) {
              initial_loop = false;
              dmax = dist;
            } else if (dist < dmax) {
              dmax = dist;
            }
          }
        } else {  // e.g. initial_loop == false && dist > dmax
          val = 0;
        }
        IMP_INTERNAL_CHECK(!IMP::isnan(val),
                           "derivative matrix is nan at position("
                               << i << "," << j << ").");
        ret(i, j) = val;
        ret(j, i) = val;
      }
    }
    return ret;
  }

  FloatsList get_derivative_matrix(unsigned particle_no,
                                   const FloatsList& xlist, bool) const {
    Eigen::MatrixXd mat(get_derivative_matrix(particle_no, xlist));
    FloatsList ret;
    for (int i = 0; i < mat.rows(); i++) {
      Floats line;
      for (int j = 0; j < mat.cols(); j++) line.push_back(mat(i, j));
      ret.push_back(line);
    }
    return ret;
  }

  Eigen::MatrixXd get_second_derivative_matrix(
      unsigned particle_a, unsigned particle_b, const FloatsList& xlist) const {
    unsigned N(xlist.size());
    Eigen::MatrixXd ret(N, N);
    if (particle_a > 1) IMP_THROW("Invalid particle 1 number", ModelException);
    if (particle_b > 1) IMP_THROW("Invalid particle 2 number", ModelException);
    // d2f/dtau2
    if (particle_a == 0 && particle_b == 0) {
      for (unsigned i = 0; i < N; i++) {
        for (unsigned j = i; j < N; j++) {
          double dist = std::abs(xlist[i][0] - xlist[j][0]);
          double exponent = std::pow(dist / lambda_val_, alpha_);
          double expterm = std::exp(-0.5 * exponent);
          ret(i, j) = 2 * expterm;
          if (i != j) ret(j, i) = ret(i, j);
        }
      }
    } else if (particle_a == 1 && particle_b == 1) {  // d2f/dlambda2
      for (unsigned i = 0; i < N; i++) {
        for (unsigned j = i; j < N; j++) {
          double dist = std::abs(xlist[i][0] - xlist[j][0]);
          double exponent = std::pow(dist / lambda_val_, alpha_);
          double expterm = std::exp(-0.5 * exponent);
          ret(i, j) = tau_val_ * tau_val_ * expterm * exponent /
                      (lambda_val_ * lambda_val_) * alpha_ / 2 *
                      (alpha_ / 2 * exponent - (alpha_ + 1));
          if (i != j) ret(j, i) = ret(i, j);
        }
      }
    } else {  // d2f/d(tau)d(lambda)
      for (unsigned i = 0; i < N; i++) {
        for (unsigned j = i; j < N; j++) {
          double dist = std::abs(xlist[i][0] - xlist[j][0]);
          double exponent = std::pow(dist / lambda_val_, alpha_);
          double expterm = std::exp(-0.5 * exponent);
          ret(i, j) = tau_val_ * alpha_ * expterm / lambda_val_ * exponent;
          if (i != j) ret(j, i) = ret(i, j);
        }
      }
    }
    return ret;
  }

  FloatsList get_second_derivative_matrix(unsigned particle_a,
                                          unsigned particle_b,
                                          const FloatsList& xlist, bool) const {
    Eigen::MatrixXd mat(
        get_second_derivative_matrix(particle_a, particle_b, xlist));
    FloatsList ret;
    for (int i = 0; i < mat.rows(); i++) {
      Floats line;
      for (int j = 0; j < mat.cols(); j++) line.push_back(mat(i, j));
      ret.push_back(line);
    }
    return ret;
  }

  unsigned get_ndims_x1() const { return 1; }
  unsigned get_ndims_x2() const { return 1; }
  unsigned get_ndims_y() const { return 1; }

  unsigned get_number_of_particles() const { return 2; }

  bool get_particle_is_optimized(unsigned particle_no) const {
    switch (particle_no) {
      case 0:  // tau
        return Scale(tau_).get_nuisance_is_optimized();
      case 1:  // lambda
        return Scale(lambda_).get_nuisance_is_optimized();
      default:
        IMP_THROW("Invalid particle number", ModelException);
    }
  }

  unsigned get_number_of_optimized_particles() const {
    unsigned count = 0;
    if (Scale(tau_).get_nuisance_is_optimized()) count++;
    if (Scale(lambda_).get_nuisance_is_optimized()) count++;
    return count;
  }

  ModelObjectsTemp get_inputs() const {
    ModelObjectsTemp ret;
    ret.push_back(tau_);
    ret.push_back(lambda_);
    return ret;
  }

  /*IMP_OBJECT_INLINE(Covariance1DFunction,
          out << "covariance function with alpha = "
          << alpha_ << std::endl, {});*/
  IMP_OBJECT_METHODS(Covariance1DFunction);

 private:
  inline double get_value(double x1, double x2) const {
    double dist = std::abs(x1 - x2);
    double ret = dist / lambda_val_;
    if (alpha_square_) {
      ret *= ret;
    } else {
      ret = std::pow(ret, alpha_);
    }
    ret = IMP::square(tau_val_) * std::exp(-0.5 * ret);
    if (do_jitter && dist < IMP_ISD_BIVARIATE_FUNCTIONS_MINIMUM) {
      ret += IMP::square(tau_val_) * J_;
    }
    IMP_INTERNAL_CHECK(!IMP::isnan(ret),
                       "function value is nan. tau = "
                           << tau_val_ << " lambda = " << lambda_val_
                           << " q1 = " << x1 << " q2 = " << x2);
    return ret;
  }

 private:
  double alpha_;
  Pointer<Particle> tau_, lambda_;
  double tau_val_, lambda_val_, J_, cutoff_, alpha_square_;
  bool do_jitter;
};

IMPISD_END_NAMESPACE

#endif /* IMPISD_BIVARIATE_FUNCTIONS_H */