finite_differences.hpp

/*
 *    This file is part of CasADi.
 *
 *    CasADi -- A symbolic framework for dynamic optimization.
 *    Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl,
 *                            KU Leuven. All rights reserved.
 *    Copyright (C) 2011-2014 Greg Horn
 *
 *    CasADi is free software; you can redistribute it and/or
 *    modify it under the terms of the GNU Lesser General Public
 *    License as published by the Free Software Foundation; either
 *    version 3 of the License, or (at your option) any later version.
 *
 *    CasADi is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *    Lesser General Public License for more details.
 *
 *    You should have received a copy of the GNU Lesser General Public
 *    License along with CasADi; if not, write to the Free Software
 *    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */
 
 
#ifndef CASADI_FINITE_DIFFERENCES_HPP
#define CASADI_FINITE_DIFFERENCES_HPP
 
#include "function_internal.hpp"
 
 
namespace casadi {
 
enum class FdMode {FORWARD, BACKWARD, CENTRAL, SMOOTHING, NUMEL};
 
CASADI_EXPORT std::string to_string(FdMode v);
 
CASADI_EXPORT casadi_int n_fd_points(FdMode v);
 
CASADI_EXPORT casadi_int fd_offset(FdMode v);
 
template<typename T1>
CASADI_EXPORT void finite_diff(FdMode v, const T1** yk, T1* J, T1 h, casadi_int n_y,
    T1 smoothing) {
  switch (v) {
    case FdMode::FORWARD:
    case FdMode::BACKWARD:
      return casadi_forward_diff(yk, J, h, n_y);
    case FdMode::CENTRAL:
      return casadi_central_diff(yk, J, h, n_y);
    case FdMode::SMOOTHING:
      return casadi_smoothing_diff(yk, J, h, n_y, eps);
    default:
      casadi_error("FD mode " + to_string(v) + " not implemented");
  }
}
 
class CASADI_EXPORT FiniteDiff : public FunctionInternal {
public:
  // Constructor (protected, use create function)
  FiniteDiff(const std::string& name, casadi_int n);
 
  ~FiniteDiff() override;
 
 
  static const Options options_;
  const Options& get_options() const override { return options_;}
 
 
  Sparsity get_sparsity_in(casadi_int i) override;
  Sparsity get_sparsity_out(casadi_int i) override;
 
  double get_default_in(casadi_int ind) const override;
 
 
  size_t get_n_in() override;
  size_t get_n_out() override;
 
 
  std::string get_name_in(casadi_int i) override;
  std::string get_name_out(casadi_int i) override;
 
  void init(const Dict& opts) override;
 
  // Evaluate numerically
  int eval(const double** arg, double** res, casadi_int* iw, double* w, void* mem) const override;
 
  bool uses_output() const override {return true;}
 
  bool has_codegen() const override { return true;}
 
  void codegen_declarations(CodeGenerator& g) const override;
 
  void codegen_body(CodeGenerator& g) const override;
 
protected:
  // Number of function evaluations needed
  virtual casadi_int n_pert() const = 0;
 
  // Get perturbation expression
  virtual std::string pert(const std::string& k) const = 0;
 
  // Get perturbation expression
  virtual double pert(casadi_int k, double h) const = 0;
 
  // Calculate finite difference approximation
  virtual double calc_fd(double** yk, double* y0, double* J, double h) const = 0;
 
  // Codegen finite difference approximation
  virtual std::string calc_fd() const = 0;
 
  // Is an error estimate available?
  virtual casadi_int has_err() const = 0;
 
  // Calculate step size from absolute tolerance
  virtual double calc_stepsize(double abstol) const = 0;
 
  // Number of directional derivatives
  casadi_int n_;
 
  // Iterations to improve h
  casadi_int h_iter_;
 
  // Perturbation
  double h_;
 
  // Dimensions
  casadi_int n_z_, n_y_;
 
  // Target ratio of truncation error to roundoff error
  double u_aim_;
 
  // Allowed step size range
  double h_min_, h_max_;
 
  // Memory object
  casadi_finite_diff_mem<double> m_;
};
 
class CASADI_EXPORT ForwardDiff : public FiniteDiff {
public:
  // Constructor
  ForwardDiff(const std::string& name, casadi_int n) : FiniteDiff(name, n) {}
 
  ~ForwardDiff() override {}
 
  std::string class_name() const override {return "ForwardDiff";}
 
  // Number of function evaluations needed
  casadi_int n_pert() const override {return 1;};
 
  // Get perturbation expression
  std::string pert(const std::string& k) const override {
    return str(h_);
  }
 
  // Get perturbation expression
  double pert(casadi_int k, double h) const override {
    return h;
  }
 
  // Calculate finite difference approximation
  double calc_fd(double** yk, double* y0, double* J, double h) const override;
 
  // Codegen finite difference approximation
  std::string calc_fd() const override {return "casadi_forward_diff_old";}
 
  // Is an error estimate available?
  casadi_int has_err() const override {return false;}
 
  // Calculate step size from absolute tolerance
  double calc_stepsize(double abstol) const override { return sqrt(abstol);}
 
  double get_abstol() const override { return h_;}
 
 
  bool has_forward(casadi_int nfwd) const override { return true;}
  Function get_forward(casadi_int nfwd, const std::string& name,
                        const std::vector<std::string>& inames,
                        const std::vector<std::string>& onames,
                        const Dict& opts) const override;
};
 
class CASADI_EXPORT BackwardDiff : public ForwardDiff {
public:
  // Constructor
  BackwardDiff(const std::string& name, casadi_int n) : ForwardDiff(name, n) {}
 
  ~BackwardDiff() override {}
 
  std::string class_name() const override {return "BackwardDiff";}
 
  // Calculate step size from absolute tolerance
  double calc_stepsize(double abstol) const override {
    return -ForwardDiff::calc_stepsize(abstol);
  }
};
 
class CASADI_EXPORT CentralDiff : public FiniteDiff {
public:
  // Constructor
  CentralDiff(const std::string& name, casadi_int n) : FiniteDiff(name, n) {}
 
  ~CentralDiff() override {}
 
  std::string class_name() const override {return "CentralDiff";}
 
  // Number of function evaluations needed
  casadi_int n_pert() const override {return 2;};
 
  // Get perturbation expression
  std::string pert(const std::string& k) const override {
    return "(2*" + k + "-1)*" + str(h_);
  }
 
  // Get perturbation expression
  double pert(casadi_int k, double h) const override {
    return (2*static_cast<double>(k)-1)*h;
  }
 
  // Calculate finite difference approximation
  double calc_fd(double** yk, double* y0, double* J, double h) const override;
 
  // Codegen finite difference approximation
  std::string calc_fd() const override {return "casadi_central_diff_old";}
 
  // Is an error estimate available?
  casadi_int has_err() const override {return true;}
 
  // Calculate step size from absolute tolerance
  double calc_stepsize(double abstol) const override { return pow(abstol, 1./3);}
 
  double get_abstol() const override { return h_*h_;}
 
 
  bool has_forward(casadi_int nfwd) const override { return true;}
  Function get_forward(casadi_int nfwd, const std::string& name,
                        const std::vector<std::string>& inames,
                        const std::vector<std::string>& onames,
                        const Dict& opts) const override;
};
 
class CASADI_EXPORT Smoothing : public FiniteDiff {
public:
  // Constructor
  Smoothing(const std::string& name, casadi_int n) : FiniteDiff(name, n) {}
 
  ~Smoothing() override {}
 
  std::string class_name() const override {return "Smoothing";}
 
  // Number of function evaluations needed
  casadi_int n_pert() const override {return 4;};
 
  // Get perturbation expression
  std::string pert(const std::string& k) const override;
 
  // Get perturbation expression
  double pert(casadi_int k, double h) const override;
 
  // Calculate finite difference approximation
  double calc_fd(double** yk, double* y0, double* J, double h) const override;
 
  // Codegen finite difference approximation
  std::string calc_fd() const override {return "casadi_smoothing_diff_old";}
 
  // Is an error estimate available?
  casadi_int has_err() const override {return true;}
 
  // Calculate step size from absolute tolerance
  double calc_stepsize(double abstol) const override { return pow(abstol, 1./3);}
 
  double get_abstol() const override { return h_*h_;}
 
 
  bool has_forward(casadi_int nfwd) const override { return true;}
  Function get_forward(casadi_int nfwd, const std::string& name,
                        const std::vector<std::string>& inames,
                        const std::vector<std::string>& onames,
                        const Dict& opts) const override;
};
 
 
} // namespace casadi
 
#endif // CASADI_FINITE_DIFFERENCES_HPP