function_internal.hpp

/*
 *    This file is part of CasADi.
 *
 *    CasADi -- A symbolic framework for dynamic optimization.
 *    Copyright (C) 2010-2014 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_FUNCTION_INTERNAL_HPP
#define CASADI_FUNCTION_INTERNAL_HPP
 
#include "function.hpp"
#include <set>
#include <stack>
#include "code_generator.hpp"
#include "importer.hpp"
#include "options.hpp"
#include "shared_object.hpp"
#include "timing.hpp"
#ifdef CASADI_WITH_THREAD
#ifdef CASADI_WITH_THREAD_MINGW
#include <mingw.mutex.h>
#else // CASADI_WITH_THREAD_MINGW
#include <mutex>
#endif // CASADI_WITH_THREAD_MINGW
#endif //CASADI_WITH_THREAD
 
// This macro is for documentation purposes
#define INPUTSCHEME(name)
 
// This macro is for documentation purposes
#define OUTPUTSCHEME(name)
 
 
namespace casadi {
  template<typename T>
  std::vector<std::pair<std::string, T>> zip(const std::vector<std::string>& id,
                                             const std::vector<T>& mat) {
    casadi_assert_dev(id.size()==mat.size());
    std::vector<std::pair<std::string, T>> r(id.size());
    for (casadi_uint i=0; i<r.size(); ++i) r[i] = std::make_pair(id[i], mat[i]);
    return r;
  }
 
  struct CASADI_EXPORT ProtoFunctionMemory {
    // Function specific statistics
    std::map<std::string, FStats> fstats;
 
    // Short-hand for "total" fstats
    FStats* t_total;
 
    // Add a statistic
    void add_stat(const std::string& s) {
      bool added = fstats.insert(std::make_pair(s, FStats())).second;
      casadi_assert(added, "Duplicate stat: '" + s + "'");
    }
  };
 
  struct CASADI_EXPORT FunctionMemory : public ProtoFunctionMemory {
    bool stats_available;
    // Shared sequence number for input, output and instruction dumps.
    casadi_int dump_id;
    FunctionMemory() : stats_available(false), dump_id(-1) {}
  };
 
  class CASADI_EXPORT ProtoFunction : public SharedObjectInternal {
  public:
    ProtoFunction(const std::string& name);
 
    ~ProtoFunction() override = 0;
 
    void construct(const Dict& opts);
 
 
    static const Options options_;
    virtual const Options& get_options() const { return options_;}
 
    virtual Dict generate_options(const std::string& target) const;
 
    void print_options(std::ostream &stream) const;
 
    void print_option(const std::string &name, std::ostream &stream) const;
 
    bool has_option(const std::string &option_name) const;
 
    virtual void change_option(const std::string& option_name, const GenericType& option_value);
 
    virtual void init(const Dict& opts);
 
    virtual void finalize();
 
    int checkout() const;
 
    void release(int mem) const;
 
    void* memory(int ind) const;
 
    bool has_memory(int ind) const;
 
    virtual void check_mem_count(casadi_int n) const { }
 
    virtual void* alloc_mem() const { return new ProtoFunctionMemory(); }
 
    virtual int init_mem(void* mem) const;
 
    virtual void free_mem(void *mem) const { delete static_cast<ProtoFunctionMemory*>(mem); }
 
    virtual Dict get_stats(void* mem) const;
 
    void clear_mem();
 
    void print(const char* fmt, ...) const;
 
    void sprint(char* buf, size_t buf_sz, const char* fmt, ...) const;
 
    void format_time(char* buffer, double time) const;
 
    void print_time(const std::map<std::string, FStats>& fstats) const;
 
    void serialize(SerializingStream &s) const;
 
    virtual void serialize_body(SerializingStream &s) const;
    virtual void serialize_type(SerializingStream &s) const {}
 
    virtual std::string serialize_base_function() const {
      return class_name();
    }
 
    std::string name_;
 
    bool verbose_;
 
    // Print timing statistics
    bool print_time_;
 
    // Print timing statistics
    bool record_time_;
 
    bool regularity_check_;
 
    bool error_on_fail_;
 
  protected:
    explicit ProtoFunction(DeserializingStream& s);
 
#ifdef CASADI_WITH_THREAD
    mutable std::mutex mtx_;
#endif // CASADI_WITH_THREAD
 
  private:
    mutable std::vector<void*> mem_;
 
    mutable std::stack<int> unused_;
  };
 
  class CASADI_EXPORT FunctionInternal : public ProtoFunction {
    friend class Function;
  public:
    FunctionInternal(const std::string& name);
 
    ~FunctionInternal() override = 0;
 
    virtual std::string getAdaptorSolverName() const { return ""; }
 
 
    static const Options options_;
    const Options& get_options() const override { return options_;}
 
    Dict generate_options(const std::string& target) const override;
 
    void change_option(const std::string& option_name, const GenericType& option_value) override;
 
    void reset_dump_count();
 
    void init(const Dict& opts) override;
 
    void finalize() override;
 
    void* alloc_mem() const override { return new FunctionMemory(); }
 
    void free_mem(void *mem) const override { delete static_cast<FunctionMemory*>(mem); }
 
    Dict get_stats(void* mem) const override;
 
    Function self() const { return shared_from_this<Function>();}
 
    // Factory
    virtual Function factory(const std::string& name,
                             const std::vector<std::string>& s_in,
                             const std::vector<std::string>& s_out,
                             const Function::AuxOut& aux,
                             const Dict& opts) const;
 
    // Get list of dependency functions
    virtual std::vector<std::string> get_function() const;
 
    // Get a dependency function
    virtual const Function& get_function(const std::string &name) const;
 
    // Check if a particular dependency exists
    virtual bool has_function(const std::string& fname) const {return false;}
 
    // Add embedded function to map, helper function
    void add_embedded(std::map<FunctionInternal*, std::pair<Function, size_t> >& all_fun,
      const Function& dep, casadi_int max_depth) const;
 
    // Get all embedded functions, recursively
    virtual void find(std::map<FunctionInternal*, std::pair<Function, size_t> >& all_fun,
      casadi_int max_depth) const;
 
    virtual std::vector<bool> which_depends(const std::string& s_in,
                                           const std::vector<std::string>& s_out,
                                           casadi_int order, bool tr=false) const;
 
    virtual Function simplify_passes(
        const std::vector<std::pair<std::string, casadi_int> >& tasks) const;
 
 
    virtual bool has_spfwd() const { return false;}
    virtual bool has_sprev() const { return false;}
 
 
    int eval_gen(const double** arg, double** res, casadi_int* iw, double* w, void* mem,
      bool always_inline, bool never_inline) const;
    virtual int eval(const double** arg, double** res, casadi_int* iw, double* w, void* mem) const;
 
 
    virtual int eval_sx(const SXElem** arg, SXElem** res,
      casadi_int* iw, SXElem* w, void* mem, bool always_inline, bool never_inline) const;
 
    virtual void eval_mx(const MXVector& arg, MXVector& res,
                         bool always_inline, bool never_inline) const;
 
 
    virtual std::vector<DM> eval_dm(const std::vector<DM>& arg) const;
    virtual bool has_eval_dm() const { return false;}
 
 
    int eval_gen(const SXElem** arg, SXElem** res, casadi_int* iw, SXElem* w, void* mem,
        bool always_inline, bool never_inline) const {
      return eval_sx(arg, res, iw, w, mem, always_inline, never_inline);
    }
    int eval_gen(const bvec_t** arg, bvec_t** res, casadi_int* iw, bvec_t* w, void* mem,
        bool always_inline, bool never_inline) const {
      return sp_forward(arg, res, iw, w, mem);
    }
 
 
    void call_gen(const MXVector& arg, MXVector& res, casadi_int npar,
                  bool always_inline, bool never_inline) const;
 
    template<typename D>
    void call_gen(const std::vector<Matrix<D> >& arg, std::vector<Matrix<D> >& res,
                  casadi_int npar, bool always_inline, bool never_inline) const;
 
    template<typename M>
      void call(const std::vector<M>& arg, std::vector<M>& res,
               bool always_inline, bool never_inline) const;
 
 
    static bool check_mat(const Sparsity& arg, const Sparsity& inp, casadi_int& npar);
 
 
    template<typename M>
    void check_arg(const std::vector<M>& arg, casadi_int& npar) const;
 
 
    template<typename M>
    void check_res(const std::vector<M>& res, casadi_int& npar) const;
 
    template<typename M> bool
    matching_arg(const std::vector<M>& arg, casadi_int& npar) const;
 
    template<typename M> bool
    matching_res(const std::vector<M>& arg, casadi_int& npar) const;
 
    template<typename M> std::vector<M>
    replace_arg(const std::vector<M>& arg, casadi_int npar) const;
 
    template<typename M> std::vector<M>
    project_arg(const std::vector<M>& arg, casadi_int npar) const;
 
    template<typename M> std::vector<M>
    project_res(const std::vector<M>& arg, casadi_int npar) const;
 
    template<typename M> std::vector<M>
    replace_res(const std::vector<M>& res, casadi_int npar) const;
 
    template<typename M> std::vector<std::vector<M>>
    replace_fseed(const std::vector<std::vector<M>>& fseed, casadi_int npar) const;
 
    template<typename M> std::vector<std::vector<M>>
    replace_aseed(const std::vector<std::vector<M>>& aseed, casadi_int npar) const;
 
    template<typename M>
    std::map<std::string, M> convert_arg(const std::vector<M>& arg) const;
    template<typename M>
    std::vector<M> convert_arg(const std::map<std::string, M>& arg) const;
    template<typename M>
    std::map<std::string, M> convert_res(const std::vector<M>& res) const;
    template<typename M>
    std::vector<M> convert_res(const std::map<std::string, M>& res) const;
 
    std::vector<double> nz_in(const std::vector<DM>& arg) const;
    std::vector<double> nz_out(const std::vector<DM>& res) const;
    std::vector<DM> nz_in(const std::vector<double>& arg) const;
    std::vector<DM> nz_out(const std::vector<double>& res) const;
 
 
    virtual void call_forward(const std::vector<MX>& arg, const std::vector<MX>& res,
                            const std::vector<std::vector<MX> >& fseed,
                            std::vector<std::vector<MX> >& fsens,
                            bool always_inline, bool never_inline) const;
    virtual void call_forward(const std::vector<SX>& arg, const std::vector<SX>& res,
                            const std::vector<std::vector<SX> >& fseed,
                            std::vector<std::vector<SX> >& fsens,
                            bool always_inline, bool never_inline) const;
 
 
    virtual void call_reverse(const std::vector<MX>& arg, const std::vector<MX>& res,
                            const std::vector<std::vector<MX> >& aseed,
                            std::vector<std::vector<MX> >& asens,
                            bool always_inline, bool never_inline) const;
    virtual void call_reverse(const std::vector<SX>& arg, const std::vector<SX>& res,
                            const std::vector<std::vector<SX> >& aseed,
                            std::vector<std::vector<SX> >& asens,
                            bool always_inline, bool never_inline) const;
 
    std::vector<MX> mapsum_mx(const std::vector<MX > &arg, const std::string& parallelization);
 
    virtual bool uses_output() const {return false;}
 
 
    Function jacobian() const;
    virtual bool has_jacobian() const { return false;}
    virtual Function get_jacobian(const std::string& name,
                                  const std::vector<std::string>& inames,
                                  const std::vector<std::string>& onames,
                                  const Dict& opts) const;
 
 
    Sparsity& jac_sparsity(casadi_int oind, casadi_int iind, bool compact, bool symmetric) const;
    virtual bool has_jac_sparsity(casadi_int oind, casadi_int iind) const { return false;}
    virtual Sparsity get_jac_sparsity(casadi_int oind, casadi_int iind, bool symmetric) const;
 
    static std::string forward_name(const std::string& fcn, casadi_int nfwd) {
      return "fwd" + str(nfwd) + "_" + fcn;
    }
 
    std::string diff_prefix(const std::string& prefix) const;
 
 
    Function forward(casadi_int nfwd) const;
    virtual bool has_forward(casadi_int nfwd) const { return false;}
    virtual 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;
 
    static std::string reverse_name(const std::string& fcn, casadi_int nadj) {
      return "adj" + str(nadj) + "_" + fcn;
    }
 
 
    Function reverse(casadi_int nadj) const;
    virtual bool has_reverse(casadi_int nadj) const { return false;}
    virtual Function get_reverse(casadi_int nadj, const std::string& name,
                                 const std::vector<std::string>& inames,
                                 const std::vector<std::string>& onames,
                                 const Dict& opts) const;
 
    template<typename MatType>
    static MatType ensure_stacked(const MatType& v, const Sparsity& sp, casadi_int n);
 
    virtual Function slice(const std::string& name, const std::vector<casadi_int>& order_in,
                           const std::vector<casadi_int>& order_out, const Dict& opts) const;
 
    virtual const Function& oracle() const;
 
    bool has_derivative() const;
 
    virtual double ad_weight() const;
 
    virtual double sp_weight() const;
 
 
    virtual const SX sx_in(casadi_int ind) const;
    virtual const SX sx_out(casadi_int ind) const;
    virtual const std::vector<SX> sx_in() const;
    virtual const std::vector<SX> sx_out() const;
    virtual const MX mx_in(casadi_int ind) const;
    virtual const MX mx_out(casadi_int ind) const;
    virtual const std::vector<MX> mx_in() const;
    virtual const std::vector<MX> mx_out() const;
    const DM dm_in(casadi_int ind) const;
    const DM dm_out(casadi_int ind) const;
    const std::vector<DM> dm_in() const;
    const std::vector<DM> dm_out() const;
 
    virtual std::vector<MX> free_mx() const;
 
    virtual std::vector<SX> free_sx() const;
 
    virtual bool has_free() const { return false;}
 
    virtual void generate_lifted(Function& vdef_fcn, Function& vinit_fcn) const;
 
    virtual casadi_int n_instructions() const;
 
    virtual casadi_int instruction_id(casadi_int k) const;
 
    virtual std::vector<casadi_int> instruction_input(casadi_int k) const;
 
    virtual double instruction_constant(casadi_int k) const;
 
    virtual std::vector<casadi_int> instruction_output(casadi_int k) const;
 
    virtual casadi_int n_nodes() const;
 
    virtual MX instruction_MX(casadi_int k) const;
 
    virtual SX instructions_sx() const;
 
    Function wrap(const std::string& name) const;
    Function wrap() const;
 
    Function wrap_as_needed(const std::string& name, const Dict& opts) const;
    Function wrap_as_needed(const Dict& opts) const;
 
    Dict cache() const;
 
    bool incache(const std::string& fname, Function& f, const std::string& suffix="") const;
 
    void tocache(const Function& f, const std::string& suffix="") const;
 
 
    void tocache_if_missing(Function& f, const std::string& suffix="") const;
 
    void codegen(CodeGenerator& g, const std::string& fname) const;
 
    void codegen_meta(CodeGenerator& g) const;
 
    void codegen_sparsities(CodeGenerator& g) const;
 
    virtual std::string codegen_name(const CodeGenerator& g, bool ns=true) const;
 
    std::string codegen_mem(CodeGenerator& g, const std::string& index="mem") const;
 
    virtual void codegen_incref(CodeGenerator& g) const;
 
    virtual void codegen_decref(CodeGenerator& g) const;
 
    virtual void codegen_alloc_mem(CodeGenerator& g) const;
 
    virtual void codegen_init_mem(CodeGenerator& g) const;
 
    virtual void codegen_free_mem(CodeGenerator& g) const {}
 
    virtual void codegen_checkout(CodeGenerator& g) const;
 
    virtual void codegen_release(CodeGenerator& g) const;
 
    std::string signature(const std::string& fname) const;
 
    std::string signature_unrolled(const std::string& fname) const;
 
    virtual void codegen_declarations(CodeGenerator& g) const;
 
    virtual void codegen_body(CodeGenerator& g) const;
 
    virtual std::string codegen_mem_type() const { return ""; }
 
    virtual bool codegen_needs_mem() const { return false; }
 
    virtual bool codegen_mem_is_opaque() const { return false; }
 
    virtual std::string generate_dependencies(const std::string& fname, const Dict& opts) const;
 
    virtual bool has_codegen() const { return false;}
 
    virtual void jit_dependencies(const std::string& fname) {}
 
    static std::string get_jit_directory(const Dict& jit_options);
 
    virtual void export_code(const std::string& lang,
      std::ostream &stream, const Dict& options) const;
 
    void serialize_type(SerializingStream &s) const override;
 
    void serialize_body(SerializingStream &s) const override;
 
    void disp(std::ostream& stream, bool more) const override;
 
    virtual void disp_more(std::ostream& stream) const {}
 
    std::string definition() const;
 
    void print_dimensions(std::ostream &stream) const;
 
    virtual std::vector<std::string> get_free() const;
 
    void get_partition(casadi_int iind, casadi_int oind, Sparsity& D1, Sparsity& D2,
                      bool compact, bool symmetric,
                      bool allow_forward, bool allow_reverse) const;
 
 
    casadi_int nnz_in() const;
    casadi_int nnz_in(casadi_int ind) const { return sparsity_in(ind).nnz(); }
    casadi_int nnz_out() const;
    casadi_int nnz_out(casadi_int ind) const { return sparsity_out(ind).nnz(); }
 
 
    casadi_int numel_in() const;
    casadi_int numel_in(casadi_int ind) const { return sparsity_in(ind).numel(); }
    casadi_int numel_out(casadi_int ind) const { return sparsity_out(ind).numel(); }
    casadi_int numel_out() const;
 
 
    casadi_int size1_in(casadi_int ind) const { return sparsity_in(ind).size1(); }
    casadi_int size2_in(casadi_int ind) const { return sparsity_in(ind).size2(); }
    casadi_int size1_out(casadi_int ind) const { return sparsity_out(ind).size1(); }
    casadi_int size2_out(casadi_int ind) const { return sparsity_out(ind).size2(); }
    std::pair<casadi_int, casadi_int> size_in(casadi_int ind) const {
      return sparsity_in(ind).size();
    }
    std::pair<casadi_int, casadi_int> size_out(casadi_int ind) const {
      return sparsity_out(ind).size();
    }
 
 
    const Sparsity& sparsity_in(casadi_int ind) const { return sparsity_in_.at(ind); }
    const Sparsity& sparsity_out(casadi_int ind) const { return sparsity_out_.at(ind); }
 
 
    bool all_scalar() const;
 
    virtual bool jac_is_symm(casadi_int oind, casadi_int iind) const;
 
    Sparsity to_compact(casadi_int oind, casadi_int iind, const Sparsity& sp) const;
 
    Sparsity from_compact(casadi_int oind, casadi_int iind, const Sparsity& sp) const;
 
    template<bool fwd>
    Sparsity get_jac_sparsity_gen(casadi_int oind, casadi_int iind) const;
 
    Sparsity get_jac_sparsity_hierarchical(casadi_int oind, casadi_int iind) const;
 
    Sparsity get_jac_sparsity_hierarchical_symm(casadi_int oind, casadi_int iind) const;
 
    virtual std::vector<MX> symbolic_output(const std::vector<MX>& arg) const;
 
 
    virtual size_t get_n_in();
    virtual size_t get_n_out();
 
 
 
    virtual std::string get_name_in(casadi_int i);
    virtual std::string get_name_out(casadi_int i);
 
    virtual double get_default_in(casadi_int ind) const {
      return 0;
    }
 
    virtual double get_max_in(casadi_int ind) const {
      return inf;
    }
 
    virtual double get_min_in(casadi_int ind) const {
      return -inf;
    }
 
    virtual std::vector<double> get_nominal_in(casadi_int ind) const {
      return std::vector<double>(nnz_in(ind), 1.);
    }
 
    virtual std::vector<double> get_nominal_out(casadi_int ind) const {
      return std::vector<double>(nnz_out(ind), 1.);
    }
 
    virtual double get_reltol() const {
      return eps;
    }
 
    virtual double get_abstol() const {
      return eps;
    }
 
    virtual Sparsity get_sparsity_in(casadi_int i);
 
    virtual Sparsity get_sparsity_out(casadi_int i);
 
    virtual bool get_diff_in(casadi_int i) { return true; }
 
    virtual bool get_diff_out(casadi_int i) { return true; }
 
    casadi_int index_in(const std::string &name) const {
      for (casadi_int i=0; i<name_in_.size(); ++i) {
        if (name_in_[i]==name) return i;
      }
      casadi_error("FunctionInternal::index_in: could not find entry \""
                   + name + "\". Available names are: " + str(name_in_) + ".");
      return -1;
    }
 
    casadi_int index_out(const std::string &name) const {
      for (casadi_int i=0; i<name_out_.size(); ++i) {
        if (name_out_[i]==name) return i;
      }
      casadi_error("FunctionInternal::index_out: could not find entry \""
                   + name + "\". Available names are: " + str(name_out_) + ".");
      return -1;
    }
 
    virtual int sp_forward(const bvec_t** arg, bvec_t** res,
                            casadi_int* iw, bvec_t* w, void* mem) const;
 
    virtual int eval_activity(const bvec_t** arg, bvec_t** res,
                            casadi_int* iw, bvec_t* w, void* mem) const;
 
    virtual int sp_forward_block(const bvec_t** arg, bvec_t** res,
      casadi_int* iw, bvec_t* w, void* mem, casadi_int oind, casadi_int iind) const;
 
    virtual int sp_reverse(bvec_t** arg, bvec_t** res, casadi_int* iw, bvec_t* w, void* mem) const;
 
    void sz_work(size_t& sz_arg, size_t& sz_res, size_t& sz_iw, size_t& sz_w) const;
 
    size_t sz_arg() const { return sz_arg_per_ + sz_arg_tmp_;}
 
    size_t sz_res() const { return sz_res_per_ + sz_res_tmp_;}
 
    size_t sz_iw() const { return sz_iw_per_ + sz_iw_tmp_;}
 
    size_t sz_w() const { return sz_w_per_ + sz_w_tmp_;}
 
    virtual size_t codegen_sz_arg(const CodeGenerator& g) const;
    virtual size_t codegen_sz_res(const CodeGenerator& g) const;
    virtual size_t codegen_sz_iw(const CodeGenerator& g) const;
    virtual size_t codegen_sz_w(const CodeGenerator& g) const;
 
    void alloc_arg(size_t sz_arg, bool persistent=false);
 
    void alloc_res(size_t sz_res, bool persistent=false);
 
    void alloc_iw(size_t sz_iw, bool persistent=false);
 
    void alloc_w(size_t sz_w, bool persistent=false);
 
    void alloc(const Function& f, bool persistent=false, int num_threads=1);
 
    virtual void set_work(void* mem, const double**& arg, double**& res,
                          casadi_int*& iw, double*& w) const {}
 
    virtual void set_temp(void* mem, const double** arg, double** res,
                          casadi_int* iw, double* w) const {}
 
    void setup(void* mem, const double** arg, double** res, casadi_int* iw, double* w) const;
 
 
    virtual bool fwdViaJac(casadi_int nfwd) const;
    virtual bool adjViaJac(casadi_int nadj) const;
 
    virtual Dict info() const;
 
    Function map(casadi_int n, const std::string& parallelization) const;
 
    void generate_in(const std::string& fname, const double** arg) const;
    void generate_out(const std::string& fname, double** res) const;
 
    bool always_inline_, never_inline_;
 
    size_t n_in_, n_out_;
 
    std::vector<bool> is_diff_in_, is_diff_out_;
 
    std::vector<Sparsity> sparsity_in_, sparsity_out_;
 
    std::vector<std::string> name_in_, name_out_;
 
    bool jit_;
 
    bool jit_cleanup_;
 
    std::string jit_serialize_;
 
    std::string jit_name_;
    std::string jit_directory_;
    std::string jit_base_name_;
 
    bool jit_temp_suffix_;
 
    eval_t eval_;
 
    casadi_checkout_t checkout_;
 
    casadi_release_t release_;
 
    signal_t incref_, decref_;
 
    Dict stats_;
 
    bool has_refcount_;
 
    bool has_refcount_in_deps_;
 
    Dict cache_init_;
 
    mutable WeakCache<std::string, Function> cache_;
 
    mutable std::vector<Sparsity> jac_sparsity_[2];
 
#ifdef CASADI_WITH_THREADSAFE_SYMBOLICS
    mutable std::mutex jac_sparsity_mtx_;
#endif // CASADI_WITH_THREADSAFE_SYMBOLICS
 
    Function derivative_of_;
 
    void* user_data_;
 
    std::string compiler_plugin_;
    Importer compiler_;
    Dict jit_options_;
 
    double jac_penalty_;
 
    // Types of derivative calculation permitted
    bool enable_forward_, enable_reverse_, enable_jacobian_, enable_fd_;
    bool enable_forward_op_, enable_reverse_op_, enable_jacobian_op_, enable_fd_op_;
 
    double ad_weight_, ad_weight_sp_;
 
    casadi_int max_num_dir_;
 
    bool inputs_check_;
 
    // Finite difference step
    Dict fd_options_;
 
    // Finite difference step size
    double fd_step_;
 
    // Finite difference method
    std::string fd_method_;
 
    // Print input/output
    bool print_in_;
    bool print_out_;
 
    // Print canonical form
    bool print_canonical_;
 
    // Warn when number of inputs or outputs exceed this value
    casadi_int max_io_;
 
    // Dump input/output
    bool dump_in_, dump_out_, dump_;
 
    // Directory to dump to
    std::string dump_dir_;
 
    // Format to dump with
    std::string dump_format_;
 
    // Forward/reverse/Jacobian options
    Dict forward_options_, reverse_options_, jacobian_options_, der_options_;
 
    // Store a reference to a custom Jacobian
    Function custom_jacobian_;
 
    // Registered functions
    std::vector<Function> registered_functions_;
 
    // Counter for unique names for dumping inputs and output
#ifdef CASADI_WITH_THREAD
    mutable std::atomic<casadi_int> dump_count_;
#else
    mutable casadi_int dump_count_;
#endif // CASADI_WITH_THREAD
 
    virtual bool is_a(const std::string& type, bool recursive) const;
 
    virtual void merge(const std::vector<MX>& arg,
      std::vector<MX>& subs_from, std::vector<MX>& subs_to) const;
 
    template<typename MatType>
    static bool purgable(const std::vector<MatType>& seed);
 
    template<typename MatType>
    std::vector<std::vector<MatType> >
    fwd_seed(casadi_int nfwd) const;
 
    template<typename MatType>
    std::vector<std::vector<MatType> >
    symbolicAdjSeed(casadi_int nadj, const std::vector<MatType>& v) const;
 
    static std::string string_from_UnifiedReturnStatus(UnifiedReturnStatus status);
 
    explicit FunctionInternal(DeserializingStream& e);
 
    static Function deserialize(DeserializingStream& s);
    static std::map<std::string, ProtoFunction* (*)(DeserializingStream&)> deserialize_map;
 
    void print_in(std::ostream &stream, const double** arg, bool truncate) const;
 
    void print_out(std::ostream &stream, double** res, bool truncate) const;
 
    static void print_canonical(std::ostream &stream, const Sparsity& sp, const double* nz);
 
    static void print_canonical(std::ostream &stream, casadi_int sz, const double* nz);
 
    static void print_canonical(std::ostream &stream, double a);
 
  protected:
    void set_jac_sparsity(casadi_int oind, casadi_int iind, const Sparsity& sp);
 
    std::unique_ptr<std::ostream> open_trace(const double** arg, casadi_int dump_id) const;
    void finish_trace(std::ostream& trace, double** res, int ret) const;
    static void trace_values(std::ostream& trace, const double* values, casadi_int nnz);
 
  private:
    // @{
    casadi_int get_dump_id() const;
    void dump_in(casadi_int id, const double** arg) const;
    void dump_out(casadi_int id, double** res) const;
    void dump() const;
    // @}
 
    size_t sz_arg_per_, sz_res_per_, sz_iw_per_, sz_w_per_;
 
    size_t sz_arg_tmp_, sz_res_tmp_, sz_iw_tmp_, sz_w_tmp_;
  };
 
  // Template implementations
  template<typename MatType>
  bool FunctionInternal::purgable(const std::vector<MatType>& v) {
    for (auto i=v.begin(); i!=v.end(); ++i) {
      if (!i->is_zero()) return false;
    }
    return true;
  }
 
  template<typename MatType>
  std::vector<std::vector<MatType> >
  FunctionInternal::
  fwd_seed(casadi_int nfwd) const {
    std::vector<std::vector<MatType>> fseed(nfwd);
    for (casadi_int dir=0; dir<nfwd; ++dir) {
      fseed[dir].resize(n_in_);
      for (casadi_int iind=0; iind<n_in_; ++iind) {
        std::string n = "f" + str(dir) + "_" +  name_in_[iind];
        Sparsity sp = is_diff_in_[iind] ? sparsity_in(iind) : Sparsity(size_in(iind));
        fseed[dir][iind] = MatType::sym(n, sp);
      }
    }
    return fseed;
  }
 
  template<typename MatType>
  std::vector<std::vector<MatType> >
  FunctionInternal::
  symbolicAdjSeed(casadi_int nadj, const std::vector<MatType>& v) const {
    std::vector<std::vector<MatType> > aseed(nadj, v);
    for (casadi_int dir=0; dir<nadj; ++dir) {
      // Replace symbolic inputs
      casadi_int oind=0;
      for (typename std::vector<MatType>::iterator i=aseed[dir].begin();
          i!=aseed[dir].end();
          ++i, ++oind) {
        // Name of the adjoint seed
        std::stringstream ss;
        ss << "a";
        if (nadj>1) ss << dir << "_";
        ss << oind;
 
        // Save to matrix
        *i = MatType::sym(ss.str(), is_diff_out_[oind] ? i->sparsity() : Sparsity(i->size()));
 
      }
    }
    return aseed;
  }
 
  template<typename M>
  void FunctionInternal::call(const std::vector<M>& arg, std::vector<M>& res,
                              bool always_inline, bool never_inline) const {
    // If all inputs are scalar ...
    if (all_scalar()) {
      // ... and some arguments are matrix-valued with matching dimensions ...
      bool matrix_call = false;
      std::pair<casadi_int, casadi_int> sz;
      for (auto&& a : arg) {
        if (!a.is_scalar() && !a.is_empty()) {
          if (!matrix_call) {
            // Matrix call
            matrix_call = true;
            sz = a.size();
          } else if (a.size()!=sz) {
            // Not same dimensions
            matrix_call = false;
            break;
          }
        }
      }
 
      // ... then, call multiple times
      if (matrix_call) {
        // Start with zeros
        res.resize(n_out_);
        M z = M::zeros(sz);
        for (auto&& a : res) a = z;
        // Call multiple times
        std::vector<M> arg1 = arg, res1;
        for (casadi_int c=0; c<sz.second; ++c) {
          for (casadi_int r=0; r<sz.first; ++r) {
            // Get scalar arguments
            for (casadi_int i=0; i<arg.size(); ++i) {
              if (arg[i].size()==sz) arg1[i] = arg[i](r, c);
            }
            // Call recursively with scalar arguments
            call(arg1, res1, always_inline, never_inline);
            // Get results
            casadi_assert_dev(res.size() == res1.size());
            for (casadi_int i=0; i<res.size(); ++i) res[i](r, c) = res1[i];
          }
        }
        // All elements assigned
        return;
      }
    }
 
    // Check if inputs need to be replaced
    casadi_int npar = 1;
    if (!matching_arg(arg, npar)) {
      return call(replace_arg(arg, npar), res, always_inline, never_inline);
    }
 
    // Call the type-specific method
    call_gen(arg, res, npar, always_inline, never_inline);
  }
 
  template<typename M>
  std::vector<M> FunctionInternal::
  project_arg(const std::vector<M>& arg, casadi_int npar) const {
    casadi_assert_dev(arg.size()==n_in_);
 
    // Which arguments require mapped evaluation
    std::vector<bool> mapped(n_in_);
    for (casadi_int i=0; i<n_in_; ++i) {
      mapped[i] = arg[i].size2()!=size2_in(i);
    }
 
    // Check if matching input sparsity
    std::vector<bool> matching(n_in_);
    bool any_mismatch = false;
    for (casadi_int i=0; i<n_in_; ++i) {
      if (mapped[i]) {
        matching[i] = arg[i].sparsity().is_stacked(sparsity_in(i), npar);
      } else {
        matching[i] = arg[i].sparsity()==sparsity_in(i);
      }
      any_mismatch = any_mismatch || !matching[i];
    }
 
    // Correct input sparsity
    if (any_mismatch) {
      std::vector<M> arg2(arg);
      for (casadi_int i=0; i<n_in_; ++i) {
        if (!matching[i]) {
          if (mapped[i]) {
            arg2[i] = project(arg2[i], repmat(sparsity_in(i), 1, npar));
          } else {
            arg2[i] = project(arg2[i], sparsity_in(i));
          }
        }
      }
      return arg2;
    }
    return arg;
  }
 
  template<typename M>
    std::vector<M> FunctionInternal::
    project_res(const std::vector<M>& arg, casadi_int npar) const {
      return arg;
  }
 
  template<typename D>
  void FunctionInternal::
  call_gen(const std::vector<Matrix<D> >& arg, std::vector<Matrix<D> >& res,
           casadi_int npar, bool always_inline, bool never_inline) const {
    std::vector< Matrix<D> > arg2 = project_arg(arg, npar);
 
    // Which arguments require mapped evaluation
    std::vector<bool> mapped(n_in_);
    for (casadi_int i=0; i<n_in_; ++i) {
      mapped[i] = arg[i].size2()!=size2_in(i);
    }
 
    // Allocate results
    res.resize(n_out_);
    for (casadi_int i=0; i<n_out_; ++i) {
      if (!res[i].sparsity().is_stacked(sparsity_out(i), npar)) {
        res[i] = Matrix<D>::zeros(repmat(sparsity_out(i), 1, npar));
      }
    }
 
    // Allocate temporary memory if needed
    std::vector<casadi_int> iw_tmp(sz_iw());
    std::vector<D> w_tmp(sz_w());
 
    // Get pointers to input arguments
    std::vector<const D*> argp(sz_arg());
    for (casadi_int i=0; i<n_in_; ++i) argp[i]=get_ptr(arg2[i]);
 
    // Get pointers to output arguments
    std::vector<D*> resp(sz_res());
    for (casadi_int i=0; i<n_out_; ++i) resp[i]=get_ptr(res[i]);
 
    // For all parallel calls
    for (casadi_int p=0; p<npar; ++p) {
      // Call memory-less
      if (eval_gen(get_ptr(argp), get_ptr(resp),
                   get_ptr(iw_tmp), get_ptr(w_tmp), memory(0),
                   always_inline, never_inline)) {
        if (error_on_fail_) casadi_error("Evaluation failed");
      }
      // Update offsets
      if (p==npar-1) break;
      for (casadi_int i=0; i<n_in_; ++i) if (mapped[i]) argp[i] += nnz_in(i);
      for (casadi_int i=0; i<n_out_; ++i) resp[i] += nnz_out(i);
    }
  }
 
  template<typename M>
  void FunctionInternal::check_arg(const std::vector<M>& arg, casadi_int& npar) const {
    casadi_assert(arg.size()==n_in_, "Incorrect number of inputs: Expected "
                          + str(n_in_) + ", got " + str(arg.size()));
    for (casadi_int i=0; i<n_in_; ++i) {
      if (!check_mat(arg[i].sparsity(), sparsity_in(i), npar)) {
        // Dimensions
        std::string d_arg = str(arg[i].size1()) + "-by-" + str(arg[i].size2());
        std::string d_in = str(size1_in(i)) + "-by-" + str(size2_in(i));
        std::string e = "Input " + str(i) + " (" + name_in_[i] + ") has mismatching shape. "
                     "Got " + d_arg + ". Allowed dimensions, in general, are:\n"
                     " - The input dimension N-by-M (here " + d_in + ")\n"
                     " - A scalar, i.e. 1-by-1\n"
                     " - M-by-N if N=1 or M=1 (i.e. a transposed vector)\n"
                     " - N-by-M1 if K*M1=M for some K (argument repeated horizontally)\n";
        if (npar!=-1) {
          e += " - N-by-P*M, indicating evaluation with multiple arguments (P must be a "
                     "multiple of " + str(npar) + " for consistency with previous inputs)";
        }
        casadi_error(e);
      }
    }
  }
 
  template<typename M>
  void FunctionInternal::check_res(const std::vector<M>& res, casadi_int& npar) const {
    casadi_assert(res.size()==n_out_, "Incorrect number of outputs: Expected "
                          + str(n_out_) + ", got " + str(res.size()));
    for (casadi_int i=0; i<n_out_; ++i) {
      casadi_assert(check_mat(res[i].sparsity(), sparsity_out(i), npar),
                    "Output " + str(i) + " (" + name_out_[i] + ") has mismatching shape. "
                    "Expected " + str(size_out(i)) + ", got " + str(res[i].size()));
    }
  }
 
  template<typename M>
  bool FunctionInternal::matching_arg(const std::vector<M>& arg, casadi_int& npar) const {
    check_arg(arg, npar);
    for (casadi_int i=0; i<n_in_; ++i) {
      if (arg.at(i).size1()!=size1_in(i)) return false;
      if (arg.at(i).size2()!=size2_in(i) && arg.at(i).size2()!=npar*size2_in(i)) return false;
    }
    return true;
  }
 
  template<typename M>
  bool FunctionInternal::matching_res(const std::vector<M>& res, casadi_int& npar) const {
    check_res(res, npar);
    for (casadi_int i=0; i<n_out_; ++i) {
      if (res.at(i).size1()!=size1_out(i)) return false;
      if (res.at(i).size2()!=size2_out(i) && res.at(i).size2()!=npar*size2_out(i)) return false;
    }
    return true;
  }
 
  template<typename M>
  M replace_mat(const M& arg, const Sparsity& inp, casadi_int npar) {
    if (arg.size()==inp.size()) {
      // Matching dimensions already
      return arg;
    } else if (arg.is_scalar()) {
      // Scalar assign means set all
      return M(inp, arg);
    } else if (arg.is_vector() && inp.size()==std::make_pair(arg.size2(), arg.size1())) {
      // Transpose vector
      return arg.T();
    } else if (arg.size1()==inp.size1() && arg.size2()>0 && inp.size2()>0
               && inp.size2()%arg.size2()==0) {
      // Horizontal repmat
      return repmat(arg, 1, inp.size2()/arg.size2());
    } else if (npar!=-1 && arg.size1()==inp.size1() && arg.size2()>0 && inp.size2()>0
               && (npar*inp.size2())%arg.size2()==0) {
      // Multiple evaluation: grow argument horizontally to npar*inp columns
      return repmat(arg, 1, (npar*inp.size2())/arg.size2());
    } else {
      // Empty matrix means set zero (kept last so a 0-by-N argument is first given the
      // chance to be recognised as a parallel/repmat call above)
      casadi_assert_dev(arg.is_empty());
      return M(inp.size());
    }
  }
 
  template<typename M>
  std::vector<M> FunctionInternal::
  replace_arg(const std::vector<M>& arg, casadi_int npar) const {
    std::vector<M> r(arg.size());
    for (casadi_int i=0; i<r.size(); ++i) r[i] = replace_mat(arg[i], sparsity_in(i), npar);
    return r;
  }
 
  template<typename M>
  std::vector<M> FunctionInternal::
  replace_res(const std::vector<M>& res, casadi_int npar) const {
    std::vector<M> r(res.size());
    for (casadi_int i=0; i<r.size(); ++i) r[i] = replace_mat(res[i], sparsity_out(i), npar);
    return r;
  }
 
  template<typename M>
  std::vector<std::vector<M> > FunctionInternal::
  replace_fseed(const std::vector<std::vector<M> >& fseed, casadi_int npar) const {
    std::vector<std::vector<M> > r(fseed.size());
    for (casadi_int d=0; d<r.size(); ++d) r[d] = replace_arg(fseed[d], npar);
    return r;
  }
 
  template<typename M>
  std::vector<std::vector<M> > FunctionInternal::
  replace_aseed(const std::vector<std::vector<M> >& aseed, casadi_int npar) const {
    std::vector<std::vector<M> > r(aseed.size());
    for (casadi_int d=0; d<r.size(); ++d) r[d] = replace_res(aseed[d], npar);
    return r;
  }
 
  template<typename M>
  std::map<std::string, M> FunctionInternal::
  convert_arg(const std::vector<M>& arg) const {
    casadi_assert(arg.size()==n_in_, "Incorrect number of inputs: Expected "
                      + str(n_in_) + ", got " + str(arg.size()));
    std::map<std::string, M> ret;
    for (casadi_int i=0;i<n_in_;++i) {
      ret[name_in_[i]] = arg[i];
    }
    return ret;
  }
 
  template<typename M>
  std::vector<M> FunctionInternal::
  convert_arg(const std::map<std::string, M>& arg) const {
    // Get default inputs
    std::vector<M> arg_v(n_in_);
    for (casadi_int i=0; i<arg_v.size(); ++i) {
      arg_v[i] = get_default_in(i);
    }
 
    // Assign provided inputs
    for (auto&& e : arg) {
      arg_v.at(index_in(e.first)) = e.second;
    }
 
    return arg_v;
  }
 
  template<typename M>
  std::map<std::string, M> FunctionInternal::
  convert_res(const std::vector<M>& res) const {
    casadi_assert(res.size()==n_out_, "Incorrect number of outputs: Expected "
                      + str(n_out_) + ", got " + str(res.size()));
    std::map<std::string, M> ret;
    for (casadi_int i=0;i<n_out_;++i) {
      ret[name_out_[i]] = res[i];
    }
    return ret;
  }
 
  template<typename M>
  std::vector<M> FunctionInternal::
  convert_res(const std::map<std::string, M>& res) const {
    // Get default inputs
    std::vector<M> res_v(n_out_);
    for (casadi_int i=0; i<res_v.size(); ++i) {
      res_v[i] = std::numeric_limits<double>::quiet_NaN();
    }
 
    // Assign provided inputs
    for (auto&& e : res) {
      M a = e.second;
      res_v.at(index_out(e.first)) = a;
    }
    return res_v;
  }
 
  template<typename MatType>
  MatType FunctionInternal::ensure_stacked(const MatType& v, const Sparsity& sp, casadi_int n) {
    // Check dimensions
    if (v.size1() == sp.size1() && v.size2() == n * sp.size2()) {
      // Ensure that sparsity is a horizontal multiple of original input, or has no entries
      if (v.nnz() != 0 && !v.sparsity().is_stacked(sp, n)) {
        return project(v, repmat(sp, 1, n));
      }
    } else {
      // Correct empty sparsity
      casadi_assert_dev(v.is_empty());
      return MatType(sp.size1(), sp.size2() * n);
    }
    // No correction needed
    return v;
  }
 
} // namespace casadi
 
 
#endif // CASADI_FUNCTION_INTERNAL_HPP