determinant.cpp

/*
 *    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
 *    Copyright (C) 2018 Robert Bosch GmbH
 *
 *    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
 *
 */
 
 
#include "determinant.hpp"
#include "linsol_internal.hpp"
 
namespace casadi {
 
  Determinant::Determinant(const MX& x, const Linsol& linsol) : linsol_(linsol) {
    casadi_assert(x.is_square(), "Dimension mismatch. Matrix must be square, "
      "but got " + x.dim() + " instead.");
    set_dep(x);
    set_sparsity(Sparsity::dense(1, 1));
  }
 
  std::string Determinant::disp(const std::vector<std::string>& arg) const {
    return "det(" + arg.at(0) + ")";
  }
 
  int Determinant::eval(const double** arg, double** res, casadi_int* iw, double* w) const {
    scoped_checkout<Linsol> mem(linsol_);
 
    // Peform LU decomposition
    if (linsol_.sfact(arg[0], mem)) return 1;
    if (linsol_.nfact(arg[0], mem)) return 1;
 
    // Compute determinant
    res[0][0] = linsol_.det(arg[0], mem);
 
    return 0;
  }
 
  int Determinant::eval_sx(const SXElem** arg, SXElem** res, casadi_int* iw, SXElem* w) const {
    // Symbolic determinant via the sparse-QR plugin (cheap O(n^3), unlike cofactor)
    SX A = SX::zeros(dep(0).sparsity());
    std::copy(arg[0], arg[0]+dep(0).nnz(), A.ptr());
    *res[0] = det(A, "symbolicqr").scalar();
    return 0;
  }
 
  size_t Determinant::codegen_sz_w() const {
    return linsol_->sz_w_fact();
  }
 
  void Determinant::generate(CodeGenerator& g,
                             const std::vector<casadi_int>& arg,
                             const std::vector<casadi_int>& res,
                             const std::vector<bool>& arg_is_ref,
                             std::vector<bool>& res_is_ref) const {
    linsol_->generate_det(g, g.work(arg[0], dep(0).nnz(), arg_is_ref[0]),
                          g.workel(res[0]));
  }
 
  void Determinant::eval_mx(const std::vector<MX>& arg, std::vector<MX>& res,
      const std::vector<bool>& unique) const {
    res[0] = linsol_.det(arg[0]);
  }
 
  void Determinant::ad_forward(const std::vector<std::vector<MX> >& fseed,
                            std::vector<std::vector<MX> >& fsens) const {
    const MX& X = dep();
    MX det_X = shared_from_this<MX>();
    MX trans_inv_X = inv(X).T();
    for (casadi_int d=0; d<fsens.size(); ++d) {
      fsens[d][0] = det_X * dot(trans_inv_X, fseed[d][0]);
    }
  }
 
  void Determinant::ad_reverse(const std::vector<std::vector<MX> >& aseed,
                            std::vector<std::vector<MX> >& asens) const {
    const MX& X = dep();
    MX det_X = shared_from_this<MX>();
    MX trans_inv_X = inv(X).T();
    for (casadi_int d=0; d<aseed.size(); ++d) {
      asens[d][0] += aseed[d][0]*det_X * trans_inv_X;
    }
  }
 
  void Determinant::serialize_body(SerializingStream& s) const {
    MXNode::serialize_body(s);
    s.pack("Determinant::linsol", linsol_);
  }
 
  Determinant::Determinant(DeserializingStream& s) : MXNode(s) {
    s.unpack("Determinant::linsol", linsol_);
  }
 
} // namespace casadi