dynare/mex/sources/libkorder/sylv/GeneralSylvester.cc

/*
 * Copyright © 2004-2011 Ondra Kamenik
 * Copyright © 2019 Dynare Team
 *
 * This file is part of Dynare.
 *
 * Dynare is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * Dynare 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with Dynare.  If not, see <https://www.gnu.org/licenses/>.
 */

#include "GeneralSylvester.hh"
#include "IterativeSylvester.hh"
#include "SchurDecomp.hh"
#include "SylvException.hh"
#include "TriangularSylvester.hh"
#include "int_power.hh"

#include <ctime>

GeneralSylvester::GeneralSylvester(int ord, int n, int m, int zero_cols, const ConstVector& da,
                                   const ConstVector& db, const ConstVector& dc,
                                   const ConstVector& dd, const SylvParams& ps) :
    pars(ps),
    order(ord),
    a(Vector {da}, n),
    b(Vector {db}, n, n - zero_cols),
    c(Vector {dc}, m),
    d(Vector {dd}, n, power(m, order)),
    solved(false)
{
  init();
}

GeneralSylvester::GeneralSylvester(int ord, int n, int m, int zero_cols, const ConstVector& da,
                                   const ConstVector& db, const ConstVector& dc, Vector& dd,
                                   const SylvParams& ps) :
    pars(ps),
    order(ord),
    a(Vector {da}, n),
    b(Vector {db}, n, n - zero_cols),
    c(Vector {dc}, m),
    d(dd, n, power(m, order)),
    solved(false)
{
  init();
}

GeneralSylvester::GeneralSylvester(int ord, int n, int m, int zero_cols, const ConstVector& da,
                                   const ConstVector& db, const ConstVector& dc,
                                   const ConstVector& dd, bool alloc_for_check) :
    pars(alloc_for_check),
    order(ord),
    a(Vector {da}, n),
    b(Vector {db}, n, n - zero_cols),
    c(Vector {dc}, m),
    d(Vector {dd}, n, power(m, order)),
    solved(false)
{
  init();
}

GeneralSylvester::GeneralSylvester(int ord, int n, int m, int zero_cols, const ConstVector& da,
                                   const ConstVector& db, const ConstVector& dc, Vector& dd,
                                   bool alloc_for_check) :
    pars(alloc_for_check),
    order(ord),
    a(Vector {da}, n),
    b(Vector {db}, n, n - zero_cols),
    c(Vector {dc}, m),
    d(dd, n, power(m, order)),
    solved(false)
{
  init();
}

void
GeneralSylvester::init()
{
  GeneralMatrix ainvb(b);
  double rcond1;
  double rcondinf;
  a.multInvLeft2(ainvb, d, rcond1, rcondinf);
  pars.rcondA1 = rcond1;
  pars.rcondAI = rcondinf;
  bdecomp = std::make_unique<SchurDecompZero>(ainvb);
  cdecomp = std::make_unique<SimilarityDecomp>(c.getData(), c.nrows(), *(pars.bs_norm));
  cdecomp->check(pars, c);
  cdecomp->infoToPars(pars);
  if (*(pars.method) == SylvParams::solve_method::recurse)
    sylv = std::make_unique<TriangularSylvester>(*bdecomp, *cdecomp);
  else
    sylv = std::make_unique<IterativeSylvester>(*bdecomp, *cdecomp);
}

void
GeneralSylvester::solve()
{
  if (solved)
    throw SYLV_MES_EXCEPTION("Attempt to run solve() more than once.");

  clock_t start = clock();
  // multiply d
  d.multLeftITrans(bdecomp->getQ());
  d.multRightKron(cdecomp->getQ(), order);
  // convert to KronVector
  KronVector dkron(d.getData(), getM(), getN(), order);
  // solve
  sylv->solve(pars, dkron);
  // multiply d back
  d.multLeftI(bdecomp->getQ());
  d.multRightKron(cdecomp->getInvQ(), order);
  clock_t end = clock();
  pars.cpu_time = static_cast<double>(end - start) / CLOCKS_PER_SEC;

  solved = true;
}

void
GeneralSylvester::check(const ConstVector& ds)
{
  if (!solved)
    throw SYLV_MES_EXCEPTION("Cannot run check on system, which is not solved yet.");

  // calculate xcheck = A·X+B·X·⊗ⁱC−D
  SylvMatrix dcheck(d.nrows(), d.ncols());
  dcheck.multLeft(b.nrows() - b.ncols(), b, d);
  dcheck.multRightKron(c, order);
  dcheck.multAndAdd(a, d);
  dcheck.getData().add(-1.0, ds);
  // calculate relative norms
  pars.mat_err1 = dcheck.getNorm1() / d.getNorm1();
  pars.mat_errI = dcheck.getNormInf() / d.getNormInf();
  pars.mat_errF = dcheck.getData().getNorm() / d.getData().getNorm();
  pars.vec_err1 = dcheck.getData().getNorm1() / d.getData().getNorm1();
  pars.vec_errI = dcheck.getData().getMax() / d.getData().getMax();
}