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/*
* 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 <http://www.gnu.org/licenses/>.
*/
#include "SimilarityDecomp.hh"
#include "SchurDecomp.hh"
#include "SchurDecompEig.hh"
#include "SylvException.hh"
#include <dynlapack.h>
#include <cmath>
SimilarityDecomp::SimilarityDecomp(const ConstVector &d, int d_size, double log10norm)
{
SchurDecomp sd(SqSylvMatrix(Vector{d}, d_size));
q = std::make_unique<SqSylvMatrix>(sd.getQ());
b = std::make_unique<BlockDiagonal>(sd.getT());
invq = std::make_unique<SqSylvMatrix>(d_size);
invq->setUnit();
invq->multLeftTrans(sd.getQ());
double norm = pow(10.0, log10norm);
diagonalize(norm);
}
void
SimilarityDecomp::getXDim(diag_iter start, diag_iter end,
int &rows, int &cols) const
{
int si = start->getIndex();
int ei = end->getIndex();
cols = b->nrows() - ei;
rows = ei - si;
}
/* Find solution of X for diagonal block given by start(incl.) and
end(excl.). If the solution cannot be found, or it is greater than
norm, X is not changed and flase is returned.
*/
bool
SimilarityDecomp::solveX(diag_iter start, diag_iter end,
GeneralMatrix &X, double norm) const
{
int si = start->getIndex();
int ei = end->getIndex();
SqSylvMatrix A(const_cast<const BlockDiagonal &>(*b), si, si, X.nrows());
SqSylvMatrix B(const_cast<const BlockDiagonal &>(*b), ei, ei, X.ncols());
GeneralMatrix C(const_cast<const BlockDiagonal &>(*b), si, ei, X.nrows(), X.ncols());
lapack_int isgn = -1;
lapack_int m = A.nrows();
lapack_int n = B.nrows();
lapack_int lda = A.getLD(), ldb = B.getLD();
double scale;
lapack_int info;
dtrsyl("N", "N", &isgn, &m, &n, A.base(), &lda, B.base(), &ldb,
C.base(), &m, &scale, &info);
if (info < -1)
throw SYLV_MES_EXCEPTION("Wrong parameter to LAPACK dtrsyl.");
if (info == 1 || scale < 1)
return false;
if (C.getData().getMax() > norm)
return false;
X = C;
return true;
}
/* ⎛I −X⎞ ⎛I X⎞
Multiply Q and invQ with ⎝0 I⎠ and ⎝0 I⎠ respectively. This also sets X=−X. */
void
SimilarityDecomp::updateTransform(diag_iter start, diag_iter end,
GeneralMatrix &X)
{
int si = start->getIndex();
int ei = end->getIndex();
SqSylvMatrix iX(q->nrows());
iX.setUnit();
iX.place(X, si, ei);
invq->GeneralMatrix::multLeft(iX);
iX.setUnit();
X.mult(-1.0);
iX.place(X, si, ei);
q->multRight(iX);
}
void
SimilarityDecomp::bringGuiltyBlock(diag_iter start, diag_iter &end)
{
double av = b->getAverageDiagSize(start, end);
diag_iter guilty = b->findClosestDiagBlock(end, b->diag_end(), av);
SchurDecompEig sd(*b); // works on b including diagonal structure
end = sd.bubbleEigen(guilty, end); // iterators are valid
++end;
q->multRight(sd.getQ());
invq->multLeftTrans(sd.getQ());
}
void
SimilarityDecomp::diagonalize(double norm)
{
diag_iter start = b->diag_begin();
diag_iter end = start;
++end;
while (end != b->diag_end())
{
int xrows;
int xcols;
getXDim(start, end, xrows, xcols);
GeneralMatrix X(xrows, xcols);
if (solveX(start, end, X, norm))
{
updateTransform(start, end, X);
b->setZeroBlockEdge(end);
start = end;
++end;
}
else
bringGuiltyBlock(start, end); // moves with end
}
}
void
SimilarityDecomp::check(SylvParams &pars, const GeneralMatrix &m) const
{
// M − Q·B·Q⁻¹
SqSylvMatrix c(getQ() * getB());
c.multRight(getInvQ());
c.add(-1.0, m);
pars.f_err1 = c.getNorm1();
pars.f_errI = c.getNormInf();
// I − Q·Q⁻¹
c.setUnit();
c.mult(-1);
c.multAndAdd(getQ(), getInvQ());
pars.viv_err1 = c.getNorm1();
pars.viv_errI = c.getNormInf();
// I − Q⁻¹·Q
c.setUnit();
c.mult(-1);
c.multAndAdd(getInvQ(), getQ());
pars.ivv_err1 = c.getNorm1();
pars.ivv_errI = c.getNormInf();
}
void
SimilarityDecomp::infoToPars(SylvParams &pars) const
{
pars.f_blocks = getB().getNumBlocks();
pars.f_largest = getB().getLargestBlock();
pars.f_zeros = getB().getNumZeros();
pars.f_offdiag = getB().getNumOffdiagonal();
}
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