600 lines
15 KiB
C++
600 lines
15 KiB
C++
/*
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* Copyright © 2004-2011 Ondra Kamenik
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* Copyright © 2019 Dynare Team
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*
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* This file is part of Dynare.
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*
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* Dynare is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Dynare is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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*/
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#include "SylvException.hh"
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#include "GeneralMatrix.hh"
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#include <dynblas.h>
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#include <dynlapack.h>
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#include <iostream>
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#include <iomanip>
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#include <cstdlib>
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#include <cmath>
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#include <limits>
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GeneralMatrix::GeneralMatrix(const GeneralMatrix &m)
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: data(m.rows*m.cols), rows(m.rows), cols(m.cols), ld(m.rows)
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{
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copy(m);
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}
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GeneralMatrix::GeneralMatrix(const ConstGeneralMatrix &m)
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: data(m.rows*m.cols), rows(m.rows), cols(m.cols), ld(m.rows)
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{
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copy(m);
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}
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GeneralMatrix::GeneralMatrix(const GeneralMatrix &m, int i, int j, int nrows, int ncols)
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: data(nrows*ncols), rows(nrows), cols(ncols), ld(nrows)
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{
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copy(m, i, j);
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}
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GeneralMatrix::GeneralMatrix(GeneralMatrix &m, int i, int j, int nrows, int ncols)
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: data(m.data, m.ld*j+i, m.ld*(ncols-1)+nrows), rows(nrows), cols(ncols), ld(m.ld)
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{
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}
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GeneralMatrix &
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GeneralMatrix::operator=(const ConstGeneralMatrix &m)
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{
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data = m.data;
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rows = m.rows;
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cols = m.cols;
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ld = m.ld;
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return *this;
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}
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Vector
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GeneralMatrix::getRow(int row)
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{
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return Vector{data, row, ld, cols};
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}
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Vector
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GeneralMatrix::getCol(int col)
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{
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return Vector{data, ld*col, rows};
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}
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ConstVector
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GeneralMatrix::getRow(int row) const
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{
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return ConstVector{data, row, ld, cols};
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}
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ConstVector
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GeneralMatrix::getCol(int col) const
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{
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return ConstVector{data, ld*col, rows};
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}
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void
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GeneralMatrix::place(const ConstGeneralMatrix &m, int i, int j)
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{
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if (i + m.nrows() > nrows()
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|| j + m.ncols() > ncols())
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throw SYLV_MES_EXCEPTION("Bad submatrix placement, matrix dimensions exceeded.");
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GeneralMatrix tmpsub(*this, i, j, m.nrows(), m.ncols());
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tmpsub.copy(m);
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}
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void
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GeneralMatrix::mult(const ConstGeneralMatrix &a, const ConstGeneralMatrix &b)
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{
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gemm("N", a, "N", b, 1.0, 0.0);
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}
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void
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GeneralMatrix::multAndAdd(const ConstGeneralMatrix &a, const ConstGeneralMatrix &b,
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double mult)
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{
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gemm("N", a, "N", b, mult, 1.0);
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}
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void
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GeneralMatrix::multAndAdd(const ConstGeneralMatrix &a, const ConstGeneralMatrix &b,
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const std::string &dum, double mult)
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{
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gemm("N", a, "T", b, mult, 1.0);
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}
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void
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GeneralMatrix::multAndAdd(const ConstGeneralMatrix &a, const std::string &dum,
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const ConstGeneralMatrix &b, double mult)
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{
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gemm("T", a, "N", b, mult, 1.0);
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}
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void
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GeneralMatrix::multAndAdd(const ConstGeneralMatrix &a, const std::string &dum1,
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const ConstGeneralMatrix &b, const std::string &dum2, double mult)
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{
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gemm("T", a, "T", b, mult, 1.0);
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}
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void
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GeneralMatrix::addOuter(const ConstVector &a, double mult)
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{
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if (nrows() != ncols())
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throw SYLV_MES_EXCEPTION("Matrix is not square in GeneralMatrix::addOuter.");
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if (nrows() != a.length())
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throw SYLV_MES_EXCEPTION("Wrong length of a vector in GeneralMatrix::addOuter.");
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// since BLAS dsyr (symmetric rank 1 update) assumes symmetricity, we do this manually
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for (int i = 0; i < nrows(); i++)
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for (int j = i; j < nrows(); j++)
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{
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double s = mult*a[i]*a[j];
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get(i, j) = get(i, j) + s;
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if (i != j)
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get(j, i) = get(j, i) + s;
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}
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}
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void
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GeneralMatrix::multRight(const ConstGeneralMatrix &m)
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{
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gemm_partial_right("N", m, 1.0, 0.0);
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}
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void
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GeneralMatrix::multLeft(const ConstGeneralMatrix &m)
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{
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gemm_partial_left("N", m, 1.0, 0.0);
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}
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void
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GeneralMatrix::multRightTrans(const ConstGeneralMatrix &m)
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{
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gemm_partial_right("T", m, 1.0, 0.0);
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}
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void
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GeneralMatrix::multLeftTrans(const ConstGeneralMatrix &m)
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{
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gemm_partial_left("T", m, 1.0, 0.0);
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}
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// here we must be careful for ld
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void
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GeneralMatrix::zeros()
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{
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if (ld == rows)
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data.zeros();
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else
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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get(i, j) = 0;
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}
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void
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GeneralMatrix::unit()
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{
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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if (i == j)
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get(i, j) = 1.0;
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else
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get(i, j) = 0.0;
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}
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void
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GeneralMatrix::nans()
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{
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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get(i, j) = std::numeric_limits<double>::quiet_NaN();
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}
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void
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GeneralMatrix::infs()
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{
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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get(i, j) = std::numeric_limits<double>::infinity();
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}
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// here we must be careful for ld
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void
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GeneralMatrix::mult(double a)
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{
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if (ld == rows)
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data.mult(a);
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else
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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get(i, j) *= a;
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}
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// here we must be careful for ld
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void
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GeneralMatrix::add(double a, const ConstGeneralMatrix &m)
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{
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if (m.nrows() != rows || m.ncols() != cols)
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throw SYLV_MES_EXCEPTION("Matrix has different size in GeneralMatrix::add.");
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if (ld == rows && m.ld == m.rows)
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data.add(a, m.data);
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else
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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get(i, j) += a*m.get(i, j);
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}
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void
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GeneralMatrix::add(double a, const ConstGeneralMatrix &m, const std::string &dum)
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{
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if (m.nrows() != cols || m.ncols() != rows)
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throw SYLV_MES_EXCEPTION("Matrix has different size in GeneralMatrix::add.");
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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get(i, j) += a*m.get(j, i);
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}
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void
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GeneralMatrix::copy(const ConstGeneralMatrix &m, int ioff, int joff)
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{
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for (int i = 0; i < rows; i++)
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for (int j = 0; j < cols; j++)
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get(i, j) = m.get(i+ioff, j+joff);
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}
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void
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GeneralMatrix::gemm(const std::string &transa, const ConstGeneralMatrix &a,
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const std::string &transb, const ConstGeneralMatrix &b,
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double alpha, double beta)
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{
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int opa_rows = a.nrows();
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int opa_cols = a.ncols();
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if (transa == "T")
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{
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opa_rows = a.ncols();
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opa_cols = a.nrows();
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}
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int opb_rows = b.nrows();
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int opb_cols = b.ncols();
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if (transb == "T")
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{
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opb_rows = b.ncols();
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opb_cols = b.nrows();
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}
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if (opa_rows != nrows()
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|| opb_cols != ncols()
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|| opa_cols != opb_rows)
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throw SYLV_MES_EXCEPTION("Wrong dimensions for matrix multiplication.");
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blas_int m = opa_rows;
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blas_int n = opb_cols;
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blas_int k = opa_cols;
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blas_int lda = a.ld;
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blas_int ldb = b.ld;
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blas_int ldc = ld;
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if (lda > 0 && ldb > 0 && ldc > 0)
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dgemm(transa.c_str(), transb.c_str(), &m, &n, &k, &alpha, a.data.base(), &lda,
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b.data.base(), &ldb, &beta, data.base(), &ldc);
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else if (nrows()*ncols() > 0)
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{
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if (beta == 0.0)
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zeros();
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else
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mult(beta);
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}
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}
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void
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GeneralMatrix::gemm_partial_left(const std::string &trans, const ConstGeneralMatrix &m,
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double alpha, double beta)
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{
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int icol;
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for (icol = 0; icol + md_length < cols; icol += md_length)
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{
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GeneralMatrix incopy(const_cast<const GeneralMatrix &>(*this), 0, icol, rows, md_length);
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GeneralMatrix inplace(*this, 0, icol, rows, md_length);
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inplace.gemm(trans, m, "N", ConstGeneralMatrix(incopy), alpha, beta);
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}
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if (cols > icol)
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{
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GeneralMatrix incopy(const_cast<const GeneralMatrix &>(*this), 0, icol, rows, cols - icol);
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GeneralMatrix inplace(*this, 0, icol, rows, cols - icol);
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inplace.gemm(trans, m, "N", ConstGeneralMatrix(incopy), alpha, beta);
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}
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}
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void
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GeneralMatrix::gemm_partial_right(const std::string &trans, const ConstGeneralMatrix &m,
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double alpha, double beta)
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{
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int irow;
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for (irow = 0; irow + md_length < rows; irow += md_length)
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{
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GeneralMatrix incopy(const_cast<const GeneralMatrix &>(*this), irow, 0, md_length, cols);
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GeneralMatrix inplace(*this, irow, 0, md_length, cols);
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inplace.gemm("N", ConstGeneralMatrix(incopy), trans, m, alpha, beta);
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}
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if (rows > irow)
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{
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GeneralMatrix incopy(const_cast<const GeneralMatrix &>(*this), irow, 0, rows - irow, cols);
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GeneralMatrix inplace(*this, irow, 0, rows - irow, cols);
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inplace.gemm("N", ConstGeneralMatrix(incopy), trans, m, alpha, beta);
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}
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}
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ConstGeneralMatrix::ConstGeneralMatrix(const GeneralMatrix &m, int i, int j, int nrows, int ncols)
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: data(m.getData(), j*m.getLD()+i, (ncols-1)*m.getLD()+nrows), rows(nrows), cols(ncols), ld(m.getLD())
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{
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// FIXME: check that the submatrix is fully in the matrix
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}
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ConstGeneralMatrix::ConstGeneralMatrix(const ConstGeneralMatrix &m, int i, int j, int nrows, int ncols)
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: data(m.getData(), j*m.getLD()+i, (ncols-1)*m.getLD()+nrows), rows(nrows), cols(ncols), ld(m.getLD())
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{
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// FIXME: check that the submatrix is fully in the matrix
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}
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ConstGeneralMatrix::ConstGeneralMatrix(const GeneralMatrix &m)
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: data(m.data), rows(m.rows), cols(m.cols), ld(m.ld)
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{
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}
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ConstVector
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ConstGeneralMatrix::getRow(int row) const
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{
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return ConstVector{data, row, ld, cols};
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}
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ConstVector
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ConstGeneralMatrix::getCol(int col) const
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{
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return ConstVector{data, ld*col, rows};
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}
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double
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ConstGeneralMatrix::getNormInf() const
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{
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double norm = 0.0;
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for (int i = 0; i < nrows(); i++)
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{
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double normi = getRow(i).getNorm1();
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norm = std::max(normi, norm);
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}
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return norm;
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}
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double
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ConstGeneralMatrix::getNorm1() const
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{
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double norm = 0.0;
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for (int j = 0; j < ncols(); j++)
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{
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double normj = getCol(j).getNorm1();
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norm = std::max(normj, norm);
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}
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return norm;
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}
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void
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ConstGeneralMatrix::multVec(double a, Vector &x, double b, const ConstVector &d) const
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{
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if (x.length() != rows || cols != d.length())
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throw SYLV_MES_EXCEPTION("Wrong dimensions for vector multiply.");
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if (rows > 0)
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{
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blas_int mm = rows;
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blas_int nn = cols;
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double alpha = b;
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blas_int lda = ld;
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blas_int incx = d.skip();
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double beta = a;
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blas_int incy = x.skip();
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dgemv("N", &mm, &nn, &alpha, data.base(), &lda, d.base(), &incx,
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&beta, x.base(), &incy);
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}
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}
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void
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ConstGeneralMatrix::multVecTrans(double a, Vector &x, double b,
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const ConstVector &d) const
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{
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if (x.length() != cols || rows != d.length())
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throw SYLV_MES_EXCEPTION("Wrong dimensions for vector multiply.");
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if (rows > 0)
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{
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blas_int mm = rows;
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blas_int nn = cols;
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double alpha = b;
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blas_int lda = ld;
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blas_int incx = d.skip();
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double beta = a;
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blas_int incy = x.skip();
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dgemv("T", &mm, &nn, &alpha, data.base(), &lda, d.base(), &incx,
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&beta, x.base(), &incy);
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}
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}
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/* m = inv(this)*m */
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void
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ConstGeneralMatrix::multInvLeft(const std::string &trans, int mrows, int mcols, int mld, double *d) const
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{
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if (rows != cols)
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throw SYLV_MES_EXCEPTION("The matrix is not square for inversion.");
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if (cols != mrows)
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throw SYLV_MES_EXCEPTION("Wrong dimensions for matrix inverse mutliply.");
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if (rows > 0)
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{
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GeneralMatrix inv(*this);
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auto ipiv = std::make_unique<lapack_int[]>(rows);
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lapack_int info;
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lapack_int rows2 = rows, mcols2 = mcols, mld2 = mld, lda = inv.ld;
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dgetrf(&rows2, &rows2, inv.getData().base(), &lda, ipiv.get(), &info);
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dgetrs(trans.c_str(), &rows2, &mcols2, inv.base(), &lda, ipiv.get(), d,
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&mld2, &info);
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}
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}
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/* m = inv(this)*m */
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void
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ConstGeneralMatrix::multInvLeft(GeneralMatrix &m) const
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{
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multInvLeft("N", m.nrows(), m.ncols(), m.getLD(), m.getData().base());
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}
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/* m = inv(this')*m */
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void
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ConstGeneralMatrix::multInvLeftTrans(GeneralMatrix &m) const
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{
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multInvLeft("T", m.nrows(), m.ncols(), m.getLD(), m.getData().base());
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}
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/* d = inv(this)*d */
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void
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ConstGeneralMatrix::multInvLeft(Vector &d) const
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{
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if (d.skip() != 1)
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throw SYLV_MES_EXCEPTION(u8"Skip≠1 not implemented in ConstGeneralMatrix::multInvLeft(Vector&)");
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multInvLeft("N", d.length(), 1, d.length(), d.base());
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}
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/* d = inv(this')*d */
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void
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ConstGeneralMatrix::multInvLeftTrans(Vector &d) const
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{
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if (d.skip() != 1)
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throw SYLV_MES_EXCEPTION(u8"Skip≠1 not implemented in ConstGeneralMatrix::multInvLeft(Vector&)");
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multInvLeft("T", d.length(), 1, d.length(), d.base());
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}
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bool
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ConstGeneralMatrix::isFinite() const
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{
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for (int i = 0; i < nrows(); i++)
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for (int j = 0; j < ncols(); j++)
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if (!std::isfinite(get(i, j)))
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return false;
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return true;
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}
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bool
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ConstGeneralMatrix::isZero() const
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{
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for (int i = 0; i < nrows(); i++)
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for (int j = 0; j < ncols(); j++)
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if (get(i, j) != 0.0)
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return false;
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return true;
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}
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void
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ConstGeneralMatrix::print() const
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{
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auto ff = std::cout.flags();
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std::cout << "rows=" << rows << ", cols=" << cols << std::endl;
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for (int i = 0; i < rows; i++)
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{
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std::cout << "row " << i << ':' << std::endl
|
|
<< std::setprecision(3);
|
|
for (int j = 0; j < cols; j++)
|
|
std::cout << std::setw(6) << get(i, j) << ' ';
|
|
std::cout << std::endl;
|
|
}
|
|
std::cout.flags(ff);
|
|
}
|
|
|
|
void
|
|
SVDDecomp::construct(const GeneralMatrix &A)
|
|
{
|
|
// quick exit if empty matrix
|
|
if (minmn == 0)
|
|
{
|
|
U.unit();
|
|
VT.unit();
|
|
conv = true;
|
|
return;
|
|
}
|
|
|
|
// make copy of the matrix
|
|
GeneralMatrix AA(A);
|
|
|
|
lapack_int m = AA.nrows();
|
|
lapack_int n = AA.ncols();
|
|
double *a = AA.base();
|
|
lapack_int lda = AA.getLD();
|
|
double *s = sigma.base();
|
|
double *u = U.base();
|
|
lapack_int ldu = U.getLD();
|
|
double *vt = VT.base();
|
|
lapack_int ldvt = VT.getLD();
|
|
double tmpwork;
|
|
lapack_int lwork = -1;
|
|
lapack_int info;
|
|
|
|
auto iwork = std::make_unique<lapack_int[]>(8*minmn);
|
|
// query for optimal lwork
|
|
dgesdd("A", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, &tmpwork,
|
|
&lwork, iwork.get(), &info);
|
|
lwork = static_cast<lapack_int>(tmpwork);
|
|
Vector work(lwork);
|
|
// do the decomposition
|
|
dgesdd("A", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work.base(),
|
|
&lwork, iwork.get(), &info);
|
|
if (info < 0)
|
|
throw SYLV_MES_EXCEPTION("Internal error in SVDDecomp constructor");
|
|
if (info == 0)
|
|
conv = true;
|
|
}
|
|
|
|
void
|
|
SVDDecomp::solve(const ConstGeneralMatrix &B, GeneralMatrix &X) const
|
|
{
|
|
if (B.nrows() != U.nrows())
|
|
throw SYLV_MES_EXCEPTION("Incompatible number of rows ");
|
|
|
|
/* Reciprocal condition number for determination of zeros in the
|
|
end of sigma */
|
|
constexpr double rcond = 1e-13;
|
|
|
|
// determine nz=number of zeros in the end of sigma
|
|
int nz = 0;
|
|
while (nz < minmn && sigma[minmn-1-nz] < rcond*sigma[0])
|
|
nz++;
|
|
// take relevant B for sigma inversion
|
|
int m = U.nrows();
|
|
int n = VT.ncols();
|
|
GeneralMatrix Bprime(transpose(U) * B, m-minmn, 0, minmn-nz, B.ncols());
|
|
// solve sigma
|
|
for (int i = 0; i < minmn-nz; i++)
|
|
Bprime.getRow(i).mult(1.0/sigma[i]);
|
|
// solve VT
|
|
X.zeros();
|
|
//- copy Bprime to right place of X
|
|
for (int i = 0; i < minmn-nz; i++)
|
|
X.getRow(n-minmn+i) = Bprime.getRow(i);
|
|
//- multiply with VT
|
|
X.multLeftTrans(VT);
|
|
}
|