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

/*
 * Copyright © 2004-2011 Ondra Kamenik
 * Copyright © 2019-2023 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 "QuasiTriangular.hh"
#include "SchurDecomp.hh"
#include "SylvException.hh"
#include "int_power.hh"

#include <dynblas.h>

#include <cmath>
#include <iostream>
#include <limits>
#include <sstream>

double
DiagonalBlock::getDeterminant() const
{
  return (*alpha) * (*alpha) + getSBeta();
}

double
DiagonalBlock::getSBeta() const
{
  return -(*beta1) * (*beta2);
}

double
DiagonalBlock::getSize() const
{
  if (real)
    return std::abs(*alpha);
  else
    return std::sqrt(getDeterminant());
}

/* This function makes Diagonal inconsistent, it should only be used
   on temorary matrices, which will not be used any more, e.g. in
   QuasiTriangular::solve() (we need fast performance) */
void
DiagonalBlock::setReal()
{
  *beta1 = 0;
  *beta2 = 0;
  real = true;
}

void
DiagonalBlock::checkBlock(const double* d, int d_size)
{
  const double* a1 = d + jbar * d_size + jbar;
  const double* b1 = a1 + d_size;
  const double* b2 = a1 + 1;
  const double* a2 = b1 + 1;
  if (a1 != alpha.a1)
    throw SYLV_MES_EXCEPTION("Bad alpha1.");
  if (!real && b1 != beta1)
    throw SYLV_MES_EXCEPTION("Bad beta1.");
  if (!real && b2 != beta2)
    throw SYLV_MES_EXCEPTION("Bad beta2.");
  if (!real && a2 != alpha.a2)
    throw SYLV_MES_EXCEPTION("Bad alpha2.");
}

Diagonal::Diagonal(double* data, int d_size)
{
  int nc = getNumComplex(data, d_size); // return nc ≤ d_size/2
  num_all = d_size - nc;
  num_real = d_size - 2 * nc;

  int jbar = 0;
  int j = 0;
  while (j < num_all)
    {
      int id = jbar * d_size + jbar; // index of diagonal block in data
      int ill = id + 1;              // index of element below the diagonal
      int iur = id + d_size;         // index of element right to diagonal
      int idd = id + d_size + 1;     // index of element next on diagonal
      if ((jbar < d_size - 1) && !isZero(data[ill]))
        {
          // it is not last column and we have nonzero below diagonal
          blocks.emplace_back(jbar, false, &data[id], &data[idd], &data[iur], &data[ill]);
          jbar++;
        }
      else
        // it is last column or we have zero below diagonal
        blocks.emplace_back(jbar, true, &data[id], &data[id], nullptr, nullptr);
      jbar++;
      j++;
    }
}

Diagonal::Diagonal(double* data, const Diagonal& d)
{
  num_all = d.num_all;
  num_real = d.num_real;
  int d_size = d.getSize();
  for (const auto& block : d)
    {
      double* beta1 = nullptr;
      double* beta2 = nullptr;
      int id = block.getIndex() * (d_size + 1);
      int idd = id;
      if (!block.isReal())
        {
          beta1 = &data[id + d_size];
          beta2 = &data[id + 1];
          idd = id + d_size + 1;
        }
      blocks.emplace_back(block.getIndex(), block.isReal(), &data[id], &data[idd], beta1, beta2);
    }
}

int
Diagonal::getNumComplex(const double* data, int d_size)
{
  int num_complex = 0;
  int in = 1;
  for (int i = 0; i < d_size - 1; i++, in = in + d_size + 1)
    if (!isZero(data[in]))
      {
        num_complex++;
        if (in < d_size - 2 && !isZero(data[in + d_size + 1]))
          throw SYLV_MES_EXCEPTION("Matrix is not quasi-triangular");
      }
  return num_complex;
}

void
Diagonal::changeBase(double* p)
{
  int d_size = getSize();
  for (auto& it : *this)
    {
      const DiagonalBlock& b = it;
      int jbar = b.getIndex();
      int base = d_size * jbar + jbar;
      if (b.isReal())
        {
          DiagonalBlock bnew(jbar, true, &p[base], &p[base], nullptr, nullptr);
          it = bnew;
        }
      else
        {
          DiagonalBlock bnew(jbar, false, &p[base], &p[base + d_size + 1], &p[base + d_size],
                             &p[base + 1]);
          it = bnew;
        }
    }
}

void
Diagonal::getEigenValues(Vector& eig) const
{
  if (int d_size {getSize()}; eig.length() != 2 * d_size)
    {
      std::ostringstream mes;
      mes << "Wrong length of vector for eigenvalues len=" << eig.length()
          << ", should be=" << 2 * d_size << '.' << std::endl;
      throw SYLV_MES_EXCEPTION(mes.str());
    }
  for (const auto& b : *this)
    {
      int ind = b.getIndex();
      eig[2 * ind] = *(b.getAlpha());
      if (b.isReal())
        eig[2 * ind + 1] = 0.0;
      else
        {
          double beta = std::sqrt(b.getSBeta());
          eig[2 * ind + 1] = beta;
          eig[2 * ind + 2] = eig[2 * ind];
          eig[2 * ind + 3] = -beta;
        }
    }
}

/* Swaps logically blocks ‘it’, and ‘++it’. remember to move also
   addresses, alpha, beta1, beta2. This is a dirty (but most
   effective) way how to do it. */
void
Diagonal::swapLogically(diag_iter it)
{
  auto itp = it;
  ++itp;

  if (it->isReal() && !itp->isReal())
    {
      // first is real, second is complex
      double* d1 = it->alpha.a1;
      double* d2 = itp->alpha.a1;
      double* d3 = itp->alpha.a2;
      // swap
      DiagonalBlock new_it(it->jbar, d1, d2);
      *it = new_it;
      DiagonalBlock new_itp(itp->jbar + 1, d3);
      *itp = new_itp;
    }
  else if (!it->isReal() && itp->isReal())
    {
      // first is complex, second is real
      double* d1 = it->alpha.a1;
      double* d2 = it->alpha.a2;
      double* d3 = itp->alpha.a1;
      // swap
      DiagonalBlock new_it(it->jbar, d1);
      *it = new_it;
      DiagonalBlock new_itp(itp->jbar - 1, d2, d3);
      *itp = new_itp;
    }
}

void
Diagonal::checkConsistency(diag_iter it)
{
  if (!it->isReal() && isZero(it->getBeta2()))
    {
      it->getBeta2() = 0.0; // put exact zero
      int jbar = it->getIndex();
      double* d2 = it->alpha.a2;
      it->alpha.a2 = it->alpha.a1;
      it->real = true;
      it->beta1 = nullptr;
      it->beta2 = nullptr;
      blocks.emplace(++it, jbar + 1, d2);
      num_real += 2;
      num_all++;
    }
}

double
Diagonal::getAverageSize(diag_iter start, diag_iter end)
{
  double res = 0;
  int num = 0;
  for (auto run = start; run != end; ++run)
    {
      num++;
      res += run->getSize();
    }
  if (num > 0)
    res = res / num;
  return res;
}

Diagonal::diag_iter
Diagonal::findClosestBlock(diag_iter start, diag_iter end, double a)
{
  auto closest = start;
  double minim {std::numeric_limits<double>::infinity()};
  for (auto run = start; run != end; ++run)
    if (double dist = std::abs(a - run->getSize()); dist < minim)
      {
        minim = dist;
        closest = run;
      }
  return closest;
}

Diagonal::diag_iter
Diagonal::findNextLargerBlock(diag_iter start, diag_iter end, double a)
{
  auto closest = start;
  double minim {std::numeric_limits<double>::infinity()};
  for (auto run = start; run != end; ++run)
    if (double dist = run->getSize() - a; 0 <= dist && dist < minim)
      {
        minim = dist;
        closest = run;
      }
  return closest;
}

void
Diagonal::print() const
{
  auto ff = std::cout.flags();
  std::cout << "Num real: " << getNumReal() << ", num complex: " << getNumComplex() << std::endl
            << std::fixed;
  for (const auto& it : *this)
    if (it.isReal())
      std::cout << "real: jbar=" << it.getIndex() << ", alpha=" << *(it.getAlpha()) << std::endl;
    else
      std::cout << "complex: jbar=" << it.getIndex() << ", alpha=" << *(it.getAlpha())
                << ", beta1=" << it.getBeta1() << ", beta2=" << it.getBeta2() << std::endl;
  std::cout.flags(ff);
}

bool
Diagonal::isZero(double p)
{
  return (std::abs(p) < EPS);
}

QuasiTriangular::const_col_iter
QuasiTriangular::col_begin(const DiagonalBlock& b) const
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  return {&getData()[jbar * d_size], d_size, b.isReal(), 0};
}

QuasiTriangular::col_iter
QuasiTriangular::col_begin(const DiagonalBlock& b)
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  return {&getData()[jbar * d_size], d_size, b.isReal(), 0};
}

QuasiTriangular::const_row_iter
QuasiTriangular::row_begin(const DiagonalBlock& b) const
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  int off = jbar * d_size + jbar + d_size;
  int col = jbar + 1;
  if (!b.isReal())
    {
      off = off + d_size;
      col++;
    }
  return {&getData()[off], d_size, b.isReal(), col};
}

QuasiTriangular::row_iter
QuasiTriangular::row_begin(const DiagonalBlock& b)
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  int off = jbar * d_size + jbar + d_size;
  int col = jbar + 1;
  if (!b.isReal())
    {
      off = off + d_size;
      col++;
    }
  return {&getData()[off], d_size, b.isReal(), col};
}

QuasiTriangular::const_col_iter
QuasiTriangular::col_end(const DiagonalBlock& b) const
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  return {getData().base() + jbar * d_size + jbar, d_size, b.isReal(), jbar};
}

QuasiTriangular::col_iter
QuasiTriangular::col_end(const DiagonalBlock& b)
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  return {&getData()[jbar * d_size + jbar], d_size, b.isReal(), jbar};
}

QuasiTriangular::const_row_iter
QuasiTriangular::row_end(const DiagonalBlock& b) const
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  return {&getData()[d_size * d_size + jbar], d_size, b.isReal(), d_size};
}

QuasiTriangular::row_iter
QuasiTriangular::row_end(const DiagonalBlock& b)
{
  int jbar = b.getIndex();
  int d_size = diagonal.getSize();
  return {&getData()[d_size * d_size + jbar], d_size, b.isReal(), d_size};
}

QuasiTriangular::QuasiTriangular(double r, const QuasiTriangular& t) :
    SqSylvMatrix(t.nrows()), diagonal(getData().base(), t.diagonal)
{
  setMatrix(r, t);
}

QuasiTriangular::QuasiTriangular(double r, const QuasiTriangular& t, double r2,
                                 const QuasiTriangular& t2) :
    SqSylvMatrix(t.nrows()), diagonal(getData().base(), t.diagonal)
{
  setMatrix(r, t);
  addMatrix(r2, t2);
}

QuasiTriangular::QuasiTriangular(const QuasiTriangular& t) :
    SqSylvMatrix(t), diagonal(getData().base(), t.diagonal)
{
}

QuasiTriangular::QuasiTriangular(const ConstVector& d, int d_size) :
    SqSylvMatrix(Vector {d}, d_size), diagonal(getData().base(), d_size)
{
}

QuasiTriangular::QuasiTriangular([[maybe_unused]] const std::string& dummy,
                                 const QuasiTriangular& t) :
    SqSylvMatrix(t.nrows()), diagonal(getData().base(), t.diagonal)
{
  Vector aux(t.getData());
  blas_int d_size = diagonal.getSize();
  double alpha = 1.0;
  double beta = 0.0;
  blas_int lda = t.getLD(), ldb = t.getLD(), ldc = ld;
  dgemm("N", "N", &d_size, &d_size, &d_size, &alpha, aux.base(), &lda, t.getData().base(), &ldb,
        &beta, getData().base(), &ldc);
}

QuasiTriangular::QuasiTriangular(const SchurDecomp& decomp) :
    SqSylvMatrix(decomp.getT()), diagonal(getData().base(), decomp.getDim())
{
}

// This pads matrix with intial columns with zeros
QuasiTriangular::QuasiTriangular(const SchurDecompZero& decomp) : SqSylvMatrix(decomp.getDim())
{
  // nullify first decomp.getZeroCols() columns
  int zeros = decomp.getZeroCols() * decomp.getDim();
  Vector zv(getData(), 0, zeros);
  zv.zeros();
  // fill right upper part with decomp.getRU()
  for (int i = 0; i < decomp.getRU().nrows(); i++)
    for (int j = 0; j < decomp.getRU().ncols(); j++)
      getData()[(j + decomp.getZeroCols()) * decomp.getDim() + i] = decomp.getRU().get(i, j);

  // fill right lower part with decomp.getT()
  for (int i = 0; i < decomp.getT().nrows(); i++)
    for (int j = 0; j < decomp.getT().ncols(); j++)
      getData()[(j + decomp.getZeroCols()) * decomp.getDim() + decomp.getZeroCols() + i]
          = decomp.getT().get(i, j);

  // construct diagonal
  diagonal = Diagonal {getData().base(), decomp.getDim()};
}

void
QuasiTriangular::setMatrix(double r, const QuasiTriangular& t)
{
  getData().zeros();
  getData().add(r, t.getData());
}

void
QuasiTriangular::addMatrix(double r, const QuasiTriangular& t)
{
  getData().add(r, t.getData());
}

void
QuasiTriangular::addUnit()
{
  for (auto di = diag_begin(); di != diag_end(); ++di)
    di->getAlpha() = *(di->getAlpha()) + 1.0;
}

void
QuasiTriangular::solve(Vector& x, const ConstVector& b, double& eig_min)
{
  x = b;
  solvePre(x, eig_min);
}

void
QuasiTriangular::solveTrans(Vector& x, const ConstVector& b, double& eig_min)
{
  x = b;
  solvePreTrans(x, eig_min);
}

void
QuasiTriangular::solvePre(Vector& x, double& eig_min)
{
  addUnit();
  for (auto di = diag_begin(); di != diag_end(); ++di)
    {
      double eig_size;
      if (!di->isReal())
        {
          eig_size = di->getDeterminant();
          eliminateLeft(di->getIndex() + 1, di->getIndex(), x);
        }
      else
        eig_size = *di->getAlpha() * (*di->getAlpha());
      eig_min = std::min(eig_min, eig_size);
    }

  blas_int nn = diagonal.getSize();
  blas_int lda = ld;
  blas_int incx = x.skip();
  dtrsv("U", "N", "N", &nn, getData().base(), &lda, x.base(), &incx);
}

void
QuasiTriangular::solvePreTrans(Vector& x, double& eig_min)
{
  addUnit();
  for (auto di = diag_begin(); di != diag_end(); ++di)
    {
      double eig_size;
      if (!di->isReal())
        {
          eig_size = di->getDeterminant();
          eliminateRight(di->getIndex() + 1, di->getIndex(), x);
        }
      else
        eig_size = *di->getAlpha() * (*di->getAlpha());
      if (eig_size < eig_min)
        eig_min = eig_size;
    }

  blas_int nn = diagonal.getSize();
  blas_int lda = ld;
  blas_int incx = x.skip();
  dtrsv("U", "T", "N", &nn, getData().base(), &lda, x.base(), &incx);
}

// Calculates x = T·b
void
QuasiTriangular::multVec(Vector& x, const ConstVector& b) const
{
  x = b;
  blas_int nn = diagonal.getSize();
  blas_int lda = ld;
  blas_int incx = x.skip();
  dtrmv("U", "N", "N", &nn, getData().base(), &lda, x.base(), &incx);
  for (auto di = diag_begin(); di != diag_end(); ++di)
    if (!di->isReal())
      {
        int jbar = di->getIndex();
        x[jbar + 1] += di->getBeta2() * (b[jbar]);
      }
}

void
QuasiTriangular::multVecTrans(Vector& x, const ConstVector& b) const
{
  x = b;
  blas_int nn = diagonal.getSize();
  blas_int lda = ld;
  blas_int incx = x.skip();
  dtrmv("U", "T", "N", &nn, getData().base(), &lda, x.base(), &incx);
  for (auto di = diag_begin(); di != diag_end(); ++di)
    if (!di->isReal())
      {
        int jbar = di->getIndex();
        x[jbar] += di->getBeta2() * b[jbar + 1];
      }
}

void
QuasiTriangular::multaVec(Vector& x, const ConstVector& b) const
{
  Vector tmp(const_cast<const Vector&>(x)); // new copy
  multVec(x, b);
  x.add(1.0, tmp);
}

void
QuasiTriangular::multaVecTrans(Vector& x, const ConstVector& b) const
{
  Vector tmp(const_cast<const Vector&>(x)); // new copy
  multVecTrans(x, b);
  x.add(1.0, tmp);
}

// Calculates x=x+(this⊗I)·b, where size of I is given by b (KronVector)
void
QuasiTriangular::multaKron(KronVector& x, const ConstKronVector& b) const
{
  int id = b.getN() * power(b.getM(), b.getDepth() - 1);
  ConstGeneralMatrix b_resh(b, id, b.getM());
  GeneralMatrix x_resh(x, id, b.getM());
  x_resh.multAndAdd(b_resh, ConstGeneralMatrix(*this), "trans");
}

// Calculates x=x+(this⊗I)·b, where size of I is given by b (KronVector)
void
QuasiTriangular::multaKronTrans(KronVector& x, const ConstKronVector& b) const
{
  int id = b.getN() * power(b.getM(), b.getDepth() - 1);
  ConstGeneralMatrix b_resh(b, id, b.getM());
  GeneralMatrix x_resh(x, id, b.getM());
  x_resh.multAndAdd(b_resh, ConstGeneralMatrix(*this));
}

void
QuasiTriangular::multKron(KronVector& x) const
{
  KronVector b(const_cast<const KronVector&>(x)); // make copy
  x.zeros();
  multaKron(x, b);
}

void
QuasiTriangular::multKronTrans(KronVector& x) const
{
  KronVector b(const_cast<const KronVector&>(x)); // make copy
  x.zeros();
  multaKronTrans(x, b);
}

void
QuasiTriangular::multLeftOther(GeneralMatrix& a) const
{
  a.multLeft(*this);
}

void
QuasiTriangular::multLeftOtherTrans(GeneralMatrix& a) const
{
  a.multLeftTrans(*this);
}

void
QuasiTriangular::swapDiagLogically(diag_iter it)
{
  diagonal.swapLogically(it);
}

void
QuasiTriangular::checkDiagConsistency(diag_iter it)
{
  diagonal.checkConsistency(it);
}

double
QuasiTriangular::getAverageDiagSize(diag_iter start, diag_iter end)
{
  return diagonal.getAverageSize(start, end);
}

QuasiTriangular::diag_iter
QuasiTriangular::findClosestDiagBlock(diag_iter start, diag_iter end, double a)
{
  return diagonal.findClosestBlock(start, end, a);
}

QuasiTriangular::diag_iter
QuasiTriangular::findNextLargerBlock(diag_iter start, diag_iter end, double a)
{
  return diagonal.findNextLargerBlock(start, end, a);
}

int
QuasiTriangular::getNumOffdiagonal() const
{
  return diagonal.getSize() * (diagonal.getSize() - 1) / 2 - diagonal.getNumComplex();
}