rdkit/Code/GraphMol/RascalMCES/lap_a_la_scipy.cpp

// This is a mildly modified version of the code in SciPy's
// scipy.optimize.linear_sum_assignment, extracted from
// rectangular_lsap.cpp.
// https://github.com/scipy/scipy/blob/main/scipy/optimize/rectangular_lsap/rectangular_lsap.cpp
// As such it is subject to the following notice:
/*
Copyright (c) 2001-2002 Enthought, Inc. 2003-2023, SciPy Developers.
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This code implements the shortest augmenting path algorithm for the
rectangular assignment problem.  This implementation is based on the
pseudocode described in pages 1685-1686 of:

    DF Crouse. On implementing 2D rectangular assignment algorithms.
    IEEE Transactions on Aerospace and Electronic Systems
    52(4):1679-1696, August 2016
    doi: 10.1109/TAES.2016.140952

Author: PM Larsen
*/

#include <algorithm>
#include <limits>
#include <numeric>
#include <vector>

namespace RDKit {
namespace RascalMCES {
template <typename T>
std::vector<size_t> argsortIter(const std::vector<T> &v) {
  std::vector<size_t> index(v.size());
  std::iota(index.begin(), index.end(), 0);
  std::sort(index.begin(), index.end(),
            [&v](size_t i, size_t j) { return v[i] < v[j]; });
  return index;
}

static int augmentingPath(size_t nc, std::vector<int> &cost,
                          std::vector<double> &u, std::vector<double> &v,
                          std::vector<size_t> &path,
                          std::vector<size_t> &row4col,
                          std::vector<double> &shortestPathCosts, size_t i,
                          std::vector<bool> &SR, std::vector<bool> &SC,
                          std::vector<size_t> &remaining, double *p_minVal) {
  double minVal = 0;

  // Crouse's pseudocode uses set complements to keep track of remaining
  // nodes.  Here we use a vector, as it is more efficient in C++.
  size_t numRemaining = nc;
  for (size_t it = 0; it < nc; it++) {
    // Filling this up in reverse order ensures that the solution of a
    // constant cost matrix is the identity matrix (c.f. #11602).
    remaining[it] = nc - it - 1;
  }

  std::fill(SR.begin(), SR.end(), false);
  std::fill(SC.begin(), SC.end(), false);
  std::fill(shortestPathCosts.begin(), shortestPathCosts.end(),
            std::numeric_limits<double>::max());

  // find shortest augmenting path
  int sink = -1;
  while (sink == -1) {
    // Clearly this will produce an overflow and set index to a large integer.
    // It is how the original code did it, and I assume whoever wrote it knew
    // what they were doing.
    size_t index = -1;
    double lowest = std::numeric_limits<double>::max();
    SR[i] = true;

    for (size_t it = 0; it < numRemaining; it++) {
      size_t j = remaining[it];

      double r = minVal + cost[i * nc + j] - u[i] - v[j];
      if (r < shortestPathCosts[j]) {
        path[j] = i;
        shortestPathCosts[j] = r;
      }

      // When multiple nodes have the minimum cost, we select one which
      // gives us a new sink node. This is particularly important for
      // integer cost matrices with small co-efficients.
      if (shortestPathCosts[j] < lowest ||
          (shortestPathCosts[j] == lowest &&
           row4col[j] == static_cast<size_t>(-1))) {
        lowest = shortestPathCosts[j];
        index = it;
      }
    }

    minVal = lowest;
    if (minVal ==
        std::numeric_limits<double>::max()) {  // infeasible cost matrix
      return -1;
    }

    size_t j = remaining[index];
    if (row4col[j] == static_cast<size_t>(-1)) {
      sink = j;
    } else {
      i = row4col[j];
    }

    SC[j] = true;
    remaining[index] = remaining[--numRemaining];
  }

  *p_minVal = minVal;
  return sink;
}

int lapMaximize(const std::vector<std::vector<int>> &costsMat,
                std::vector<size_t> &a, std::vector<size_t> &b) {
  if (costsMat.empty() || costsMat.front().empty()) {
    return 0;
  }
  size_t nr = costsMat.size();
  size_t nc = costsMat.front().size();
  bool transpose = nc < nr;
  std::vector<int> cost(nc * nr);
  // for maximization, take -ve of costs.
  for (size_t i = 0; i < nr; ++i) {
    for (size_t j = 0; j < nc; ++j) {
      if (transpose) {
        cost[j * nr + i] = -costsMat[i][j];
      } else {
        cost[i * nc + j] = -costsMat[i][j];
      }
    }
  }
  if (transpose) {
    std::swap(nc, nr);
  }
  // initialize variables
  std::vector<double> u(nr, 0);
  std::vector<double> v(nc, 0);
  std::vector<double> shortestPathCosts(nc);
  std::vector<size_t> path(nc, -1);
  std::vector<size_t> col4row(nr, -1);
  std::vector<size_t> row4col(nc, -1);
  std::vector<bool> SR(nr);
  std::vector<bool> SC(nc);
  std::vector<size_t> remaining(nc);

  // iteratively build the solution
  for (size_t curRow = 0; curRow < nr; curRow++) {
    double minVal;
    int sink = augmentingPath(nc, cost, u, v, path, row4col, shortestPathCosts,
                              curRow, SR, SC, remaining, &minVal);
    if (sink < 0) {
      return -1;
    }

    // update dual variables
    u[curRow] += minVal;
    for (size_t i = 0; i < nr; i++) {
      if (SR[i] && i != curRow) {
        u[i] += minVal - shortestPathCosts[col4row[i]];
      }
    }

    for (size_t j = 0; j < nc; j++) {
      if (SC[j]) {
        v[j] -= minVal - shortestPathCosts[j];
      }
    }

    // augment previous solution
    size_t j = sink;
    while (1) {
      size_t i = path[j];
      row4col[j] = i;
      std::swap(col4row[i], j);
      if (i == curRow) {
        break;
      }
    }
  }

  if (transpose) {
    size_t i = 0;
    for (auto v : argsortIter(col4row)) {
      a[i] = col4row[v];
      b[i] = v;
      i++;
    }
  } else {
    for (size_t i = 0; i < nr; i++) {
      a[i] = i;
      b[i] = col4row[i];
    }
  }

  return 0;
}
}  // namespace RascalMCES
}  // namespace RDKit