// BSD 2-Clause License
//
// Copyright 2020 James Melville
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice,
//    this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright notice,
//    this list of conditions and the following disclaimer in the documentation
//    and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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#ifndef UWOT_PERPLEXITY_H
#define UWOT_PERPLEXITY_H

#include <atomic>
#include <cmath>
#include <limits>
#include <vector>

namespace uwot {

auto find_beta(const std::vector<double> &d2, double target, double tol,
               std::size_t n_iter,
               std::size_t &n_window_search_fails) -> double {
  constexpr auto double_max = (std::numeric_limits<double>::max)();
  double beta = 1.0;
  double lo = 0.0;
  double hi = double_max;

  // best value seen is used only if binary search fails
  // (usually only happens if there are multiple degenerate distances)
  double beta_best = beta;
  double adiff_min = double_max;
  bool converged = false;

  // neighbors of i not including itself
  auto n_true_neighbors = d2.size();

  for (std::size_t iter = 0; iter < n_iter; iter++) {
    double Z = 0.0;
    double H = 0.0;
    double sum_D2_W = 0.0;
    for (std::size_t k = 0; k < n_true_neighbors; k++) {
      double W = std::exp(-d2[k] * beta);
      Z += W;
      sum_D2_W += d2[k] * W;
    }
    if (Z > 0) {
      H = std::log(Z) + beta * sum_D2_W / Z;
    }

    double adiff = std::abs(H - target);
    if (adiff < tol) {
      converged = true;
      break;
    }

    // store best beta in case binary search fails
    if (adiff < adiff_min) {
      adiff_min = adiff;
      beta_best = beta;
    }

    if (H < target) {
      hi = beta;
      beta = 0.5 * (lo + hi);
    } else {
      lo = beta;
      if (hi == double_max) {
        beta *= 2.0;
      } else {
        beta = 0.5 * (lo + hi);
      }
    }
  }
  if (!converged) {
    ++n_window_search_fails;
    beta = beta_best;
  }

  return beta;
}

void perplexity_search(std::size_t i, const std::vector<double> &nn_dist,
                       std::size_t n_neighbors, double target, double tol,
                       std::size_t n_iter, std::vector<double> &d2,
                       std::vector<double> &nn_weights, bool save_sigmas,
                       std::vector<double> &sigmas,
                       std::size_t &n_window_search_fails) {
  auto i_begin = n_neighbors * i;

  // log-sum-exp trick
  // shift squared distances by minimum (distances are already sorted)
  // D2, W and Z are their shifted versions
  // but P (and hence Shannon entropy) is unchanged
  // the self neighbor is ignored leading to some +/- 1 in loops and indexing
  double dmin = nn_dist[i_begin + 1] * nn_dist[i_begin + 1];
  for (std::size_t k = 1; k < n_neighbors; k++) {
    d2[k - 1] = nn_dist[i_begin + k] * nn_dist[i_begin + k] - dmin;
  }

  double beta = find_beta(d2, target, tol, n_iter, n_window_search_fails);

  double Z = 0.0;
  for (std::size_t k = 0; k < n_neighbors - 1; k++) {
    double W = std::exp(-d2[k] * beta);
    Z += W;
    // no longer need d2 at this point, store final W there
    d2[k] = W;
  }
  for (std::size_t k = 1; k < n_neighbors; k++) {
    nn_weights[i_begin + k] = d2[k - 1] / Z;
  }

  if (save_sigmas) {
    sigmas[i] = 1 / sqrt(beta);
  }
}

void perplexity_search(std::size_t begin, std::size_t end,
                       const std::vector<double> &nn_dist,
                       std::size_t n_neighbors, double target, double tol,
                       std::size_t n_iter, std::vector<double> &res,
                       bool save_sigmas, std::vector<double> &sigmas,
                       std::atomic_size_t &n_search_fails) {
  // number of binary search failures in this window
  std::size_t n_window_search_fails = 0;
  std::vector<double> d2(n_neighbors - 1, 0.0);

  for (std::size_t i = begin; i < end; i++) {
    perplexity_search(i, nn_dist, n_neighbors, target, tol, n_iter, d2, res,
                      save_sigmas, sigmas, n_window_search_fails);
  }

  // Update global count of failures
  n_search_fails += n_window_search_fails;
}

} // namespace uwot

#endif // UWOT_PERPLEXITY_H
