kll/include/kolmogorov_smirnov_impl.hpp

/*
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 * distributed with this work for additional information
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 * to you under the Apache License, Version 2.0 (the
 * "License"); you may not use this file except in compliance
 * with the License.  You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
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 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.  See the License for the
 * specific language governing permissions and limitations
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#ifndef KOLMOGOROV_SMIRNOV_IMPL_HPP_
#define KOLMOGOROV_SMIRNOV_IMPL_HPP_

namespace datasketches {

// type resolver
template<typename T, typename C, typename S, typename A>
kll_quantile_calculator<T, C, A> make_quantile_calculator(const kll_sketch<T, C, S, A>& sketch) {
  return kll_quantile_calculator<T, C, A>(sketch);
}

template<typename Sketch>
double kolmogorov_smirnov::delta(const Sketch& sketch1, const Sketch& sketch2) {
  using Comparator = typename Sketch::comparator;
  auto calc1 = make_quantile_calculator(sketch1);
  auto calc2 = make_quantile_calculator(sketch2);
  auto it1 = calc1.begin();
  auto it2 = calc2.begin();
  const auto n1 = sketch1.get_n();
  const auto n2 = sketch2.get_n();
  double delta = 0;
  while (it1 != calc1.end() && it2 != calc2.end()) {
    const double norm_cum_wt1 = static_cast<double>((*it1).second) / n1;
    const double norm_cum_wt2 = static_cast<double>((*it2).second) / n2;
    delta = std::max(delta, std::abs(norm_cum_wt1 - norm_cum_wt2));
    if (Comparator()((*it1).first, (*it2).first)) {
      ++it1;
    } else if (Comparator()((*it2).first, (*it1).first)) {
      ++it2;
    } else {
      ++it1;
      ++it2;
    }
  }
  const double norm_cum_wt1 = it1 == calc1.end() ? 1 : static_cast<double>((*it1).second) / n1;
  const double norm_cum_wt2 = it2 == calc2.end() ? 1 : static_cast<double>((*it2).second) / n2;
  delta = std::max(delta, std::abs(norm_cum_wt1 - norm_cum_wt2));
  return delta;
}

template<typename Sketch>
double kolmogorov_smirnov::threshold(const Sketch& sketch1, const Sketch& sketch2, double p) {
  const double r1 = sketch1.get_num_retained();
  const double r2 = sketch2.get_num_retained();
  const double alpha_factor = sqrt(-0.5 * log(0.5 * p));
  const double delta_area_threshold = alpha_factor * sqrt((r1 + r2) / (r1 * r2));
  const double eps1 = sketch1.get_normalized_rank_error(false);
  const double eps2 = sketch2.get_normalized_rank_error(false);
  return delta_area_threshold + eps1 + eps2;
}

template<typename Sketch>
bool kolmogorov_smirnov::test(const Sketch& sketch1, const Sketch& sketch2, double p) {
  return delta(sketch1, sketch2) > threshold(sketch1, sketch2, p);
}

} /* namespace datasketches */

#endif