THUAI6/CAPI/cpp/grpc/include/absl/random/internal/chi_square.h

// Copyright 2017 The Abseil Authors.
//
// Licensed 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
//
//      https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "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 under the License.

#ifndef ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
#define ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_

// The chi-square statistic.
//
// Useful for evaluating if `D` independent random variables are behaving as
// expected, or if two distributions are similar.  (`D` is the degrees of
// freedom).
//
// Each bucket should have an expected count of 10 or more for the chi square to
// be meaningful.

#include <cassert>

#include "absl/base/config.h"

namespace absl
{
    ABSL_NAMESPACE_BEGIN
    namespace random_internal
    {

        constexpr const char kChiSquared[] = "chi-squared";

        // Returns the measured chi square value, using a single expected value.  This
        // assumes that the values in [begin, end) are uniformly distributed.
        template<typename Iterator>
        double ChiSquareWithExpected(Iterator begin, Iterator end, double expected)
        {
            // Compute the sum and the number of buckets.
            assert(expected >= 10);  // require at least 10 samples per bucket.
            double chi_square = 0;
            for (auto it = begin; it != end; it++)
            {
                double d = static_cast<double>(*it) - expected;
                chi_square += d * d;
            }
            chi_square = chi_square / expected;
            return chi_square;
        }

        // Returns the measured chi square value, taking the actual value of each bucket
        // from the first set of iterators, and the expected value of each bucket from
        // the second set of iterators.
        template<typename Iterator, typename Expected>
        double ChiSquare(Iterator it, Iterator end, Expected eit, Expected eend)
        {
            double chi_square = 0;
            for (; it != end && eit != eend; ++it, ++eit)
            {
                if (*it > 0)
                {
                    assert(*eit > 0);
                }
                double e = static_cast<double>(*eit);
                double d = static_cast<double>(*it - *eit);
                if (d != 0)
                {
                    assert(e > 0);
                    chi_square += (d * d) / e;
                }
            }
            assert(it == end && eit == eend);
            return chi_square;
        }

        // ======================================================================
        // The following methods can be used for an arbitrary significance level.
        //

        // Calculates critical chi-square values to produce the given p-value using a
        // bisection search for a value within epsilon, relying on the monotonicity of
        // ChiSquarePValue().
        double ChiSquareValue(int dof, double p);

        // Calculates the p-value (probability) of a given chi-square value.
        double ChiSquarePValue(double chi_square, int dof);

    }  // namespace random_internal
    ABSL_NAMESPACE_END
}  // namespace absl

#endif  // ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_