90 lines
3.0 KiB
C++
90 lines
3.0 KiB
C++
// Copyright 2017 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#ifndef ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
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#define ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
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// The chi-square statistic.
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//
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// Useful for evaluating if `D` independent random variables are behaving as
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// expected, or if two distributions are similar. (`D` is the degrees of
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// freedom).
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//
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// Each bucket should have an expected count of 10 or more for the chi square to
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// be meaningful.
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#include <cassert>
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#include "absl/base/config.h"
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namespace absl {
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ABSL_NAMESPACE_BEGIN
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namespace random_internal {
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constexpr const char kChiSquared[] = "chi-squared";
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// Returns the measured chi square value, using a single expected value. This
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// assumes that the values in [begin, end) are uniformly distributed.
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template <typename Iterator>
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double ChiSquareWithExpected(Iterator begin, Iterator end, double expected) {
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// Compute the sum and the number of buckets.
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assert(expected >= 10); // require at least 10 samples per bucket.
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double chi_square = 0;
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for (auto it = begin; it != end; it++) {
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double d = static_cast<double>(*it) - expected;
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chi_square += d * d;
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}
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chi_square = chi_square / expected;
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return chi_square;
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}
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// Returns the measured chi square value, taking the actual value of each bucket
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// from the first set of iterators, and the expected value of each bucket from
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// the second set of iterators.
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template <typename Iterator, typename Expected>
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double ChiSquare(Iterator it, Iterator end, Expected eit, Expected eend) {
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double chi_square = 0;
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for (; it != end && eit != eend; ++it, ++eit) {
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if (*it > 0) {
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assert(*eit > 0);
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}
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double e = static_cast<double>(*eit);
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double d = static_cast<double>(*it - *eit);
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if (d != 0) {
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assert(e > 0);
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chi_square += (d * d) / e;
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}
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}
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assert(it == end && eit == eend);
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return chi_square;
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}
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// ======================================================================
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// The following methods can be used for an arbitrary significance level.
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//
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// Calculates critical chi-square values to produce the given p-value using a
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// bisection search for a value within epsilon, relying on the monotonicity of
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// ChiSquarePValue().
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double ChiSquareValue(int dof, double p);
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// Calculates the p-value (probability) of a given chi-square value.
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double ChiSquarePValue(double chi_square, int dof);
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} // namespace random_internal
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ABSL_NAMESPACE_END
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} // namespace absl
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#endif // ABSL_RANDOM_INTERNAL_CHI_SQUARE_H_
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