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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Gang Liang
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/math/statistics/histogram.hpp>
#include <ql/math/statistics/incrementalstatistics.hpp>
#include <ql/math/comparison.hpp>
#include <algorithm>
namespace QuantLib {
namespace {
/* The discontinuous quantiles use the method (type 8) as
recommended by Hyndman and Fan (1996). The resulting
quantile estimates are approximately median-unbiased
regardless of the distribution of 'samples'.
If quantile function is called multiple times for the same
dataset, it is recommended to pre-sort the sample vector.
*/
Real quantile(const std::vector<Real>& samples, Real prob) {
Size nsample = samples.size();
QL_REQUIRE(prob >= 0.0 && prob <= 1.0,
"Probability has to be in [0,1].");
QL_REQUIRE(nsample > 0, "The sample size has to be positive." );
if (nsample == 1)
return samples[0];
// two special cases: close to boundaries
const Real a = 1. / 3, b = 2*a / (nsample+a);
if (prob < b)
return *std::min_element(samples.begin(), samples.end());
else if (prob > 1-b)
return *std::max_element(samples.begin(), samples.end());
// general situation: middle region and nsample >= 2
Size index = static_cast<Size>(std::floor((nsample+a)*prob+a));
std::vector<Real> sorted(index+1);
std::partial_sort_copy(samples.begin(), samples.end(),
sorted.begin(), sorted.end());
// use "index & index+1"th elements to interpolate the quantile
Real weight = nsample*prob + a - index;
return (1-weight) * sorted[index-1] + weight * sorted[index];
}
}
Size Histogram::bins() const {
return bins_;
}
const std::vector<Real>& Histogram::breaks() const {
return breaks_;
}
Histogram::Algorithm Histogram::algorithm() const {
return algorithm_;
}
bool Histogram::empty() const {
return bins_ == 0;
}
Size Histogram::counts(Size i) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
return counts_.at(i);
#else
return counts_[i];
#endif
}
Real Histogram::frequency(Size i) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
return frequency_.at(i);
#else
return frequency_[i];
#endif
}
void Histogram::calculate() {
QL_REQUIRE(!data_.empty(), "no data given");
Real min = *std::min_element(data_.begin(), data_.end());
Real max = *std::max_element(data_.begin(), data_.end());
// calculate number of bins if necessary
if (bins_ == Null<Size>()) {
switch (algorithm_) {
case Sturges: {
bins_ = static_cast<Size>(
std::ceil(std::log(static_cast<Real>(data_.size()))
/std::log(2.0) + 1));
break;
}
case FD: {
Real r1 = quantile(data_, 0.25);
Real r2 = quantile(data_, 0.75);
Real h = 2.0 * (r2-r1) * std::pow(static_cast<Real>(data_.size()), -1.0/3.0);
bins_ = static_cast<Size>(std::ceil((max-min)/h));
break;
}
case Scott: {
IncrementalStatistics summary;
summary.addSequence(data_.begin(), data_.end());
Real variance = summary.variance();
Real h = 3.5 * std::sqrt(variance)
* std::pow(static_cast<Real>(data_.size()), -1.0/3.0);
bins_ = static_cast<Size>(std::ceil((max-min)/h));
break;
}
case None:
QL_FAIL("a bin-partition algorithm is required");
default:
QL_FAIL("unknown bin-partition algorithm");
};
bins_ = std::max<Size>(bins_,1);
}
if (breaks_.empty()) {
// set breaks if not provided
breaks_.resize(bins_-1);
// ensure breaks_ evenly span over the range of data_
// TODO: borrow the idea of pretty in R.
Real h = (max-min)/bins_;
for (Size i=0; i<breaks_.size(); ++i) {
breaks_[i] = min + (i+1)*h;
}
} else {
// or ensure they're sorted if given
std::sort(breaks_.begin(), breaks_.end());
auto end = std::unique(breaks_.begin(), breaks_.end(),
static_cast<bool (*)(Real, Real)>(close_enough));
breaks_.resize(end - breaks_.begin());
}
// finally, calculate counts and frequencies
counts_.resize(bins_);
std::fill(counts_.begin(), counts_.end(), 0);
for (Real p : data_) {
bool processed = false;
for (Size i=0; i<breaks_.size(); ++i) {
if (p < breaks_[i]) {
++counts_[i];
processed = true;
break;
}
}
if (!processed)
++counts_[bins_-1];
}
frequency_.resize(bins_);
Size totalCounts = data_.size();
for (Size i=0; i<bins_; ++i)
frequency_[i] = static_cast<Real>(counts_[i])/totalCounts;
}
}
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