/usr/include/ql/math/fastfouriertransform.hpp is in libquantlib0-dev 1.7.1-1.
This file is owned by root:root, with mode 0o644.
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/*
Copyright (C) 2006 Joseph Wang
Copyright (C) 2009 Liquidnet Holdings, Inc.
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.
*/
/*! \file fastfouriertransform.hpp
\brief Fast Fourier Transform
*/
// Based on public domain code by Christopher Diggins
#ifndef quantlib_fast_fourier_transform_hpp
#define quantlib_fast_fourier_transform_hpp
#include <ql/errors.hpp>
#include <ql/types.hpp>
#include <vector>
#include <iterator>
namespace QuantLib {
//! FFT implementation
class FastFourierTransform {
public:
//! the minimum order required for the given input size
static std::size_t min_order(std::size_t inputSize) {
return static_cast<std::size_t>(
std::ceil(std::log(static_cast<Real>(inputSize)) / M_LN2));
}
FastFourierTransform(std::size_t order)
: cs_(order), sn_(order) {
std::size_t m = 1 << order;
cs_[order - 1] = std::cos (2 * M_PI / m);
sn_[order - 1] = std::sin (2 * M_PI / m);
for (std::size_t i = order - 1; i > 0; --i) {
cs_ [i - 1] = cs_[i]*cs_[i] - sn_[i]*sn_[i];
sn_ [i - 1] = 2*sn_[i]*cs_[i];
}
}
//! The required size for the output vector
std::size_t output_size() const {
return ((std::size_t)1 << cs_.size());
}
//! FFT transform.
/*! The output sequence must be allocated by the user */
template<typename InputIterator, typename RandomAccessIterator>
void transform(InputIterator inBegin, InputIterator inEnd,
RandomAccessIterator out) const {
transform_impl(inBegin, inEnd, out, false);
}
//! Inverse FFT transform.
/*! The output sequence must be allocated by the user. */
template<typename InputIterator, typename RandomAccessIterator>
void inverse_transform(InputIterator inBegin, InputIterator inEnd,
RandomAccessIterator out) const {
transform_impl(inBegin, inEnd, out, true);
}
private:
std::vector<double> cs_, sn_;
template<typename InputIterator, typename RandomAccessIterator>
void transform_impl(InputIterator inBegin, InputIterator inEnd,
RandomAccessIterator out,
bool inverse) const {
typedef
typename std::iterator_traits<RandomAccessIterator>::value_type
complex;
const std::size_t order = cs_.size();
const std::size_t N = std::size_t(1 << order);
std::size_t i = 0;
for (; inBegin != inEnd; ++i, ++inBegin) {
*(out + bit_reverse(i, order)) = *inBegin;
}
QL_REQUIRE (i <= N, "FFT order is too small");
for (std::size_t s = 1; s <= order; ++s) {
std::size_t m = 1 << s;
complex w(1.0);
complex wm(cs_[s-1], inverse ? sn_[s-1] : -sn_[s-1]);
for (std::size_t j = 0; j < m/2; ++j) {
for (std::size_t k = j; k < N; k += m) {
complex t = w * (*(out + k + m/2));
complex u = *(out + k);
*(out + k) = u + t;
*(out + k + m/2) = u - t;
}
w *= wm;
}
}
}
static std::size_t bit_reverse(std::size_t x, std::size_t order) {
std::size_t n = 0;
for (std::size_t i = 0; i < order; ++i) {
n <<= 1;
n |= (x & 1);
x >>= 1;
}
return n;
}
};
}
#endif
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