add boost on mac

macx64/include/boost/math/tools/signal_statistics.hpp

@@ -0,0 +1,346 @@
+//  (C) Copyright Nick Thompson 2018.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_TOOLS_SIGNAL_STATISTICS_HPP
+#define BOOST_MATH_TOOLS_SIGNAL_STATISTICS_HPP
+
+#include <algorithm>
+#include <iterator>
+#include <boost/type_traits/is_complex.hpp>
+#include <boost/assert.hpp>
+#include <boost/multiprecision/detail/number_base.hpp>
+#include <boost/math/tools/roots.hpp>
+#include <boost/math/tools/univariate_statistics.hpp>
+
+
+namespace boost::math::tools {
+
+template<class ForwardIterator>
+auto absolute_gini_coefficient(ForwardIterator first, ForwardIterator last)
+{
+    using std::abs;
+    using RealOrComplex = typename std::iterator_traits<ForwardIterator>::value_type;
+    BOOST_ASSERT_MSG(first != last && std::next(first) != last, "Computation of the Gini coefficient requires at least two samples.");
+
+    std::sort(first, last,  [](RealOrComplex a, RealOrComplex b) { return abs(b) > abs(a); });
+
+
+    decltype(abs(*first)) i = 1;
+    decltype(abs(*first)) num = 0;
+    decltype(abs(*first)) denom = 0;
+    for (auto it = first; it != last; ++it)
+    {
+        decltype(abs(*first)) tmp = abs(*it);
+        num += tmp*i;
+        denom += tmp;
+        ++i;
+    }
+
+    // If the l1 norm is zero, all elements are zero, so every element is the same.
+    if (denom == 0)
+    {
+        decltype(abs(*first)) zero = 0;
+        return zero;
+    }
+    return ((2*num)/denom - i)/(i-1);
+}
+
+template<class RandomAccessContainer>
+inline auto absolute_gini_coefficient(RandomAccessContainer & v)
+{
+    return boost::math::tools::absolute_gini_coefficient(v.begin(), v.end());
+}
+
+template<class ForwardIterator>
+auto sample_absolute_gini_coefficient(ForwardIterator first, ForwardIterator last)
+{
+    size_t n = std::distance(first, last);
+    return n*boost::math::tools::absolute_gini_coefficient(first, last)/(n-1);
+}
+
+template<class RandomAccessContainer>
+inline auto sample_absolute_gini_coefficient(RandomAccessContainer & v)
+{
+    return boost::math::tools::sample_absolute_gini_coefficient(v.begin(), v.end());
+}
+
+
+// The Hoyer sparsity measure is defined in:
+// https://arxiv.org/pdf/0811.4706.pdf
+template<class ForwardIterator>
+auto hoyer_sparsity(const ForwardIterator first, const ForwardIterator last)
+{
+    using T = typename std::iterator_traits<ForwardIterator>::value_type;
+    using std::abs;
+    using std::sqrt;
+    BOOST_ASSERT_MSG(first != last && std::next(first) != last, "Computation of the Hoyer sparsity requires at least two samples.");
+
+    if constexpr (std::is_unsigned<T>::value)
+    {
+        T l1 = 0;
+        T l2 = 0;
+        size_t n = 0;
+        for (auto it = first; it != last; ++it)
+        {
+            l1 += *it;
+            l2 += (*it)*(*it);
+            n += 1;
+        }
+
+        double rootn = sqrt(n);
+        return (rootn - l1/sqrt(l2) )/ (rootn - 1);
+    }
+    else {
+        decltype(abs(*first)) l1 = 0;
+        decltype(abs(*first)) l2 = 0;
+        // We wouldn't need to count the elements if it was a random access iterator,
+        // but our only constraint is that it's a forward iterator.
+        size_t n = 0;
+        for (auto it = first; it != last; ++it)
+        {
+            decltype(abs(*first)) tmp = abs(*it);
+            l1 += tmp;
+            l2 += tmp*tmp;
+            n += 1;
+        }
+        if constexpr (std::is_integral<T>::value)
+        {
+            double rootn = sqrt(n);
+            return (rootn - l1/sqrt(l2) )/ (rootn - 1);
+        }
+        else
+        {
+            decltype(abs(*first)) rootn = sqrt(static_cast<decltype(abs(*first))>(n));
+            return (rootn - l1/sqrt(l2) )/ (rootn - 1);
+        }
+    }
+}
+
+template<class Container>
+inline auto hoyer_sparsity(Container const & v)
+{
+    return boost::math::tools::hoyer_sparsity(v.cbegin(), v.cend());
+}
+
+
+template<class Container>
+auto oracle_snr(Container const & signal, Container const & noisy_signal)
+{
+    using Real = typename Container::value_type;
+    BOOST_ASSERT_MSG(signal.size() == noisy_signal.size(),
+                     "Signal and noisy_signal must be have the same number of elements.");
+    if constexpr (std::is_integral<Real>::value)
+    {
+        double numerator = 0;
+        double denominator = 0;
+        for (size_t i = 0; i < signal.size(); ++i)
+        {
+            numerator += signal[i]*signal[i];
+            denominator += (noisy_signal[i] - signal[i])*(noisy_signal[i] - signal[i]);
+        }
+        if (numerator == 0 && denominator == 0)
+        {
+            return std::numeric_limits<double>::quiet_NaN();
+        }
+        if (denominator == 0)
+        {
+            return std::numeric_limits<double>::infinity();
+        }
+        return numerator/denominator;
+    }
+    else if constexpr (boost::is_complex<Real>::value ||
+                       boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_complex)
+
+    {
+        using std::norm;
+        typename Real::value_type numerator = 0;
+        typename Real::value_type denominator = 0;
+        for (size_t i = 0; i < signal.size(); ++i)
+        {
+            numerator += norm(signal[i]);
+            denominator += norm(noisy_signal[i] - signal[i]);
+        }
+        if (numerator == 0 && denominator == 0)
+        {
+            return std::numeric_limits<typename Real::value_type>::quiet_NaN();
+        }
+        if (denominator == 0)
+        {
+            return std::numeric_limits<typename Real::value_type>::infinity();
+        }
+
+        return numerator/denominator;
+    }
+    else
+    {
+        Real numerator = 0;
+        Real denominator = 0;
+        for (size_t i = 0; i < signal.size(); ++i)
+        {
+            numerator += signal[i]*signal[i];
+            denominator += (signal[i] - noisy_signal[i])*(signal[i] - noisy_signal[i]);
+        }
+        if (numerator == 0 && denominator == 0)
+        {
+            return std::numeric_limits<Real>::quiet_NaN();
+        }
+        if (denominator == 0)
+        {
+            return std::numeric_limits<Real>::infinity();
+        }
+
+        return numerator/denominator;
+    }
+}
+
+template<class Container>
+auto mean_invariant_oracle_snr(Container const & signal, Container const & noisy_signal)
+{
+    using Real = typename Container::value_type;
+    BOOST_ASSERT_MSG(signal.size() == noisy_signal.size(), "Signal and noisy signal must be have the same number of elements.");
+
+    Real mu = boost::math::tools::mean(signal);
+    Real numerator = 0;
+    Real denominator = 0;
+    for (size_t i = 0; i < signal.size(); ++i)
+    {
+        Real tmp = signal[i] - mu;
+        numerator += tmp*tmp;
+        denominator += (signal[i] - noisy_signal[i])*(signal[i] - noisy_signal[i]);
+    }
+    if (numerator == 0 && denominator == 0)
+    {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+    if (denominator == 0)
+    {
+        return std::numeric_limits<Real>::infinity();
+    }
+
+    return numerator/denominator;
+
+}
+
+template<class Container>
+auto mean_invariant_oracle_snr_db(Container const & signal, Container const & noisy_signal)
+{
+    using std::log10;
+    return 10*log10(boost::math::tools::mean_invariant_oracle_snr(signal, noisy_signal));
+}
+
+
+// Follows the definition of SNR given in Mallat, A Wavelet Tour of Signal Processing, equation 11.16.
+template<class Container>
+auto oracle_snr_db(Container const & signal, Container const & noisy_signal)
+{
+    using std::log10;
+    return 10*log10(boost::math::tools::oracle_snr(signal, noisy_signal));
+}
+
+// A good reference on the M2M4 estimator:
+// D. R. Pauluzzi and N. C. Beaulieu, "A comparison of SNR estimation techniques for the AWGN channel," IEEE Trans. Communications, Vol. 48, No. 10, pp. 1681-1691, 2000.
+// A nice python implementation:
+// https://github.com/gnuradio/gnuradio/blob/master/gr-digital/examples/snr_estimators.py
+template<class ForwardIterator>
+auto m2m4_snr_estimator(ForwardIterator first, ForwardIterator last, decltype(*first) estimated_signal_kurtosis=1, decltype(*first) estimated_noise_kurtosis=3)
+{
+    BOOST_ASSERT_MSG(estimated_signal_kurtosis > 0, "The estimated signal kurtosis must be positive");
+    BOOST_ASSERT_MSG(estimated_noise_kurtosis > 0, "The estimated noise kurtosis must be positive.");
+    using Real = typename std::iterator_traits<ForwardIterator>::value_type;
+    using std::sqrt;
+    if constexpr (std::is_floating_point<Real>::value ||
+       boost::multiprecision::number_category<Real>::value == boost::multiprecision::number_kind_floating_point)
+    {
+        // If we first eliminate N, we obtain the quadratic equation:
+        // (ka+kw-6)S^2 + 2M2(3-kw)S + kw*M2^2 - M4 = 0 =: a*S^2 + bs*N + cs = 0
+        // If we first eliminate S, we obtain the quadratic equation:
+        // (ka+kw-6)N^2 + 2M2(3-ka)N + ka*M2^2 - M4 = 0 =: a*N^2 + bn*N + cn = 0
+        // I believe these equations are totally independent quadratics;
+        // if one has a complex solution it is not necessarily the case that the other must also.
+        // However, I can't prove that, so there is a chance that this does unnecessary work.
+        // Future improvements: There are algorithms which can solve quadratics much more effectively than the naive implementation found here.
+        // See: https://stackoverflow.com/questions/48979861/numerically-stable-method-for-solving-quadratic-equations/50065711#50065711
+        auto [M1, M2, M3, M4] = boost::math::tools::first_four_moments(first, last);
+        if (M4 == 0)
+        {
+            // The signal is constant. There is no noise:
+            return std::numeric_limits<Real>::infinity();
+        }
+        // Change to notation in Pauluzzi, equation 41:
+        auto kw = estimated_noise_kurtosis;
+        auto ka = estimated_signal_kurtosis;
+        // A common case, since it's the default:
+        Real a = (ka+kw-6);
+        Real bs = 2*M2*(3-kw);
+        Real cs = kw*M2*M2 - M4;
+        Real bn = 2*M2*(3-ka);
+        Real cn = ka*M2*M2 - M4;
+        auto [S0, S1] = boost::math::tools::quadratic_roots(a, bs, cs);
+        if (S1 > 0)
+        {
+            auto N = M2 - S1;
+            if (N > 0)
+            {
+                return S1/N;
+            }
+            if (S0 > 0)
+            {
+                N = M2 - S0;
+                if (N > 0)
+                {
+                    return S0/N;
+                }
+            }
+        }
+        auto [N0, N1] = boost::math::tools::quadratic_roots(a, bn, cn);
+        if (N1 > 0)
+        {
+            auto S = M2 - N1;
+            if (S > 0)
+            {
+                return S/N1;
+            }
+            if (N0 > 0)
+            {
+                S = M2 - N0;
+                if (S > 0)
+                {
+                    return S/N0;
+                }
+            }
+        }
+        // This happens distressingly often. It's a limitation of the method.
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+    else
+    {
+        BOOST_ASSERT_MSG(false, "The M2M4 estimator has not been implemented for this type.");
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+}
+
+template<class Container>
+inline auto m2m4_snr_estimator(Container const & noisy_signal,  typename Container::value_type estimated_signal_kurtosis=1, typename Container::value_type estimated_noise_kurtosis=3)
+{
+    return m2m4_snr_estimator(noisy_signal.cbegin(), noisy_signal.cend(), estimated_signal_kurtosis, estimated_noise_kurtosis);
+}
+
+template<class ForwardIterator>
+inline auto m2m4_snr_estimator_db(ForwardIterator first, ForwardIterator last, decltype(*first) estimated_signal_kurtosis=1, decltype(*first) estimated_noise_kurtosis=3)
+{
+    using std::log10;
+    return 10*log10(m2m4_snr_estimator(first, last, estimated_signal_kurtosis, estimated_noise_kurtosis));
+}
+
+
+template<class Container>
+inline auto m2m4_snr_estimator_db(Container const & noisy_signal,  typename Container::value_type estimated_signal_kurtosis=1, typename Container::value_type estimated_noise_kurtosis=3)
+{
+    using std::log10;
+    return 10*log10(m2m4_snr_estimator(noisy_signal, estimated_signal_kurtosis, estimated_noise_kurtosis));
+}
+
+}
+#endif