added autocorrelation unit test.

add_subdirectory(nfft)

add_subdirectory(random)

add_subdirectory(statistical_testing)

add_subdirectory(statistics)

add_subdirectory(util)

dca_add_gtest(autocorrelation_test

        GTEST_MAIN

        LIBS)

// Copyright (C) 2019 ETH Zurich

// Copyright (C) 2019 UT-Battelle, LLC

// All rights reserved.

//

// See LICENSE for terms of usage.

// See CITATION.md for citation guidelines, if DCA++ is used for scientific publications.

//

// Author: Giovanni Balduzzi (gbalduzz@itp.phys.ethz.ch)

//

// This file tests autocorrelation.hpp by generating a time series of known autocorrelation time.

#include "dca/math/statistics/autocorrelation.hpp"

#include <random>

#include "gtest/gtest.h"

TEST(AutocorrelationTest, All) {

  const std::vector<double> tau_exp_vals{1, 5, 3};

  const std::vector<double> means{0, 1, -1};

  const std::vector<double> stdevs{1, 0.5, 2};

  const int n_samples = 5e4;

  std::mt19937_64 rng(42);

  for (int test_id = 0; test_id < tau_exp_vals.size(); ++test_id) {

    const double tau_exp = tau_exp_vals[test_id];

    std::vector<double> independent_series(n_samples);

    std::normal_distribution<double> distro(means[test_id], stdevs[test_id]);

    const int n_corr = 100;

    dca::math::statistics::Autocorrelation<double> autocorr(n_corr);

    // Compute and accumulate time series.

    for (auto& x : independent_series) {

      x = distro(rng);

    }

    for (int i = n_corr; i < independent_series.size(); ++i) {

      double correlated = 0;

      for (int j = i - n_corr; j <= i; ++j) {

        correlated += std::exp(-(i - j) / tau_exp) * independent_series[j];

      }

      autocorr.addSample(correlated);

    }

    // See: http://www.hep.fsu.edu/~berg/teach/mcmc08/material/lecture07mcmc3.pdf

    const auto tau_integrated = 1. + (2 * std::exp(-1. / tau_exp)) / (1 - std::exp(-1. / tau_exp));

    const double tau_computed = autocorr.computeAutocorrelationTime();

    const double rel_diff = 2 * (tau_computed - tau_integrated) / (tau_computed + tau_integrated);

    EXPECT_NEAR(rel_diff, 0, 0.1);

  }

}

TEST(AutocorrelationTest, ComplexCompiles) {

  dca::math::statistics::Autocorrelation<std::complex<float>> corr(10);

  corr.addSample(std::complex<float>(1, 0));

  corr.addSample(std::complex<float>(1, -1));

  // Note: this computation will fail to converge.

  corr.computeAutocorrelationTime();

}