/*

* xtensor-fftw

* Copyright (c) 2017, Patrick Bos

* Distributed under the terms of the BSD 3-Clause License.

*

* The full license is in the file LICENSE, distributed with this software.

*/

// real life examples

#define _USE_MATH_DEFINES // for MSVC ("Math Constants are not defined in Standard C/C++")

#include <cmath> // M_PI

#include <complex>

#include <xtensor-fftw/basic.hpp>

#include <xtensor-fftw/helper.hpp>

#include <xtensor/xarray.hpp>

#include <xtensor/xbuilder.hpp> // xt::arange

#include <xtensor/xmath.hpp> // xt::sin, cos

#include <xtensor/xio.hpp>

#include "gtest/gtest.h"

TEST(examples, sin_derivative) {

// generate a sinusoid field

double dx = M_PI/100;

xt::xarray<double> x = xt::arange(0., 2*M_PI, dx);

xt::xarray<double> sin = xt::sin(x);

// transform to Fourier space

auto sin_fs = xt::fftw::rfft(sin);

// multiply by i*k

std::complex<double> i {0, 1};

auto k = xt::fftw::rfftscale<double>(sin.shape()[0], dx);

xt::xarray< std::complex<double> > sin_derivative_fs = xt::eval(i * k * sin_fs);

// transform back to normal space

auto sin_derivative = xt::fftw::irfft(sin_derivative_fs);

EXPECT_TRUE(xt::allclose(xt::cos(x), sin_derivative));

// std::cout << "x: " << x << std::endl;

// std::cout << "sin: " << sin << std::endl;

// std::cout << "cos: " << xt::cos(x) << std::endl;

// std::cout << "sin_derivative: " << sin_derivative << std::endl;

}