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test_fft.cc
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	#include "my_types.hh"
	#include "fft.hh"
	#include <gtest/gtest.h>

	/*****************************************************************/
	TEST(FFT, transform) {
	UInt N = 512;
	Matrix<complex> m(N);

	Real k = 2 * M_PI / N;
	for (auto&& entry : index(m)) {
	int i = std::get<0>(entry);
	int j = std::get<1>(entry);
	auto& val = std::get<2>(entry);
	val = cos(k * i);
	}

	Matrix<complex> res = FFT::transform(m);

	for (auto&& entry : index(res)) {
	int i = std::get<0>(entry);
	int j = std::get<1>(entry);
	auto& val = std::get<2>(entry);
	if (std::abs(val) > 1e-10)
	std::cout << i << "," << j << " = " << val << std::endl;

	if (i == 1 && j == 0)
	ASSERT_NEAR(std::abs(val), N * N / 2, 1e-10);
	else if (i == N - 1 && j == 0)
	ASSERT_NEAR(std::abs(val), N * N / 2, 1e-10);
	else
	ASSERT_NEAR(std::abs(val), 0, 1e-10);
	}
	}
	/*****************************************************************/

	TEST(FFT, inverse_transform) {
	// going in reverse
	UInt N = 512;
	Matrix<complex> m(N);
	Real k = 2 * M_PI / N;

	for (auto&& entry : index(m)) {
	int i = std::get<0>(entry);
	int j = std::get<1>(entry);
	auto& val = std::get<2>(entry);
	if (i == 1 && j == 0)
	val = N * N / 2;
	else if (i == N - 1 && j == 0)
	val = N * N / 2;
	else
	val = 0;
	}
	// Inverse analysis
	Matrix<complex> ires = FFT::itransform(m);

	for (auto&& entry : index(ires)) {
	int i = std::get<0>(entry);
	int j = std::get<1>(entry);
	auto& val = std::get<2>(entry);
	ASSERT_NEAR(std::abs(val), std::abs(cos(k * i)), 1e-10); //Normalizing Results
	}
	}

	/*****************************************************************/