/*
	File                 : nsl_hilbert.c
	Project              : LabPlot
	Description          : NSL Hilbert transform
	--------------------------------------------------------------------
	SPDX-FileCopyrightText: 2021 Stefan Gerlach <stefan.gerlach@uni.kn>
	SPDX-License-Identifier: GPL-2.0-or-later
*/

#include "nsl_hilbert.h"
#include "nsl_common.h"
#include <gsl/gsl_fft_complex.h>
#include <gsl/gsl_fft_halfcomplex.h>
#ifdef HAVE_FFTW3
#include <fftw3.h>
#endif

const char* nsl_hilbert_result_type_name[] = {i18n("Imaginary Part"), i18n("Envelope")};

/* algorithm from https://de.wikipedia.org/wiki/Hilbert-Transformation#Berechnung_%C3%BCber_Fouriertransformation */
int nsl_hilbert_transform(double data[], size_t stride, size_t n, nsl_hilbert_result_type type) {
	if (n < 2) /* we need at least 2 points */
		return 1;

	/* 1. DFT of data: dft_transform returns gsl_halfcomplex (raw) */
	nsl_dft_transform(data, stride, n, 1, nsl_dft_result_raw);

	const size_t N = 2 * n;
	double* result = (double*)malloc(N * sizeof(double));
	gsl_fft_halfcomplex_unpack(data, result, stride, n);

	size_t i;
	/*	for (i = 0; i < N; i++)
			printf(" %g", result[i]);
		printf("\n");
	*/
	/* 2. manipulate values */
	for (i = 2; i < 2 * ceil(n / 2.); i++)
		result[i] *= 2;

	/*	for (i = 0; i < N; i++)
			printf(" %g", result[i]);
		printf("\n");
	*/
	for (i = n + 1; i < N; i++)
		result[i] = 0;

		/*	for (i = 0; i < N; i++)
				printf(" %g", result[i]);
			printf("\n");
		*/
		/* 3. back transform */
#ifdef HAVE_FFTW3
	fftw_complex* o = (fftw_complex*)malloc(N * sizeof(double));
	fftw_plan pb = fftw_plan_dft_1d((int)n, o, o, FFTW_BACKWARD, FFTW_ESTIMATE);

	fftw_execute_dft(pb, (fftw_complex*)result, (fftw_complex*)result);
	fftw_destroy_plan(pb);
	free(o);
#else
	gsl_fft_complex_workspace* work = gsl_fft_complex_workspace_alloc(n);
	gsl_fft_complex_wavetable* hc = gsl_fft_complex_wavetable_alloc(n);
	gsl_fft_complex_inverse(result, 1, n, hc, work);
	gsl_fft_complex_wavetable_free(hc);
	gsl_fft_complex_workspace_free(work);
#endif

	/*	for (i = 0; i < N; i++)
	#ifdef HAVE_FFTW3
			printf(" %g", result[i]/n);
	#else
			printf(" %g", result[i]);
	#endif
		printf("\n");
	*/
	/* copy back (Hilbert transform is imag part) */
	switch (type) {
	case nsl_hilbert_result_imag:
		for (i = 0; i < n; i++)
#ifdef HAVE_FFTW3
			data[i] = result[2 * i + 1] / n;
#else
			data[i] = result[2 * i + 1];
#endif
		break;
	case nsl_hilbert_result_envelope:
		for (i = 0; i < n; i++)
#ifdef HAVE_FFTW3
			data[i] = hypot(result[2 * i], result[2 * i + 1]) / n;
#else
			data[i] = hypot(result[2 * i], result[2 * i + 1]);
#endif
	}

	free(result);

	return 0;
}
