m-thesis-introduction/fourier/05_sine_fitting.py

#!/usr/bin/env python3
# vim: fdm=indent ts=4

__doc__ = \
"""
Sample sine wave + noise
Filter it
Then fit in t-domain to resolve \\varphi_0
"""

import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import numpy as np
if not True:
    import numpy.fft as ft
else:
    import scipy.fftpack as ft
import scipy.optimize as opt

from mylib import *

rng = np.random.default_rng()

def guess_sine_parameters(samples, fft=None, fft_freqs=None, guess=[None,None,None,None]):
    """Use crude methods to guess the parameters to a sine wave
    from properties of both samples and their fourier transform.

    Parameters:
    -----------
    samples - arraylike

    guess - arraylike or float or None
        If float, this is interpreted as a frequency
        Order of parameters: [amplitude, frequency, phase, offset]
        If one parameter is None, it is filled with an approximate value if available.

    Returns:
    -----------
    guess - arraylike
        An updated version of init_guess: [amplitude, frequency, phase, offset]
    """

    if not hasattr(guess, '__len__'):
        # interpret as a frequency (might still be None)
        guess = [None, guess, None, None]

    assert len(guess) == 4, "Wrong length for initial guess (should be 4)"

    nearest_f, nearest_phase = None, None
    if fft is not None and (guess[1] is None or guess[2] is None):
        nearest_idx = None
        if guess[1] is not None:
            if fft_freqs is not None:
                nearest_idx = find_nearest(guess[1], fft_freqs)
        else:
            # We'll take the strongest peak by default
            if fft is not None:
                nearest_idx = np.argmax(fft*2)

        if nearest_idx is not None:
            if fft_freqs is not None:
                nearest_f = fft_freqs[nearest_idx]

            nearest_phase = np.angle(fft[nearest_idx])

    for i in range(4):
        if guess[i] is not None:
            continue

        if i == 0: # amplitude
            guess[i] = np.std(samples) * (2 ** 1/2)
        elif i == 1: # frequency
            guess[i] = nearest_f
        elif i == 2: # phase
            guess[i] = nearest_phase
        elif i == 3: # offset   samples
            guess[i] = np.mean(samples)

    return guess

def curvefit_sine(time, samples, init_guess, fitfunc=sine_fitfunc, bounds=(-np.inf, np.inf), **curve_kwargs):
    """Fit a sine to samples with a supplied initial guess.

    This function sets bounds for the phase.
    """
    if bounds is None or bounds == (-np.inf, np.inf):
        high_bounds = np.array([np.inf, np.inf, +1*np.pi, np.inf])
        low_bounds = -1*high_bounds

        bounds = (low_bounds, high_bounds)

    return opt.curve_fit(fitfunc, time, samples, p0=init_guess, bounds=bounds, **curve_kwargs)

def fit_sine_to_samples(time, samples, samplerate=1, bandpass=None, guess=[None,None,None,None], fitfunc=sine_fitfunc, fft=None, freqs=None,**curve_kwargs):
    if bandpass is not None or guess[1] is None or guess[2] is None:
        if fft is None:
            fft = ft.rfft(samples)
        if freqs is None:
            freqs = ft.rfftfreq(samples.size, 1/samplerate)

        if bandpass:
            fft[(freqs < bandpass[0]) | (freqs > bandpass[1])] = 0
            samples = ft.irfft(fft, samples.size)

    old_guess = guess.copy()
    guess = guess_sine_parameters(samples, fft=fft, fft_freqs=freqs, guess=guess)

    try:
        fit = curvefit_sine(time, samples, guess, fitfunc=fitfunc, **curve_kwargs)
    except RuntimeError:
        fit = None

    return fit, guess, (fft, freqs, samples)

def chi_sq(observed, expected):
    """
    Simple \Chi^2 test
    """
    return np.sum( (observed-expected)**2  / expected)

def dof(observed, n_parameters=1):
    return len(observed) - n_parameters

def simulate_noisy_sine_fitting_SNR_and_residuals(
        N=1, snr_band=passband(), noise_band=passband(),
        t_length=1e-6, f_sample=250e6,
        noise_sigma=1, init_params=[1, 50e6, None, 0],
        show_original_signal_figure=True, show_bandpassed_signal_figure=True
        ):
    residuals = np.empty( (int(N), len(init_params)) )
    real_snrs = np.empty( (int(N)) )

    axs1, axs2 = None, None
    for j, _ in enumerate(residuals):

        if j % 500 == 0:
            print("Iteration {} running".format(j))

        # set random phase
        init_params[2] = 2*np.pi*rng.random()

        samples = sine_fitfunc(time, *init_params)
        noise = None
        if noise_sigma: # noise
            noise = rng.normal(0,noise_sigma, size=(len(samples)))

        real_snrs[j] = signal_to_noise(samples, noise, signal_band=snr_band, samplerate=f_sample, noise_band=noise_band)

        # plot original
        if show_original_signal_figure and (j==0 or N == 1):
            fig, axs1 = plot_signal_and_spectrum(
                    samples+noise, f_sample, "Original",
                    freq_unit='MHz', freq_scaler=freq_scaler
                    )
            for ax in axs1[[1,2]]:
                ax.axvline(f_sine/freq_scaler, color='r', alpha=0.4) # f_beacon
                ax.axvspan(snr_band[0]/freq_scaler,snr_band[1]/freq_scaler, color='purple', alpha=0.3, label='signalband') # snr
                ax.axvspan(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler, color='orange', alpha=0.3, label='noiseband') # noise_band

            # indicate initial phase
            axs1[2].axhline(init_params[2], color='r', alpha=0.4)

            axs1[1].legend()

        fit, guess, (fft, freqs, bandpassed) = fit_sine_to_samples(time, samples+noise, f_sample, guess=[None,f_sine,None,None], bandpass=snr_band)

        if fit is None:
            residuals[j] = np.nan
            continue

        residuals[j] = normalise_sine_params(init_params - fit[0])

        if show_bandpassed_signal_figure and (j==0 or N == 1):
            fitted_sine = sine_fitfunc(time, *fit[0])

            fig2, axs2 = plot_signal_and_spectrum(
                    bandpassed, f_sample, "Bandpassed samples\nS/N:{:.2e}".format(real_snrs[j]),
                    freq_unit='MHz', freq_scaler=freq_scaler
                    )
            for ax in axs2[[1,2]]:
                ax.axvline(f_sine/freq_scaler, color='r', alpha=0.4) # f_beacon
                ax.axvspan(snr_band[0]/freq_scaler,snr_band[1]/freq_scaler, color='purple', alpha=0.3, label='signalband') # snr
                ax.axvspan(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler, color='orange', alpha=0.3, label='noiseband') # noise_band

            l = axs2[0].plot(time, fitted_sine, label='fit')
            axs2[0].text(1, 1, '$\chi/d.o.f. = {:.2e}/{:.2e}$'.format(chi_sq(fitted_sine, samples), dof(samples,4)), transform=axs2[0].transAxes, ha='right', va='top')

            # indicate initial phase
            axs2[2].axhline(init_params[2], color='r', alpha=0.4)
            axs2[2].axhline(init_params[2], color=l[0].get_color(), alpha=0.4)

            axs2[0].legend(loc='upper left')
            axs2[1].legend()

            print("init:", init_params)
            print("fit :", fit[0])
            print("res :", residuals[j])

    return residuals, real_snrs, (axs1, axs2)


if __name__ == "__main__":
    from argparse import ArgumentParser
    from myscriptlib import save_all_figs_to_path_or_show

    rng = np.random.default_rng(1)

    parser = ArgumentParser(description=__doc__)
    parser.add_argument("fname", metavar="path/to/figure[/]", nargs="?", help="Location for generated figure, will append __file__ if a directory. If not supplied, figure is shown.")
    parser.add_argument("-n", "--n-rand", dest='N', default=1, type=int, nargs='?', help='Number of random sines to fit')
    args = parser.parse_args()
    default_extensions = ['.pdf', '.png']

    if args.fname == 'none':
        args.fname = None

    report_N_nan = True

    f_sine = 53.123456 # MHz
    sine_amplitude = 0.2
    sine_offset = 0
    init_params = np.array([sine_amplitude, f_sine, None, sine_offset])

    N = int(args.N)
    f_sample = 250 # MHz
    t_length = 10 # us
    noise_sigma = 1

    f_delta = 1/t_length
    noise_band = (30,80) # MHz
    snr_band = (f_sine -2*f_delta, f_sine + 2*f_delta)

    time = sampled_time(f_sample, end=t_length)

    freq_scaler = 1

    ###### End of inputs

    residuals, real_snrs, _ = simulate_noisy_sine_fitting_SNR_and_residuals(N=N, snr_band=snr_band, noise_band=noise_band, t_length=t_length, f_sample=f_sample, noise_sigma=noise_sigma, init_params=init_params)

    # Filter NaNs from fit attempts that failed
    nan_mask = ~np.isnan(residuals).any(axis=1)
    if report_N_nan:
        ## report how many NaNs were found
        print("NaNs: {}/{}".format(np.count_nonzero(~nan_mask), len(real_snrs)))

    residuals = residuals[ nan_mask ]
    real_snrs = real_snrs [ nan_mask ]

    ## Plot Signal-to-Noise vs Residuals of the fit paramters
    fig, axs = plt.subplots(1,4, sharey=True)
    fig.suptitle("S/N vs Residuals, S/N Band ({:.2e},{:.2e})MHz".format(snr_band[0]/freq_scaler, snr_band[-1]/freq_scaler))
    axs[0].set_ylabel("S/N")
    for i in range(len(init_params)):
        unit_scaler = [1, 1][i==1]
        unit_string = ['', '[MHz]'][i==1]
        xlabel = ["Amplitude", "Frequency", "Phase", "Offset"][i]

        axs[i].set_xlabel(xlabel + unit_string)
        axs[i].plot(residuals[:,i]/unit_scaler, real_snrs, ls='none', marker='o')

    ## Plot Histograms of the Residuals
    if True and N > 1:
        for j in range(len(init_params)):
            if j == 0 or j == 3:
                continue

            unit_scaler = [1, freq_scaler][j==1]
            unit_string = ['', '[MHz]'][j==1]
            xlabel = ["Amplitude", "Frequency", "Phase", "Offset"][j]

            title = xlabel + " residuals"
            title += "\n"
            title += "f: {:.2e}MHz, amp/sigma: {:.2e}".format(f_sine/freq_scaler, sine_amplitude/noise_sigma)
            if noise_band:
                title += " Band ({:.2e},{:.2e})MHz".format(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler)

            fig, ax = plt.subplots()
            ax.set_title(title)
            ax.hist(residuals[:,j]/unit_scaler, density=False, histtype='step', bins='sqrt')
            ax.set_xlabel(xlabel + unit_string)
            ax.set_ylabel("Counts")

            # make it symmetric around 0
            xmax = max(*ax.get_xlim())
            ax.set_xlim(-xmax, xmax)

            if j == 2: # Phase
                xmin, xmax = ax.get_xlim()
                maj_div = max(1, 2**np.ceil(np.log2(np.pi/(xmax-xmin)) + 1 ))
                min_div = maj_div*12

                axis_pi_ticker(ax.xaxis, major_divider=maj_div, minor_divider=min_div)

        # Plot histogram between phase and frequency
        if True and N > 10:
            fig, ax = plt.subplots()
            title = "Residuals\n"
            title += "f: {:.2e}MHz, amp/sigma: {:.2e}".format(f_sine/freq_scaler, sine_amplitude/noise_sigma)
            if noise_band:
                title += "\n Band ({},{})MHz".format(noise_band[0]/freq_scaler, noise_band[1]/freq_scaler)
            title += ", N={:.1e}".format(N)
            ax.set_title(title)
            ax.set_xlabel('Frequency [MHz]')
            ax.set_ylabel('Phase')
            _, _, _, sc = ax.hist2d(residuals[:,1]/freq_scaler, residuals[:,2], bins=np.sqrt(len(residuals)))
            fig.colorbar(sc, ax=ax, label='Counts')

            #ax.set_xlim(-np.pi, np.pi)
            axis_pi_ticker(ax.yaxis)
            ax.set_ylim(-np.pi, np.pi)

    ## Save or show figures
    save_all_figs_to_path_or_show(args.fname, default_basename=__file__, default_extensions=default_extensions)