cpp/python/ste.py

import pathlib

import numpy
import numpy as np
from matplotlib import pyplot as plt
from scipy.optimize import curve_fit

from python.helpers import read_parameter_file


def ste_decay(x: np.ndarray, m0: float, t: float, beta: float, finfty: float) -> np.ndarray:
    """
    Calculate stimulated-echo decay.

    :param x: Mixing times in seconds.
    :param m0: Amplitude
    :param t: Correlation time in seconds
    :param beta: Stretching parameter
    :param finfty: Final plateau
    :return: Stimulated-echo decay
    """
    return m0 * ((1-finfty) * np.exp(-(x/t)**beta) + finfty)


def fit_decay(x: np.ndarray, y: np.ndarray, tevo: np.ndarray, verbose: bool = True) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
    num_evo = y.shape[1]
    if num_evo != tevo.size:
        tevo = np.arange(num_evo)

    tau_fit = np.empty((num_evo, 2))
    tau_fit[:, 0] = tevo

    beta_fit = np.empty((num_evo, 2))
    beta_fit[:, 0] = tevo

    finfty_fit = np.empty((num_evo, 2))
    finfty_fit[:, 0] = tevo

    scaled_y = (y-y[-1, :]) / (y[0, :]-y[-1, :])

    for j in range(num_evo):
        p0 = [y[0, 0], x[np.argmin(np.abs(scaled_y[:, j]-np.exp(-1)))], 0.8, 0.1]

        try:
            res = curve_fit(ste_decay, x, y[:, j], p0, bounds=[(0, 0, 0., 0), (np.inf, np.inf, 1, 1)])
        except RuntimeError as e:
            print(f'Fit {j+1} of {num_evo} failed with {e.args}')
            continue

        m0, tauc, beta, finfty = res[0]

        if verbose:
            print(f'Fit {j+1} of {num_evo}: tau_c = {tauc:.6e}, beta={beta:.4e}, amplitude = {m0: .4e}, f_infty={finfty:.4e}')

        tau_fit[j, 1] = tauc
        beta_fit[j, 1] = beta
        finfty_fit[j, 1] = finfty

    return tau_fit, beta_fit, finfty_fit


def fit_ste(
        parameter_file: pathlib.Path,
        prefix: str,
        plot_decays: bool = True,
        verbose: bool = True,
    ) -> tuple[str, np.ndarray, np.ndarray, np.ndarray]:
    # read simulation parameters
    parameter = read_parameter_file(parameter_file)

    # files have form ste_arg=0.000000e+01_parameter.txt, first remove ste part then parameter.txt to get variables
    varied_string = str(parameter_file).partition('_')[-1].rpartition('_')[0]

    # make evolution times
    tevo = np.linspace(parameter['tevo_start'], parameter['tevo_stop'], num=int(parameter['tevo_steps']))

    raw_data = np.loadtxt(f'{prefix}_{varied_string}.dat')

    t_mix = raw_data[:, 0]
    decay = raw_data[:, 1:]

    if plot_decays:
        fig, ax = plt.subplots()
        ax.set_title(prefix)
        ax.semilogx(t_mix, decay, '.')

        fig.show()

    print(f'Fit {prefix}')
    tau, beta, finfty = fit_decay(t_mix, decay, tevo, verbose=verbose)

    return varied_string, tau, beta, finfty