232 lines
9.8 KiB
Python
232 lines
9.8 KiB
Python
import numpy as np
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import uncertainties as u
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from lmfit import Model, Parameters
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from scipy.integrate import simps
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def bin_data(array, binsize):
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if isinstance(binsize, int) and 0 < binsize < len(array):
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return [
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np.mean(array[binsize * i : binsize * i + binsize])
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for i in range(int(np.ceil(len(array) / binsize)))
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]
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else:
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print("Binsize need to be positive integer smaller than lenght of array")
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return array
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def find_nearest(array, value):
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# find nearest value and return index
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array = np.asarray(array)
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idx = (np.abs(array - value)).argmin()
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return idx
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def create_uncertanities(y, y_err):
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# create array with uncertanities for error propagation
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combined = np.array([])
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for i in range(len(y)):
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part = u.ufloat(y[i], y_err[i])
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combined = np.append(combined, part)
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return combined
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def fitccl(
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scan,
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guess,
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vary,
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constraints_min,
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constraints_max,
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numfit_min=None,
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numfit_max=None,
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binning=None,
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):
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"""Made for fitting of ccl date where 1 peak is expected. Allows for combination of gaussian and linear model combination
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:param scan: scan in the data dict (i.e. M123)
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:param guess: initial guess for the fitting, if none, some values are added automatically in order (see below)
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:param vary: True if parameter can vary during fitting, False if it to be fixed
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:param numfit_min: minimal value on x axis for numerical integration - if none is centre of gaussian minus 3 sigma
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:param numfit_max: maximal value on x axis for numerical integration - if none is centre of gaussian plus 3 sigma
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:param constraints_min: min constranits value for fit
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:param constraints_max: max constranits value for fit
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:param binning : binning of the data
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:return data dict with additional values
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order for guess, vary, constraints_min, constraints_max:
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[Gaussian centre, Gaussian sigma, Gaussian amplitude, background slope, background intercept]
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examples:
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guess = [None, None, 100, 0, None]
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vary = [True, True, True, True, True]
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constraints_min = [23, None, 50, 0, 0]
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constraints_min = [80, None, 1000, 0, 100]
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"""
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if "peak_indexes" not in scan:
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scan["peak_indexes"] = []
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if len(scan["peak_indexes"]) > 1:
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# return in case of more than 1 peaks
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return
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if binning is None or binning == 0 or binning == 1:
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x = list(scan["omega"])
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y = list(scan["Counts"])
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y_err = list(np.sqrt(y)) if scan.get("sigma", None) is None else list(scan["sigma"])
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if not scan["peak_indexes"]:
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centre = np.mean(x)
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else:
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centre = x[int(scan["peak_indexes"])]
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else:
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x = list(scan["omega"])
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if not scan["peak_indexes"]:
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centre = np.mean(x)
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else:
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centre = x[int(scan["peak_indexes"])]
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x = bin_data(x, binning)
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y = list(scan["Counts"])
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y_err = list(np.sqrt(y)) if scan.get("sigma", None) is None else list(scan["sigma"])
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combined = bin_data(create_uncertanities(y, y_err), binning)
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y = [combined[i].n for i in range(len(combined))]
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y_err = [combined[i].s for i in range(len(combined))]
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if len(scan["peak_indexes"]) == 0:
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# Case for no peak, gaussian in centre, sigma as 20% of range
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peak_index = find_nearest(x, np.mean(x))
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guess[0] = centre if guess[0] is None else guess[0]
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guess[1] = (x[-1] - x[0]) / 5 if guess[1] is None else guess[1]
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guess[2] = 50 if guess[2] is None else guess[2]
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guess[3] = 0 if guess[3] is None else guess[3]
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guess[4] = np.mean(y) if guess[4] is None else guess[4]
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constraints_min[2] = 0
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elif len(scan["peak_indexes"]) == 1:
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# case for one peak, takse into account users guesses
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peak_height = scan["peak_heights"]
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guess[0] = centre if guess[0] is None else guess[0]
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guess[1] = 0.1 if guess[1] is None else guess[1]
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guess[2] = float(peak_height / 10) if guess[2] is None else float(guess[2])
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guess[3] = 0 if guess[3] is None else guess[3]
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guess[4] = np.median(x) if guess[4] is None else guess[4]
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constraints_min[0] = np.min(x) if constraints_min[0] is None else constraints_min[0]
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constraints_max[0] = np.max(x) if constraints_max[0] is None else constraints_max[0]
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def gaussian(x, g_cen, g_width, g_amp):
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"""1-d gaussian: gaussian(x, amp, cen, wid)"""
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return (g_amp / (np.sqrt(2 * np.pi) * g_width)) * np.exp(
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-((x - g_cen) ** 2) / (2 * g_width ** 2)
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)
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def background(x, slope, intercept):
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"""background"""
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return slope * (x - centre) + intercept
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mod = Model(gaussian) + Model(background)
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params = Parameters()
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params.add_many(
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("g_cen", guess[0], bool(vary[0]), np.min(x), np.max(x), None, None),
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("g_width", guess[1], bool(vary[1]), constraints_min[1], constraints_max[1], None, None),
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("g_amp", guess[2], bool(vary[2]), constraints_min[2], constraints_max[2], None, None),
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("slope", guess[3], bool(vary[3]), constraints_min[3], constraints_max[3], None, None),
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("intercept", guess[4], bool(vary[4]), constraints_min[4], constraints_max[4], None, None),
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)
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# the weighted fit
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weights = [np.abs(1 / val) if val != 0 else 1 for val in y_err]
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try:
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result = mod.fit(y, params, weights=weights, x=x, calc_covar=True)
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except ValueError:
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print(f"Couldn't fit scan {scan['idx']}")
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return
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if result.params["g_amp"].stderr is None:
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result.params["g_amp"].stderr = result.params["g_amp"].value
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elif result.params["g_amp"].stderr > result.params["g_amp"].value:
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result.params["g_amp"].stderr = result.params["g_amp"].value
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# u.ufloat to work with uncertanities
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fit_area = u.ufloat(result.params["g_amp"].value, result.params["g_amp"].stderr)
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comps = result.eval_components()
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if len(scan["peak_indexes"]) == 0:
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# for case of no peak, there is no reason to integrate, therefore fit and int are equal
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int_area = fit_area
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elif len(scan["peak_indexes"]) == 1:
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gauss_3sigmamin = find_nearest(
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x, result.params["g_cen"].value - 3 * result.params["g_width"].value
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)
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gauss_3sigmamax = find_nearest(
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x, result.params["g_cen"].value + 3 * result.params["g_width"].value
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)
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# numfit_min = gauss_3sigmamin if numfit_min is None else find_nearest(x, numfit_min)
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# numfit_max = gauss_3sigmamax if numfit_max is None else find_nearest(x, numfit_max)
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numfit_min = 0 if numfit_min is None else find_nearest(x, numfit_min)
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numfit_max = len(x)-1 if numfit_max is None else find_nearest(x, numfit_max)
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it = -1
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while abs(numfit_max - numfit_min) < 3:
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# in the case the peak is very thin and numerical integration would be on zero omega
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# difference, finds closes values
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it = it + 1
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numfit_min = find_nearest(
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x,
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result.params["g_cen"].value - 3 * (1 + it / 10) * result.params["g_width"].value,
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)
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numfit_max = find_nearest(
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x,
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result.params["g_cen"].value + 3 * (1 + it / 10) * result.params["g_width"].value,
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)
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if x[numfit_min] < np.min(x):
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# makes sure that the values supplied by user lay in the omega range
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# can be ommited for users who know what they're doing
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numfit_min = gauss_3sigmamin
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print("Minimal integration value outside of x range")
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elif x[numfit_min] >= x[numfit_max]:
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numfit_min = gauss_3sigmamin
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print("Minimal integration value higher than maximal")
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else:
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pass
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if x[numfit_max] > np.max(x):
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numfit_max = gauss_3sigmamax
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print("Maximal integration value outside of x range")
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elif x[numfit_max] <= x[numfit_min]:
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numfit_max = gauss_3sigmamax
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print("Maximal integration value lower than minimal")
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else:
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pass
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count_errors = create_uncertanities(y, y_err)
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# create error vector for numerical integration propagation
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num_int_area = simps(count_errors[numfit_min:numfit_max], x[numfit_min:numfit_max])
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slope_err = u.ufloat(result.params["slope"].value, result.params["slope"].stderr)
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# pulls the nominal and error values from fit (slope)
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intercept_err = u.ufloat(
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result.params["intercept"].value, result.params["intercept"].stderr
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)
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# pulls the nominal and error values from fit (intercept)
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background_errors = np.array([])
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for j in range(len(x[numfit_min:numfit_max])):
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# creates nominal and error vector for numerical integration of background
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bg = slope_err * (x[j] - centre) + intercept_err
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background_errors = np.append(background_errors, bg)
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num_int_background = simps(background_errors, x[numfit_min:numfit_max])
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int_area = num_int_area - num_int_background
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d = {}
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for pars in result.params:
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d[str(pars)] = (result.params[str(pars)].value, result.params[str(pars)].vary)
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print("Scan", scan["idx"])
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print(result.fit_report())
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d["ratio"] = (result.params["g_amp"].value - int_area.n) / result.params["g_amp"].value
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d["int_area"] = int_area
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d["fit_area"] = u.ufloat(result.params["g_amp"].value, result.params["g_amp"].stderr)
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d["full_report"] = result.fit_report()
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d["result"] = result
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d["comps"] = comps
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d["numfit"] = [numfit_min, numfit_max]
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d["x_fit"] = x
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scan["fit"] = d
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