Added fitting with lmfit (#128)

- added stand alone fitting using:
https://jugit.fz-juelich.de/mlz/lmfit.git
- fit_gaus, fit_pol1 with and without errors
- multi threaded fitting

---------

Co-authored-by: JulianHeymes <julian.heymes@psi.ch>

python/examples/fits.py

@@ -0,0 +1,79 @@
+import matplotlib.pyplot as plt
+import numpy as np
+from aare import fit_gaus, fit_pol1
+from aare import gaus, pol1
+
+textpm = f"±"  #
+textmu = f"μ"  #
+textsigma = f"σ"  #
+
+
+
+# ================================= Gauss fit =================================
+# Parameters
+mu = np.random.uniform(1, 100)  # Mean of Gaussian
+sigma = np.random.uniform(4, 20)  # Standard deviation
+num_points = 10000  # Number of points for smooth distribution
+noise_sigma = 100
+
+# Generate Gaussian distribution
+data = np.random.normal(mu, sigma, num_points)
+
+# Generate errors for each point
+errors = np.abs(np.random.normal(0, sigma, num_points))  # Errors with mean 0, std 0.5
+
+# Create subplot
+fig0, ax0 = plt.subplots(1, 1, num=0, figsize=(12, 8))
+
+x = np.histogram(data, bins=30)[1][:-1] + 0.05
+y = np.histogram(data, bins=30)[0]
+yerr = errors[:30]
+
+
+# Add the errors as error bars in the step plot
+ax0.errorbar(x, y, yerr=yerr, fmt=". ", capsize=5)
+ax0.grid()
+
+par, err = fit_gaus(x, y, yerr)
+print(par, err)
+
+x = np.linspace(x[0], x[-1], 1000)
+ax0.plot(x, gaus(x, par), marker="")
+ax0.set(xlabel="x", ylabel="Counts", title=f"A0 = {par[0]:0.2f}{textpm}{err[0]:0.2f}\n"
+                                           f"{textmu} = {par[1]:0.2f}{textpm}{err[1]:0.2f}\n"
+                                           f"{textsigma} = {par[2]:0.2f}{textpm}{err[2]:0.2f}\n"
+                                           f"(init: {textmu}: {mu:0.2f}, {textsigma}: {sigma:0.2f})")
+fig0.tight_layout()
+
+
+
+# ================================= pol1 fit =================================
+# Parameters
+n_points = 40
+
+# Generate random slope and intercept (origin)
+slope = np.random.uniform(-10, 10)  # Random slope between 0.5 and 2.0
+intercept = np.random.uniform(-10, 10)  # Random intercept between -10 and 10
+
+# Generate random x values
+x_values = np.random.uniform(-10, 10, n_points)
+
+# Calculate y values based on the linear function y = mx + b + error
+errors = np.abs(np.random.normal(0, np.random.uniform(1, 5), n_points))
+var_points = np.random.normal(0, np.random.uniform(0.1, 2), n_points)
+y_values = slope * x_values + intercept + var_points
+
+fig1, ax1 = plt.subplots(1, 1, num=1, figsize=(12, 8))
+ax1.errorbar(x_values, y_values, yerr=errors, fmt=". ", capsize=5)
+par, err = fit_pol1(x_values, y_values, errors)
+
+
+x = np.linspace(np.min(x_values), np.max(x_values), 1000)
+ax1.plot(x, pol1(x, par), marker="")
+ax1.set(xlabel="x", ylabel="y", title=f"a = {par[0]:0.2f}{textpm}{err[0]:0.2f}\n"
+                                      f"b = {par[1]:0.2f}{textpm}{err[1]:0.2f}\n"
+                                      f"(init: {slope:0.2f}, {intercept:0.2f})")
+fig1.tight_layout()
+
+plt.show()
+