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"""
Fit Multiple Data Sets
======================
Fitting multiple (simulated) Gaussian data sets simultaneously.
All minimizers require the residual array to be one-dimensional. Therefore, in
the ``objective`` function we need to ``flatten`` the array before returning it.
"""
import matplotlib.pyplot as plt
import numpy as np
from lmfit import Parameters, minimize, report_fit
def gauss(x, amp, cen, sigma):
"""Gaussian lineshape."""
return amp * np.exp(-(x-cen)**2 / (2.*sigma**2))
def gauss_dataset(params, i, x):
"""Calculate Gaussian lineshape from parameters for data set."""
amp = params[f'amp_{i+1}']
cen = params[f'cen_{i+1}']
sig = params[f'sig_{i+1}']
return gauss(x, amp, cen, sig)
def objective(params, x, data):
"""Calculate total residual for fits of Gaussians to several data sets."""
ndata, _ = data.shape
resid = 0.0*data[:]
# make residual per data set
for i in range(ndata):
resid[i, :] = data[i, :] - gauss_dataset(params, i, x)
# now flatten this to a 1D array, as minimize() needs
return resid.flatten()
###############################################################################
# Create five simulated Gaussian data sets
np.random.seed(2021)
x = np.linspace(-1, 2, 151)
data = []
for _ in np.arange(5):
amp = 0.60 + 9.50*np.random.rand()
cen = -0.20 + 1.20*np.random.rand()
sig = 0.25 + 0.03*np.random.rand()
dat = gauss(x, amp, cen, sig) + np.random.normal(size=x.size, scale=0.1)
data.append(dat)
data = np.array(data)
###############################################################################
# Create five sets of fitting parameters, one per data set
fit_params = Parameters()
for iy, y in enumerate(data):
fit_params.add(f'amp_{iy+1}', value=0.5, min=0.0, max=200)
fit_params.add(f'cen_{iy+1}', value=0.4, min=-2.0, max=2.0)
fit_params.add(f'sig_{iy+1}', value=0.3, min=0.01, max=3.0)
###############################################################################
# Constrain the values of sigma to be the same for all peaks by assigning
# sig_2, ..., sig_5 to be equal to sig_1.
for iy in (2, 3, 4, 5):
fit_params[f'sig_{iy}'].expr = 'sig_1'
###############################################################################
# Run the global fit and show the fitting result
out = minimize(objective, fit_params, args=(x, data))
report_fit(out.params)
###############################################################################
# Plot the data sets and fits
plt.figure()
for i in range(5):
y_fit = gauss_dataset(out.params, i, x)
plt.plot(x, data[i, :], 'o', x, y_fit, '-')
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