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"""Example fitting to multiple (simulated) data sets"""
import numpy as np
from lmfit import Parameters, minimize
from lmfit.lineshapes import gaussian
def gauss_dataset(params, i, x):
"""calc gaussian from params for data set i
using simple, hardwired naming convention"""
amp = params['amp_%i' % (i+1)]
cen = params['cen_%i' % (i+1)]
sig = params['sig_%i' % (i+1)]
return gaussian(x, amp, cen, sig)
def objective(params, x, data):
""" calculate total residual for fits to several data sets held
in a 2-D array, and modeled by Gaussian functions"""
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()
def test_multidatasets():
# create 5 datasets
x = np.linspace(-1, 2, 151)
data = []
for _ in np.arange(5):
amp = 2.60 + 1.50*np.random.rand()
cen = -0.20 + 1.50*np.random.rand()
sig = 0.25 + 0.03*np.random.rand()
dat = gaussian(x, amp, cen, sig) + np.random.normal(size=len(x),
scale=0.1)
data.append(dat)
# data has shape (5, 151)
data = np.array(data)
assert data.shape == (5, 151)
# create 5 sets of parameters, one per data set
pars = Parameters()
for iy, _ in enumerate(data):
pars.add('amp_%i' % (iy+1), value=0.5, min=0.0, max=200)
pars.add('cen_%i' % (iy+1), value=0.4, min=-2.0, max=2.0)
pars.add('sig_%i' % (iy+1), value=0.3, min=0.01, max=3.0)
# but now constrain all values of sigma to have the same value
# by assigning sig_2, sig_3, .. sig_5 to be equal to sig_1
for iy in (2, 3, 4, 5):
pars['sig_%i' % iy].expr = 'sig_1'
# run the global fit to all the data sets
out = minimize(objective, pars, args=(x, data))
assert len(pars) == 15
assert out.nvarys == 11
assert out.nfev > 15
assert out.chisqr > 1.0
assert pars['amp_1'].value > 0.1
assert pars['sig_1'].value > 0.1
assert pars['sig_2'].value == pars['sig_1'].value
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