I would like to use the lmfit module to fit a function to a variable number of data-sets, with some shared and some individual parameters.
Here is an example generating Gaussian data, and fitting to each data-set individually:
import numpy as np
import matplotlib.pyplot as plt
from lmfit import minimize, Parameters, report_fit
def func_gauss(params, x, data=[]):
A = params['A'].value
mu = params['mu'].value
sigma = params['sigma'].value
model = A*np.exp(-(x-mu)**2/(2.*sigma**2))
if data == []:
return model
return data-model
x = np.linspace( -1, 2, 100 )
data = []
for i in np.arange(5):
params = Parameters()
params.add( 'A' , value=np.random.rand() )
params.add( 'mu' , value=np.random.rand()+0.1 )
params.add( 'sigma', value=0.2+np.random.rand()*0.1 )
data.append(func_gauss(params,x))
plt.figure()
for y in data:
fit_params = Parameters()
fit_params.add( 'A' , value=0.5, min=0, max=1)
fit_params.add( 'mu' , value=0.4, min=0, max=1)
fit_params.add( 'sigma', value=0.4, min=0, max=1)
minimize(func_gauss, fit_params, args=(x, y))
report_fit(fit_params)
y_fit = func_gauss(fit_params,x)
plt.plot(x,y,'o',x,y_fit,'-')
plt.show()
# ideally I would like to write:
#
# fit_params = Parameters()
# fit_params.add( 'A' , value=0.5, min=0, max=1)
# fit_params.add( 'mu' , value=0.4, min=0, max=1)
# fit_params.add( 'sigma', value=0.4, min=0, max=1, shared=True)
# minimize(func_gauss, fit_params, args=(x, data))
#
# or:
#
# fit_params = Parameters()
# fit_params.add( 'A' , value=0.5, min=0, max=1)
# fit_params.add( 'mu' , value=0.4, min=0, max=1)
#
# fit_params_shared = Parameters()
# fit_params_shared.add( 'sigma', value=0.4, min=0, max=1)
# call_function(func_gauss, fit_params, fit_params_shared, args=(x, data))
I think you're most of the way there. You need to put the data sets into an array or structure that can be used in a single, global objective function that you give to minimize() and fits all data sets with a single set of Parameters for all the data sets. You can share this set among data sets as you like. Expanding on your example a bit, the code below does work to do a single fit to the 5 different Gaussian functions. For an example of tying parameters across data sets, I used nearly identical value for sigma the 5 datasets the same value. I created 5 different sigma Parameters ('sig_1', 'sig_2', ..., 'sig_5'), but then forced these to have the same values using a mathematical constraint. Thus there are 11 variables in the problem, not 15.
import numpy as np
import matplotlib.pyplot as plt
from lmfit import minimize, Parameters, report_fit
def gauss(x, amp, cen, sigma):
"basic gaussian"
return amp*np.exp(-(x-cen)**2/(2.*sigma**2))
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)].value
cen = params['cen_%i' % (i+1)].value
sig = params['sig_%i' % (i+1)].value
return gauss(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, nx = 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 5 datasets
x = np.linspace( -1, 2, 151)
data = []
for i in np.arange(5):
params = Parameters()
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=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
fit_params = Parameters()
for iy, y in enumerate(data):
fit_params.add( 'amp_%i' % (iy+1), value=0.5, min=0.0, max=200)
fit_params.add( 'cen_%i' % (iy+1), value=0.4, min=-2.0, max=2.0)
fit_params.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):
fit_params['sig_%i' % iy].expr='sig_1'
# run the global fit to all the data sets
result = minimize(objective, fit_params, args=(x, data))
report_fit(result)
# plot the data sets and fits
plt.figure()
for i in range(5):
y_fit = gauss_dataset(fit_params, i, x)
plt.plot(x, data[i, :], 'o', x, y_fit, '-')
plt.show()
For what it's worth, I would consider holding the multiple data sets in a dictionary or list of DataSet class instead of a multi-dimensional array. Anyway, I hope this helps get you going onto what you really need to do.