For this particular work, I am using scipy optimize to try find the best parameters that fit two different models at the same time.
model_func_par = lambda t, total, r0, theta: np.multiply((total/3),(1+2*r0),np.exp(-t/theta))
model_func_perp = lambda t, total, r0, theta: np.multiply((total/3),(1-r0),np.exp(-t/theta))
After this I create two error functions by subtractig the raw data, and plug it into scipy.optimize.leastsq(). As you can see I have two different equations with the same r0 and theta parameters - I have to find the parameters that fit best both equations (in theory, r0 and theta should be the same for both equations, but because of noise and experimental errors etc I am sure this won't be quite the case.
I guess I could do a separate optimization for each equation and perhaps take an average of the two results, but I wanted to see if anyone knows of a way to do one optimization for both.
Thanks in advance!
Is there any specific reason to use np.multiply? Since the typical mathematical operators are overloaded for np.ndarrays, it's more convenient to write (and read):
model1 = lambda t, total, r0, theta: (total/3) * (1+2*r0) * np.exp(-t/theta)
model2 = lambda t, total, r0, theta: (total/3) * (1-r0) * np.exp(-t/theta)
To answer your question: AFAIK this isn't possible with scipy.optimize.least_squares. However, a very simple approach would be to minimize the sum of least squares residuals
min || model1(xdata, *coeffs) - ydata ||^2 + || model2(xdata, *coeffs) - ydata ||^2
like this:
import numpy as np
from scipy.optimize import minimize
from scipy.linalg import norm
# your xdata and ydata as np.ndarrays
# xdata = np.array([...])
# ydata = np.array([...])
# the objective function to minimize
def obj(coeffs):
return norm(model1(xdata,*coeffs)-ydata)**2 + norm(model2(xdata,*coeffs)-ydata)**2
# the initial point (coefficients)
coeffs0 = np.ones(3)
# res.x contains your coefficients
res = minimize(obj, x0=coeffs0)
However, note that this isn't a complete answer. A better approach would be to formulate it as a multi-objective optimization problem. You may take a look at pymoo for this purpose.