How to fit data to model with analytical gradient in basinhopping or with another gradient descent method? - tensorflow

Question

I'd like to fit experimental data to a model and extract the optimal model parameters, the parameters that result in minimal error between model function and experimental data. To get the optimal parameters, I'd like to use a gradient descent method, tensorflow, Bayesian inference or basinhopping or something that deals well with bad initial estimates and is rigid. To speed things up, I'd like to use the analytical gradient for example in basinhopping. How do I do that with the basinghopping routine from scipy. In the following example code, I have some example function and I'd like to use the analytical Jacobian instead of the numerical one, but I get an error. Do I have to sum up the Jacobian components?
Example code (my actual function is much more complex)
import random
import matplotlib.pyplot as plt
import numpy as np
# symbolic math
from sympy import lambdify, symbols, cos
from sympy.tensor.array import derive_by_array
# fitting
from scipy.optimize import basinhopping
# symbolic math with sympy ---
s_lst = x, a, b, c, d = symbols('x, a, b, c d', positive=True)
# mathematical function
y = a*x + cos(b*x)**2 * c*x**2 + d
# jacobian (derivatives after model parameters)
params = s_lst[1:]
jac_y = derive_by_array(y, params)
# translate sympy expression to python function
# function
get_y = lambdify(s_lst, y)
# jacobian (derivatives in a, b, c, d)
get_jac_y = [lambdify(s_lst, element) for element in jac_y]
#print(len(get_jac_y))
# data ---
x = np.linspace(0, 1, 500)
# measurement data
a = [random.randrange(4, 6, 1) for i in range(len(x))]
b = [random.randrange(3190, 3290, 1) for i in range(len(x))]
c = [random.randrange(90, 109, 1) for i in range(len(x))]
d = [0.1*random.randrange(0, 2, 1) for i in range(len(x))]
y_measured = get_y(x, a, b, c, d)
# exemplary model data
a, b, c, d = 5, 3200, 100, 1
y_model = get_y(x, a, b, c, d)
# plot
plt.plot(x, y_measured)
plt.plot(x, y_model)
plt.title('exemplary model and measured data')
plt.show()
# functions for fitting
def func(params, args1, args2=None):
a, b, c, d = params
y = get_y(args1, a, b, c, d)
if args2 is None:
return y
return np.sum((y - args2)**2)
# derivatives
def dfunc(params, args1, args2):
a, b, c, d = params
jac = [jac(args1, a, b, c, d) for jac in get_jac_y]
# because derviative in d is one
jac[-1] = np.ones(len(args1))
return np.asarray(jac)
# function and derivatives
def objective_func(params, args1, args2):
f = func(params, args1, args2)
df = dfunc(params, args1, args2)
return f, df
# fit with basinhopping and scipy ---
# initial model parameters
x0 = [1, 2, 33, 4]
# minimization with numerical jacobian, gives a result
minimizer_kwargs = {"args":(x, y_measured), 'method':'L-BFGS-B'}
ret = basinhopping(func, x0, minimizer_kwargs=minimizer_kwargs)
# minimization with analytical jacobian, fails,
# error: failed in converting 7th argument `g' of _lbfgsb.setulb to C/Fortran array
minimizer_kwargs = {"args":(x, y_measured), 'method':'L-BFGS-B', 'jac':True}
ret = basinhopping(objective_func, x0, minimizer_kwargs=minimizer_kwargs)
If I put in dfunc something like return [np.sum((j)) for j in jac] the program runs but fails. What would be the correct expression?