Symbolic model for Exponential Integral, expi(x)

Question

I am trying to do a global fit with shared parameters using objective functions that contain exponential integrals. If I were using, curve_fit, I would simply include the line:

from scipy.special import expi

I haven't been able to get the equivalent symbolic function in Symfit, 'symfit.Ei' to work.

import numpy as np
import scipy.optimize
from scipy.special import expi
import numpy as np
import symfit as sf

y1 = np.array(data1)

y3 = np.array(ydata3)

x1 = np.array(xdata1)

x3 = np.array(xdata3)

t1 = 50     # AOM 1st OFF Time
t2 = 100    # AOM 2nd ON Time
t3 = 150    # AOM 2nd OFF Time 
t4 = 450


def mod1(data, a_decay, b_decay, constant, on1_a_amplitude, on1_b_amplitude, ARE_A, ARE_B): 
    first_term_a =  sf.Ei(-data/a_decay) 
    second_term_a = sf.Ei(-data*(1+ARE_A*a_decay)/a_decay)) 
    first_term_b =  sf.Ei(-data/b_decay)) 
    second_term_b = (sf.Ei(-data*(1+ARE_B*b_decay)/b_decay))
 return constant+on1_a_amplitude*(first_term_a-second_term_a+sf.log(1+ARE_A*a_decay)) + on1_b_amplitude*(first_term_b-second_term_b+sf.log(1+ARE_B*b_decay))

def mod2(data, a_decay, b_decay, constant, on2_a_amplitude, on2_b_amplitude, ARE_A, ARE_B): # not all parameters are used here
    first_term_a =  (sf.Ei((t2-t1-data)/a_decay)) - (sf.Ei((t2-data)/a_decay))
    second_term_a = (sf.Ei((t2-data)*(1+ARE_A*a_decay)/a_decay)) - (sf.Ei((t2-t1-data)*(1+ARE_A*a_decay)/a_decay))
    third_term_a = (sf.Ei((t2-data)/a_decay)) -(sf.Ei((t2-data)*(1+ARE_A*a_decay)/a_decay)) + sf.log(ARE_A*a_decay)

    first_term_b =  (sf.Ei((t2-t1-data)/b_decay)) - (sf.Ei((t2-data)/b_decay))
    second_term_b = (sf.Ei((t2-data)*(1+ARE_B*b_decay)/b_decay)) - (sf.Ei((t2-t1-data)*(1+ARE_B*b_decay)/a_decay))
    third_term_b = (sf.Ei((t2-data)/b_decay)) - (sf.Ei((t2-data)*(1+ARE_B*b_decay)/b_decay)) + sf.log(ARE_B*b_decay)

return constant+on2_a_amplitude*(sf.exp((t1-t2)/a_decay)*(first_term_a+second_term_a)+third_term_a)+on2_b_amplitude*(sf.exp((t1-t2)/b_decay)*(first_term_b+second_term_b)+third_term_b)  

x_1, x_3, y_1, y_3 = sf.variables('x_1, x_3, y_1, y_3')

a_dec = sf.Parameter(value=64.32, min=0.0, max=100)
b_dec = sf.Parameter(value=53.88, min=0.0, max=100)
con = sf.Parameter(value=2.911E-4, min=0.0, max=1)
off1_a_amp = sf.Parameter(value=0.015, min=0.0, max=1)
off1_b_amp = sf.Parameter(value=0.015, min=0.0, max=1)
off2_a_amp = sf.Parameter(value=0.015, min=0.0, max=1)
off2_b_amp = sf.Parameter(value=0.015, min=0.0, max=1)
AR_A = sf.Parameter(value=0.032, min=0.0, max=1)
AR_B = sf.Parameter(value=0.1, min=0.0, max=1)


model = sf.Model({
y_1: mod1(x_1, a_dec, b_dec, con, off1_a_amp, off1_b_amp, AR_A, AR_B),
y_3: mod2(x_3, a_dec, b_dec, con, off2_a_amp, off2_b_amp, AR_A, AR_B ),
})


fit = sf.Fit(model, x_1=x1, x_3=x3, y_1=y1, y_3=y3)
fit_result = fit.execute()
print(fit_result)

For some reason 'sf.Ei' throws a name error. i.e. 'Name Error: name 'Ei' is not defined.

Symbolic model for Exponential Integral, expi(x)

Answers (1)

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