optimization - scipy.optimize.minimize keeps returning math error, going out of bounds -


i'm using scipy.opimize.minimize find best fit parameters negative log-likelihood of dataset (which has given pdf). functions calculating pdf , negative log-likelihood given below:

def density(time, x, y, z):     w = (z/x)*mt.exp(-time/x) + ((1-z)/y)*mt.exp(-time/y)     return w   def nll2(params):      sig = 0     a, b, c = params[0], params[1], params[2]     in range(0, 100):         sig = sig - mt.log(density(xval[i], a, b, c))     return sig

where xval dataset (list of 100time values between 0-10). it's worth, pdf of double decay process.

i have been given starting values x, y , z (stored in list called "initial_guesses" given nll2 function "param" argument), , have find best-fit values of x, y , z (i.e. values minimise nll2 given dataset xval).

i try following line of code:

initial_guesses = [1.30719636,  0.19783642,  0.25150731]  best_fit = sci.optimize.minimize(nll2, initial_guesses, bounds = [(0.1, 20), (0.1, 20), (0.1, 1)], method = 'l-bfgs-b').x

the bounds have been chosen i'm "supposed" come [1.3, 0.2, 0.25] i.e. close initial values. however, when this, end error message:

file "newcode2.py", line 125, in nll2 sig = sig - mt.log(density(xval[i], x, y, z)) valueerror: math domain error

i know happening because logarithm being taken of negative value, bounds i've given minimizer should prevent happening.

to investigate further, changed nll2 function following:

def nll2(params):      sig = 0     a, b, c = params[0], params[1], params[2]     in range(0, 100):         if density(xval[i], a, b, c) > 0:             sig = sig - mt.log(density(xval[i], a, b, c))         else:             print density(xval[i], a, b, c), xval[i], params, '\n'     return sig

an example of terminal prints out following:

-4.25654045048e-10 2.76533572107 [ 0.1 20. 1.00000001]

so somehow parameters going limits of bounds i've set, in last case going on 1e-8. causing density function return minutely negative number, causing crash.

does know how can stop minimizer doing this? i've tried using slsqp method, same problem.

i apologize if i've given detail, i'm tired , want give out information might useful.

nb i've imported math class mt.


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