Deal with overflow in exp using numpy

Question

Using numpy, I have this definition of a function:

def powellBadlyScaled(X):
    f1 = 10**4 * X[0] * X[1] - 1
    f2 = numpy.exp(-numpy.float(X[0])) + numpy.exp(-numpy.float(X[1])) - 1.0001
    return f1 + f2

This function is evaluated a huge number of times on an optimization routine. It often raises exception:

RuntimeWarning: overflow encountered in exp

I understand that operand cannot be stored in allocated space for a float. But how can I overcome the problem?

Answer 1

You can use the bigfloat package. It supports arbitrary precision floating point operations.

http://packages.python.org/bigfloat/

import bigfloat
bigfloat.exp(5000,bigfloat.precision(100))
# -> BigFloat.exact('2.9676283840236670689662968052896e+2171', precision=100)

Are you using a function optimization framework? They usually implement value boundaries (using penalty terms). Try that. Are the relevant values really that extreme? In optimization it's not uncommon to minimize log(f). (approximate log likelihood etc etc). Are you sure you want to optimize on that exp value and not log(exp(f)) == f. ?

Have a look at my answer to this question: logit and inverse logit functions for extreme values

Btw, if all you do is minimize powellBadlyScaled(x,y) then the minimum is at x -> + inf and y -> + inf, so no need for numerics.