Exponential of large negative numbers

Question

How does one compute a number such as np.exp(-28000) on Python? The answer is around 5E-12161. I've been told that due to the double-precision floating point format, I would only be able to calculate a number > 1e-2048

What are you going to do with this number? Can you arrange your calculations so that you only need to work with the logarithms of the numbers? -28000 is much easier to work with than exp(-28000). — Warren Weckesser, Mar 29 '17 at 04:55
I am trying to create a damped sinusoid with a given time array going up to 28000 — Daniel George, Mar 29 '17 at 04:59
@WarrenWeckesser: Please see my full question: http://stackoverflow.com/q/43100725/6943476 — Daniel George, Mar 29 '17 at 18:03

arduinolover · Answer 1 · 2017-03-29T07:09:29.620

2

Try mpmath for floating-point arithmetic with arbitrary precision

Edit 1:

>>> import mpmath as mp 
>>> import numpy as np
>>> a = np.matrix((0,0)) 
>>> print(a)
[0.0 0.0]
>>> b = mp.matrix(a.tolist())
>>> c = b.apply(mp.exp)
>>> print(c)
[1.0]
[1.0]

edited Mar 29 '17 at 07:09

answered Mar 29 '17 at 04:43

arduinolover

176
2
5

I tried installing that module using pip but it did not show up during compilation. Also, I am trying to find the exponential of an array and I heard mpmath does not do this. – Daniel George Mar 29 '17 at 04:46
For mpmath array, array wise operations can be done. Please see the above example – arduinolover Mar 29 '17 at 04:58
@arduinolover : This didn't work for numpy arrays and I don't know how to convert the numpy arrays to mp format. – kmario23 Mar 29 '17 at 07:00
@arduinolover: Is there an easy way to convert arrays into matrices? Please see my full question: http://stackoverflow.com/q/43100725/6943476 – Daniel George Mar 29 '17 at 18:02

score 0 · Accepted Answer · answered Mar 29 '17 at 04:39

0

Try the decimal module.

Decimal(math.exp(1))**-28000

answered Mar 29 '17 at 04:39

phg1024

169
6

Thank you! Now I need to figure out how to do this for an array – Daniel George Mar 29 '17 at 04:43
@DanielGeorge : I added an approach to make it to work on arrays. Please have a look. – kmario23 Mar 29 '17 at 06:52

score 0 · Answer 3 · answered Mar 29 '17 at 06:49

You could define a function to calculate the "bigexponent" and apply it to the array (along an axis). But, note that the input array has to be of type int.

# solution courtesy: http://stackoverflow.com/a/43084475/2956066
In [97]: def bigexp(x):
    ...:     return Decimal(math.exp(1))**x


In [98]: np.apply_along_axis(bigexp, 1, arr)

Efficiency (in descending order)

# twice faster than applying along axis 0
In [115]: %timeit np.apply_along_axis(bigexp, 1, a)
1000 loops, best of 3: 272 µs per loop

In [116]: %timeit np.apply_along_axis(bigexp, 0, a)
1000 loops, best of 3: 465 µs per loop

I tried using your method but am getting this error: ValueError: axis must be less than arr.ndim; axis=1, rank=1. Please see the full question I posted: http://stackoverflow.com/q/43100725/6943476 — Daniel George, Mar 29 '17 at 17:57

Exponential of large negative numbers

3 Answers3

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