Question

I have a numpy array (actually imported from a GIS raster map) which contains
probability values of occurrence of a species like following example:

a = random.randint(1.0,20.0,1200).reshape(40,30)
b = (a*1.0)/sum(a)

Now I want to get a discrete version for that array again. Like if I have
e.g. 100 individuals which are located on the area of that array (1200 cells) how are they
distributed? Of course they should be distributed according to their probability,
meaning lower values indicated lower probability of occurrence. However, as everything is statistics there is still the chance that a individual is located at a low probability
cell. It should be possible that multiple individuals can occupy on cell…

It is like transforming a continuous distribution curve into a histogram again. Like many different histograms may result in a certain distribution curve it should also be the other way round. Accordingly applying the algorithm I am looking for will produce different discrete values each time.

…is there any algorithm in python which can do that? As I am not that familiar with discretization maybe someone can help.

Answer 1

Use random.choice with bincount:

np.bincount(np.random.choice(b.size, 100, p=b.flat),
            minlength=b.size).reshape(b.shape)

If you don’t have NumPy 1.7, you can replace random.choice with:

np.searchsorted(np.cumsum(b), np.random.random(100))

giving:

np.bincount(np.searchsorted(np.cumsum(b), np.random.random(100)),
            minlength=b.size).reshape(b.shape)