Minimum and Maximum of an Array

Question

How do you find the minimum or maximum of an array?

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Answer

Although this should be a trivial task, things are complicated by the fact that of the multiple min/max functions you can use, each behaves slightly differently.

The built-in Python functions min and max will work on a sequence or a series of arguments. However, you will get a type error if you try it on a single scalar, so you have to test ahead of time whether a single-argument call is operating on a sequence. Additionally, if the sequence is an array of more than one dimension, min and max will not operate in a "meaningful" way:

>>> import Numeric as N
>>> a = N.reshape(N.arange(12), (4,3))
>>> a
[[ 0, 1, 2,]
 [ 3, 4, 5,]
 [ 6, 7, 8,]
 [ 9,10,11,]]
>>> min(a)
[0,1,2,]
>>> max(a)
[ 9,10,11,]

What rules did min and max use to obtain this result? Konrad Hinsen explains it's the result of an address comparison! Very odd (at least to an earth scientist).

The Numeric minimum and maximum functions do not use this address comparison method, but rather do element-wise comparison between two arguments, returning an array of the same size:

>>> import Numeric as N
>>> a = N.array([2,  5, 23, 7,-2])
>>> b = N.array([12, 2, -3,37,-2])
>>> N.minimum(a,b)
[ 2, 2,-3, 7,-2,]
>>> N.maximum(a,b)
[12, 5,23,37,-2,]

However, if you want the min/max of all the elements in a single array, calling these Numeric functions with a single argument won't work:

>>> N.minimum(a)
Traceback (most recent call last):
  ...
ValueError: invalid number of arguments

The Numeric min/max functions will, however, accept a single argument array with the reduce attribute, since reduce effectively considers the sub-array associated with each position along axis 0 (by default) as an argument to the function, in pairwise blocks, and returns the result. Thus:

>>> import Numeric as N
>>> c = N.array([[2,4,1,-4], [5,9,-2,4], [2,5,-3,12]])
>>> N.maximum.reduce(c)
[ 5, 9, 1,12,]

gives the same result as:

>>> import Numeric as N
>>> c1 = N.array([2,4,1,-4])
>>> c2 = N.array([5,9,-2,4])
>>> c3 = N.array([2,5,-3,12])
>>> N.maximum(N.maximum(c1,c2), c3)
[ 5, 9, 1,12,]

If you want to get the min/max of all the elements in a single array, regardless of how many dimensions the array is, one way is to use the minimum and maximum functions in the MA module. Like their Numeric counterparts, if the functions are called with two arguments an element-wise comparison is returned. However, in MA the functions can be called with one argument to obtain the overall min/max:

>>> import MA
>>> c = N.array([[2,4,1,-4], [5,9,-2,4], [2,5,-3,12]])
>>> MA.maximum(c)
12