Universal functions in in numpy
Martin McBride, 2021-01-27
Tags arrays, ufunc, universal function, vectorisation, out
Categories numpy
In section Python libraries
The section on vectorisation looked to apply arithmetic operators across a whole array in a single expression. Universal functions allow us to apply mathematical functions across a whole array in a similar way. Universal functions, or ufuncs for short, special NumPy versions of standard maths functions.
Example universal function - sqrt
The sqrt ufunc calculates the square root of each element in an array. For example:
a = np.array([1, 2, 3, 4]) b = np.sqrt(a)
This calculates the square root of each element 1, 2, 3, 4, giving the result:
b = [1. 1.41421356 1.73205081 2. ]
Of course this can be applied to multi-dimensional arrays too, for example a 2 by 3 array:
a = np.array([[10, 20, 33], [40, 50, 60]]) b = np.sqrt(a)
This again calculates the square root of each element and returns another 2 by 3 array:
b = [[3.16227766 4.47213595 5.74456265]
[6.32455532 7.07106781 7.74596669]]
Example universal function of two arguments - power
Some ufuncs take two arguments, for example the power function:
a = np.array([5, 10, 5, 10]) b = np.array([2, 2, 3, 3]) c = np.power(a, b)
power(x, y) calculates x to the power y. The function is equivalent to x**y.
So power(5, 2) is 5 squared, or 25, and so on:
b = [ 25 100 125 1000]
Summary of ufuncs
There are quite a number of ufuncs, and they are all described in the official NumPy documentation. The main groups of functions are:
- Maths operations
- Trigonometric functions
- Bit manipulation
- Comparison functions
- Logical functions
- Float functions
Additional arguments
ufuncs can be called with additional, optional arguments:
out, covered below.where, see Advanced vectorisation.
out
Normally, a ufunc creates a new NumPy array to hold its result:
a = np.array([1, 2, 3, 4]) b = np.array([2, 4, 6, 8]) c = a + b
The out parameter allows us to specify an existing array for the output. To use this feature, we must use the add ufunc rather than the + operator:
a = np.array([1, 2, 3, 4]) b = np.array([2, 4, 6, 8]) r = np.zeros_like(a) np.add(a, b, out=r)
This fills the array r with the result of a + b. The shape of the output array must be compatible with the input arrays.
One case where this is useful is if you want to re-use an existing array, for example to add a to b and leave the result in a. This is particularly useful if the arrays are very large. Here is how to do it:
a = np.array([1, 2, 3, 4]) b = np.array([2, 4, 6, 8]) np.add(a, b, out=a)
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If you found this article useful, you might be interested in the book NumPy Recipes, or other books, by the same author.
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