Functions acting on arrays

There are different types of functions acting on arrays. Some act elementwise, and they return an array of the same shape. Those are called universal functions. Other array functions return an array of a different shape.

Universal functions

Universal functions are functions that act elementwise on arrays. They thus have an output array that has the same shape as the input array. These functions allow us to compute the result of a scalar function on a whole array at once.

Built-in universal functions

A typical example is the cos function (the one provided by NumPy):

cos(pi) # -1
cos(array([[0, pi/2, pi]])) # array([[1, 0, -1]])

Note that universal functions work on arrays in a componentwise manner. This is also true for operators, such as multiplication or exponent:

2 * array([2, 4]) # array([4, 8])
array([1, 2]) * array([1, 8]) # array([1, 16])
array([1, 2])**2 # array([1, 4])
2**array([1, 2]) # array([1, 4])
array([1, 2])**array([1, 2]) # array...