Operations on NumPy arrays

Overview

Teaching: 15 min
Exercises: 15 min

Questions

Objectives

• Apply reduction functions (mean, min, max) along a given axis

• Find a specialised numerical algorithm from the ones available in numpy

• Sort arrays along given axis

Multiplication of two arrays is elementwise. For example, to calculate a square of each element we may use:

a = np.arange(3)
b = a * a

Axis-based reductions

The np.sum function sums all elements regardless of the number of array dimensions:

b = np.arange(9).reshape(3,3)
np.sum(b)

If you want to sum only columns or rows, you need to pass the index of the axis over which you want to sum:

np.sum(b, 0)
np.sum(b, 1)

Other similar reduction functions are np.min, np.max or np.mean:

np.min(b)
np.min(b, 0)
np.min(b, 1)

You can also find the index of the minimum element in each axis:

np.argmin(b, 0)
array([0, 0, 0])

Sorting

NumPy also implement various sorting algorithms. To sort elements of an array you can use np.sort functions:

a = np.random.rand(4)
a
array([ 0.9490829 ,  0.07528673,  0.17463988,  0.95964801])
np.sort(a)
array([ 0.07528673,  0.17463988,  0.9490829 ,  0.95964801])

Similarly to the reduction functions, you can also pass the axis index to sort along:

b = a.reshape(2, 2)
np.sort(b, 0)
np.sort(b, 1)

np.argsort returns the order of elements in a sorted array:

np.argsort(a)

Special modules

NumPy also provides extra modules implementing basic numerical methods:

• np.linalg – linear algebra,
• np.fft – fast Fourier transform,
• np.random – random number generators.

Finding closest element

Generate a 10 x 3 array of random numbers (using np.random.rand). From each row, find the column index of the element closest to 0.75. Make use of np.abs and np.argmin. The result should be a one-dimensional array of integers from 0 to 2.

Solving linear equations

Solve the following system of linear equations using np.linalg.solve. Test the solution. $2x + 3y = 3$ $5x - y = 6$

Key Points