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How to handle Data, and Images(2) - Numpy and Math

How to use Math operations on Numpy, and how matrix operations work.

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By Hyeonu(Eric) Kim
4 min read

Lesson Notes in .ipynb file

How to handle Data, and Images(2) - Numpy and Math

Topics

Python’s Numpy library can do basic operations

Adding or Multiplying array with constant results in adding or multiplying every element

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import numpy as np

# create a 2 x 2 array from random integer 1 to 10
arr = np.random.randint(1, 10, size=4).reshape(2, 2)
print("arr\n", arr)

# arr * 10
arr_10 = arr*10
print("arr * 10\n", arr_10)

Output:

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arr
 [[2 7]
 [7 4]]
arr * 10
 [[20 70]
 [70 40]]

We can also use operations on Numpy arrays

Though for matrix to perform addition to another matrix, they have to be in same dimension, Numpy allows this with feature called broadcasting. This allows Numpy to perform operations on arrays of different shapes by automatically expanding the smaller array to match the shape of the larger one

Key rule for broadcasting:

  1. The arrays are compared element-wise from right to left.
  2. Two dimensions are compatible if:
    • They are equal, or
    • One of them is 1.
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# create a 2 x 2 array [[0,1]
#                       [2,3]]
arr1 = np.arange(4).reshape(2,2)

# create a 1 x 2 array [0, 1]
arr2 = np.arange(2)

# adding arr1 + arr2
arr3 = arr1 + arr2

print(arr3)

Output:

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[[0 2]
 [2 4]]

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# create a 2 x 4 array [[0, 1, 2, 3]
#                       [4, 5, 6, 7]]
arr1 = np.arange(0, 8).reshape(2, 4)

# create a 2 x 4 array [[0, 1, 2, 3]
#                       [4, 5, 6, 7]]
arr2 = np.arange(0, 8).reshape(2, 4)

# merge arr1, arr2 [[0, 1, 2, 3]
#                   [4, 5, 6, 7]
#                   [0, 1, 2, 3]
#                   [4, 5, 6, 7]]
arr3 = np.concatenate([arr1, arr2], axis=0)

# create a 4 x 1 array [[0]
#                       [1]
#                       [2]
#                       [3]]
arr4 = np.arange(0, 4).reshape(4, 1)

# adding arr3 and arr4
print(arr3 + arr4)

Output:

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[[ 0  1  2  3]
 [ 5  6  7  8]
 [ 2  3  4  5]
 [ 7  8  9 10]]

Using Numpy’s masking operation

Instead of using for loop to change value of elements, we can use Numpy, which is much faster. It is mostly used in Image processing

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# create a 4 x 4 array with elements 0-15
arr1 = np.arange(16).reshape(4, 4)
print("arr1\n", arr1)

# changes elements to boolean that are less than 10 to True else False
arr2 = arr1 < 10
print("arr2\n", arr2)

# changes elements that are true from arr2 to 100
arr1[arr2] = 100
print("arr1\n", arr1)

Output:

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arr1
 [[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]
 [12 13 14 15]]
arr2
 [[ True  True  True  True]
 [ True  True  True  True]
 [ True  True False False]
 [False False False False]]
arr1
 [[100 100 100 100]
 [100 100 100 100]
 [100 100  10  11]
 [ 12  13  14  15]]

Numpy’s statistical functions

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# create a 4 x 4 array from 0-15
arr = np.arange(16).reshape(4,4)

print("Max value:", np.max(arr))
print("Min value:", np.min(arr))
print("Summation:", np.sum(arr))
print("Average value:", np.mean(arr))

Output:

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Max value: 15
Min value: 0
Summation: 120
Average value: 7.5

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# create a 4 x 4 array from 0-15
arr = np.arange(16).reshape(4,4)

print(arr)
print("Sum of each column:", np.sum(arr, axis=0))
print("Sum of each row:", np.sum(arr, axis=1))

Output:

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[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]
 [12 13 14 15]]
Sum of each column: [24 28 32 36]
Sum of each row: [24 28 32 36]

Summary

  • Adding or Multiplying array with constant results in adding or multiplying every element

  • numpy.max: returns the maximum of an array or maximum along an axis

  • numpy.min: returns the minimum of an array or minimum along an axis

  • numpy.sum: sum of array elements over a given axis

  • numpy.mean: compute the arithmetic mean along the specified axis.

Handling Data and Images, Numpy
Python Study Handling Data and Images Numpy
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