Visual Explanation of Python NumPy Library

NumPy is one of the popular Python libraries. In this article, we’ll understand its usage with graphics and more practical approach. So you can visually relate and remember it.

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import numpy as np

python numpy array create

You can create numpy array by passing an array, or an array of array for multi-dimension array. It supports many formats.

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np.array(list(range(4))) #array([0, 1, 2, 3])
np.array((0, 1, 2, 3))   #array([0, 1, 2, 3])
np.fromstring('1 4 ', sep=' ')
np.fromstring('1, 2', dtype=int, sep=',')
numpy.frombuffer(buffer, dtype = float, count = -1, offset = 0)
numpy.fromiter(iterable, dtype, count = -1) #from iterator

Some quick ways to create NumPy arrays are

python numpy array create

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site = np.array([
    [
      ["S","O","L","O"],["T","H","O","T"]
    ],
    [
      ['.','c','o','m'],['b','l','o','g']
    ]
  ]);

site.shape # (2, 2, 4)
site.size  # 16
site.ndim  # 3
len(site)  # 2

You can also create an array with random values

python numpy array create

Some more functions

  • arange: (a range) To create NumPy array.

    np.arange(from ,to(not included), step)

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np.arange(1 ,15, 2) #array([ 1,  3,  5,  7,  9, 11, 13])
a = np.arange(1,17).reshape(4,4)
a
# array([[ 1,  2,  3,  4],
#        [ 5,  6,  7,  8],
#        [ 9, 10, 11, 12],
#        [13, 14, 15, 16]])

Arithmetic Operations

python numpy direct operation

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np.array((1,2,3,4)) - 1 # array([0, 1, 2, 3])

You can apply the other operations in the same way. However, remember that the right side array shape should be acceptable. This is also called Broadcasting.

python numpy wrong shape operation

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A(2-D array): 4 x 3
B(1-D array):     3
Result      : 4 x 3

A(4-D array): 7 x 1 x 6 x 1
B(3-D array):     3 x 1 x 5
Result      : 7 x 3 x 6 x 5

Other operations

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np.subtract(a, b) #or a - b
np.add(a, b) #or a + b
np.divide(a, b) #or a / b
np.multiply(a, b) #or a * b
a.dot(b)    #dot product between a,b

python numpy dot operation

You can also perform many math operations on all the elements of NumPy;

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np.exp(a)   #Exponentiation
np.sqrt(a)  #Square root
np.sin(a)
np.cos(a)  
np.log(a)

Selection

To access an emelement from the array, you can use following patterns;

  • arr[from:to:step] - To create another array from the original array.
    • If from is not specified, it means 0
    • If to is not specified, it means length of that dimension
    • If step is not specified, it means 1
  • arr[at] - To select an elemnt at specific index
  • arr[:] - all the elements of that dimension.
  • arr[…] - all the elements of that dimension.

arr[:] means from start to end with step 1. arr[::] also mean the same.

python numpy selection

Isn’t it confusing that we can use multiple different expressions to select the same data from an array? Let’s understand why and how with examples.

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site = np.array([
    [
      ["S","O","L","O"],["T","H","O","T"]
    ],
    [
      ['.', 'c', 'o', 'm'], ['b', 'l', 'o', 'g']
    ]
  ]);

# All below expressions result ['T', 'H', 'O', 'T']
site[0][1]
site[0:1][0][1]
site[0:2][0][1]

# All below expressions result [['T', 'H', 'O', 'T']]
site[0:1,1]

Did you understand the difference between site[0][1] and site[0:1,1]?

In case of site[0:1,1], we first create a new NumPy array then select it’s 2nd element.

python numpy selection difference

In case of site[0,1], we just refer the 2nd column of 1st element and return it.

python numpy selection difference

Negative index and direction

Nump array indexing work in the same way of python native lists. You can use negative step to reverse the list, or a negative index to select an item from reverse direction.

python numpy negative step, negative index

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site = np.array([
    [
      ["S","O","L","O"],["T","H","O","T"]
    ],
    [
      ['.', 'c', 'o', 'm'], ['b', 'l', 'o', 'g']
    ]
  ]);
site[:,:,::-1]

Output

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array([[['O', 'L', 'O', 'S'],
        ['T', 'O', 'H', 'T']],

       [['m', 'o', 'c', '.'],
        ['g', 'o', 'l', 'b']]], dtype='<U1')

Aggregation

NumPy provides direct function to perform an aggregation opperation and return the result.

python numpy aggregation

fn Description
a.sum() sum
a.min() min
a.max() max
a.cumsum() Cumulative sum
a.mean() Mean
a.median() Median
a.corrcoef() Correlation coefficient
np.std(a) Standard deviation

Axis

You can perform aggregation on particular dimension as well.

python numpy aggregation

For a 3d array, there are 3 axis. When you select a particular axis, an operation is performed that axis-wise.

python numpy aggregation

Let’s understand with one more example of max operation.

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npr=np.array([1,3,4,5,7,8,4,2,4,5,3,8])
npr.reshape(2,3,2).max(axis=0)

python numpy aggregation

Restructure

Remember that each dimension should have same number of elements.

  • resize: Change the original array
  • reshape: Returns a new array
  • transpose: Rows into columns and vice versa

python numpy resize reshape transpose

You can append or concatenate 2 arrays in following ways;

python numpy resize reshape transpose

insert and delete works in the same way. For a 2d array, you can consider axis 0 as row and axis 1 as column. If you insert a single value, numpy automatically fill remaining items with the same value. Otherwise you need to take care of the size.

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a = np.arange(1,10).reshape(3,3)
a = np.insert(a,1,[9,9,9],axis=0)

Output

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array([[1, 2, 3],
       [9, 9, 9],
       [4, 5, 6],
       [7, 8, 9]])

Since each row has 3 items, you can insert either 9 or [9,9,9]. any other shape will give error.

python numpy insert axis 0

python numpy insert axis 0

To understand delete operation, reverse the animation above.

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a = np.arange(1,10).reshape(3,3)
a2 = np.insert(a,1,[9,9,9],axis=0)
a3 = np.delete(a2,1,axis=0)
a == a3

Output

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array([[ True,  True,  True],
       [ True,  True,  True],
       [ True,  True,  True]])

If you want single value output

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np.array_equal(a,a3) # True

Sort operation can also be performed on whole array or only on particular axis.

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a.sort()
a2.sort(axis=0)

Advance Selection

Values from NumPy array can be selected by passing truth values array.

python numpy advance selection

Clone

  • Deep copy: b = a[:] or b = a.copy()
  • View: b = a.view(). Any change in b will reflect on a other than change in shape
  • Shallow copy (or reference): b = a.

NumPy has many useful functions that reduce a lot of effort of managing and manipulating data. What you need to understand is

  • Direct operations
  • Axis
  • Selection

Once these concepts are clear, you can understand and use it’s any function easily. But still if you feel I should cover more functions, leave a message on discussion forum.

There are many other things that you can do with numpy like storing and manipulating dates, solving math expressions, matrix, loafin or saving numpy array from/to a file etc.



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Amit
Amit Author & Maintainer of many opensourse projects like fast-xml-parser, imglab, stubmatic etc. Very much interested in research & innovations.

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