Matrix Operations in Python Numpy

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We often perform matrix operations in python. In this post, we will take a look at the simple matrix operations in Python.

First, let’s import the module as follows:

import numpy as np

Now, let’s check out the matrix creation and operation procedures.

Creating Matrix

  1. Creating Matrix from list of lists
     >>> matrix = [[1,2,3],[4,5,6],[7,8,9]]
     >>> np.array(matrix)
     array([[ 1,  2,  3],
            [ 4,  5,  6],
            [ 7,  8,  9]])
    
  2. Creating matrix using np.arrange() and np.reshape(array,(m,n)) where $m \times n$ is the size of the matrix.
     >>> import numpy as np
     >>> nums = np.arange(0,16)
     >>> matrix = np.reshape(nums,(4,4))
     >>> matrix
     array([[ 0,  1,  2,  3],
            [ 4,  5,  6,  7],
            [ 8,  9, 10, 11],
            [12, 13, 14, 15]])
    
  3. Zero Matrix using np.zeros()
     >>> np.zeros((4,3))
     array([[0., 0., 0.],
             [0., 0., 0.],
             [0., 0., 0.],
             [0., 0., 0.]])
    
  4. One matrix using np.ones()

     >>> np.ones((2,3))
     array([[1., 1., 1.],
             [1., 1., 1.]])
    
  5. Identity matrix using np.eye(m) where $m \times m$ is the size of matrix

     >>> np.eye(4)
     array([[1., 0., 0., 0.],
         [0., 1., 0., 0.],
         [0., 0., 1., 0.],
         [0., 0., 0., 1.]])
    
  6. Transpose matrix
     >>> matrix.T
     array([[ 0,  4,  8, 12],
            [ 1,  5,  9, 13],
            [ 2,  6, 10, 14],
            [ 3,  7, 11, 15]])
    
  7. all possible (0,1)-matrices of size (3,2)
     [np.reshape(np.array(i), (3, 2)) for i in itertools.product([0, 1], repeat = 3 * 2)]
    

max/min and argmax/argmin

in numpy, array_variable.max() and array_variable.min() are used to return the maximum/minimum values respectively. array_variable.argmax() and array_variable.argmin() are used to return the indices of maximum/minimum values respectively.

>>> test = np.random.randint(1,100,9)
>>> test.reshape(3,3)
>>> test
array([[34, 12, 22],
       [69, 36, 27],
       [26, 57, 53]])
>>> test.max()
69
>>> test.min()
12
>>> test.argmax()
3
>>> test.argmin()
1

Accessing Values

matrix = np.reshape(np.arange(0,16),(4,4))
print(matrix[0]) # first row
print(matrix[1][2]) # third element of second row
print(matrix[:,1]) # second column
print(matrix[:,-1]) # last column
# [0 1 2 3]
# 6
# [ 1  5  9 13]
# [ 3  7 11 15]

Slicing of Matrix

print(matrix[:3, :2])  # three rows, two columns
print(matrix[:2,])  # two rows, all columns
print(matrix[:,3])  # all rows, third column
print(matrix[:, 1:3])  # all rows, second to the third column

Element-wise Addition, Subtraction, and Division

>>> print(np.add(matrix,matrix))
[[ 0  2  4  6]
 [ 8 10 12 14]
 [16 18 20 22]
 [24 26 28 30]]
>>>
>>> print(np.subtract(matrix,matrix))
[[0 0 0 0]
 [0 0 0 0]
 [0 0 0 0]
 [0 0 0 0]]
>>>
>>> print(np.divide(matrix,matrix))
[[nan  1.  1.  1.]
 [ 1.  1.  1.  1.]
 [ 1.  1.  1.  1.]
 [ 1.  1.  1.  1.]]

Multiplication

  1. Element-wise Multiplication (Hadamard Product)
     >>> print(np.multiply(matrix,matrix))
     [[  0   1   4   9]
      [ 16  25  36  49]
      [ 64  81 100 121]
      [144 169 196 225]]
    
  2. Dot Product
     >>> print(np.dot(matrix,matrix))
     [[ 56  62  68  74]
      [152 174 196 218]
      [248 286 324 362]
      [344 398 452 506]]
    

Other Notable Operations

  1. Axis-wise Addition
     >>> np.sum(matrix,axis=0)  # column sum
     array([24, 28, 32, 36])
     >>>
     >>> np.sum(matrix,axis=1)  # row sum
     array([ 6, 22, 38, 54])
    
  2. Matrix rank
     >>> np.linalg.matrix_rank(matrix)
     2
    
  3. Determinant of a square matrix
     >>> np.linalg.det(np.eye(5))
     1.0
    
  4. Numpy offers direct filtering/mapping options. Let’s take a look at the examples:
     >>> test > 30
     array([[ True, False, False],
            [ True,  True, False],
            [False,  True,  True]])
    

Input a Matrix from a Input File

Let’s create a input file named T.txt that contains the following input

1,0,2,0,0,0,0
1,1,2,2,0,0,1
2,2,1,1,0,0,2
1,1,2,1,0,2,1

Now, in the python script, do the following

with  open('T.txt', 'r') as  f:
	T = np.array([[int(num) for  num  in  line.split(',')] for  line  in  f])
print(T)

References

  1. Python Matrices and NumPy Arrays
  2. Matrix manipulation in Python

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