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pankaj kumar
pankaj kumar

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How to Perform Basic Matrix Operations with Pytorch Tensor

#machinelearning #pytorch #tensor #matrix

In this Notebook, I try to Explain Basic Matrix Operations using PyTorch tensor.

Lets Discuss Tensor First!

Tensor is a multi-dimensional matrix containing elements of a single data type.
like tensor is multidimensional so you can Easily handle number Which is a zero-dimensional matrix, vector Which is a single-dimensional matrix, matrix Which is a two-dimensional matrix, or multi-dimensions matrix.



# Import torch and other required modules
import torch
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# Number
t1 = torch.tensor(9.)
t1
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tensor(9.)
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# vector
t2 = torch.tensor([1,2,3,4,5])
t2
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tensor([1, 2, 3, 4, 5])
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# matrix
t3 = torch.tensor([[2., 6], 
                   [8, 9], 
                   [9, 4]])
t3
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tensor([[2., 6.],
        [8., 9.],
        [9., 4.]])
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# n-dimentional
t4 = torch.tensor([[[11., 12., 13.],
         [13., 14., 15.]],

        [[15., 16., 17.],
         [17., 18., 19.]]])
t4
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tensor([[[11., 12., 13.],
         [13., 14., 15.]],

        [[15., 16., 17.],
         [17., 18., 19.]]])
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In the ML/DL you can use CPU or GPU for processing and torch can handle both devices with using torch.device for more detail go to https://pytorch.org/docs/stable/tensors.html

Let's Discuss Matrix and Operations of Matrix

Matrix

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. --Wikipedia
Alt Text

Image Source: Wikipedia
In the above matrix, you can see an m × n matrix: The m is the number of Horizontal are rows and the n is verticals are columns. In the matrix, each element is denoted by a variable with two subscripts like a 2,1 that means second row and first column

The Ml/DL matrix is very important because with matrix data handling and representation are very easy so Pytorch provides a tensor for handling matrix or higher dimensional matrix as I discussed above.
now Let's discuss a different type of matrix and how to create and handle with tensor

Matrix Operations

Scalar Operations

  • Addition
  • Subtraction
  • Multiplication
  • division
  • other mathematical function

Matrix Operations (in the addition, subtraction, scalar matrix Multiplication snd division must be dimension order is same)

  • Addition of Matrices
  • Subtraction of Matrices
  • scaler Multiplication of Matrices
  • scaler Multiplication of Matrices
  • Multiplication of Matrices

Read more:
https://byjus.com/jee/matrix-operations/

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Mathematical_Methods_in_Chemistry_(Levitus)/15%3A_Matrices/15.03%3A_Matrix_Multiplication



# for example let's take 2x4 matrix 
x = torch.randn((2,3))

x, x.shape
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(tensor([[-2.7610e-01,  7.4592e-01,  4.8388e-01],
         [ 8.7141e-01, -6.2898e-04,  8.8964e-01]]), torch.Size([2, 3]))
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y = torch.randn((2,3))
y, x.shape
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(tensor([[-0.3368, -0.8528, -0.3528],
         [ 0.4487, -1.1638, -0.8607]]), torch.Size([2, 3]))
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Scaler Opretions of Matrix

Addition of scaler number with matrix element 



# add constant with matrix
x+2
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tensor([[1.7239, 2.7459, 2.4839],
        [2.8714, 1.9994, 2.8896]])
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2*x
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tensor([[-5.5220e-01,  1.4918e+00,  9.6776e-01],
        [ 1.7428e+00, -1.2580e-03,  1.7793e+00]])
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Subtract scaler number with matrix element 



# Subtract constant with matrix
x-2
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tensor([[-2.2761, -1.2541, -1.5161],
        [-1.1286, -2.0006, -1.1104]])
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Multiplication of scaler number with matrix element 



x*3
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tensor([[-8.2830e-01,  2.2377e+00,  1.4516e+00],
        [ 2.6142e+00, -1.8869e-03,  2.6689e+00]])
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x*-1
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tensor([[ 2.7610e-01, -7.4592e-01, -4.8388e-01],
        [-8.7141e-01,  6.2898e-04, -8.8964e-01]])
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Division of scaler number with matrix element 



x/2
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tensor([[-1.3805e-01,  3.7296e-01,  2.4194e-01],
        [ 4.3571e-01, -3.1449e-04,  4.4482e-01]])
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Other Math function

Absolute Function

Alt Text
Images Sauce:pytorch.org



torch.abs(x)
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tensor([[2.7610e-01, 7.4592e-01, 4.8388e-01],
        [8.7141e-01, 6.2898e-04, 8.8964e-01]])
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Ceiling

Alt Text
Images Sauce:pytorch.org



torch.ceil(x)
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tensor([[-0., 1., 1.],
        [1., -0., 1.]])
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Similarly, you can use other math functions like Cos(x), sin(x), etc.

Matrix opretions 



m1 = torch.tensor([[2., 6], 
                   [8, 9], 
                   [9, 4]])
m1
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tensor([[2., 6.],
        [8., 9.],
        [9., 4.]])
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m2 = torch.tensor([[1., 6], 
                   [8, 4], 
                   [3, 4]])
m2
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tensor([[1., 6.],
        [8., 4.],
        [3., 4.]])
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Addition of Matrices 



# add self witch is similar  to 2*m1
m1+m1
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tensor([[ 4., 12.],
        [16., 18.],
        [18.,  8.]])
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m1+m2
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tensor([[ 3., 12.],
        [16., 13.],
        [12.,  8.]])
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Subtraction of Matrices 



m1-m2
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tensor([[1., 0.],
        [0., 5.],
        [6., 0.]])
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# Subtract with self
x-x
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tensor([[0., 0., 0.],
        [0., 0., 0.]])
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Division of Matrices 



# this is scaler Multiplication don't be confused with matrix Multiplication. in scaler, Multiplication must be the dimensions  are the same  
x*x
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tensor([[7.6231e-02, 5.5639e-01, 2.3414e-01],
        [7.5936e-01, 3.9561e-07, 7.9146e-01]])
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x*y
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tensor([[ 9.2995e-02, -6.3612e-01, -1.7071e-01],
        [ 3.9101e-01,  7.3199e-04, -7.6575e-01]])
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Division of Matrices 



x/x
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tensor([[1., 1., 1.],
        [1., 1., 1.]])
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x/y
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tensor([[ 8.1973e-01, -8.7466e-01, -1.3716e+00],
        [ 1.9420e+00,  5.4046e-04, -1.0336e+00]])
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Multiplication of Matrices

If X and Y are matrix and X has dimensions m×n and Y have dimensions n×p, then the product of X and Y has dimensions m×p.
The entry (XY)ij is obtained by multiplying row I of X by column j of Y, which is done by multiplying corresponding entries together and then adding the results:

Alt Text

Images Sauce:chem.libretexts.org

For Matrix multipication you can use @ oprator and * oparetor is scaler multipication



#let's take X 
X = torch.tensor([[2., 6], 
                   [8, 9], 
                   [9, 4]])
X, X.shape
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(tensor([[2., 6.],
         [8., 9.],
         [9., 4.]]), torch.Size([3, 2]))
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#let's take X 
Y = torch.tensor([[2., 6, 9], 
                   [8, 9, 4]])
, X.shape
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'X.shape'
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#multiply X ans Y 
X@Y
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tensor([[ 52.,  66.,  42.],
        [ 88., 129., 108.],
        [ 50.,  90.,  97.]])
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If dimention of matrix is not according to the rul then you can not perform matrix multipication 



# example with error
m1@m2
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---------------------------------------------------------------------------

RuntimeError                              Traceback (most recent call last)

<ipython-input-29-f3553d88c578> in <module>
      1 # example with error
----> 2 m1@m2


RuntimeError: size mismatch, m1: [3 x 2], m2: [3 x 2] at /opt/conda/conda-bld/pytorch_1587428266983/work/aten/src/TH/generic/THTensorMath.cpp:41
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m1.shape
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torch.Size([3, 2])
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m2.shape
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torch.Size([3, 2])
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The dimension of m1 is 3x2 and the dimension of m2 is 3x2 so m1 column is not matched with m2 rows 3!=2 that's why this is fire dimension error

For live code click here

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