How to Perform Basic Matrix Operations with Pytorch Tensor

pankaj kumar — Sat, 30 May 2020 10:28:58 +0000

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



# Number
t1 = torch.tensor(9.)
t1

tensor(9.)



# vector
t2 = torch.tensor([1,2,3,4,5])
t2

tensor([1, 2, 3, 4, 5])



# matrix
t3 = torch.tensor([[2., 6], 
                   [8, 9], 
                   [9, 4]])
t3

tensor([[2., 6.],
        [8., 9.],
        [9., 4.]])



# n-dimentional
t4 = torch.tensor([[[11., 12., 13.],
         [13., 14., 15.]],

        [[15., 16., 17.],
         [17., 18., 19.]]])
t4

tensor([[[11., 12., 13.],
         [13., 14., 15.]],

        [[15., 16., 17.],
         [17., 18., 19.]]])

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

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

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

(tensor([[-2.7610e-01,  7.4592e-01,  4.8388e-01],
         [ 8.7141e-01, -6.2898e-04,  8.8964e-01]]), torch.Size([2, 3]))



y = torch.randn((2,3))
y, x.shape

(tensor([[-0.3368, -0.8528, -0.3528],
         [ 0.4487, -1.1638, -0.8607]]), torch.Size([2, 3]))

Scaler Opretions of Matrix

Addition of scaler number with matrix element



# add constant with matrix
x+2

tensor([[1.7239, 2.7459, 2.4839],
        [2.8714, 1.9994, 2.8896]])

2*x

tensor([[-5.5220e-01,  1.4918e+00,  9.6776e-01],
        [ 1.7428e+00, -1.2580e-03,  1.7793e+00]])

Subtract scaler number with matrix element



# Subtract constant with matrix
x-2

tensor([[-2.2761, -1.2541, -1.5161],
        [-1.1286, -2.0006, -1.1104]])

Multiplication of scaler number with matrix element

x*3

tensor([[-8.2830e-01,  2.2377e+00,  1.4516e+00],
        [ 2.6142e+00, -1.8869e-03,  2.6689e+00]])



x*-1

tensor([[ 2.7610e-01, -7.4592e-01, -4.8388e-01],
        [-8.7141e-01,  6.2898e-04, -8.8964e-01]])

Division of scaler number with matrix element

x/2

tensor([[-1.3805e-01,  3.7296e-01,  2.4194e-01],
        [ 4.3571e-01, -3.1449e-04,  4.4482e-01]])

Other Math function

Absolute Function

Images Sauce:pytorch.org



torch.abs(x)

tensor([[2.7610e-01, 7.4592e-01, 4.8388e-01],
        [8.7141e-01, 6.2898e-04, 8.8964e-01]])

Ceiling

Images Sauce:pytorch.org



torch.ceil(x)

tensor([[-0., 1., 1.],
        [1., -0., 1.]])

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

tensor([[2., 6.],
        [8., 9.],
        [9., 4.]])



m2 = torch.tensor([[1., 6], 
                   [8, 4], 
                   [3, 4]])
m2

tensor([[1., 6.],
        [8., 4.],
        [3., 4.]])

Addition of Matrices



# add self witch is similar  to 2*m1
m1+m1

tensor([[ 4., 12.],
        [16., 18.],
        [18.,  8.]])



m1+m2

tensor([[ 3., 12.],
        [16., 13.],
        [12.,  8.]])

Subtraction of Matrices



m1-m2

tensor([[1., 0.],
        [0., 5.],
        [6., 0.]])



# Subtract with self
x-x

tensor([[0., 0., 0.],
        [0., 0., 0.]])

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

tensor([[7.6231e-02, 5.5639e-01, 2.3414e-01],
        [7.5936e-01, 3.9561e-07, 7.9146e-01]])

x*y

tensor([[ 9.2995e-02, -6.3612e-01, -1.7071e-01],
        [ 3.9101e-01,  7.3199e-04, -7.6575e-01]])

Division of Matrices

x/x

tensor([[1., 1., 1.],
        [1., 1., 1.]])

x/y

tensor([[ 8.1973e-01, -8.7466e-01, -1.3716e+00],
        [ 1.9420e+00,  5.4046e-04, -1.0336e+00]])

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:

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

(tensor([[2., 6.],
         [8., 9.],
         [9., 4.]]), torch.Size([3, 2]))



#let's take X 
Y = torch.tensor([[2., 6, 9], 
                   [8, 9, 4]])
, X.shape

'X.shape'



#multiply X ans Y 
X@Y

tensor([[ 52.,  66.,  42.],
        [ 88., 129., 108.],
        [ 50.,  90.,  97.]])

If dimention of matrix is not according to the rul then you can not perform matrix multipication



# example with error
m1@m2

---------------------------------------------------------------------------

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



m1.shape

torch.Size([3, 2])



m2.shape

torch.Size([3, 2])

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

DEV Community: pankaj kumar

How to Perform Basic Matrix Operations with Pytorch Tensor

Lets Discuss Tensor First!

Let's Discuss Matrix and Operations of Matrix

Matrix

Matrix Operations

Scaler Opretions of Matrix

Addition of scaler number with matrix element

Subtract scaler number with matrix element

Multiplication of scaler number with matrix element

Division of scaler number with matrix element

Other Math function

Absolute Function

Ceiling

Matrix opretions

Addition of Matrices

Subtraction of Matrices

Division of Matrices

Division of Matrices

Multiplication of Matrices