## Introduction

In this tutorial, we will explain how to multiply tensors in PyTorch with torch.matmul() function. We will see its syntax and see various examples to understand its functionality in a better way.

**Syntax of torch.matmul() function**

The syntax of torch matmul function is as follows –

*torch.matmul(tensor1, tensor2, out)*

**tensor1 –**The first tensor for multiplication**tensor2 –**The second tensor for multiplication**out –**Output tensor, result of multiplication of tensor1 with tensor2

**Functionality of torch matmul function**

The functionality of torch matmul depends on the dimensions of the two input tensors as follows –

- When both tensor1 and tensor2 are of 1-Dimension then the dot product is done whose output is a scalar.
*[See example 1 below]* - When both tensor1 and tensor2 are of 2-Dimension then the matrix multiplication is done. However the inner dimension of the two tensors should be the same, i.e. the number of columns in tensor1 should match the number of rows of tensor2. (It is the fundamental rule of matrix multiplication)
*[See example 2 below]* - When tensor1 is 1-Dimension and tensor2 is 2-Dimension then internally one dimension is added to tensor1 to make it 2-Dimension. After that, matrix multiplication is performed between the two tensors, and the extra dimension is removed from the final result. It should be noted that the 1-Dimension tensor should be such that when an extra dimension is added it should match the number of rows of tensor2 to obey the matrix multiplication rule. Otherwise, it will throw an error.
*[See example 3 below]* - When tensor1 is 2-Dimension and tensor2 is 1-Dimension then the matrix-vector multiplication is done.
*[See example 4 below]* - When at least one tensor has dimension N where N>2 then batched matrix multiplication is done where broadcasting logic is used.
*[See example 5 & 6 below]*

**Examples**

To start with the examples, let us first of all import PyTorch library.

In [0]:

import torch;

**Example – 1: Multiplying Two 1-Dimension Tensors with torch.matmul()**

In the first example, we multiply two 1-D dimension tensors with torch matmul and the resulting output is scalar.

In [1]:

tensor1 = torch.tensor([2,3]) tensor1

tensor([2, 3])

tensor2 = torch.tensor([4,4]) tensor2

Out[2]:

tensor([4, 4])

In[3]:

output = torch.matmul(tensor1,tensor2) output

Out[3]:

tensor(20)

**Example – 2: Multiplying Two 2-Dimension Tensors with torch.matmul**

In this example, we generate two 2-D tensors with randint function of size 4×3 and 3×2 respectively. Do notice that their inner dimension is of the same size i.e. 3 thus making them eligible for matrix multiplication. The output tensor after multiplying with torch matmul is of size 4×2.

In [4]:

tensor1 = torch.randint(high = 20, size=(4,3)) tensor1

Out[4]:

tensor([[13, 15, 12], [ 6, 13, 19], [ 8, 10, 18], [ 8, 17, 17]])

tensor2 = torch.randint(high = 20, size=(3,2)) tensor2

Out[5]:

tensor([[ 2, 18], [ 5, 2], [ 9, 10]])

output = torch.matmul(tensor1,tensor2) output

tensor([[209, 384], [248, 324], [228, 344], [254, 348]])

**Example – 3: Multiplying 1D Tensor with 2D Tensor**

Here we create a 1D tensor and a 2D tensor of size 2×3 and then multiply them with matmul function.

In [7]:

tensor1 = torch.tensor([6,5]) tensor1

tensor([6, 5])

tensor2 = torch.randint(high = 20, size=(2,3)) tensor2

tensor([[10, 12, 12], [18, 13, 12]])

output = torch.matmul(tensor1,tensor2) output

tensor([150, 137, 132])

**Example – 4: Multiplying 2D Tensor with 1D Tensor**

Here we create a 2D tensor of size 3×2 and a 1D tensor and then multiply them with PyTorch matmul function.

In [10]:

tensor1 = torch.randint(high = 20, size=(3,2)) tensor1

tensor([[ 5, 10], [13, 0], [ 7, 1]])

tensor2 = torch.tensor([2,5]) tensor2

tensor([2, 5])

output = torch.matmul(tensor1,tensor2) output

tensor([60, 26, 19])

**Example – 5: Multiplying 2D Tensor with 3D Tensor**

In this example, we create a 2D tensor of size 4×3 and a 3D tensor of size 2x3x2 and then multiply them.

In [13]:

tensor1 = torch.randint(high = 20, size=(4,3)) tensor1

tensor([[16, 18, 8], [ 5, 12, 12], [17, 7, 5], [15, 5, 14]])

tensor2 = torch.randint(high = 20, size=(2,3,2)) tensor2

Out[14]:

tensor([[[14, 15], [13, 3], [ 8, 13]], [[ 2, 12], [ 4, 7], [ 1, 3]]])

output = torch.matmul(tensor1,tensor2) output

tensor([[[522, 398], [322, 267], [369, 341], [387, 422]], [[112, 342], [ 70, 180], [ 67, 268], [ 64, 257]]])

**Example – 6: Multiplying Two 3D Tensors**

In this example, we create two 3D tensors and then multiply them with PyTorch matmul function.

In [16]:

tensor1 = torch.randint(high = 20, size=(2,4,3)) tensor1

tensor([[[ 6, 14, 8], [16, 19, 7], [ 2, 1, 13], [ 0, 17, 19]], [[ 4, 16, 12], [14, 16, 15], [18, 18, 5], [ 4, 8, 8]]])

tensor2 = torch.randint(high = 20, size=(2,3,2)) tensor2

tensor([[[18, 19], [17, 5], [ 4, 8]], [[ 1, 8], [ 2, 13], [14, 2]]])

output = torch.matmul(tensor1,tensor2) output

tensor([[[378, 248], [639, 455], [105, 147], [365, 237]], [[204, 264], [256, 350], [124, 388], [132, 152]]])