Code for the Blog at:

final_code.py

from torch import nn
from time import time
import torch
import numpy as np
import matplotlib.pyplot as plt
from tqdm import tqdm
from skimage.util.shape import view_as_windows
torch.manual_seed(42)


def conv_2d(kernel, bias, x):
    kernel_shape = kernel.shape[0]
    output_shape = x.shape[0] - kernel_shape + 1
    result = np.zeros((output_shape, output_shape))
    for row in range(x.shape[0] - 1):
        for col in range(x.shape[1] - 1):
            window = x[row: row + kernel_shape, col: col + kernel_shape]
            result[row, col] = np.sum(np.multiply(kernel, window))
    return result + bias


def memory_strided_im2col(x, kernel):
    output_shape = (x.shape[0] - kernel.shape[0]) + 1
    return view_as_windows(x, kernel.shape).reshape(kernel.shape[0]*2, output_shape*output_shape)


def naive_im2col(x, kernel):
    kernel_shape = kernel.shape[0]
    rows = []

    # Assuming Padding = 0, stride = 1
    for row in range(x.shape[0] - 1):
        for col in range(x.shape[1] - 1):
            window = x[row: row + kernel_shape, col: col + kernel_shape]
            rows.append(window.flatten())
    return np.transpose(np.array(rows))


if __name__ == "__main__":

    naive_time_log = []
    torch_time_log = []
    strided_time_log = []
    naive_im2col_time_log = []
    MAX_INPUT_SIZE = 300
    NUM_RUNS = 20
    input_size_list = list(range(3, MAX_INPUT_SIZE, 5))

    for input_size in tqdm(input_size_list):
        torch_time = np.zeros(NUM_RUNS)
        naive_time = np.zeros(NUM_RUNS)
        im2col_time = np.zeros(NUM_RUNS)
        strided_time = np.zeros(NUM_RUNS)
        for run in range(NUM_RUNS):
            conv = nn.Conv2d(1, 1, 2)
            ip = torch.randint(low=0, high=10, size=(
                1, 1, input_size, input_size),  dtype=torch.float32)
            conv.weight = nn.Parameter(torch.randint(
                low=0, high=10, size=(1, 1, 2, 2),  dtype=torch.float32))
            ip_np = ip.numpy().reshape(-1, ip.shape[-1])
            kernel_np = conv.weight.detach().squeeze().numpy()
            bias_np = conv.bias.detach().squeeze().numpy()

            start = time()
            naive_conv = conv_2d(kernel_np, bias_np, ip_np)
            naive_time[run] = time() - start

            start = time()
            np.dot(kernel_np.flatten(), naive_im2col(ip_np, kernel_np)) + bias_np
            im2col_time[run]= time() - start

            start = time()
            torch_conv = conv(ip)
            torch_time[run] = time() - start

            start = time()
            np.dot(kernel_np.flatten(), memory_strided_im2col(ip_np, kernel_np)) + bias_np
            strided_time[run]= time() - start

        naive_time_log.append(naive_time.mean())
        torch_time_log.append(torch_time.mean())
        strided_time_log.append(strided_time.mean())
        naive_im2col_time_log.append(im2col_time.mean())
   
    plt.plot(input_size_list, naive_time_log,
             label='Naive Conv 2D', color='red')
    plt.plot(input_size_list, torch_time_log,
             label='PyTorch Conv 2D', color='blue')
    plt.plot(input_size_list, naive_im2col_time_log,
             label='Im2Col Conv 2D', color='green')
    plt.plot(input_size_list, strided_time_log,
             label='Mem Strided Im2Col Conv 2D', color='purple')
    plt.xlabel('Size of Input (n x n)')
    plt.ylabel('Execution Time (secs) - Log Scale')
    plt.yscale("log")
    plt.legend()
    plt.show()

When input shape is higher than 3 - then output from your convolution is not the same as output from pytorch convolution. Try to print line 77 and 73. They should be same but they are not. I know output from numpy convolution is vector and output from pytorch convolution is tensor, simply even if you reshape numpy convolution product to (1, 1, Input_size, input_size) the numbers in matrix are not the same. But the naive_im2col is working fine.