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MA2108 Note 1

Definitions

1. A set is an unordered collection of unique elements. Examples are natural numbers, integers, rational numbers, and real numbers
2. Cartesian product of $A$ and $B$ is $A \times B = \lbrace(a, b) : a \in A, b \in B\rbrace$
3. A function from set $A$ to set $B$ is a rule of correspondence that assigns each element $x \in A$ to uniquely determined element $f(x) \in B$
4. Set $A$ is called the domain of $f$
5. Set $B$ is the codomain of $f$
6. The set $f(A) = \lbrace(x) : x \in A\rbrace$ is called the range of $f$
7. Althought $D(f) = A$, we only have $R(f) \subseteq B$

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import torch
import torch.nn as nn
import torch.nn.functional as F

"""
Creating tensors
"""
a = torch.rand(...) # returns a torch.Tensor
b = torch.LongTensor(10).random_(0, 2) # 10-dim vector from [0, 1]

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Leetcode Libraries

Here's a tiny compilation of all the libraries and tools that can be used on Leetcode to make life simpler. This README covers the following:

1. requests
2. collections
3. itertools

---

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import os
import numpy as np
import random
import tensorflow as tf
from tfdeterminism import patch

def seed(s=42):
  random.seed(s)
  np.random.seed(s)
  tf.random.set_seed(s)

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import torch
import torch.nn as nn
import torch.nn.functional as F
from torchvision import transforms

import numpy as np
from PIL import Image
import matplotlib.pyplot as plt
from patchify import patchify, unpatchify # pip install patchify

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!wget http://www.some_dataset_website.com/my_dataset.tar.gz
!tar -xvzf my_dataset.tar.gz

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PATH = "./my_dataset/" # path to dataset on Colab instance
TRAIN_PATH = PATH + "train/"
VAL_PATH = PATH + "val/"

# your custom augmentations
T = transforms.Compose([
      transforms.ToTensor(),
      ...
    ])

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'''
Configures some pipeline hyper-parameters. You
can set them to whatever you please.

You have the option of either mentioning it here
or creating variables inside the map_fn function.

This is entirely up to you. I do both for demonstration purposes.
'''

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# hlper function to get the testing accuracy at the end of the epoch
def get_test_stats(model, loader):
  total_samples = 0
  correct = 0
  model.eval() # switch to eval mode
    
  for (batch_idx, data) in enumerate(loader, 0):
      x, y = data
      logits = model(x)
      preds = torch.argmax(logits, 1)

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device = xm.xla_device()

# define some hyper-params you'd feed into your model
in_channels = ...
random_param = ...

# create model using appropriate hyper-params
net = MyCustomNet(...)

# seat it atop the TPU worker device and switch it to train mode