DATA130011.01-Lab 1 Solved

Lab 1 – The Basics of Python and Pytorch

This lab aims to help the students refresh the basics of python, particularly, NumPy. 

1.       Write a Python function to sum all the numbers in a list.

2.       Write a Python function that takes a list and returns a new list with unique elements of the first list. e.g.,

Input:[1, 2, 3, 3, 3, 3, 4, 5].

Output: [1, 2, 3, 4, 5].

3.       Write a Python function that checks whether a passed string is palindrome or not. A palindrome is a word, phrase, or sequence that reads the same backward as forward, e.g., madam or nurses run.

4.       Write a NumPy program to find the real and imaginary parts of an array of complex numbers. e.g.,

Input: array [ 1.00000000+0.j 0.70710678+0.70710678j] Output: array [[1, 0], [0.70710678, 0.70710678]]

5.       Write a Python program to add two binary numbers. e.g.,

Input : (’11’, ’1’)

Output : 100

6.       You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order and each of their nodes contain a single digit. Add the two numbers and return it as a linked list. You may assume the two numbers do not contain any leading zero, except the number 0 itself. e.g.,

Input: (2 -> 4 -> 3) + (5 -> 6 -> 4)

Output: 7 -> 0 -> 8

Explanation: 342 + 465 = 807.

Linked list is defined as follow # Definition for singly-linked list.

# class ListNode:

# def __init__(self, x):

# self.val = x

# self.next = None

7.       Implement bubble sort

8.       Implement merge sort

9.       Implement quick sort

10.   Implement shell sort

11.   Implement linear regression model and use autograd to optimize it by Pytorch.

12.   Implement logistic regression model and use autograd to optimize it by Pytorch.

13.   Implement linear SVM model for binary classification task and use autograd to optimize it by Pytorch. Hint: you may use the loss of Pmax[0,1 − y (wx + b)]

14.   Add a Frobenius norm penalty for the weight w in your SVM model by two different ways..

Hint: Frobenius norm of a matrix .

15.   Learn how to use linear regression[1], logistic regression[2], and SVM[3] by scikit-learn.

16.   Download CIFAR-10 dataset[4] and visualize some of its images.

17.   Write a dataset class for loading CIFAR-10. Make sure it could be transferred to Pytorch Dataloader.

Hint: If you find this part a little hard, check the official code[5] and make sure you understand each part.

18.   Read6 and learn how to use torchvision.transforms to transform images.

19.   Run one epoch for loading CIFAR-10 with Pytorch Dataloader and test the loading time of different batch_size (1, 4, 64, 1024), different num_workers (0,1,4,16), and whether use pin_memory or not.

20.   Calculate the mean and std of CIFAR-10’ training set within each RGB channel.

21.   Image to character painting

(a) Target

Converting the RGB color image to character painting with Python code

• Character painting is a combination of a series of characters. We can think of characters as relatively large pixels. A character can represent a color. The more types of characters, the more colors can be represented, and the picture will be more hierarchical sense

(b) Requirements

•    Python 3.5

•    pillow 5.1.0

(c) Method

i.      Use PIL (pillow) to get the input picture

ii.    Use the following formula to map RGB values to gray values (note that this formula is not a real algorithm, but a simplified sRGB IEC61966-2.1 formula)

• gray = 0.2126 * r + 0.7152 * g + 0.0722 * b

iii. Create a character list (length and content are customized) iv. Map the gray value to characters and save the result with a string (note the corresponding picture size, add line breaks)

v. Export character painting to a .txt file (d) Result

 

22.   Numpy exercises

•    Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates.

•    Create a 2D array subclass such that Z[i, j] == Z[j, i].

•    Consider 2 sets of points P0, P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])?

23.   Bilinear Interpolation

Please implement the bilinear interpolation algorithm using python. Check this for an introduction to bilinear interpolation.

Test samples:

A =

((110, 120, 130),

(210, 220, 230),

(310, 320, 330))

BilinearInterpolation(A, (1, 1)) == 110

BilinearInterpolation(A, (2.5, 2.5)) == 275

24.   Cartesian product

Given an arbitrary number of vectors, build the cartesian product (every combinations of every item).

e.g. [1, 2, 3], [4, 5], [6, 7] ==> [[1 4 6] [1 4 7] [1 5 6] [1 5 7] [2 4 6] [2 4 7] [2 5 6] [2 5 7] [3 4 6] [3 4 7] [3 5 6] [3 5 7]]

25.   Extracting a subpart of an array

Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a fill value when necessary) e.g.

In:

>‌> Z = np.random.randint(0, 10, (5, 5))

>‌> shape = (4, 4)

>‌> fill = 0

>‌> position = (1,1)

>‌> Z

[[3 6 8 5 9]

[4 9 0 0 9]

[6 1 4 0 8]

[9 1 2 0 9] [4 1 7 5 0]] Out:

[[0 0 0 0]

[0 3 6 8]

[0 4 9 0]

[0 6 1 4]]

26.   Matrix operations

Please implement following matrix (just 2D) operations without numpy:

•    add

•    subtract

•    scalar multiply

•    multiply

•    identity

•    transpose

•    inverse

Test samples:

In:

>‌> matrix_a = [[12, 10], [3, 9]]

>‌> matrix_b = [[3, 4], [7, 4]]

>‌> matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]

>‌> matrix_d = [[3, 0, 2], [2, 0, -2], [0, 1, 1]] Out:

add(matrix_a, matrix_b) == [[15, 14], [10, 13]] subtract(matrix_a, matrix_b) == [[9, 6], [-4, 5]] scalar_multiply(matrix_b, 3) == [[9, 12], [21, 12]] multiply(matrix_a, matrix_b) == [[106, 88], [72, 48]] identity(3) == [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

transpose(matrix_c) == [[11, 21, 31, 41], [12, 22, 32, 42], [13, 23, 33, 43], [14, 24, 34, 44]] inverse(matrix_d) == [[0.2, 0.2, 0.0], [-0.2, 0.30000000000000004, 1.0], [0.2, -0.30000000000000004, 0.0]]

27.   Greatest common divisor

Find the greatest common divisor(gcd) of two integers.

Test samples:

•    GCD(3, 5) = 1

•    GCD(6, 3) = 3

•    GCD(-2, 6) = 2

•    GCD(0, 3) = 3

28.   Find all consecutive positive number sequences whose sum is N

e.g. 18+19...+22 = 9+10+...+16 = 100

Find all consecutive positive number sequences whose sum is 1000, and report your results.

29.   Password checking

A website requires the users to input username and password to register. Write a program to check the validity of password input by users. Following are the criteria for checking the password:

•    At least 1 letter between [a-z]

•    At least 1 number between [0-9] • At least 1 letter between [A-Z]

•    At least 1 character from [$#@]

•    Minimum length of transaction password: 6

•    Maximum length of transaction password: 12

Your program should accept a sequence of comma separated passwords and will check them according to the above criteria. Passwords that match the criteria are to be printed, each separated by a comma. e.g.

If the following passwords are given as input to the program: ABd1234@1,a F1#,2w3E*,2We3345

Then, the output of the program should be: ABd1234@1


 
[1] https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression
[2] https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html#sklearn.linear_model.LogisticRegression
[3] https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html
[4] https://www.cs.toronto.edu/~kriz/cifar.html
[5] https://pytorch.org/docs/stable/_modules/torchvision/datasets/cifar.html#CIFAR10 6https://pytorch.org/docs/stable/torchvision/transforms.html