Introductory Labs

We will be using the Python programming language with the NumPy library during the whole semester. Make sure you are comfortable with these so that you don't spend more time dealing with python/numpy issues than solving the assignment tasks.

For the case you are not too sure about your Python/NumPy skills, have a look here: http://cs231n.github.io/python-numpy-tutorial/, search for other materials (duckduckgo, google) or ask your teacher.

Start by reading General information for Python development and cloning the assignment template repository.

We strongly recommend using the .ipynb notebooks provided in the template. ($ pip install jupyter, then $ jupyter notebook in the directory containing basics.ipynb. Or you can use your favorite IDE jupyter notebook plugin.)

We provide unit tests in the assignment template, see test_basics.py. To execute the tests, run $ python -m unittest. The tests are provided to simplify local development and debugging of your code. Passing all the unit tests does not automatically mean that your code will pass all BRUTE tests, feel free to write additional tests into test_basics.py if needed. Make sure that all the unittests pass OK, before uploading to BRUTE.

In the first part of today’s assignment, you will start with some simple matrix manipulation tasks.

TRY TO AVOID USING LOOPS FOR MATRIX MANIPULATION IN YOUR PROGRAM! (some hints on how to do that here).

Although numpy has a matrix class, we will not be using that. Instead, we will use the array class for representing matrices, vectors, images, lists, etc. We will import numpy using

import numpy as np

Your goal is to complete a function output = matrix_manip(A, B), where A and B are input matrices (represented by np.array). The matrix_manip function should return a python dict containing the results of the operations described below.

To have some data to work with, lets use the following matrices A and B:

A = np.array([[16,  2,  3, 13],
              [ 5, 11, 10,  8],
              [ 9,  7,  6, 12],
              [ 4, 14, 15,  1]])
 
B = np.array([[3, 4,  9, 4, 3, 6, 6, 2, 3, 4],
              [9, 2, 10, 1, 4, 3, 7, 1, 3, 5]])

Your function should work on general input matrices, not only for the A and B shown here or for matrices with the same dimensions.

1. Find the transpose of the matrix A and return it in output['A_transpose']. Example result:

   >> output['A_transpose']
   array([[16,  5,  9,  4],
          [ 2, 11,  7, 14],
          [ 3, 10,  6, 15],
          [13,  8, 12,  1]])
    

2. Select the third column of the matrix A and return it in output['A_3rd_col'].

   >> output['A_3rd_col']
   array([[ 3],
          [10],
          [ 6],
          [15]])
    

   Hint: Don't forget python and numpy use 0-based indexing. Make sure your output dimensions are correct!
3. Select last two rows from last three columns of the matrix A and return the matrix in output['A_slice'].

   >> output['A_slice']
   array([[ 7,  6, 12],
          [14, 15,  1]])

4. Find all positions in A greater then 3 and increment them by 1. Afterwards add a new column of ones to the matrix (from right). Save the result to output['A_gr_inc'].

   >> output['A_gr_inc']
   array([[17,  2,  3, 14,  1],
          [ 6, 12, 11,  9,  1],
          [10,  8,  7, 13,  1],
          [ 5, 15, 16,  1,  1]])
    

   Hint: Try > operator on the whole matrix. The output dtype should be the same as the input dtype. Some numpy functions do not make copies of the inputs, but return 'views' of the input arrays instead. Make sure you don't corrupt the other results when computing output['A_gr_inc']
5. Create matrix C such that $C_{i,j} = \sum_{k=1}^n A\_gr\_inc_{i,k} \cdot (A\_gr\_inc^T)_{k,j}$ and store it in output['C'].

   >> output['C']
   array([[499, 286, 390, 178],
          [286, 383, 351, 396],
          [390, 351, 383, 296],
          [178, 396, 296, 508]])
    

   Hint: No loops are needed, use appropriate numpy matrix function. Try it on a paper with a 2×2 matrix.
6. Compute $\sum_{c=1}^n c \cdot \sum_{r=1}^m A\_gr\_inc_{r,c}$, store in output['A_weighted_col_sum']:

   >> output['A_weighted_col_sum']
   391
    

   Hint: Look at np.arange and np.sum. Finally convert the output to Python float (as indicated in the docstring) by calling float(…).
7. Subtract a vector $(4,6)^T$ from all columns of matrix B. Save the result to matrix output['D'].

   >> output['D']
   array([[-1,  0,  5,  0, -1,  2,  2, -2, -1,  0],
          [ 3, -4,  4, -5, -2, -3,  1, -5, -3, -1]])
    

   Hint: numpy broadcasting.
8. Select all column vectors in the matrix D, which have greater euclidean length than the average length of column vectors in D. Store the results in output['D_select']

   >> output['D_select']
   array([[ 0,  5,  0, -2],
          [-4,  4, -5, -5]])
    

In this part of the assignment, you are supposed to work with a simple input data which contains images of letters. We will use similar data structures later on during the labs. Do the following:

1. The following variables are stored in the data_33rpz_basics.npz data file:
   • images (3D array of 2000 10×10 grayscale images)
   • alphabet (letters contained in the images, not full alphabet is included)
   • labels (indexes of the images into Alphabet array).
2. Load and access them as follows

   loaded_data = np.load("data_33rpz_basics.npz")
   loaded_data['images']

3. Have look at the image with the montage function supplied in the template:

   import matplotlib.pyplot as plt
   plt.imshow(montage(images), cmap='gray')
   plt.show()

   Hint: Try to use

   %matplotlib notebook

   after importing matplotlib.
4. For a given letter, compute its mean image. This means taking all images in the dataset displaying that letter, and making pixel-wise mean. Use your name initials (if present in the dataset) and save them as initial1_mean.png and initial2_mean.png (use any letter if any of your initials is not present in the dataset). Round the mean image to integers and return it in the uint8 type.
   • hint: Image generation is already prepared in basics.ipynb
   • For the purpose of mean image calculation, complete the function compute_letter_mean:

     letter_mean = compute_letter_mean(letter_char, alphabet, images, labels)

     where letter_char is a character (e.g. 'A', 'B', 'C') representing the letter whose mean we want to compute, alphabet, images and labels are loaded from the provided data, and letter_mean is the resulting mean image.
5. Compute features (from images) for all occurrences of a given letter. For a single image, it is an image feature x - a single number characterizing an image. It is defined as

   x = sum of pixel values in the left half of image - sum of pixel values in the right half of image

   warning: The images are stored in unsigned type (uint8), make sure to convert the values to suitable signed type before doing the subtraction. E.g. np.int32(sum_left) - np.int32(sum_right).
   Complete a function for the features computation:

   lr_features = compute_lr_features(letter_char, alphabet, images, labels)

   where letter_char is a character representing the letter whose feature histogram we want to compute, alphabet, images and labels are loaded from the provided data, and lr_features is the resulting vector of features for a given letter.
   • For reference the following feature vector was computed for a letter A

     >> compute_lr_features('A', alphabet, images, labels)
     array([  120  1223  -144  -161   197 -2921  -998  -944  -120  -304  -884 -1461
            -1233  1444  1705  1332   881   212    92   319 -3104 -2829   255     1
            -1763  2230  1916  -335  -257 -3568 -5204 -1144  -641   525   182  -768
             -844  1536  1139   522   495   353  -251  1345   439  1114 -2087  -107
             -563  1491 -1935 -1640  1979  2215   906  1726  1332   365   825  2776
             1282   708  1010   429  1141  1145  1896     7  -642  -657    36   368
             1079    79  -483   327  -135   888  2270  2211  3860  1248  1371  -857
              100  -134  -946  1954  1979 -1575  -837  1363   803   546 -1916 -1808
              370  -435  -363   497])
      

6. Plot feature histograms of your initials into one figure to compare them and save the figure as initials_histograms.png.
   • Code for plotting histograms already prepared for you as plot_letter_feature_histogram(features_1, features_2, letters)
   • Look at the generated histogram image. Do the histogram plots make sense? Could you recognize the letter only by looking at its lr_histogram?