matrix_basics.md

Background

The information above concerning basic mathematical operations on matrices should be enough to take on the tasks below. These are a bit more involved, and also more relevant to operations we'll use in data compression.

Task

• Type: Implement

• Tasks: Write functions to ...

  1. Get the shape (m- and n-dimensions) of any 1- or 2-D array.
  2. 'Pad' (expand) an array to double the length and width (4x the size in total) with zeros to the right and below.
  3. Reduce an array to half the length and width (1/4 total), taking the top and left most block.
  4. Implement the dot product above for 2-D arrays from scratch.

• Reference implementations:

  1. matrix_basics.get_m_n()
  2. matrix_basics.pad_2x2()
  3. matrix_basics.back_to_half() (this complements pad_2x2)
  4. Locally matrix_basics.dot_from_scratch(), as well as in numpy:
     • np.dot(a, b), np.matmul(a, b) and a @ b (where a and b are np.arrays)
     • Bonus: check your work with np.allclose.