[Solved] CT5132/CT5148 Lab Week 03

Solutions are available in the /code directory in our .zip.

1. Last week we calculated a list containing e^x x [0.0,0.1,,1.0], using range, lambda, map and math.exp. Now, lets do the Numpy way, using np.linspace and np.exp. Solution: exp_np.py.
2. In the ECG (heartbeat) example, we saw how to use a Boolean expression to give a new array telling us where the Boolean expression is true:

We can also create a new array consisting of the values where it is true:

x = np.array([3, -2, -1, 0, 1, 2, 3]) x[x > 0]

# array([1, 2, 3])

We can use the same idea now on the left-hand side of an assignment, to overwrite only values in an array where the Boolean expression is true. Use this to set all negative values in x to zero. Solution: numpy_boolean_lhs.py.

3. Find the biggest jump between any two consecutive values in the heartbeat (ECG) data. When does it occur? What were the before and after values? Hint: recall we have seen np.diff and np.argmax. I suggest np.diff(x, prepend=x[0]) this time instead of prepend=0. Solution: heartbeat_jump.py.
4. Use Numpy to create a chessboard pattern like this:

[[0 1 0 1 0 1 0 1]

[1 0 1 0 1 0 1 0]

• 1 0 1 0 1 0 1]
• 0 1 0 1 0 1 0]
• 1 0 1 0 1 0 1]
• 0 1 0 1 0 1 0]
• 1 0 1 0 1 0 1]
• 0 1 0 1 0 1 0]]

Hints: use np.linspace, np.meshgrid, and the % operator. For the final touch, look up astype so that your array is int-valued, not float. Solution: chessboard.py.

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5. Create the 2d array a_ij, a vertical 1d array b_i, a horizontal 1d array c_j, and a scalar d. Calculate the new 2d array q where q_ij = a_ij +b_i +c_j +d. (This scenario will be familiar to CT5141 Optimisation students as it occurs in linear objective functions.) Solution: 2d_1d_scalar.py.

6. In our fractals example, we claimed that when a point escapes from a circle of radius 2, it will never come back, but in test_escape_and_return(), thats exactly what seemed to happen. Why? Solution: fractal_escape_and_return.py.
7. Try different values for zmin and zmax in the Julia example. What is the effect?
8. Try different values for c. Do you get any interesting images? I liked c = -0.015 + 0.66j.
9. Try different colourmaps in the Julia set. Look up:

https://matplotlib.org/3.1.0/tutorials/colors/colormaps.html

to see a gallery.

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