exersises_adv.md

Advanced Exercises: High-performance computing

a. Given a list of XYZ-coordinates, p,

[[1.0, 2.0, 10],
 [3.0, 4.0, 20],
 [5.0, 6.0, 30],
 [7.0, 8.0, 40]]

Normalise each coordinate by dividing with its Z (3rd) element. For example, the first row becomes:

[1/10, 2/10, 10/10] Hint: extract the last column into a variable z, and then change its dimensions so that p / z works.

b. Create a 3x3 ndarray. Use fancy indexing to slice out the diagonal elements.

c. Generate a 10 x 3 array of random numbers (all between 0 and 1). From each row, pick the number closest to 0.75. Make use of np.abs and np.argmax to find the column j which contains the closest element in each row.

d. Predict and verify the shape of the following slicing operation.

x = np.empty((10, 8, 6))

idx0 = np.zeros((3, 8)).astype(int)
idx1 = np.zeros((3, 1)).astype(int)
idx2 = np.zeros((1, 1)).astype(int)

x[idx0, idx1, idx2]

e. Very Advanced Construct an array:

x = np.arange(12, dtype=np.int32).reshape((3, 4)) so that x is

array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

Now, provide to np.lib.stride_tricks.as_strided the strides necessary to view a sliding 2x2 window over this array. The output should be

array([[[[ 0,  1],
         [ 4,  5]],

        [[ 1,  2],
         [ 5,  6]],

        [[ 2,  3],
         [ 6,  7]]],


       [[[ 4,  5],
         [ 8,  9]],

        [[ 5,  6],
         [ 9, 10]],

        [[ 6,  7],
         [10, 11]]]], dtype=int32)

The code is of the form

z = as_strided(x, shape=(2, 3, 2, 2),
                  strides=(..., ..., ..., ...))

This sort of stride manipulation is handy for implementing techniques such as region based statistics, convolutions, etc.