Speedup the lake_problem function in the example_lake_model.py example.

This is an one-on-one adaptation of https://github.com/quaquel/epa1361/pull/4.

Speed up the lake_problem function by around 30x, by flattening a loop and computing those values in NumPy arrays.

Average duration of 100 lake_model experiments: 0.940 seconds vs 0.030 seconds (speed up: 31.41).

I validated the output and it is consistent with the previous function:

def validate_new_function():
    result_original = lake_problem()
    result_optimized = lake_problem_fast()

    # Check if the results are the same within a given tolerance
    assert np.allclose(result_original, result_optimized, rtol=1e-3, atol=1e-3), "Outputs are not the same: {} vs. {}".format(result_original, result_optimized)

for _ in range(10):
    try:
        validate_new_function()
    except AssertionError as e:
        print(e)

It prints nothing, which means all outputs are withing 0.1% of each other (due to the stochastic nature of the random.lognormal() draw it's never exactly the same).

The full analysis can be viewed in this notebook.

This over an order of magnitude speedup will help students iterate faster when learning and playing with the exercises, and might enable some new assignments and examples previously out of scope due to performance limitations.

Also add a warning on the decisions KeyError.