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Exercise solutions

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Please don't look as these solutions until you have attempted the exercises.

Perfect numbers

Perfect numbers are equal to the sum of their proper divisors — all divisors except the number itself.

For example, 6 is a perfect number. Its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.

The mistake here is that the divisors_of() function only returns divisors greater than one, and so the code fails to identify any of the true perfect numbers.

Interestingly, this mistake did not result in the code mistakenly identifying any other numbers as perfect numbers.

Python vs R

If you're only familiar with one of these two languages, you may be surprised to discover that they have some fundamental differences. In this exercise we demonstrated one consequence of the ways that these languages handle function arguments.

The R Language Definition

The semantics of invoking a function in R argument are call-by-value. In general, supplied arguments behave as if they are local variables initialized with the value supplied and the name of the corresponding formal argument. Changing the value of a supplied argument within a function will not affect the value of the variable in the calling frame.

— Argument Evaluation

Python Programming FAQ

Remember that arguments are passed by assignment in Python. Since assignment just creates references to objects, there's no alias between an argument name in the caller and callee, and so no call-by-reference per se.

— How do I write a function with output parameters (call by reference)?

  • In R the run_model_scaled_beta() and run_model_scaled_gamma() functions do not modify the value of settings in the demonstration() function. This produces model outputs for the following parameter combinations:

    • β = 1.0 and γ = 0.5;
    • β = 1.5 and γ = 0.5; and
    • β = 1.0 and γ = 0.35.

  • In Python the run_model_scaled_beta() and run_model_scaled_gamma() functions do modify the value of settings in the demonstration() function. This produces model outputs for the following parameter combinations:

    • β = 1.0 and γ = 0.5;
    • β = 1.5 and γ = 0.5; and
    • β = 1.5 and γ = 0.35.

Answer

The value of β is different in the third combination.