Generate Random Real Numbers

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Problem to Solve

I want a real number (a float) randomly chosen from some range.

In the earlier recipe Generate Random Integers, we saw how to randomly choose an integer from a range of integers. Physics applications tend to use real numbers (floats) more often than integers, so randomly generating those is important too.

These recipes assume you want to pick a number with in some range of values, with all possibilities in that range being equally likely. The technical term for that is "sampling from a uniform distribution." If you need to weight some values more than others, see the next recipe, Draw From a Weighted Distribution.

Again, we're assuming import random has been done.

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Recipe: Generate a Real Number Between 0 (inclusive) and 1 (exclusive)

Under the hood, this is the most fundamental of all pseudorandom number tasks; all the rest are built upon this. As a result, this is one is the fastest.

zero_to_one = random.random()

That's it. The random() function returns a float in the range [0.0, 1.0) every time it's called. No arguments.

Recipe: Flip a Biased Coin

One common application of this "flipping a biased coin", i.e., choosing between two alternatives where one outcome has probability \(p\) and the other has probability \(1 - p\). The recipe is:

if random.random() < p:
    result = "heads"
else:
    result = "tails"

or, more compactly using python's "ternary operator" for one-line if/else,

result = "heads" if random.random() < p else "tails"

You could accomplish the same thing with result = random.choices(["heads", "tails"], [p, 1 - p]), but that's considerably slower — by my tests, about 13 times slower.

Recipe: Generate a Real Number Between Two Arbitrary Values

This is the most common need: Randomly pick a number between \(a\) and \(b\) (inclusive of endpoints), with all values in that range equally likely. The recipe is:

# assuming `a` and `b` are already defined,
random_value = random.uniform(a, b)

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