How to implement the following hyperbolic function in Python?

Question

I am a Python beginner, and I have the following problem: I have a set of values between 0 and 1, and I want to implement a nonlinear function that outputs values between 0 and 100 as follows:

(Sorry for the lack of mathematical description of this function, I'm not sure how it's called - the curve is essentially a quarter of a circle)

I feel like this should be very straightforward, but I'm at a loss about how to proceed.

Many thanks in advance!

score 1 · Accepted Answer · answered Apr 04 '20 at 11:54

1

The equation you are looking for is

sqrt(100**2 - 100**2(x-1)**2)

As such:

arr = np.random.random_sample(100) #100 numbers between 0 and 1
hyp = lambda x: (100**2 - 100**2*(x-1)**2)**0.5
print(hyp(arr)) #[98.18880326, 68.95051961, 98.81540216, 26.98951239...]

answered Apr 04 '20 at 11:54

A.J. Uppal

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or more simply `100 * sqrt(1 - (x-1)**2)` – Thierry Lathuille Apr 04 '20 at 11:57
Quick follow-up question: how could I make the curve a little bit flatter? For example for x = 0.55, with this function y is almost 90. I'd like y to be closer to 80 with a slightly flatter curve. Many thanks in advance! – Paul Miller Apr 04 '20 at 14:20
That's a mathematical question; how would you describe such an equation? – A.J. Uppal Apr 04 '20 at 21:09

How to implement the following hyperbolic function in Python?

1 Answers1