Generating sequence of numbers in Python (curved)

Question

I am trying to generate, say a non-linear sequence of 120 numbers in a range between 7 and 20.

I have already tried using numpy geomspace and logspace, which gave me pretty much the same outcome. It does what I want, but the resulted "curve" is not "sharp" enough so to speak.

import numpy as np
TILE_NONLINEAR = np.geomspace(7, 20, num=120)

I need to control an acceding and descending. A slow start and fast acceleration at the end and/or vice versa. Like for instance, outcome should be something like:

[7, 7.001, 7.003, 7.01 ..... 17.1, 17.3, 17.8, 18.7, 20]

or

[7, 7.8, 8.5, 9, ..... 19.9, 19.95, 19.98, 20]

The resulted sequences are off the top of my head just to give an idea.

Answer 1

There are bunch of nonlinear function that can be used for the task (some are listed here). Below is a simple exponential function to generate nonlinear array between two numbers. You can control curvature in the function:

import numpy as np

def nonlinspace(start, stop, num):
    linear = np.linspace(0, 1, num)
    my_curvature = 1
    curve = 1 - np.exp(-my_curvature*linear)
    curve = curve/np.max(curve)   #  normalize between 0 and 1
    curve  = curve*(stop - start-1) + start
    return curve

arr = nonlinspace(7, 21, 10)

#rounded result : [ 7., 9.16, 11.1, 12.83, 14.38, 15.77, 17.01, 18.12, 19.11, 20.]