Golang中模拟钟形曲线上的值

Question

My math is a bit elementary so I apologize for any assumptions in advance.

I want to fetch values that exist on a simulated bell curve. I don't want to actually create a bell curve or plot one, I'd just like to use a function that given an input value can tell me the corresponding Y axis value on a hypothetical bell curve.

Here's the full problem statement:

I am generating floating point values between 0.0 and 1.0.

0.50 represents 2.0 on the bell curve, which is the maximum. The values < 0.50 and > 0.50 start dropping on this bell curve, so for example 0.40 and 0.60 are the same and could be something like 1.8. 1.8 is arbitrarily chosen for this example, and I'd like to know how I can tweak this 'gradient'.

Right now Im doing a very crude implementation, for example, for any value > 0.40 and < 0.60 the function returns 2.0, but I'd like to 'smooth' this and gain more 'control' over the descent/gradient

Any ideas how I can achieve this in Go

Answer 1

Gaussian function described here : https://en.wikipedia.org/wiki/Gaussian_function
has a bell-curve shape. Example of implementation :

package main
import (
    "math"
)

const (
    a = 2.0 // height of curve's peak
    b = 0.5 // position of the peak
    c = 0.1 // standart deviation controlling width of the curve 
            //( lower abstract value of c -> "longer" curve)
)

func curveFunc(x float64) float64 {
    return a *math.Exp(-math.Pow(x-b, 2)/2.0*math.Pow(c, 2))
}