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c#mappinglogarithm

mapping numbers on a scale

I have an array of numbers up to 20000 and I'm trying to assign a weight to these numbers:

The closer a number is to 0 the higher should the weight be. My problem is that I'm trying to make it such that the higher the number is, the smaller should the difference in weight be, for example the weight difference between 1-100 might be 1.5 but the difference between 100-10000 might be 0.5.

I think it's a logarithmic scale, isn't it? I'm not great at math at all.. this is not a homework question, school was out long ago just a hobby question.

What I've tried is that I've mapped weights to my number array by doing a square root on 25000-value but this isn't what I'm looking for. I just put that in so I could see a gradient of weights coming back plus the numbers are just to big, ideally I want the weights between 0.01 and 3.

I don't have any code to show, any help would be appreciated.

Solution

  • While your question isn't really a C# question, I may have an answer for you. To scale a value with logarithmic spacing, you can use the following formula:

    enter image description here

    You said you maximum value is 20000 and you want to scale the values from 0.01 to a maximum of 3, so we need to insert the max and scale our formula:

    // edit: also the values should be reversed, so subtract the log from 1:

    enter image description here

    This gives the following values f(x) for values of x:

    f(0) = 3
f(1) = 2.79
f(10) = 2.27
f(100) = 1.60
f(1000) = 0.91
f(10000) = 0.21
f(20000) = 0

    Would that suffice for your case?