Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a reference number, Rx, and a series of numbers, Sx[], to compare to it. Let's call the output Ox[]. I am using a simple square root to accelerate the apparent difference between the reference number and each number in the series.

Ox[n] = Abs(Sx[n] - Rx) ^ 0.5

Besides being able to control how aggressively the curve varies from linear (by changing the root), I want to be able to define what Ox[n] should be when Sx[n] is a certain % of Rx:

e.g. when Sx[n] = 0.5 Rx, then Ox[n] = 0.1 Rx

To be clear, I want to be able to keep the root index in order to control the shape of the curve, but also be able to influence the values of the output so that at a given input % of Rx, I have a pre-desired output. This would be a question of scaling.

share|improve this question

1 Answer 1

I figured it out:

$$S=\frac{1-Ref_{tgtPer}}{\sqrt[r]{(1-Ref_{floorPer})Ref_{val}}}$$

where

$S =$ Scale

$r =$ the index

$Ref_{tgtPer}=$ The target % of the Reference (Rx)

$Ref_{floorPer}=$ The desired value of the output at $Ref_{tgtPer}$ of Rx

$Ref_{val}=$ The reference value (Rx)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.