Re: How to find a formula from a list of numbers

Article View: aus.mathematics

Article #36

#36

From: Adam Nielsen
Date: Sun, 04 Oct 2009 22:25

65 lines
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>>>  A  | B
>>> -----+-----
>>> 0   | 0
>>> 32  | 3.6
>>> 64  | 7.6
>>> 128 | 15.6
>>> 255 | 31.5
>>>
>>> And I need a formula such that I can put in any number (between 0 and 255
>>> inclusive) for A, and obtain the result B.  Unfortunately because this isn't
>>> quite straightforward division I'm a bit stuck.
>>>
> Inspecting the results, the differences in the successive B values for 
> the successive doublings of the A values are: 4, 8, 16 (actually 15.9 
> for slightly less than a doubling).  So, a simplified formula is:
>     B = A/8 - 0.4
> 
> This would produce a negative B value for A < 4, so a correct formula is:
>     B =  {A/8 - 0.4 if A >=4, 0 otherwise}
> 
> There may need to be some additional tweaking for small values of A, 
> which we don't yet have the measurements for.

Thanks Barb, that's excellent!  I've collected some extra values and it looks
like you're spot on:

  A  |  B
-----+-----
 0   | 0
 3   | 0
 4   | 0.1
 6   | 0.3
 8   | 0.6
 16  | 1.6
 32  | 3.6
 64  | 7.6
 128 | 15.6
 192 | 23.6
 255 | 31.5

The simple divide and subtract will also keep the code nice and fast.  However
I'm not so sure one of the other rails will be that easy:

  A  |  B'
-----+-----
 0   | 0
 1   | 0.1
 4   | 0.4
 8   | 0.9
 16  | 1.9
 32  | 3.8
 48  | 5.7
 64  | 7.6
 96  | 11.4
 128 | 15.2
 160 | 19.1
 192 | 22.9
 208 | 24.8
 224 | 26.7
 255 | 30.4

Many thanks for your help!

Cheers,
Adam.

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