Re: Calculating with imprecise values
Juergen Luethje wrote:
>
> Al Getz wrote:
>
> [Sensitivity Analysis]
>
> > Hi Juergen,
> >
> > Sorry i dont have a link in mind, but a quick google turned up several
> > sites including a 'forum' for Sens A. I didnt want it to sound too
> > complicated though, because basically it's not,
>
> Much appreciated. 
>
> > so here's a quick example to help show how simple it can really be....
> >
> > First a pure approach then a numerical approach that can be used in
> > an Eu program...
> >
> > I think a good example would be finding the volume of a rather long
> > box with rectangular cross section we'll say the length of is 'a',
> > and the two sides are 'b' and 'c'. This would look like a rectangular
> > pipe. We want to find the volume, but also the change in volume so
> > we can understand what happens when either of the measurements for
> > a,b, and c are either off to begin with (due to measurement inaccuracies)
> > or just to see what happens when a given dimension changes.
> >
> > For this example we'll say
> > a=100
> > b=10
> > c=10
> > in inches.
> >
> > The volume would be v=a*b*c which we'll rewrite
> > y=a*b*c
> >
> > First we take first partials:
> > dy/da=b*c
> > dy/db=a*c
> > dy/dc=a*b
> >
> > and now we can call the sensitivities:
> > Sya=dy/da=b*c
> > Syb=dy/db=a*c
> > Syc=dy/dc=a*b
> >
> > Where 'Sya' is read: "The sensitivity of y with respect to a".
> >
> > Now we look at the actual numerical value of these to see what
> > we can find out:
> > Sya=b*c=100
> > Syb=a*c=1000
> > Syc=a*b=1000
> >
> > From this we can quickly see that Sya is ten times less than Syb or
> > Syc, so the measurement in 'a' isnt as important as the measurement
> > for 'b' or 'c'.
> >
> > Going back to the original equation with the chosen values for this
> > example, we can see that a change of say 1/16 inch causes a much
> > bigger change in volume when the change occurs in either b or c, while
> > not as big of a change in volume when the change occurs in a.
>
> I see. I can imagine that this kind of approach to a problem often can
> be very useful.
>
> > Writing this out as a 'formula' we get an approximate numerical
> > method:
> > Sya=(f(a+inc,b,c)-f(a,b,c))/inc
> > Syb=(f(a,b+inc,c)-f(a,b,c))/inc
> > Syc=(f(a,b,c+inc)-f(a,b,c))/inc
> > where
> > f(a,b,c)=a*b*c (the original volume equation), and
> > 'inc' is a small number like 0.001.
> >
> > The above can be used in a program quite easily, but usually a slightly
> > more accurate method is used in programs (the 'Central Means' formula):
> > Sya=(f(a+inc,b,c)-f(a-inc,b,c))/(inc+inc)
> > Syb=(f(a,b+inc,c)-f(a,b-inc,c))/(inc+inc)
> > Syc=(f(a,b,c+inc)-f(a,b,c-inc))/(inc+inc)
> > All that's involved here is calling the function f twice for each
> > sensitivity: once using a positive inc and once a negative inc,
> > then subtracting the results and dividing by twice the inc.
>
> Al, thanks a lot for the trouble writing down this comprehensive and
> good understandable explanation!
>
> Regards,
> Juergen
>
> --
> What do you want to re-install today?
Hello again Juergen,
Oh you're welcome, and i hope you find some good uses for this.
Take care,
Al
And, good luck with your Euphoria programming!
My bumper sticker: "I brake for LED's"
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