OpenEuphoria

1. Calculating with imprecise values

• Posted by Juergen Luethje <j.lue at gmx.de> Dec 13, 2005
• 679 views

Do we already have an Eu library for calculating with imprecise values?
I couldn't find such a library in the archives. I mean something along 
the following lines:
Say we have measured two distances, 3.4 cm and 4.7 cm, and we want to
add them. Since those values are normally not 100% precise, the result
is not necessarily (3.4+4.7) cm = 8.1 cm. If the values have been
rounded, and "3.4" means something between 3.35 and 3.44, and "4.7"
means something between 4.65 and 4.74, then the result can be any value
between 8.00 cm and 8.18 cm.

If we don't already have such a library, is there any interest?

Regards,
   Juergen

3. Re: Calculating with imprecise values

• Posted by Matt Lewis <matthewwalkerlewis at gmail.com> Dec 13, 2005
• 635 views

Juergen Luethje wrote:
> 
> Do we already have an Eu library for calculating with imprecise values?
> I couldn't find such a library in the archives. I mean something along 
> the following lines:
> Say we have measured two distances, 3.4 cm and 4.7 cm, and we want to
> add them. Since those values are normally not 100% precise, the result
> is not necessarily (3.4+4.7) cm = 8.1 cm. If the values have been
> rounded, and "3.4" means something between 3.35 and 3.44, and "4.7"
> means something between 4.65 and 4.74, then the result can be any value
> between 8.00 cm and 8.18 cm.
> 
> If we don't already have such a library, is there any interest?
> 

It sounds like fuzzy numbers and fuzzy arithmetic.  I've thought about
writing something to do this, but haven't yet...

Matt Lewis

5. Re: Calculating with imprecise values

• Posted by Juergen Luethje <j.lue at gmx.de> Dec 13, 2005
• 603 views
• Last edited Dec 14, 2005

jxliv7 wrote:

> Juergen, what i think you're talking about is significant digits and
> significant
> decimals. there's some excellent discussions of them at
>    http://mathforum.org/dr.math/ 
> and in particular
>    http://mathforum.org/library/drmath/view/56375.html
>    http://mathforum.org/library/drmath/view/59014.html

I think what I mean is something mentioned on this ^^^^ page.

> there are no Euphoria libraries that i know of that deal with this, since the
> results of any multiplication, division, addition, substraction, sqare root,
> etc., can vary considerably dependent on what the user wants. figuring taxes
> is different (between Europe and the US, for example), 

Yes, of course.

> rounding is different
> (which digit to base the rounding on, round up, round down, truncate),
> scientific
> calculations are different, etc.
> 
> what i've done with my apps is basically have the user make the choice
> beforehand
> of the precision of any calculation.
> 
> hope that helps,

Thanks.
I think what I mean has got to do with what is called "error propagation".

For example, if I measure a length with a ruler that shows millimeters,
the measurement will be accurate to one millimeter. So if I measure the
value 12 mm, the "real" value is somewhere between 11.5 and 12.5 mm.
Then I measure another distance, and I get 4 mm, that means the "real" value
is somewhere between 3.5 and 4.5 mm.
Now for some reason I have ro add both values. So I am thinking of a
function like the following:

function add_with_error (atom a, atom delta_a, atom b, atom delta_b)
   atom min, max

   min = (a-delta_a) + (b-delta_b)
   max = (a+delta_a) + (b+delta_b)
   return {min, max}
end function

Given the example above, I would call the function like this:

? add_with_error(12,0.5,4,0.5)

This prints {15,17}. So I have got some *additional* information.
Normally I would get the result 12+4 => 16,
and I would have the feeling "Well, 16 might not be the exact result,
because the ruler is not 100% precise".
Using a function such as add_with_error(), I know now that the actual
result is between 15 and 17.

Does that make sense? 

Regards,
   Juergen

-- 
Have you read a good program lately?

7. Re: Calculating with imprecise values

• Posted by cklester <cklester at yahoo.com> Dec 13, 2005
• 632 views
• Last edited Dec 14, 2005

Juergen Luethje wrote:
> Matt Lewis wrote:
> > It sounds like fuzzy numbers and fuzzy arithmetic.  I've thought about
> > writing something to do this, but haven't yet...
> I'm not sure whether I understand the meaning of the expressions "fuzzy
> numbers" and "fuzzy arithmetic" correctly.

It just means they tickle when you use them.

-=ck
"Programming in a state of Euphoria."
http://www.cklester.com/euphoria/

9. Re: Calculating with imprecise values

• Posted by Elliott Sales de Andrade <quantum_analyst at hotmail.com> Dec 14, 2005
• 619 views

Juergen Luethje wrote:
> 
<snip>
> What I mean ATM is something that I think has got to do with "error
> propagation". Please see my reply to "jxliv7" for details.
> 

Well, there are no Euphoria programs that I know of, but in University we use
   this form of error propagation:
   http://www.upscale.utoronto.ca/PVB/Harrison/ErrorAnalysis/index.html

> Thanks,
>    Juergen
> 
> -- 
> Have you read a good program lately?


~[ WingZone ]~
http://wingzone.tripod.com/

11. Re: Calculating with imprecise values

• Posted by Al Getz <Xaxo at aol.com> Dec 14, 2005
• 657 views

Hello there,


I've used so called 'sensitivity' analysis in the past to measure changes
in functions with respect to a given variable and this helped understand
things better sometimes especially when human error is involved.

For example....

for the equation with some function F:
  y=F(a,b,c)

the sensitivity with change of parameter 'a' might be 100 times as great
as with parameter 'b', and perhaps the sensitivity with respect to 'c'
might be 1000 times lower than with 'a', meaning y hardly changes
with 'b' or 'c' but changes quite a bit with parameter 'a'.  Thus,
the error in measurement in 'b' or 'c' doesnt matter as much as with
the error in 'a'.  This would mean great care should be used in measuring
'a' while with 'b' or 'c' you might get away with estimating from other
parameters or whatever.


Take care,
Al

And, good luck with your Euphoria programming!

My bumper sticker: "I brake for LED's"

13. Re: Calculating with imprecise values

• Posted by Juergen Luethje <j.lue at gmx.de> Dec 14, 2005
• 619 views

Al Getz wrote:

> I've used so called 'sensitivity' analysis in the past to measure changes
> in functions with respect to a given variable and this helped understand
> things better sometimes especially when human error is involved.
> 
> For example....
> 
> for the equation with some function F:
>   y=F(a,b,c)
> 
> the sensitivity with change of parameter 'a' might be 100 times as great
> as with parameter 'b', and perhaps the sensitivity with respect to 'c'
> might be 1000 times lower than with 'a', meaning y hardly changes
> with 'b' or 'c' but changes quite a bit with parameter 'a'.  Thus,
> the error in measurement in 'b' or 'c' doesnt matter as much as with
> the error in 'a'.  This would mean great care should be used in measuring
> 'a' while with 'b' or 'c' you might get away with estimating from other
> parameters or whatever.

Interesting!
Do you have a link at hand that explains sensitivity analysis more in
detail? 

Regards,
   Juergen

15. Re: Calculating with imprecise values

• Posted by Al Getz <Xaxo at aol.com> Dec 16, 2005
• 614 views

Juergen Luethje wrote:
> 
> Al Getz wrote:
> 
> > I've used so called 'sensitivity' analysis in the past to measure changes
> > in functions with respect to a given variable and this helped understand
> > things better sometimes especially when human error is involved.
> > 
> > For example....
> > 
> > for the equation with some function F:
> >   y=F(a,b,c)
> > 
> > the sensitivity with change of parameter 'a' might be 100 times as great
> > as with parameter 'b', and perhaps the sensitivity with respect to 'c'
> > might be 1000 times lower than with 'a', meaning y hardly changes
> > with 'b' or 'c' but changes quite a bit with parameter 'a'.  Thus,
> > the error in measurement in 'b' or 'c' doesnt matter as much as with
> > the error in 'a'.  This would mean great care should be used in measuring
> > 'a' while with 'b' or 'c' you might get away with estimating from other
> > parameters or whatever.
> 
> Interesting!
> Do you have a link at hand that explains sensitivity analysis more in
> detail? 
> 
> Regards,
>    Juergen

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, 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.

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.


Take care,
Al

And, good luck with your Euphoria programming!

My bumper sticker: "I brake for LED's"

17. Re: Calculating with imprecise values

• Posted by Al Getz <Xaxo at aol.com> Dec 18, 2005
• 606 views

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"