Integration of transformed data

[ptc-1793698]

There is a problem then using splines for integration.
The problem arises because initial data should be logarithmically transformed in terms of having a nice fit.
How to use such transformed data for obtaining an integration for initial data?

KL

[ptc-1368288]

On 5/9/2010 11:36:48 AM, KristjanLaes wrote:
>There is a problem then using
>splines for integration.
>The problem arises because
>initial data should be
>logarithmically transformed in
>terms of having a nice fit.
>How to use such transformed
>data for obtaining an
>integration for initial data?
>
>KL
______________________________

If the lower limit of integration is 0, you strip the data set from negative values [which are meaningless anyway] and set the first X value to 0, then fit then integrate. There is certainly an homographic function, more visible. I will attempt. In the mean time, here is your project ... set the upper limit of integration as you wish. Use Logspace for the variable, it does not affect the function, just a convenience for plotting and eventually exporting a data set of the fit.

jmG

[ptc-1368288]

From educated knowledge, this is the fit "homographic".

jmG

[RichardJ]

I actually generated that yesterday, but then Mathcad crashed and I lost it. I walked off in disgust to do something else, figuring I would do it again today. It looks like you saved me the work 🙂

Richard

[ptc-1368288]

On 5/10/2010 9:33:36 AM, KristjanLaes wrote:
>
____________________________

Your conceptual premise is erroneous. If you integrate starting from 0, the data below this value are invalid. Consider the data I have cleaned. From there your spline idea does not apply: spline does NOT fit, spline "joins". That there would be another model: possible but that will be hard to prove because you just have data . That the numerical integration might not be exact, maybe. You could ask Mathematica but I doubt any significant difference. You are forging something that does not need and that you CAN'T reverse engineer.

Done, same as before with higher proof.
Did you miss the homographic model previously posted ?

jmG

[ptc-1368288]

"should be around +1 " ... WRONG
"should be around -1 " ... WRONG

Here is the verdict, both Mathematica and Mathcad do likely under evaluate by some unknown value. Thiele is much closer, but that does not prove your spline is correct. If I would be asked to declare, then it would be Thiele. Not all 15 decimals were entered in Mathematica.



jmG

[ptc-1793698]

jmG,

I was giving crude magnitude of the values. I expected these values to be rather close to +/-1 and not for example +/-10.

Why you think that I cant use values of i less than zero to have a meaningful answer then integrating?
And I saw your worksheets too.
It seems that it is easier to use this inbuilt spline to have "joined" data for integration. Of course, there appear some too "wrongly" "joined" regions too.
It is easier for me to use this spline. And this transformation of the data makes the result of the "joining" more visible too.
KL

[ptc-1368288]

On 5/11/2010 7:00:51 AM, KristjanLaes wrote:
>jmG,
>
>I was giving crude magnitude
>of the values. I expected
>these values to be rather
>close to +/-1 and not for
>example +/-10.
>
>Why you think that I cant use
>values of i less than zero to
>have a meaningful answer then
>integrating?

==> You mentioned on the work sheet to integrate starting at zero, then the homographic function for that segment. If you now want to integrate from the min(X), you then have to fit that segment separately and analyse a bit more that segment to discover that some points are redundant [fitting can lave with that] but at least one or two more points are critically missing to fit a model. Then integrate over the discontinuous global fit

>And I saw your worksheets too.
>It seems that it is easier to
>use this inbuilt spline to
>have "joined" data for
>integration. Of course, there
>appear some too "wrongly"
>"joined" regions too.
>It is easier for me to use
>this spline. And this
>transformation of the data
>makes the result of the
>"joining" more visible too.
>KL

==> Your data transformation is more visible but the spline is doing nothing good as you don't have a resulting function, just an interpolation that you can't export and re-use easily. What you are doing is reverse engineer a wrongdoing.

Analyse the lower segment.
It looks simple but needs a bit of research for an adequate model.

jmG

[TheodoreM.Bones]

There is too much complexity here. A few simple
model fits will do anything.