Program for Linear and Polynomial Fit

#1 Posted: 12/8/2019 7:12:39 AM

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Simple examples on Linear and Polynomial fittings included as follows. This may be useful for beginners.
Examples 1 to 3 are for comparison only. Plot of given data is necessary to guess the distribution.

1. Ex. 1: Quadratic, posted by Martin
2. Ex.2: Ex.1 using SMath
3. Ex.3. Linear
4. Ex.4: A simple program to determine a suitable Linear / Polynomial fit to such data.

1.0 Linear & Poly Fits.sm (738.92 KiB) downloaded 298 time(s).

Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka

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Alvaro Diaz Falconi 12/9/2019 3:41:00 AM

#2 Posted: 12/8/2019 12:12:47 PM

Jean Giraud

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Simple examples on Linear and Polynomial fittings included as follows.

SS 6179 does not open at all and may have crashed my session.
If SS 7251 syntax is not compatible, it just turns red.
As it looks, incompatible syntax in program is dead like a stone.
Voltaire declared [not exactly] ...
When a stone is dead, she is dead for a long time !

Why not simply open the red syntax program ?
The black regions SS 7251 have been reported many times,
still pending Doctors to come back from fishing.
Thanks Collab NDTMA

#3 Posted: 12/8/2019 12:50:12 PM

NDTM Amarasekera

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SS 6179 does not open at all and may have crashed my session.

Sorry Jean. Forgot to attach the PDF. Thanks for your observations.

1.0 Linear & Poly Fits.pdf (683.54 KiB) downloaded 286 time(s).

Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka

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Alvaro Diaz Falconi 12/9/2019 3:41:00 AM

#4 Posted: 12/8/2019 4:49:45 PM

Jean Giraud

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Sorry Jean. Forgot to attach the PDF. Thanks for your observations.

Thanks for the *.PDF
Reconstructed c/w a lot more elegant export
Jean.

Polyfit Otherwise.sm (15.6 KiB) downloaded 265 time(s).

#5 Posted: 12/8/2019 5:58:03 PM

Jean Giraud

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Reconstructed c/w a lot more elegant export
J

... a bit more/different but encountered "puzzling or bug".
Doctored but mystic.

Polyfit Otherwise.sm (22.44 KiB) downloaded 250 time(s).

#6 Posted: 12/8/2019 11:21:29 PM

Jean Giraud

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... a bit more/different but encountered "puzzling or bug".
Doctored but mystic.

... suite/reconciliation from SS 5346 [works SS 6179]
Elegant and profitable, no bug/puzzling. Export polyfit.

Polynomial fit Methods [Regress Quick].sm (17.83 KiB) downloaded 239 time(s).

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frapuano 12/9/2019 2:41:00 PM, NDTM Amarasekera 12/9/2019 1:31:00 PM

#7 Posted: 12/9/2019 10:32:33 AM

Alvaro Diaz Falconi

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Hi. This is another approach.

PolyFit.sm (18.44 KiB) downloaded 282 time(s).
PolyFit.pdf (162.98 KiB) downloaded 263 time(s).

Best regards.
Alvaro

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NDTM Amarasekera 12/9/2019 1:31:00 PM, frapuano 12/9/2019 2:41:00 PM, sergio 12/9/2019 11:46:00 AM

#8 Posted: 12/9/2019 9:11:33 PM

Jean Giraud

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This is another approach.

Thanks Alvaro ... superb ! Jean.
That black regions is really a pen in the ass.

PolyFit [Alvaro Balistic].sm (22.1 KiB) downloaded 229 time(s).

#9 Posted: 12/9/2019 11:18:06 PM

Jean Giraud

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... added HadCRU [Hadley Climate Research Unit]
Global warming 1950 ... 2019 °C deviation wrt period 1950/1960
Fit on ChebyShev ± 1 and recovered on separate document.

PolyFit [Alvaro Balistic].sm (133.63 KiB) downloaded 177 time(s).

#10 Posted: 12/10/2019 2:15:11 AM

Jean Giraud

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Fit on ChebyShev Â± 1 and recovered on separate document.

... here is HadCRU fitted in the ChebyShev ± 1
then recovered in the original 1950 ... 2019 range.
It has nothing to do with the PolyFit(X,Y,n)
simply that high order polynomials are numerically
unstable at high range of the variate 'x'.
It has nothing to do with the CAS or floating arithmetic,
simply an Edu mathematical fact.

PolyFit [Alvaro Balistic].sm (310.61 KiB) downloaded 212 time(s).

#11 Posted: 12/10/2019 12:36:43 PM

Jean Giraud

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... here is HadCRU fitted in the ChebyShev Â± 1

... the clean/refreshed Edu version.

PolyFit [Alvaro Balistic].sm (230.72 KiB) downloaded 239 time(s).

#12 Posted: 12/10/2019 1:17:44 PM

NDTM Amarasekera

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Simple examples on Linear and Polynomial fittings included as follows.

Another method

Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka

#13 Posted: 12/10/2019 6:14:55 PM

Jean Giraud

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Simple examples on Linear and Polynomial fittings included as follows.

... tested/fails [Uncertainty]

Poly 00 NDTMA.sm (112.87 KiB) downloaded 263 time(s).

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NDTM Amarasekera 12/10/2019 11:30:00 PM

#14 Posted: 12/10/2019 7:00:23 PM

Alvaro Diaz Falconi

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Wrote
Simple examples on Linear and Polynomial fittings included as follows.

... tested/fails [Uncertainty]

Poly 00 NDTMA.sm (112.87 KiB) downloaded 263 time(s).

Hi. Here

the code (el(x,r)≡0)&(c≡1) for construct the Vandermonde matrix is for avoid 0^0, which returns the error.

Also, I avoid augment in the recursive loops because it's frustratingly slow.

Finlay, the code for PolyVal it's very inefficient, it's only for pedagogical purposes. Horner must be implemented for some other application. Notice that both are matlab/octave/scilab routines too.

In my opinion, the intention of Nugegodage to replicate ms excel results in SMath is very important, to promote SMaths as better alternative to excel doing math.

Best regards.

Alvaro.

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NDTM Amarasekera 12/10/2019 11:30:00 PM

#15 Posted: 12/10/2019 7:40:48 PM

CBG

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Same exercises by Cholesky's method.

Cholesky_Function_CBG_Jean_SS7251.sm (168.3 KiB) downloaded 263 time(s).

Cholesky_Function_CBG_Jean_SS6179.sm (166.42 KiB) downloaded 251 time(s).

Best Regards

Carlos

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NDTM Amarasekera 12/10/2019 11:30:00 PM

#16 Posted: 12/10/2019 11:21:00 PM

NDTM Amarasekera

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Thank you Jean, Alvaro and Carlos for your valuable responses.
BTW, I too get "uncertainty" error in Jean's example. Hope these issues will be resolved soon.
Once again Thank You all.

Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka

#17 Posted: 12/10/2019 11:58:52 PM

Alvaro Diaz Falconi

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Hi. R2 like ms excel added. And tome other alternatives for solve the matrix.

PolyFit.sm (152.04 KiB) downloaded 263 time(s).
PolyFit.pdf (693.6 KiB) downloaded 242 time(s).

Best regards.
Alvaro.

#18 Posted: 12/11/2019 1:42:29 AM

Jean Giraud

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Thank you Jean, Alvaro and Carlos for your valuable responses.
BTW, I too get "uncertainty" error in Jean's example. Hope these issues will be resolved soon.

Resolved in the attached from coding Cholesky the right way.
Alvaro code was OK too.
All in all, purely polynomials have so few applications
that they don't worth more than a short Classroom introduction.
On the other hand, the vector of functions is lot more productive.
And BTW, it is the form for the Conjugate Gradient model fitting.
Jean.

Poly 000 jmG Conjugate Gradient.sm (49.54 KiB) downloaded 254 time(s).
Poly 000 jmG.sm (146.39 KiB) downloaded 260 time(s).

#19 Posted: 12/11/2019 5:33:00 AM

Martin_B

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That's my solution
- to separate the functions from matrix building,
- to use vectorize for speed

#20 Posted: 12/11/2019 11:44:36 AM

Jean Giraud

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That's my solution
- to separate the functions from matrix building,
- to use vectorize for speed

Thanks for your effort/contribution.
Sorry, but too much of a monkey business.
Here are the two elegant Cholesky linear solver:
1. The modular local utility [Mathcad linfit style]
2. The general algo style as an Smath native.
Works same SS 6179 from original created SS 5346.
Hope this document will tranquilize visitors/users !

Jean.

Poly 000 jmG linfit MCD.sm (34.52 KiB) downloaded 267 time(s).

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