Program for Linear and Polynomial Fit

#1 Pubblicato: 08/12/2019 07:12:39

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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) scaricato 1361 volta(e).

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

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Alvaro 09/12/2019 03:41:00

#2 Pubblicato: 08/12/2019 12:12:47

Jean Giraud

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Wrote
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 Pubblicato: 08/12/2019 12:50:12

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) scaricato 979 volta(e).

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

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Alvaro 09/12/2019 03:41:00

#4 Pubblicato: 08/12/2019 16:49:45

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) scaricato 1291 volta(e).

#5 Pubblicato: 08/12/2019 17:58:03

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) scaricato 1229 volta(e).

#6 Pubblicato: 08/12/2019 23:21:29

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) scaricato 1148 volta(e).

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frapuano 09/12/2019 14:41:00, NDTM Amarasekera 09/12/2019 13:31:00

#7 Pubblicato: 09/12/2019 10:32:33

Alvaro

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Hi. This is another approach.

PolyFit.sm (18,44 KiB) scaricato 1306 volta(e).
PolyFit.pdf (162,98 KiB) scaricato 867 volta(e).

Best regards.
Alvaro

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NDTM Amarasekera 09/12/2019 13:31:00, frapuano 09/12/2019 14:41:00, sergio 09/12/2019 11:46:00

#8 Pubblicato: 09/12/2019 21:11:33

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) scaricato 1171 volta(e).

#9 Pubblicato: 09/12/2019 23:18:06

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) scaricato 1070 volta(e).

#10 Pubblicato: 10/12/2019 02:15:11

Jean Giraud

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Wrote
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) scaricato 1077 volta(e).

#11 Pubblicato: 10/12/2019 12:36:43

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) scaricato 1117 volta(e).

#12 Pubblicato: 10/12/2019 13:17:44

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 Pubblicato: 10/12/2019 18:14:55

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) scaricato 1314 volta(e).

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NDTM Amarasekera 10/12/2019 23:30:00

#14 Pubblicato: 10/12/2019 19:00:23

Alvaro

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Wrote

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

... tested/fails [Uncertainty]

Poly 00 NDTMA.sm (112,87 KiB) scaricato 1314 volta(e).

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 10/12/2019 23:30:00

#15 Pubblicato: 10/12/2019 19:40:48

CBG

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Same exercises by Cholesky's method.

Cholesky_Function_CBG_Jean_SS7251.sm (168,3 KiB) scaricato 1340 volta(e).

Cholesky_Function_CBG_Jean_SS6179.sm (166,42 KiB) scaricato 1308 volta(e).

Best Regards

Carlos

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NDTM Amarasekera 10/12/2019 23:30:00

#16 Pubblicato: 10/12/2019 23:21:00

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 Pubblicato: 10/12/2019 23:58:52

Alvaro

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

PolyFit.sm (152,04 KiB) scaricato 1304 volta(e).
PolyFit.pdf (693,6 KiB) scaricato 837 volta(e).

Best regards.
Alvaro.

#18 Pubblicato: 11/12/2019 01:42:29

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) scaricato 1274 volta(e).
Poly 000 jmG.sm (146,39 KiB) scaricato 1278 volta(e).

#19 Pubblicato: 11/12/2019 05:33:00

Martin_B

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

#20 Pubblicato: 11/12/2019 11:44:36

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) scaricato 1321 volta(e).

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