Program for Linear and Polynomial Fit

#1 Publicado: 8/12/2019 7:12:39

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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) descargado 1358 vez(es).

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

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Alvaro 9/12/2019 3:41:00

#2 Publicado: 8/12/2019 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 Publicado: 8/12/2019 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) descargado 976 vez(es).

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

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Alvaro 9/12/2019 3:41:00

#4 Publicado: 8/12/2019 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) descargado 1289 vez(es).

#5 Publicado: 8/12/2019 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) descargado 1228 vez(es).

#6 Publicado: 8/12/2019 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) descargado 1145 vez(es).

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frapuano 9/12/2019 14:41:00, NDTM Amarasekera 9/12/2019 13:31:00

#7 Publicado: 9/12/2019 10:32:33

Alvaro

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Hi. This is another approach.

PolyFit.sm (18,44 KiB) descargado 1303 vez(es).
PolyFit.pdf (162,98 KiB) descargado 861 vez(es).

Best regards.
Alvaro

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NDTM Amarasekera 9/12/2019 13:31:00, frapuano 9/12/2019 14:41:00, sergio 9/12/2019 11:46:00

#8 Publicado: 9/12/2019 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) descargado 1169 vez(es).

#9 Publicado: 9/12/2019 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) descargado 1069 vez(es).

#10 Publicado: 10/12/2019 2:15:11

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) descargado 1074 vez(es).

#11 Publicado: 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) descargado 1115 vez(es).

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

NDTM Amarasekera

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Wrote
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 Publicado: 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) descargado 1309 vez(es).

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

#14 Publicado: 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) descargado 1309 vez(es).

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 Publicado: 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) descargado 1339 vez(es).

Cholesky_Function_CBG_Jean_SS6179.sm (166,42 KiB) descargado 1305 vez(es).

Best Regards

Carlos

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

#16 Publicado: 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 Publicado: 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) descargado 1302 vez(es).
PolyFit.pdf (693,6 KiB) descargado 831 vez(es).

Best regards.
Alvaro.

#18 Publicado: 11/12/2019 1:42:29

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) descargado 1271 vez(es).
Poly 000 jmG.sm (146,39 KiB) descargado 1276 vez(es).

#19 Publicado: 11/12/2019 5:33:00

Martin_B

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

#20 Publicado: 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) descargado 1319 vez(es).

Foro SMath

Program for Linear and Polynomial Fit - Mensajes