Matrix function (conditional)

#1 Pubblicato: 20/09/2019 15:34:48

0 apprezzamenti in 3 post.

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Hi,

I'm trying to write a function that I can use to calculate the surface area. The function is to be based on data from a matrix with n elements
I ran out of ideas. I guess the problem is in a loop.
I attach a file and an image.
I will be grateful for your help.

Integral.sm (7,23 KiB) scaricato 1145 volta(e).

#2 Pubblicato: 20/09/2019 17:22:30

Arie

94 apprezzamenti in 285 post.

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You can define piecewise function this way. Haven't figured out integration yet. Built in int() function doesn't seem to work.

Piecewise Function.sm (6,82 KiB) scaricato 1153 volta(e).

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#3 Pubblicato: 20/09/2019 19:56:29

Jean Giraud

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Wrote
I'm trying to write a function that I can use to calculate the surface area. The function is to be based on data from a matrix with n elements
I ran out of ideas. I guess the problem is in a loop.
I attach a file and an image.
I will be grateful for your help.

That was lavishly exemplified few hours ago.
Your drawing needs some project intention about,
i.e: what is what for what.

#4 Pubblicato: 20/09/2019 20:15:38

Jean Giraud

983 apprezzamenti in 6.866 post.

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Wrote
You can define piecewise function this way. Haven't figured out integration yet. Built in int() function doesn't seem to work.

Latest version is all white. Could discover the blank regions,
framed the regions, added background.

#5 Pubblicato: 20/09/2019 20:37:44

Jean Giraud

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Wrote
calculate the surface area

#6 Pubblicato: 20/09/2019 20:46:37

Вячеслав Мезенцев

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You can try something like this

Russia ☭ forever, Viacheslav N. Mezentsev

#7 Pubblicato: 20/09/2019 23:29:09

Jean Giraud

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Wrote
calculate the surface area.

Annotate the drawing [what is what in there], and what wort what.

MatrixUnknown.sm (9,19 KiB) scaricato 1151 volta(e).

#8 Pubblicato: 21/09/2019 04:37:10

XiuPer

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Thank you guys for your answers,

I will try to explain what I need.

Depending on the soil layers, I have a graph similar to the picture. At a later stage, I want to divide this chart into equal pieces (for example 0.25 m or 0.5m) to obtain "soil springs".
To simplify the example, I assumed that the elements of the K matrix are constant.

#9 Pubblicato: 21/09/2019 05:47:47

Martin Kraska

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uint.sm (9,71 KiB) scaricato 1154 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

2 utenti hanno apprezzato questo post

frapuano 21/09/2019 07:05:00, sergio 21/09/2019 08:26:00

#10 Pubblicato: 21/09/2019 11:23:03

Jean Giraud

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Wrote
Depending on the soil layers,
I have a graph similar to the picture. At a later stage,
I want to divide this chart into equal pieces
(for example 0.25 m or 0.5m) to obtain "soil springs".
To simplify the example, I assumed that the elements of the K matrix are constant.

OK ... from there, apply your skill to produce the Cartesian graph
of the piecewise soil. No problem to integrate.
Integration of discontinuous functions is deceiving.
Two models attached. The Romberg-Simpson is more accurate.
Example 2, the integration is known by inspection.
Isn't deceiving Simpson is not so good !
Cheers ... Jean

Integrate Discontinuous_2.sm (131,93 KiB) scaricato 1206 volta(e).

#11 Pubblicato: 21/09/2019 14:12:23

Jean Giraud

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Wrote
Integration of discontinuous functions is deceiving.

Total integration is often what the project needs.
Most Engineering projects require the evolution of the integration,
i.e: the cumulative integration.
The attached takes Martin data set, convex Hermite
that you can fillet [sub:=,] and populate at will [mesh 't'].
The latest step is the FD integration [Finite Differences].
The graph shows the evolution of the integration.
The end point of the cumulative = total integration
from any other best/applicable numerical integrator.
Except for trivial cases no numerical integration is exact.
FD integration is always very accurate [kind of yardstick].
Hermite polyline is very similar to CAD systems.
Please, come back on that "Soil project".
Cheers ... Jean

Integrate Discontinuous_3 [HermiteSpline, FD].sm (49,69 KiB) scaricato 1018 volta(e).

#12 Pubblicato: 21/09/2019 14:16:46

Jean Giraud

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Wrote
You can try something like this

True Viacheslav: ODE integrator(s) are very excellent.
Thanks for your input.

#13 Pubblicato: 21/09/2019 17:18:55

Jean Giraud

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... some didactic added.
OBSERVE: before the CAS numerical integration,
integration was FD [Finite Differences].
Read: F.B. Hildebrand.

Integrate Discontinuous_3 [HermiteSpline, FD].sm (114,63 KiB) scaricato 1030 volta(e).

#14 Pubblicato: 22/09/2019 06:57:11

XiuPer

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Thank you very much,
(btw the "thank" button on this page does not work)

The idea of using linterp is actually much better instead of a loop.
Below is the file with the result I needed.

Final springs.sm (20,64 KiB) scaricato 1178 volta(e).

#15 Pubblicato: 22/09/2019 09:43:08

Jean Giraud

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Wrote
Thank you very much,
(btw the "thank" button on this page does not work)

The idea of using linterp is actually much better instead of a loop.
Below is the file with the result I needed.

The "Tanks" button used to work years ago, not any more.
Good work ... two comments:
1. subscript is confusing with sub-sub index.
Very many projects are sub-sub indexed.
Reserve subscript as tutorial [exemplified].
2. variable name confusing with number is another killer.
you had 1:=max(X).
SS7030 was reputed good version, compatible SS 6179.

Final springs_1.sm (24,73 KiB) scaricato 1183 volta(e).

#16 Pubblicato: 22/09/2019 13:56:55

Jean Giraud

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... for convenience and publishing:
you can sub-space [at will] your calculated segments.
From there, you may obtain the cumulative integration
from the FD as offered before.

Final springs_1.sm (42,69 KiB) scaricato 1164 volta(e).

#17 Pubblicato: 22/09/2019 15:32:32

Jean Giraud

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Wrote
you can sub-space [at will]

... directly from the sampled data.
Subspace is a great utility.

Soil Simplifed from Sampled Data.sm (18,09 KiB) scaricato 1224 volta(e).

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