Matrix function (conditional)

#1 Posted: 9/20/2019 3:34:48 PM

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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 KiB) downloaded 35 time(s).

#2 Posted: 9/20/2019 5:22:30 PM

Arie

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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 KiB) downloaded 38 time(s).

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#3 Posted: 9/20/2019 7:56:29 PM

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 Posted: 9/20/2019 8:15:38 PM

Jean Giraud

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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 Posted: 9/20/2019 8:37:44 PM

Jean Giraud

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Wrote
calculate the surface area

#6 Posted: 9/20/2019 8:46:37 PM

Вячеслав Мезенцев

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You can try something like this

Russia ☭ forever, Viacheslav N. Mezentsev

#7 Posted: 9/20/2019 11:29:09 PM

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 KiB) downloaded 31 time(s).

#8 Posted: 9/21/2019 4:37:10 AM

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 Posted: 9/21/2019 5:47:47 AM

Martin Kraska

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uint.sm (9 KiB) downloaded 41 time(s).

Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

2 users liked this post

frapuano 9/21/2019 7:05:00 AM, sergio 9/21/2019 8:26:00 AM

#10 Posted: 9/21/2019 11:23:03 AM

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 KiB) downloaded 33 time(s).

#11 Posted: 9/21/2019 2:12:23 PM

Jean Giraud

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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 KiB) downloaded 30 time(s).

#12 Posted: 9/21/2019 2:16:46 PM

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 Posted: 9/21/2019 5:18:55 PM

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 KiB) downloaded 30 time(s).

#14 Posted: 9/22/2019 6:57:11 AM

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 KiB) downloaded 31 time(s).

#15 Posted: 9/22/2019 9:43:08 AM

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 KiB) downloaded 43 time(s).

#16 Posted: 9/22/2019 1:56:55 PM

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 KiB) downloaded 29 time(s).

#17 Posted: 9/22/2019 3:32:32 PM

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 KiB) downloaded 49 time(s).

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Matrix function (conditional) - Messages