AlgLib 3.1x - SMath

#21 Pubblicato: 17/07/2018 19:49:21

1.558 apprezzamenti in 1.868 post.

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Updated. al_nleqsolve() refactored. Try now.

File non trovato. File non trovato.

You can also specify only names of the systems (f and j).

File non trovato. File non trovato.

Russia ☭ forever, Viacheslav N. Mezentsev

4 utenti hanno apprezzato questo post

frapuano 18/07/2018 10:53:00, Fridel Selitsky 18/07/2018 02:35:00, Radovan Omorjan 18/07/2018 05:41:00, Igor Skarine 18/07/2018 10:17:00

#22 Pubblicato: 18/07/2018 02:35:44

Fridel Selitsky

520 apprezzamenti in 451 post.

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One example of V. Mezentsev (Uni)
Primer Uni.sm (13,49 KiB) scaricato 1668 volta(e).

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Radovan Omorjan 18/07/2018 05:34:00, frapuano 18/07/2018 10:53:00

#23 Pubblicato: 18/07/2018 05:40:48

Radovan Omorjan

325 apprezzamenti e 1 disapprezzamenti in 2.052 post.

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Wrote
One example of V. Mezentsev (Uni)
Primer Uni.sm (13,49 KiB) scaricato 1668 volta(e).

Fortunately, I was wrong. We could use it with different number of equations and unknowns.
I just use the Ber7 example and change it with n as a global variable. No need for zeros as non-existing functions.

Primer%20Uni-mod.sm (13,3 KiB) scaricato 1728 volta(e).

When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"

#24 Pubblicato: 18/07/2018 10:15:46

Igor Skarine

14 apprezzamenti in 97 post.

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Thanks a lot uni!
The issue listed in my post #18 has been resolved.
But for some reason simple Newton-Raphson with variable step usually
works better than al_nleqsolve.

#25 Pubblicato: 18/07/2018 15:19:47

Jean Giraud

983 apprezzamenti in 6.866 post.

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Wrote
But for some reason simple Newton-Raphson with variable step usually
works better than al_nleqsolve.

Can you demonstrate for this application ?

Solve al_nleqsolve-Electron.sm (18,41 KiB) scaricato 1635 volta(e).

#26 Pubblicato: 21/07/2018 12:45:03

Fridel Selitsky

520 apprezzamenti in 451 post.

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We find several roots at once

Primer Uni3.sm (15,93 KiB) scaricato 1631 volta(e).
Primer Jean1.sm (14,78 KiB) scaricato 1583 volta(e).

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frapuano 21/07/2018 13:44:00

#27 Pubblicato: 22/07/2018 03:50:27

Fridel Selitsky

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3d.sm (29,62 KiB) scaricato 1608 volta(e).

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NDTM Amarasekera 22/07/2018 05:00:00, frapuano 22/07/2018 05:30:00

#28 Pubblicato: 22/07/2018 23:29:32

Jean Giraud

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Thanks Ber7 for the 3D, nice.

Jean

#29 Pubblicato: 24/07/2018 13:03:26

Fridel Selitsky

520 apprezzamenti in 451 post.

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Solution of an overdetermined system of equations. The problem is taken from here
https://en.smath.info/forum/yaf_postst12745_How-to-solve-it.aspx

Overdetermined.sm (15,26 KiB) scaricato 1604 volta(e).

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Andrey Ivashov 26/07/2018 18:06:00

#30 Pubblicato: 30/07/2018 13:09:38

Fridel Selitsky

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The process of finding the roots

Primer Anim.sm (30,29 KiB) scaricato 1590 volta(e).

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frapuano 30/07/2018 14:08:00

#31 Pubblicato: 22/08/2018 04:32:16

Fridel Selitsky

520 apprezzamenti in 451 post.

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The intersection points of two curves

Primer1b.sm (33,88 KiB) scaricato 1635 volta(e).
Primer1b.pdf (212,69 KiB) scaricato 933 volta(e).

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sergio 22/08/2018 05:52:00, frapuano 22/08/2018 11:24:00

#32 Pubblicato: 22/08/2018 11:39:31

Fridel Selitsky

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Fixed. Now you can find all the intersection points.

Primer2.sm (36,58 KiB) scaricato 1662 volta(e).
Primer2.pdf (215,28 KiB) scaricato 954 volta(e).

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Davide Carpi 22/08/2018 11:41:00, sergio 22/08/2018 13:01:00

#33 Pubblicato: 23/08/2018 05:11:57

Fridel Selitsky

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Primer3.sm (20,12 KiB) scaricato 1698 volta(e).

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frapuano 23/08/2018 09:07:00

#34 Pubblicato: 23/08/2018 10:57:07

Jean Giraud

983 apprezzamenti in 6.866 post.

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... thanks Ber7

Contour SOLVE AstroidHyperbola.sm (20,85 KiB) scaricato 1689 volta(e).

#35 Pubblicato: 25/08/2018 06:22:47

Fridel Selitsky

520 apprezzamenti in 451 post.

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Primer6.sm (18,31 KiB) scaricato 1616 volta(e).

#36 Pubblicato: 06/10/2018 14:56:58

Fridel Selitsky

520 apprezzamenti in 451 post.

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Simple solutions to two problems
1.The construction of a sphere with respect to four given points
2.The construction of a circle with respect to three given points
To calculate the coordinates of the center and radius using the solver AlgLib
In the first problem, a system of four sphere equations for four given points is solved.
In the second - a system of three equations of a circle and the equation of a plane for three given points.

SphereAlglib.sm (64,36 KiB) scaricato 1618 volta(e).

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NDTM Amarasekera 06/10/2018 22:52:00

#37 Pubblicato: 08/10/2018 03:23:09

Alvaro

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Hi. The same, but without plugins.

SphereSMath.sm (75,21 KiB) scaricato 1587 volta(e).

Best regards.
Alvaro.

PD: Do you know the angles for your rotation matrix gamma? I get this, but can't put the matrix elements in the correct order nor sign:

Actually, as I know, the minus in the last atan is a mistake, but at least give the same absolute values.

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Fridel Selitsky 08/10/2018 03:35:00, NDTM Amarasekera 08/10/2018 04:19:00

#38 Pubblicato: 09/10/2018 11:42:42

Fridel Selitsky

520 apprezzamenti in 451 post.

Gruppo: User

Wrote
Hi. The same, but without plugins.

PD: Do you know the angles for your rotation matrix gamma? I get this, but can't put the matrix elements in the correct order nor sign:

Actually, as I know, the minus in the last atan is a mistake, but at least give the same absolute values.

Hi, Alvaro.
Unfortunately, I have never done reverse transformations (gamma-omega).
Your error may be caused by the use of the left coordinate system in Smath- graphs.
I selected the angles for the axial matrices empirically in order to get a good perspective ,using the gamma matrix.perspective.

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Alvaro 09/10/2018 21:14:00

#39 Pubblicato: 10/10/2018 00:40:38

Jean Giraud

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Wrote
Unfortunately, I have never done reverse transformations (gamma-omega).

Mathcad solves the Euler angles from a given γ [gamma matrix].
Smath does not immediately, it complains: Try to use a more specific algorithm.
There are 24 [4!] possible ways to define a 3D system [Mathematica].
The most common is Euler though Mathcad Mathcad ≠ Mathematica.
For common use to define some pleasant views, especially in Smath:
1. Euler [ 3 trig angles]
2. Parametric [X,Y,Z,t] very easy to manage.
3. Quaternion only two coefficients that Quaternion solves for the 3D γ matrix

Rotate Horn.sm (15,07 KiB) scaricato 1623 volta(e).
Solve Euler Fails.sm (22,54 KiB) scaricato 1668 volta(e).
Rotate Breather [Euler].sm (37,2 KiB) scaricato 1432 volta(e).
Rotate_0 Euler, xyz(t), Quaternion.sm (275,27 KiB) scaricato 1660 volta(e).

#40 Pubblicato: 12/12/2018 12:57:19

Вячеслав Мезенцев

1.558 apprezzamenti in 1.868 post.

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Updated.

Changes for al_rkckadapt():
- zero point issue fixed;
- added support for the simple D(t,x) definition.

Russia ☭ forever, Viacheslav N. Mezentsev

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frapuano 12/12/2018 14:31:00, sergio 12/12/2018 13:54:00

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AlgLib 3.1x - AlgLib Plugin (based on ALGLIB 3.1x) - Messaggi