AlgLib 3.1x - SMath

#21 Posted: 2018/7/17 19:49:21

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Updated. al_nleqsolve() refactored. Try now.

File not found. File not found.

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

File not found. File not found.

Russia ☭ forever, Viacheslav N. Mezentsev

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frapuano 2018/7/18 10:53:00, Fridel Selitsky 2018/7/18 02:35:00, Radovan Omorjan 2018/7/18 05:41:00, Igor Skarine 2018/7/18 10:17:00

#22 Posted: 2018/7/18 02:35:44

Fridel Selitsky

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One example of V. Mezentsev (Uni)
Primer Uni.sm (13.49 KiB) downloaded 969 time(s).

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Radovan Omorjan 2018/7/18 05:34:00, frapuano 2018/7/18 10:53:00

#23 Posted: 2018/7/18 05:40:48

Radovan Omorjan

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Wrote
One example of V. Mezentsev (Uni)
Primer Uni.sm (13.49 KiB) downloaded 969 time(s).

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) downloaded 952 time(s).

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

#24 Posted: 2018/7/18 10:15:46

Igor Skarine

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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 Posted: 2018/7/18 15:19:47

Jean Giraud

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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) downloaded 940 time(s).

#26 Posted: 2018/7/21 12:45:03

Fridel Selitsky

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We find several roots at once

Primer Uni3.sm (15.93 KiB) downloaded 923 time(s).
Primer Jean1.sm (14.78 KiB) downloaded 891 time(s).

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frapuano 2018/7/21 13:44:00

#27 Posted: 2018/7/22 03:50:27

Fridel Selitsky

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3d.sm (29.62 KiB) downloaded 904 time(s).

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NDTM Amarasekera 2018/7/22 05:00:00, frapuano 2018/7/22 05:30:00

#28 Posted: 2018/7/22 23:29:32

Jean Giraud

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Thanks Ber7 for the 3D, nice.

Jean

#29 Posted: 2018/7/24 13:03:26

Fridel Selitsky

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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) downloaded 896 time(s).

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Andrey Ivashov 2018/7/26 18:06:00

#30 Posted: 2018/7/30 13:09:38

Fridel Selitsky

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The process of finding the roots

Primer Anim.sm (30.29 KiB) downloaded 882 time(s).

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frapuano 2018/7/30 14:08:00

#31 Posted: 2018/8/22 04:32:16

Fridel Selitsky

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The intersection points of two curves

Primer1b.sm (33.88 KiB) downloaded 906 time(s).
Primer1b.pdf (212.69 KiB) downloaded 493 time(s).

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sergio 2018/8/22 05:52:00, frapuano 2018/8/22 11:24:00

#32 Posted: 2018/8/22 11:39:31

Fridel Selitsky

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Fixed. Now you can find all the intersection points.

Primer2.sm (36.58 KiB) downloaded 916 time(s).
Primer2.pdf (215.28 KiB) downloaded 498 time(s).

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Davide Carpi 2018/8/22 11:41:00, sergio 2018/8/22 13:01:00

#33 Posted: 2018/8/23 05:11:57

Fridel Selitsky

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Primer3.sm (20.12 KiB) downloaded 940 time(s).

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frapuano 2018/8/23 09:07:00

#34 Posted: 2018/8/23 10:57:07

Jean Giraud

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... thanks Ber7

Contour SOLVE AstroidHyperbola.sm (20.85 KiB) downloaded 907 time(s).

#35 Posted: 2018/8/25 06:22:47

Fridel Selitsky

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Primer6.sm (18.31 KiB) downloaded 909 time(s).

#36 Posted: 2018/10/6 14:56:58

Fridel Selitsky

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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) downloaded 916 time(s).

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NDTM Amarasekera 2018/10/6 22:52:00

#37 Posted: 2018/10/8 03:23:09

Alvaro

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Hi. The same, but without plugins.

SphereSMath.sm (75.21 KiB) downloaded 877 time(s).

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 2018/10/8 03:35:00, NDTM Amarasekera 2018/10/8 04:19:00

#38 Posted: 2018/10/9 11:42:42

Fridel Selitsky

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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 2018/10/9 21:14:00

#39 Posted: 2018/10/10 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) downloaded 926 time(s).
Solve Euler Fails.sm (22.54 KiB) downloaded 935 time(s).
Rotate Breather [Euler].sm (37.2 KiB) downloaded 799 time(s).
Rotate_0 Euler, xyz(t), Quaternion.sm (275.27 KiB) downloaded 886 time(s).

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

Вячеслав Мезенцев

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

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