AlgLib 3.1x - SMath

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

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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 7/18/2018 10:53:00 AM, Fridel Selitsky 7/18/2018 2:35:00 AM, Radovan Omorjan 7/18/2018 5:41:00 AM, Igor Skarine 7/18/2018 10:17:00 AM

#22 Posted: 7/18/2018 2:35:44 AM

Fridel Selitsky

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One example of V. Mezentsev (Uni)
Primer Uni.sm (13 KiB) downloaded 81 time(s).

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Radovan Omorjan 7/18/2018 5:34:00 AM, frapuano 7/18/2018 10:53:00 AM

#23 Posted: 7/18/2018 5:40:48 AM

Radovan Omorjan

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Wrote
One example of V. Mezentsev (Uni)
Primer Uni.sm (13 KiB) downloaded 81 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 KiB) downloaded 77 time(s).

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

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

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: 7/18/2018 3:19:47 PM

Jean Giraud

983 likes in 6866 posts.

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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 KiB) downloaded 65 time(s).

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

Fridel Selitsky

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We find several roots at once

Primer Uni3.sm (15 KiB) downloaded 74 time(s).
Primer Jean1.sm (14 KiB) downloaded 66 time(s).

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frapuano 7/21/2018 1:44:00 PM

#27 Posted: 7/22/2018 3:50:27 AM

Fridel Selitsky

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3d.sm (29 KiB) downloaded 68 time(s).

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NDTM Amarasekera 7/22/2018 5:00:00 AM, frapuano 7/22/2018 5:30:00 AM

#28 Posted: 7/22/2018 11:29:32 PM

Jean Giraud

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Thanks Ber7 for the 3D, nice.

Jean

#29 Posted: 7/24/2018 1:03:26 PM

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 KiB) downloaded 64 time(s).

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Andrey Ivashov 7/26/2018 6:06:00 PM

#30 Posted: 7/30/2018 1:09:38 PM

Fridel Selitsky

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The process of finding the roots

Primer Anim.sm (30 KiB) downloaded 66 time(s).

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frapuano 7/30/2018 2:08:00 PM

#31 Posted: 8/22/2018 4:32:16 AM

Fridel Selitsky

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The intersection points of two curves

Primer1b.sm (33 KiB) downloaded 67 time(s).
Primer1b.pdf (212 KiB) downloaded 56 time(s).

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sergio 8/22/2018 5:52:00 AM, frapuano 8/22/2018 11:24:00 AM

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

Fridel Selitsky

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Fixed. Now you can find all the intersection points.

Primer2.sm (36 KiB) downloaded 72 time(s).
Primer2.pdf (215 KiB) downloaded 57 time(s).

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Davide Carpi 8/22/2018 11:41:00 AM, sergio 8/22/2018 1:01:00 PM

#33 Posted: 8/23/2018 5:11:57 AM

Fridel Selitsky

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Primer3.sm (20 KiB) downloaded 66 time(s).

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frapuano 8/23/2018 9:07:00 AM

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

Jean Giraud

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... thanks Ber7

Contour SOLVE AstroidHyperbola.sm (20 KiB) downloaded 62 time(s).

#35 Posted: 8/25/2018 6:22:47 AM

Fridel Selitsky

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Primer6.sm (18 KiB) downloaded 66 time(s).

#36 Posted: 10/6/2018 2:56:58 PM

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 KiB) downloaded 64 time(s).

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

#37 Posted: 10/8/2018 3:23:09 AM

Alvaro Diaz Falconi

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Hi. The same, but without plugins.

SphereSMath.sm (75 KiB) downloaded 61 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 10/8/2018 3:35:00 AM, NDTM Amarasekera 10/8/2018 4:19:00 AM

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

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 Diaz Falconi 10/9/2018 9:14:00 PM

#39 Posted: 10/10/2018 12:40:38 AM

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 KiB) downloaded 67 time(s).
Solve Euler Fails.sm (22 KiB) downloaded 61 time(s).
Rotate Breather [Euler].sm (37 KiB) downloaded 62 time(s).
Rotate_0 Euler, xyz(t), Quaternion.sm (275 KiB) downloaded 67 time(s).

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

Вячеслав Мезенцев

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Updated.

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

[albumimg]1531[/albumimg]

Russia ☭ forever, Viacheslav N. Mezentsev

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frapuano 12/12/2018 2:31:00 PM, sergio 12/12/2018 1:54:00 PM

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