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 uni #101 Posted : 30 November 2021 08:35:46(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Originally Posted by: uni Linear interpolation and linear spline interpolation are different things. I will try to find the formulas that are used in these functions.We can restore the interpolation functions: lspline(), pspline() and cspline(). This is how the cspline() function works. Based on the attached document and file from the PTC Mathcad forum. Cubic spline interpolation using Mathcad (2009).pdf (257kb) downloaded 39 time(s). cspline1.mcdx.zip (13kb) downloaded 12 time(s). cspline.sm (39kb) downloaded 21 time(s). cspline.pdf (89kb) downloaded 15 time(s).Edited by user 10 December 2021 13:42:42(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev
 Jean Giraud #102 Posted : 30 November 2021 15:58:24(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 981 time(s) in 809 post(s) With enough points, simply cinterp Smath. ODE HIRES.sm (68kb) downloaded 15 time(s).
 uni #103 Posted : 04 December 2021 06:46:37(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) rkfixed(3|4) added, but I still don’t know which derivative symbol is better to take. (ʹ) - modifier letter prime (U+02B9) used below. I don't know how to enter it from the keyboard. Edited by user 10 December 2021 13:43:39(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 04/12/2021(UTC)
 uni #104 Posted : 04 December 2021 11:19:00(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Full set: interp(), [l,p,c]spline(). Odesolve interpolation test.sm (60kb) downloaded 27 time(s). Odesolve interpolation test.pdf (103kb) downloaded 22 time(s).(*) rkfixed() with a bug now, so you will see something differ.Edited by user 10 December 2021 13:45:44(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev
 uni #105 Posted : 05 December 2021 12:55:49(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Originally Posted by: uni (ʹ) - modifier letter prime (U 02B9) used below. I don't know how to enter it from the keyboard.This can be done in 2 steps:1. Copy \02B9\ to text region. This code will turn into a text simbol (ʹ).2. Select and copy it as variable name.PS. It looks like it's time to combine all Mathcad functions into one plugin - Mathcad Toolbox. It will contain all such functions: ODE solvers, spline functions, in/out functions and so on.Edited by user 05 December 2021 16:29:09(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 05/12/2021(UTC)
 Razonar #106 Posted : 05 December 2021 19:18:42(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 1,356Was thanked: 815 time(s) in 516 post(s) Hi. Your develop looks brillant.Originally Posted by: uni ... 1. Copy \02B9\ to text region. This code will turn into a text simbol (ʹ).2. Select and copy it as variable name. ...Also, you can get any unicode char with thisOriginally Posted by: uni ... PS. It looks like it's time to combine all Mathcad functions into one plugin - Mathcad Toolbox. It will contain all such functions: ODE solvers, spline functions, in/out functions and so on.And don't forget the possibility that the area simply returns the equations of the differential equation or a non-linear system of equations so that the user can then try to solve the ode or nle systems with the functions he chooses.Best regards.Alvaro. 1 user thanked Razonar for this useful post. on 06/12/2021(UTC)
 mkraska #107 Posted : 06 December 2021 00:30:56(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/04/2012(UTC)Posts: 1,983Was thanked: 1123 time(s) in 720 post(s) Originally Posted by: uni rkfixed(3|4) added, but I still don’t know which derivative symbol is better to take. (ʹ) - modifier letter prime (U+02B9) used below. I don't know how to enter it from the keyboard.This looks very interesting. Seems that it is not yet in the online gallery?In principle, the built-in diff(1) operator would be an option but it looks ugly if applied twice.The ordinary prime would be ok for me (just as it is used as tag in unit names), it is input as Shift # on german keyboards. diff2.sm (3kb) downloaded 10 time(s). Martin Kraska Pre-configured portable distribution of SMath Studio: https://smath.com/wiki/SMath_with_Plugins.ashx
 Jean Giraud #108 Posted : 06 December 2021 04:15:07(UTC) Rank: GuestGroups: Registered Joined: 04/07/2015(UTC)Posts: 6,866Was thanked: 981 time(s) in 809 post(s) Originally Posted by: uni I still donât know which derivative symbol is better to take. (Ê¹ - modifier letter prime (U 02B9) used below. I don't know how to enter it from the keyboard.My preference goes for book style.US keyboard D apostrophe (x):=
 uni #109 Posted : 06 December 2021 06:07:58(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Originally Posted by: mkraska This looks very interesting. Seems that it is not yet in the online gallery?I can't contact Andrey directly. The server does not allow compiling the sources, as there is no free space. Therefore, the latest changes are not yet available.I've made some changes. I liked the idea with the str2num() function. Also I can override the diff(1) function, but that can be confusing.Now it is possible to numerically solve the Cauchy problem for one variable: diff(y(x),x,n)=F(x,y(x),...,diff(y(x),x,n-1)) . Later, I will expand the rest of the ODE solvers to support this simplified form. But for this I need to combine plugins and add interpolation functions similar to Mathcad (lspline(), interp(), ...). It will be more convenient for me to test the solvers, comparing the results with Mathcad.Block region collects equations in the form of a system and substitutes it as the first parameter into the function.Edited by user 10 December 2021 13:45:12(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev
 uni #110 Posted : 06 December 2021 10:32:09(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Originally Posted by: mkraska The ordinary prime would be ok for me (just as it is used as tag in unit names), it is input as Shift # on german keyboards.I can add the ability to set this symbol directly in the document. This way you can change the default symbol. Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 06/12/2021(UTC)
 uni #111 Posted : 06 December 2021 15:11:48(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Plugin updated. Please try.Examples: Changes:- rkfixed() now works correctly;- Odesolve block renamed to Mathcad Block;- the task for the ODE solver in the usual mathematical notation is supported;- default diff symbol is apostrophe ( ' );- linterp() is used as an interpolation function;- refactored. Edited by user 10 December 2021 13:43:52(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev 2 users thanked uni for this useful post. on 06/12/2021(UTC),  on 06/12/2021(UTC)
 Razonar #112 Posted : 06 December 2021 19:41:05(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 1,356Was thanked: 815 time(s) in 516 post(s) Originally Posted by: uni - linterp() is used as an interpolation function;Hi Viacheslav, thanks, great job. One question: Why to use linterp instead cspline? The problem with cspline is about the border of the interval, where you have only diff by the left and the right, and there you can adapt the cubic splines to be linear or parabolic, but in the interior of the interval I guess that it's better cubic splines interpolation. ODEQuestion.sm (16kb) downloaded 15 time(s).Best regards.Alvaro.
 uni #113 Posted : 06 December 2021 21:44:46(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) I will add the interpolation functions ( interp(), lspline(),... ) to the plugin and rename it to Mathcad Toolbox. After that, it will be possible to test its work, comparing it with the Mathcad numerically.Edited by user 06 December 2021 21:46:41(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 06/12/2021(UTC)
 uni #114 Posted : 07 December 2021 11:56:03(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Plugin updated.Changes:- plugin renamed to Mathcad Toolbox;- version changed to 0.3.*;- interp(), lspline() functions added;- lspline() function used in any ode solvers. Russia ☭ forever Viacheslav N. Mezentsev 2 users thanked uni for this useful post. on 07/12/2021(UTC),  on 07/12/2021(UTC)
 mkraska #115 Posted : 07 December 2021 14:32:19(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/04/2012(UTC)Posts: 1,983Was thanked: 1123 time(s) in 720 post(s) Really nice generic block concept! It is a really good reason for updating the handbook and the portable distribution. This is how to use it with symbolic solutions using Solve() (Maxima plugin): Solve block.sm (6kb) downloaded 25 time(s).Looking forward to a RK integrator for multi-DOF systems. This is how I would imagine the user interface. Federpendel-block.sm (49kb) downloaded 27 time(s). Martin Kraska Pre-configured portable distribution of SMath Studio: https://smath.com/wiki/SMath_with_Plugins.ashx 1 user thanked mkraska for this useful post. on 07/12/2021(UTC)
 uni #116 Posted : 07 December 2021 15:32:51(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Originally Posted by: mkraska Looking forward to a RK integrator for multi-DOF systems. This is how I would imagine the user interface.This is the next step, but the existing solution is not stable and has some bugs. Russia ☭ forever Viacheslav N. Mezentsev
 uni #117 Posted : 07 December 2021 17:13:30(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Plugin updated.Changes:- plugin merged with Mathcad File Access (all functions are inside Mathcad Toolbox);- the condition has changed in the definition of the solver function (to support both directions of integration): (x-xmin)*(xmax-x)>=0;- pspline() function added. Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 07/12/2021(UTC)
 Razonar #118 Posted : 07 December 2021 20:00:34(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 1,356Was thanked: 815 time(s) in 516 post(s) Originally Posted by: uni Originally Posted by: mkraska Looking forward to a RK integrator for multi-DOF systems. This is how I would imagine the user interface.This is the next step, but the existing solution is not stable and has some bugs.Hi. In the meantime, we can play with things like this: Solve block.sm (55kb) downloaded 30 time(s).Best regards.Alvaro.Edited by user 07 December 2021 20:04:36(UTC)  | Reason: Not specified 1 user thanked Razonar for this useful post. on 07/12/2021(UTC)
 uni #119 Posted : 08 December 2021 08:24:11(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Originally Posted by: Razonar Hi. In the meantime, we can play with things like thisLooks great, but something is missing.Edited by user 10 December 2021 13:44:39(UTC)  | Reason: Not specified Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 08/12/2021(UTC)
 uni #120 Posted : 10 December 2021 11:59:47(UTC) Rank: Advanced MemberGroups: Registered, Advanced MemberJoined: 10/11/2010(UTC)Posts: 1,494Was thanked: 1274 time(s) in 745 post(s) Plugin updated.Changes:- fixed algorithm for selecting regions (Mathcad Block). Russia ☭ forever Viacheslav N. Mezentsev 1 user thanked uni for this useful post. on 10/12/2021(UTC)
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