Mathcad Toolbox

#1 Posted: 11/10/2010 2:39:50 AM

Вячеслав Мезенцев

1402 likes in 1708 posts.

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Mathcad Toolbox

Contents:

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CurrentDirectory(1) - Gets or sets the fully qualified path of the current working directory.
DocumentDirectory(1) - Gets the fully qualified path of the current document.
GetFolderPath(1) - Gets the path to the system special folder identified by the specified enumeration.
GETWAVINFO(1) - Creates a vector with four elements containing information about file.
interp(4) - (vs,vx,vy,x) returns an interpolated value at x from the coefficients in vector vs, and the original data in vx and vy.
Play(1) - Play sound file.
pspline(2) - (vx,vy) returns a vector of second derivatives to build a cubic spline parabolic at the endpoints.
pspline(3) - (vx,vy,x) returns a vector of second derivatives to build a cubic spline parabolic at the endpoints.
lspline(2) - (vx,vy) returns a vector of second derivatives to build a cubic spline linear at the endpoints.
lspline(3) - (vx,vy,x) returns a vector of second derivatives to build a cubic spline linear at the endpoints.
READBIN(6) - ( file, type, endian, cols, skip, maxrows ) returns an array containing the binary data in file.
READBMP(1) - Creates an array containing a grayscale representation of a bitmap format image file.
READRGB(1) - Creates an array containing a red-green-blue packed matrix representation of the image file.
READWAV(1) - Creates a matrix containing signal amplitudes in file.
READ_BLUE(1) - Returns a matrix representing the RGB blue component of the image in file.
READ_GREEN(1) - Returns a matrix representing the RGB green component of the image in file.
READ_IMAGE(1) - Creates an array containing a grayscale representation of the image file.
READ_RED(1) - Returns a matrix representing the RGB red component of the image in file.
rfile(2) - ( path, filename ) Reads an expression from the file.
Rkadapt(3) - (ode,y(x),xmax) uses the Runge-Kutta-Fehlberg method (RKF45).
Rkadapt(4) - (ode,y(x),xmax,steps) uses the Runge-Kutta-Fehlberg method (RKF45).
Rkadapt(5) - (ics,xmin,xmax,steps,D(x,y)) uses the Runge-Kutta-Fehlberg method (RKF45).
rkfixed(3) - (ode,y(x),xmax) uses the fourth-order Runge-Kutta fixed-step method.
rkfixed(4) - (ode,y(x),xmax,steps) uses the fourth-order Runge-Kutta fixed-step method.
rkfixed(5) - (ics,xmin,xmax,steps,D(x,y)) uses the fourth-order Runge-Kutta fixed-step method.
wfile(3) - ( value, path, filename ) Writes the expression to the file.
WRITEBIN(4) - ( file, type, endian, M ) writes an array of scalars to the binary data file named file.
WRITEWAV(4) - ( file, s, b, M ) Creates a WAV signal file out of a matrix.

Examples:

7-13-Three-Planets (Mathcad Block).sm (34 KiB) downloaded 170 time(s).
7-13-Three-Planets (Mathcad Block).pdf (57 KiB) downloaded 135 time(s).

7-13-Three-Planets 2 (Mathcad Block).sm (30 KiB) downloaded 110 time(s).
7-13-Three-Planets 2 (Mathcad Block).pdf (54 KiB) downloaded 84 time(s).

7-13-Three-Planets 3 (Mathcad Block).sm (25 KiB) downloaded 95 time(s).
7-13-Three-Planets 3 (Mathcad Block).pdf (55 KiB) downloaded 95 time(s).

7-13-Three-Planets 4 (Mathcad Block).sm (30 KiB) downloaded 93 time(s).
7-13-Three-Planets 4 (Mathcad Block).pdf (73 KiB) downloaded 88 time(s).

7-13-Three-Planets 5 (Mathcad Block).sm (26 KiB) downloaded 124 time(s).
7-13-Three-Planets 5 (Mathcad Block).pdf (61 KiB) downloaded 93 time(s).

7-13-Three-Planets 6 (Mathcad Block).sm (26 KiB) downloaded 112 time(s).
7-13-Three-Planets 6 (Mathcad Block).pdf (67 KiB) downloaded 96 time(s).

Utility for call dsolvers for initial and boundary values problems from a solver block.

Mathcad Block. RKA (Razonar).sm (59 KiB) downloaded 127 time(s).
Mathcad Block. RKA (Razonar).pdf (66 KiB) downloaded 121 time(s).

RKA.sm (308 KiB) downloaded 117 time(s). (last version)
RKA.pdf (931 KiB) downloaded 131 time(s).

See also:

● [topic=17088]Intel ODE Solver Library[/topic]
● [topic=1918]DotNumerics[/topic]
● [topic=13809]SADEL[/topic]
● [topic=1970]Matlab C++ Math Library[/topic]
● [topic=17063]OSLO[/topic]
● [topic=17067]lsoda[/topic]
● [topic=1997]GNU Scientific Library (GSL)[/topic]

ODE_manual.pdf (239 KiB) downloaded 755 time(s).

Russia ☭ forever, Viacheslav N. Mezentsev

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Radovan Omorjan 11/10/2010 8:14:00 AM, Thiago Pereira 6/27/2024 12:24:00 AM

#2 Posted: 11/10/2010 8:36:44 AM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Many thanks uni for this plugin

Your examples are very interesting (Russian side of the Forum) and I hope that some additional ODE solvers will be implemented as plugins in the near future.
BTW, I've noted that the function used in rkfixed (Система(t;x) in this example) is tolerant to the argument names (t;x here). Actually, rkfixed will not complain if the variables t and x have been already defined - we should be carefull about it.

Regards,
Radovan

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

#3 Posted: 11/10/2010 10:24:03 AM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

Quote
I hope that some additional ODE solvers will be implemented as plugins in the near future.

Now it's not so hard. I'll try to implement odesolversolve() from AlgLib project. At this moment I have some functions from there:

AlgLib Plugin (based on ALGLIB 3.1.0)

Дополнение обрабатывает следующие вхождения:
al_airy("число" - Returns the Airy function: Ai(x), Ai'(x), Bi(x) and Bi'(x).
al_beta("1:число"; "2:число" - Beta function
al_convr1d("1:вектор"; "2:число"; "3:вектор"; "4:число" - 1-dimensional real convolution.
al_fftc1d("1:вектор"; "2:число" - 1-dimensional complex FFT
al_fftc1dinv("1:вектор"; "2:число" - 1-dimensional complex FFT

I think I can to implement full functionality. Also (if anybody need) it's possible to create plotting functions like: CreateMesh(), CreateSpace(), implicitplot2d() and implicitplot3d().

P.S. Three functions (CreateMesh(), implicitplot2d() and implicitplot3d()) based on SMath programming tools already exists.

Russia ☭ forever, Viacheslav N. Mezentsev

#4 Posted: 11/10/2010 10:36:37 AM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Wish you good luck

Regards,
Radovan

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

#5 Posted: 11/10/2010 11:38:02 AM

frapuano

13 likes in 115 posts.

Group: User

UNI

will be wonderful if based on your experience you can write ( if possible ) a further tutorial on how to develop a plugin for Smath for super NewBie like me and probably many others.
I have seen that your program is very detailed/commented but would be nice to have a diary of how you have put toghether the bit an pieces to develop the plugin , the difficulties that you have overcome , which are the biggest problem to face in writing a plug in amd the things that one person should be more carefull to succed .

Thanks a lot for your help

Francesco

P.S. In the last months I am following the Smath forum in Russian af far as is possible through the google traslate approach ( from Russian to English ..whose traslation is better then from Russian to Italian my mother tongue) and is really very interesting . Need to try to learn better Russian language ..hope to find something useful to this aim on Internet, I guess that we are missing a universe of knowledge due to ignoring the language

#6 Posted: 11/10/2010 12:51:21 PM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

Quote
will be wonderful if based on your experience you can write ( if possible ) a further tutorial on how to develop a plugin for Smath for super NewBie like me and probably many others.

Unfortunately, I don't have the full manual for plugin development. There is a good video-manual for beginners on wiki: Tutorials for Creating Plugins. I used it and also examples from svn. As I see, in English much more materials on this subject than in Russian or other language.

Quote
I have seen that your program is very detailed/commented but would be nice to have a diary of how you have put toghether the bit an pieces to develop the plugin , the difficulties that you have overcome , which are the biggest problem to face in writing a plug in amd the things that one person should be more carefull to succed.

"Step by step" instructions you mean? It will depend on type of a plugin and algorithm of function. rkfixed() is a difficult example. The main problem was: how to work with function in a plugin? It is better to begin with simple examples like combin() function from video-manual.

Quote
In the last months I am following the Smath forum in Russian af far as is possible through the google traslate approach ( from Russian to English ..whose traslation is better then from Russian to Italian my mother tongue) and is really very interesting

I'll try to include all those examples in English in SMath Studio. You can try translate.ru.

Russia ☭ forever, Viacheslav N. Mezentsev

#7 Posted: 11/11/2010 4:39:00 PM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

For testing only: ODESolvers.dll (+ Rkadapt())

Russia ☭ forever, Viacheslav N. Mezentsev

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Radovan Omorjan 11/11/2010 5:19:00 PM

#8 Posted: 11/12/2010 5:19:55 AM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

New version: ODESolvers.dll

It works more correctly than previous.

Russia ☭ forever, Viacheslav N. Mezentsev

#9 Posted: 11/12/2010 7:31:11 AM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Hello,

Wrote
New version: ODESolvers.dll

It works more correctly than previous.

Many thanks for your efforts on making this plugin

The ODE solvers are on the top of my "wish list".

I tested it a bit and this version is indeed much faster then the previous one.
Here is one of my simple test examples for ODE solvers:

And your solvers worked as expected, thank you

The previous version was much slower and had a problem with larger "n".
This is also a test for a stiff ODE. As the rkfixed and Rkadapt are not stiff solvers, the result is as presented in the graph. Stiff ODE solver should cope with the situation when y2 is approaching zero.

Here are some of my comments, if you do not mind:
- I am not a programmer but am rather surprised how you managed to get the function as a function parameter (D(t,y) in this case - my congratulations

. I suppose the side effect is that rkfixed and Rkadapt will be working wrong if this function (D(t,y)) uses t and vector y with t,y previously defined. I thought that the ODE solver will be realized in a similar way like "roots" function.

- I tried to define function D as a multiline function but this will not work.

Anyway, I am very grateful to you for this plugin.

Regards,
Radovan

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

#10 Posted: 11/12/2010 12:17:14 PM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

Thank you, Radovan.

Quote
- I tried to define function D as a multiline function but this will not work.

I asked Andrey about it and he has explained a problem. You can try newnew version: ODESolvers.dll

About comments

feedback is necessary to me to fix errors.

Quote
I am not a programmer but am rather surprised how you managed to get the function as a function parameter (D(t,y).

It is not so simply to explain in a few words about how I do that. May be later, specially for those who is interested.

Russia ☭ forever, Viacheslav N. Mezentsev

#11 Posted: 11/12/2010 1:10:21 PM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

Rkadapt() algorithm. Unfortunately, it doesn't work.
Rkadapt prog.sm

Russia ☭ forever, Viacheslav N. Mezentsev

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Radovan Omorjan 11/12/2010 6:45:00 PM

#12 Posted: 11/12/2010 3:25:51 PM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

Experiments:

Russia ☭ forever, Viacheslav N. Mezentsev

#13 Posted: 11/12/2010 6:57:49 PM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Hello uni

Wrote
Rkadapt() algorithm. Unfortunately, it doesn't work.
Rkadapt prog.sm

I took a look at this sm file. On the basis of the error message about the function Rkadapt2 - "The matrix element does'nt exist." and by some inspection I think that there might be a mistake about vectors and row matrix. There might be that you used the single index for row matrix regarding it as a vector, and you might forgot to use two instead of one index.

Regards,
Radovan

P.S. I am not able to test the new *.dll at the moment because I do not know how to use it with portable 0.89_8 version (unfortunately, have no possibility to install SMath at my home computer).

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

#14 Posted: 11/23/2010 7:29:21 AM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Hello uni

I tested a little bit rkfixed and Rkadapt. Here is a simple picture:

It seems, as you mentioned, that Rkadapt will not work with multiline function. However, it is very good that rkfixed will work with it - a bit surprise for me. I also tried to define function f(x,t) by using "eval" - it does not work either with rkfixed or Rkadapt. Due to my previous experience, I thought it would not work. I know that this kind of functions, like you did with rkfixed and Rkadapt, will have troubles due to the SMath way of working. Never mind, I hope that SMath will have tha ability to cope with this kind of problems some day.

Regards,
Radovan

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

#15 Posted: 5/6/2013 6:16:42 PM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

Updated description.

Russia ☭ forever, Viacheslav N. Mezentsev

#16 Posted: 5/12/2013 3:08:39 PM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Just tried ODE plugin and figured out that it can accept additional parameters after the first two in D(x,y) function of derivatives.
I might miss that feature, but it should be pointed out that this is very nice and useful

[albumimg]140[/albumimg]

I hope that some stiff solvers would be available sooner or later

Regards,
Radovan

ODE-Lorentz.sm (11 KiB) downloaded 158 time(s).

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

2 users liked this post

Martin Kraska 5/12/2013 5:27:00 PM, Вячеслав Мезенцев 5/12/2013 3:50:00 PM

#17 Posted: 5/12/2013 3:48:41 PM

Вячеслав Мезенцев

1402 likes in 1708 posts.

Group: Moderator

Oh, you found a bug, well, I'll fix it

[albumimg]142[/albumimg]

Usual, in such cases I use a different way of passing parameters, but it doesn't work for this example.

EDIT: I was wrong, it works.

[albumimg]141[/albumimg]

ODE-Lorentz-uni.sm (13 KiB) downloaded 146 time(s).

Russia ☭ forever, Viacheslav N. Mezentsev

#18 Posted: 5/12/2013 4:41:11 PM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Wrote
Oh, you found a bug, well, I'll fix it Usual, in such cases I use a different way of passing parameters, but it doesn't work for this example.

EDIT: I was wrong, it works.

[albumimg]141[/albumimg]

Actually, I thought this was by design and that I missed it

, and now I am pleasantly surprised

. I would prefer my solution, if you do not mind. This way, and in this case - there is a vector with three dependent variables, the rest are parameters (resulting the matrice with four columns). Your solution would have six variables - (resulting the matrice with seven columns). Your example is like the way it works in Mathcad (I never liked this way). If you need additional parameters you must put it in the vector, and use there derivatives equal to zero - it looks a bit artificial.

I also tried this one and it worked as well

[albumimg]143[/albumimg]

Uni, please keep it this way and do not change it

Regards,
Radovan

ODE-Lorentz-2.sm (11 KiB) downloaded 151 time(s).

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

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Davide Carpi 5/12/2013 5:29:00 PM

#19 Posted: 5/12/2013 5:26:44 PM

Martin Kraska

1222 likes in 2150 posts.

Group: Moderator

How about this dirty parameter handling...
[albumimg]144[/albumimg][albumimg]145[/albumimg]

Example.sm (12 KiB) downloaded 184 time(s).

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

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Radovan Omorjan 5/13/2013 1:09:00 AM

#20 Posted: 5/13/2013 1:32:56 AM

Radovan Omorjan

325 likes in 2052 posts.

Group: Moderator

Thank you Martin,

Wrote
How about this dirty parameter handling...

Hmm... why dirty? Do not understand, sorry. This looks quite regular to me, except that it is not flexible. The third parameter must always have the same name as in the definition of D().

Regards,
Radovan

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

SMath Forum

Mathcad Toolbox - Contains analogs of functions from Mathcad - Messages