GNU Scientific Library (GSL)

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Functions list:

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Solvers for Non-Stiff Systems:

gslrk2(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta (2, 3) method.

gslrk4(init, x1, x2, intvls, D) Explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.

gslrkf45(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta-Fehlberg (4, 5) method.

gslrkck(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta Cash-Karp (4, 5) method.

gslrk8pd(init, x1, x2, intvls, D) Explicit embedded Runge-Kutta Prince-Dormand (8, 9) method.

Arguments:

- init is either a vector of n real initial values, where n is the number of unknowns (or a single scalar initial value, in the case of a single ODE).
- x1 and x2 are real, scalar endpoints of the interval over which the solution to the ODE(s) is evaluated. Initial values in init are the values of the ODE function(s) evaluated at x1.
- intvls is the integer number of discretization intervals used to interpolate the solution function. The number of solution points is the number of intervals + 1.
- D is a vector function of the form D(x,y) specifying the right-hand side of the system

Options:

- AbsTol - absolute tolerance parameter, default value 1E-7.
- RelTol - relative tolerance parameter, default value 1E-4.

Examples:

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gsl.ode.integrate.sm (11 KiB) downloaded 137 time(s).
gsl.ode.kinetic1.sm (8 KiB) downloaded 132 time(s).
gsl.ode.kinetic2.sm (14 KiB) downloaded 114 time(s).
gsl.ode.kinetic3.sm (14 KiB) downloaded 112 time(s).
gsl.ode.test1.sm (19 KiB) downloaded 116 time(s).
gsl.ode.test2.sm (18 KiB) downloaded 115 time(s).
gsl.ode.Amplitude detector.sm (20 KiB) downloaded 145 time(s).

gsl.ode.integrate.pdf (92 KiB) downloaded 121 time(s).
gsl.ode.kinetic1.pdf (77 KiB) downloaded 113 time(s).
gsl.ode.kinetic2.pdf (92 KiB) downloaded 95 time(s).
gsl.ode.kinetic3.pdf (91 KiB) downloaded 92 time(s).
gsl.ode.test1.pdf (110 KiB) downloaded 107 time(s).
gsl.ode.test2.pdf (110 KiB) downloaded 101 time(s).
gsl.ode.Amplitude detector.pdf (148 KiB) downloaded 119 time(s).

Links:

1. GNU Scientific Library – Reference Manual.
2. GSL for Windows.
3. The GSL Team.
4. Thanks.

See also:

● [topic=726]Mathcad Toolbox[/topic]
● [topic=1918]DotNumerics[/topic]
● [topic=13809]SADEL[/topic]
● [topic=1970]Matlab C++ Math Library[/topic]
● [topic=17063]OSLO[/topic]
● [topic=17067]lsoda[/topic]

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GNU Scientific Library. ODE Solvers. Arenstorf orbit.pdf (99 KiB) downloaded 318 time(s).

very very cool library, there are several interesting things

works for me (win 7 x64)


best regards,

Davide

I agree with Davide. I mentioned this library few times as well

As I said before, uni is like a man working in a candy store and giving us very good and healthy sweets for free

Regards,
Radovan

Uni,
I see you do not use prefixes any more. Does that mean, you are considering the GSL as the primary source of generic SMath functions? IMHO that would be sensible, as GSL seems to be the most vital and most free library among the ones you wrapped so far. However, I have no idea about performance issues.

Functions that are not yet implemented not have a prefix. When I add a function in the plug-in, I add a prefix to it. All the functions in this library will have the same or similar names which given in their description.

For example: gsl_sf_bessel_J0() -> gslsfJ0(), gsl_sf_airy_Ai() -> gslsfAi(), ...

I'll ask Andrey to implement the namespace for functions. This option may be enabled and disabled as the description of the region. In this case, you can specify the function names without the prefix.

Wrote

I'll ask Andrey to implement the namespace for functions. This option may be enabled and disabled as the description of the region. In this case, you can specify the function names without the prefix.

I am not sure that I understand correctly, what the namespace for functions concept is meant to be.
Is that something like local aliasing?
Is that a by-region setting?
What is the visualization concept?

I'd expect something like switching on aliasing (and perhaps enabling of the plugin) by a separate statement "with("GLS" ) or with("Matlab" ). This could be
deactivated later in the same sheet by a function without() in a traceable manner.

BTW, how about including a plugin hint in the description string of the functions. I had to search the forum in order to find out what plugin provides the erf() function (Davide, sorry for my leaking memory). Not a big deal for me, but would help to correctly direct user feedback.

Wrote

I'd expect something like switching on aliasing (and perhaps enabling of the plugin) by a separate statement "with("GLS" ) or with("Matlab" ). This could be
deactivated later in the same sheet by a function without() in a traceable manner.

I think it only works for the document in text form. It is unlikely that this method will be useful in our case.

We have one example of namespace support. Not necessarily indicate the selected space, but the user should be able to select it. We can assign a hot key to display the namespace for the selected function.

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Wrote

As I said before, uni is like a man working in a candy store and giving us very good and healthy sweets for free

I see viacheslav and davide more like fabulous dwarves blacksmiths and radovan and martin like mere mortal betatesters, thanks btw :d

Ok, it is a Mathcad concept (I was not aware of that).

The example with m as units and m as variable does not really convince me. By math standards, these items should be distinguished by type face (italic for variables, upright for units or other items that are not supposed to change. SMath has this the other way around, but at least clearly indicates the difference. Thus, the unit name space tag is the apostrophe ' in front of the name.

There is another "namespace" then in SMath, the absolute variables with ~ as tag (which would be fine to represent matrix/vector values).

An option for getting along without new features would be to leave the prefixes in the names and to provide generic names pointing to the most appropriate function from whatever plugin it may come or even to provide wrapper functions like Findroot() to choose from what is available.

The ordinary ("mortal" ) user hardly wants to choose from 20 ode solvers or from 10 nonlinear solvers.

Updated to GSL 1.16.

Updated for the fully automatic build using Release Manager.

Installing this plugin causing forced close on Arch Linux + Mono.
After forced close you cannot be able to open Smath again unless manually deleting the plugin.

Regards

Because the plugin is not compatible with Linux + Mono:

Quote

VS2013, .Net 2.0, C#, C++/CLI, Win32 + x64

Win32 + x64 - means Windows only, C++/CLI - unmanaged code used.

gslrkck simple test.

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gslrkck.test1.sm (11 KiB) downloaded 79 time(s).
gslrkck.test1.pdf (48 KiB) downloaded 85 time(s).

Updated.

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

Updated.

[albumimg]1570[/albumimg] [albumimg]1571[/albumimg] [albumimg]1572[/albumimg] [albumimg]1573[/albumimg] [albumimg]1574[/albumimg] [albumimg]1575[/albumimg]

gsl.ode.kinetic1.sm (8 KiB) downloaded 132 time(s).
gsl.ode.kinetic2.sm (14 KiB) downloaded 114 time(s).
gsl.ode.kinetic3.sm (14 KiB) downloaded 112 time(s).
gsl.ode.test1.sm (19 KiB) downloaded 116 time(s).
gsl.ode.test2.sm (18 KiB) downloaded 115 time(s).
gsl.ode.Amplitude detector.sm (20 KiB) downloaded 145 time(s).

gsl.ode.kinetic1.pdf (77 KiB) downloaded 113 time(s).
gsl.ode.kinetic2.pdf (92 KiB) downloaded 95 time(s).
gsl.ode.kinetic3.pdf (91 KiB) downloaded 92 time(s).
gsl.ode.test1.pdf (110 KiB) downloaded 107 time(s).
gsl.ode.test2.pdf (110 KiB) downloaded 101 time(s).
gsl.ode.Amplitude detector.pdf (148 KiB) downloaded 119 time(s).

Updated.

Added: gslmsadams(5), gslrk1imp(5), gslrk2imp(5), gslrk4imp(5), gslbsimp(5), gslmsbdf(5).
Fixed: gslrk1imp(6), gslrk2imp(6), gslrk4imp(6), gslbsimp(6), gslmsbdf(6).
Removed: gslmsadams(6).

Solvers with 5 arguments working with numerical Jacobian (not so good but I don't know how to improve it now).

I was on a journey.

This use of the library is beyond the scope of the forum. I will try to create a simple example, but you still need to read the original documentation to use the library.

Updated.

Changes:

- updated to GSL 2.4.

Plugin updated.

Changes:

- added support for ODE systems in mathematical form;
- refactored.