GNU Scientific Library (GSL)

#1 Опубликовано: 27.08.2013 17:53:11

Вячеслав Мезенцев

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GNU Scientific Library (GSL)

Functions list:

Показать спойлер

gslbsimp(1) - (cmd) implicit Bulirsch-Stoer method of Bader and Deuflhard.
gslbsimp(3) - (ode,y(x),xmax) implicit Bulirsch-Stoer method of Bader and Deuflhard.
gslbsimp(4) - (ode,y(x),xmax,steps) implicit Bulirsch-Stoer method of Bader and Deuflhard.
gslbsimp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Bulirsch-Stoer method of Bader and Deuflhard.
gslbsimp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Bulirsch-Stoer method of Bader and Deuflhard.
gslmsadams(1) - (cmd) variable-coefficient linear multistep Adams method in Nordsieck form.
gslmsadams(3) - (ode,y(x),xmax) variable-coefficient linear multistep Adams method in Nordsieck form.
gslmsadams(4) - (ode,y(x),xmax,steps) variable-coefficient linear multistep Adams method in Nordsieck form.
gslmsadams(5) - (ics,xmin,xmax,steps,D(x,y)) variable-coefficient linear multistep Adams method in Nordsieck form.
gslmsdbf(1) - (cmd) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
gslmsdbf(3) - (ode,y(x),xmax) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
gslmsdbf(4) - (ode,y(x),xmax,steps) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
gslmsdbf(5) - (ics,xmin,xmax,steps,D(x,y)) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
gslmsdbf(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) variable-coefficient linear multistep backward differentiation formula (BDF) method in Nordsieck form.
gslrk1imp(1) - (cmd) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
gslrk1imp(3) - (ode,y(x),xmax) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
gslrk1imp(4) - (ode,y(x),xmax,steps) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
gslrk1imp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
gslrk1imp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian first order Runge-Kutta (implicit Euler or backward Euler) method.
gslrk2(1) - (cmd) explicit embedded Runge-Kutta (2,3) method.
gslrk2(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta (2,3) method.
gslrk2(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta (2,3) method.
gslrk2(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta (2,3) method.
gslrk2imp(1) - (cmd) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk2imp(3) - (ode,y(x),xmax) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk2imp(4) - (ode,y(x),xmax,steps) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk2imp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk2imp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk4(1) - (cmd) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.
gslrk4(3) - (ode,y(x),xmax) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.
gslrk4(4) - (ode,y(x),xmax,steps) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.
gslrk4(5) - (ics,xmin,xmax,steps,D(x,y)) explicit 4th order (classical) Runge-Kutta. Error estimation is carried out by the step doubling method.
gslrk4imp(1) - (cmd) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk4imp(3) - (ode,y(x),xmax) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk4imp(4) - (ode,y(x),xmax,steps) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk4imp(5) - (ics,xmin,xmax,steps,D(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk4imp(6) - (ics,xmin,xmax,steps,D(x,y),J(x,y)) implicit Gaussian second order Runge-Kutta (implicit mid-point) method.
gslrk8pd(1) - (cmd) explicit embedded Runge-Kutta Prince-Dormand (8,9) method.
gslrk8pd(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta Prince-Dormand (8,9) method.
gslrk8pd(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Prince-Dormand (8,9) method.
gslrk8pd(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Prince-Dormand (8,9) method.
gslrkck(1) - (cmd) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gslrkck(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gslrkck(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gslrkck(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gslrkf45(1) - (cmd) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gslrkf45(3) - (ode,y(x),xmax) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gslrkf45(4) - (ode,y(x),xmax,steps) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gslrkf45(5) - (ics,xmin,xmax,steps,D(x,y)) explicit embedded Runge-Kutta Cash-Karp (4,5) method.
gsl_deriv_backward(3) - (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive backward difference algorithm with a step-size of h.
gsl_deriv_central(3) - (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive central difference algorithm with a step-size of h.
gsl_deriv_forward(3) - (f,x,h) computes the numerical derivative of the function f at the point x using an adaptive forward difference algorithm with a step-size of h.
gsl_sf_airy(1) - (cmd) compute the Airy function.
gsl_sf_airy(2) - (flags,x) compute the Airy function.
gsl_sf_bessel(1) - (cmd) compute the Bessel function.
gsl_sf_bessel(2) - (flags,x) compute the Bessel function.
gsl_sf_bessel(3) - (flags,n|nu|l,x) compute the Bessel function.
gsl_sf_clausen(1) - (x) calculate the Clausen integral.
gsl_sf_dawson(1) - (x) calculate the Dawson integral.
gsl_sf_debye(2) - (n,x) calculate the Debye function.
gsl_sf_dilog(1) - (x) calculate the Dilogarithm.
gsl_sf_ellint_D(2) - (ϕ,k) compute the incomplete elliptic integral D(ϕ,k).
gsl_sf_ellint_Dcomp(1) - (k) compute the complete elliptic integral D(k).
gsl_sf_ellint_E(2) - (ϕ,k) compute the incomplete elliptic integral E(ϕ,k).
gsl_sf_ellint_Ecomp(1) - (k) compute the complete elliptic integral E(k).
gsl_sf_ellint_F(2) - (ϕ,k) compute the incomplete elliptic integral F(ϕ,k).
gsl_sf_ellint_Kcomp(1) - (k) compute the complete elliptic integral K(k).
gsl_sf_ellint_P(3) - (ϕ,k,n) compute the incomplete elliptic integral P(ϕ,k,n).
gsl_sf_ellint_Pcomp(2) - (k,n) compute the complete elliptic integral Π(k,n).
gsl_sf_ellint_RC(2) - (x,y) compute the incomplete elliptic integral RC(x,y).
gsl_sf_ellint_RD(3) - (x,y,z) compute the incomplete elliptic integral RD(x,y,z).
gsl_sf_ellint_RF(3) - (x,y,z) compute the incomplete elliptic integral RF(x,y,z).
gsl_sf_ellint_RJ(4) - (x,y,z,p) compute the incomplete elliptic integral RJ(x,y,z,p).
gsl_sf_eta(1) - (s) calculate the eta function η(s) for arbitrary s.
gsl_sf_eta_int(1) - (n) calculate the eta function η(n) for integer n.
gsl_sf_hzeta(2) - (s,q) calculate the Hurwitz zeta function ζ(s,q) for s > 1, q > 0.
gsl_sf_zeta(1) - (s) calculate the Riemann zeta function ζ(s) for arbitrary s ≠ 1.
gsl_sf_zetam1(1) - (s) calculate the Riemann zeta function ζ(s) minus one for arbitrary s ≠ 1.
gsl_sf_zetam1_int(1) - (n) calculate the Riemann zeta function ζ(n) minus one for integer n ≠ 1.
gsl_sf_zeta_int(1) - (n) calculate the Riemann zeta function ζ(n) for integer n ≠ 1.
gsl_version - returns GSL version.

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:

[albumimg]1553[/albumimg] [albumimg]1534[/albumimg] [albumimg]1535[/albumimg] [albumimg]1536[/albumimg]
[albumimg]1570[/albumimg] [albumimg]1571[/albumimg] [albumimg]1572[/albumimg] [albumimg]1573[/albumimg] [albumimg]1574[/albumimg] [albumimg]1575[/albumimg]

gsl.ode.integrate.sm (11 КиБ) скачан 167 раз(а).
gsl.ode.kinetic1.sm (8 КиБ) скачан 155 раз(а).
gsl.ode.kinetic2.sm (14 КиБ) скачан 143 раз(а).
gsl.ode.kinetic3.sm (14 КиБ) скачан 142 раз(а).
gsl.ode.test1.sm (19 КиБ) скачан 144 раз(а).
gsl.ode.test2.sm (18 КиБ) скачан 143 раз(а).
gsl.ode.Amplitude detector.sm (20 КиБ) скачан 169 раз(а).

gsl.ode.integrate.pdf (92 КиБ) скачан 148 раз(а).
gsl.ode.kinetic1.pdf (77 КиБ) скачан 137 раз(а).
gsl.ode.kinetic2.pdf (92 КиБ) скачан 120 раз(а).
gsl.ode.kinetic3.pdf (91 КиБ) скачан 123 раз(а).
gsl.ode.test1.pdf (110 КиБ) скачан 130 раз(а).
gsl.ode.test2.pdf (110 КиБ) скачан 133 раз(а).
gsl.ode.Amplitude detector.pdf (148 КиБ) скачан 146 раз(а).

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]

GNU Scientific Library. ODE Solvers. Arenstorf orbit.pdf (99 КиБ) скачан 343 раз(а).

Russia ☭ forever, Viacheslav N. Mezentsev

4 пользователям понравился этот пост

Martin Kraska 28.08.2013 03:21:00, Radovan Omorjan 28.08.2013 00:54:00, ioan92 28.08.2013 02:54:00, Davide Carpi 27.08.2013 18:21:00

#2 Опубликовано: 27.08.2013 18:21:50

Davide Carpi

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very very cool library, there are several interesting things

works for me (win 7 x64)

best regards,

Davide

If you like my plugins please consider to support the program buying a license; for personal contributions to me: paypal.me/dcprojects

#3 Опубликовано: 28.08.2013 01:18:41

Radovan Omorjan

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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

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

2 пользователям понравился этот пост

Davide Carpi 28.08.2013 03:58:00, Вячеслав Мезенцев 28.08.2013 02:51:00

#4 Опубликовано: 28.08.2013 03:27:27

Martin Kraska

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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.

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

1 пользователям понравился этот пост

Davide Carpi 28.08.2013 03:58:00

#5 Опубликовано: 28.08.2013 03:33:37

Вячеслав Мезенцев

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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.

Russia ☭ forever, Viacheslav N. Mezentsev

1 пользователям понравился этот пост

Davide Carpi 28.08.2013 03:58:00

#6 Опубликовано: 28.08.2013 04:50:52

Martin Kraska

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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.

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

#7 Опубликовано: 28.08.2013 05:13:24

Вячеслав Мезенцев

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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.

Russia ☭ forever, Viacheslav N. Mezentsev

1 пользователям понравился этот пост

Davide Carpi 28.08.2013 13:39:00

#8 Опубликовано: 28.08.2013 05:51:42

kilele

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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

#9 Опубликовано: 28.08.2013 08:04:36

Martin Kraska

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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.

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

#10 Опубликовано: 28.08.2013 11:21:27

Вячеслав Мезенцев

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Updated to GSL 1.16.

Russia ☭ forever, Viacheslav N. Mezentsev

3 пользователям понравился этот пост

Davide Carpi 28.08.2013 13:39:00, Radovan Omorjan 28.08.2013 16:42:00, ioan92 29.08.2013 08:51:00

#11 Опубликовано: 16.09.2016 10:37:36

Вячеслав Мезенцев

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Updated for the fully automatic build using Release Manager.

Russia ☭ forever, Viacheslav N. Mezentsev

#12 Опубликовано: 23.06.2018 17:49:08

overlord

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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

#13 Опубликовано: 23.06.2018 18:36:27

Вячеслав Мезенцев

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Because the plugin is not compatible with Linux + Mono:

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

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

Russia ☭ forever, Viacheslav N. Mezentsev

#14 Опубликовано: 01.08.2018 12:19:18

Вячеслав Мезенцев

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gslrkck simple test.

[albumimg]1497[/albumimg]

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Russia ☭ forever, Viacheslav N. Mezentsev

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sergio 01.08.2018 18:07:00

#15 Опубликовано: 12.12.2018 08:12:57

Вячеслав Мезенцев

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Updated.

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

Russia ☭ forever, Viacheslav N. Mezentsev

4 пользователям понравился этот пост

Andrey Ivashov 12.12.2018 09:34:00, Radovan Omorjan 12.12.2018 09:07:00, sergio 12.12.2018 09:16:00, frapuano 12.12.2018 09:33:00

#16 Опубликовано: 24.12.2018 12:50:43

Вячеслав Мезенцев

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Updated.

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

gsl.ode.kinetic1.sm (8 КиБ) скачан 155 раз(а).
gsl.ode.kinetic2.sm (14 КиБ) скачан 143 раз(а).
gsl.ode.kinetic3.sm (14 КиБ) скачан 142 раз(а).
gsl.ode.test1.sm (19 КиБ) скачан 144 раз(а).
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gsl.ode.kinetic1.pdf (77 КиБ) скачан 137 раз(а).
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gsl.ode.kinetic3.pdf (91 КиБ) скачан 123 раз(а).
gsl.ode.test1.pdf (110 КиБ) скачан 130 раз(а).
gsl.ode.test2.pdf (110 КиБ) скачан 133 раз(а).
gsl.ode.Amplitude detector.pdf (148 КиБ) скачан 146 раз(а).

Russia ☭ forever, Viacheslav N. Mezentsev

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sergio 24.12.2018 13:23:00, frapuano 24.12.2018 14:23:00, Radovan Omorjan 24.12.2018 14:53:00, Alvaro Diaz Falconi 25.12.2018 01:33:00

#17 Опубликовано: 21.01.2019 21:23:03

Вячеслав Мезенцев

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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).

Russia ☭ forever, Viacheslav N. Mezentsev

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frapuano 22.01.2019 05:02:00, Radovan Omorjan 22.01.2019 05:32:00, Davide Carpi 22.01.2019 07:43:00

#18 Опубликовано: 14.05.2019 10:33:45

Вячеслав Мезенцев

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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.

Russia ☭ forever, Viacheslav N. Mezentsev

#19 Опубликовано: 21.05.2021 01:55:24

Вячеслав Мезенцев

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