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Cookbook: Difference between revisions
→Find Algebraic Variables from ODE State Variables
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An Octave cookbook. Each entry should go in a separate section and have the following subsection: problem, solution, discussion and maybe a see also. | An Octave cookbook. Each entry should go in a separate section and have the following subsection: problem, solution, discussion and maybe a see also. | ||
__FORCETOC__ | |||
== Programs, Libraries, and Packages == | == Programs, Libraries, and Packages == | ||
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=== List all function in Octave === | === List all function in Octave === | ||
Use the following script | Use the following script (filename <code>list_func.m</code>) | ||
<syntaxhighlight lang="Octave"> | <syntaxhighlight lang="Octave"> | ||
## List of all builtin (C++) functions and m-file functions | ## List of all builtin (C++) functions and m-file functions | ||
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Check the [[Geometry package]] for many more distance functions (points, lines, polygons, etc.). | Check the [[Geometry package]] for many more distance functions (points, lines, polygons, etc.). | ||
=== Find Algebraic Variables from ODE State Variables === | |||
==== Problem ==== | |||
When using lsode or other ODE solver to find the state variables x as a function of time t in a set of ODE's, there seems to be no simple way to return and tabulate algebraic variables y that are a function of the state variables x and time t, other than the derivatives. | |||
Consider a modified version of the spring function defined above in the section on parametric functions: | |||
<syntaxhighlight lang="Octave"> | |||
function sprime=dspring (s, t) | |||
k=1; | |||
tau=1; | |||
x = s(1); | |||
v = s(2); | |||
y=x+v*tau; | |||
sprime(1) = v; | |||
sprime(2) = -k * y; | |||
endfunction | |||
</syntaxhighlight> | |||
What would be a way to way to use this function and lsode to tabulate not just the elements of x and sprime, but also (say) y as a function of time? | |||
==== Solution ==== | |||
Modify the function sprime to return y as a second argument: | |||
<syntaxhighlight lang="Octave"> | |||
function [sprime,y]=dspring (s, t) | |||
k=1; | |||
tau=1; | |||
x = s(1); | |||
v = s(2); | |||
y=x+v*tau; | |||
sprime(1) = v; | |||
sprime(2) = -k * y; | |||
endfunction | |||
</syntaxhighlight> | |||
lsode will happily ignore the second return argument y, but after x has been tabulated, y can be tabulated using the second return argument of the spring function in a for loop, e.g. | |||
<syntaxhighlight lang="Octave"> | |||
t = linspace (0, 10, 100); | |||
x = lsode ('dspring',[1;0], t); | |||
y=zeros(length(t),1); | |||
for i=1:length(t) | |||
[xtmp,y(i,1)]=dspring(x(i,:),t(i)); | |||
end | |||
</syntaxhighlight> | |||
==== Discussion ==== | |||
This is a simple example with one algebraic variable. Others can be added by extending the second dimension of the y array. | |||
[[Category: | [[Category:Examples]] | ||