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%%
%% This is file `pst-ode.tex',
%%
%% Alexander Grahn, (C) 2012--today
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% `pst-ode' defines \pstODEsolve for integrating systems of first order
%% ODEs using the Runge-Kutta-Fehlberg (RKF45) method with automatic
%% step size adjustment
%%
\def\fileversion{0.10}
\def\filedate{2017/06/16}
\csname PSTODELoaded\endcsname
\let\PSTODELoaded\endinput
%
% Requires some packages
\ifx\PSTricksLoaded\endinput\else \input pstricks \fi
%
\message{`pst-ode' v\fileversion, \filedate\space (ag)}
%
\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax
\pst@addfams{pst-ode}
%% prologue for postcript
\pstheader{pst-ode.pro}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% pstODEsolve
%
% LaTeX command for integrating systems of first order ODEs using the Runge-
% Kutta-Fehlberg method with automatic step size adjustment;
% values of the integration parameter `t' as well as the solution (= state)
% vectors `x(t)' at output points are stored as a long list in a Postscript
% object; its content can be plotted using the listplot* functions
% of pst-plot and pst-3dplot packages.
%
% Optionally, the result can be written to a file (ps2pdf -dNOSAFER ...)
%
% Usage:
%
% \pstODEsolve[Options]
% {result}{output vector format}{ta}{tb}{number of output points}
% {initial cond.}{function}
%
% options:
% * append result appended to <result> which must already exist (e. g.
% from previous use of \pstODEsolve); usually the initial
% condition vector argument is left empty in order to continue
% integration from the last state
% * saveData result is written to file <result>.dat
% * algebraic (system of) ODE given in infix notation
% * algebraicIC initial condition vector given in infix notation
% * algebraicT integration interval limits ta, tb given in infix notation
% * algebraicOutputFormat output vector format given in infix notation
% * algebraicAll output vector format, ta, tb, initial cond., function given
% in infix notation
% * silent suppress output of stepping information
% * varsteptol relative tolerance for step size adjustment
%
% arguments:
%
% #1: Postscript identifier taking the result as a long list of state vectors
% calculated at the output points
% #2: output vector format, e. g. `(t) 0 1'; specifies which data to be written
% to #1; (t) (parentheses required) puts value of integration parameter `t'
% into the output list; 0, 1, 2, etc. specify the elements of the state
% vector to be put into the output list
% #3: start value of integration parameter (ta)
% #4: end value of integration parameter (tb)
% #5: number of output points, including ta and tb; must be >= 2
% #6: initial condition vector; if empty, continue integration from the last
% state vector of the previous \pstODEsolve usage or from state vector set
% by \pstODEsetOrRestoreState macro
% #7: right hand side of ODE system; if given in Postscript notation (algebraic=
% false), the function provided should pop (in reverse order!) the elements
% of the current state vector from the operand stack and push the first
% derivatives (right hand side of ODE system) back to it; inside the
% function, the integration parameter can be accessed using `t'
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\define@boolkey[psset]{pst-ode}[PstODE@]{append}[true]{}%
\define@boolkey[psset]{pst-ode}[PstODE@]{saveData}[true]{}%
\define@boolkey[psset]{pst-ode}[PstODE@]{algebraicT}[true]{}%
\define@boolkey[psset]{pst-ode}[PstODE@]{algebraicIC}[true]{}%
\define@boolkey[psset]{pst-ode}[PstODE@]{algebraicOutputFormat}[true]{}%
\define@boolkey[psset]{pst-ode}[PstODE@]{algebraicAll}[true]{}%
\define@boolkey[psset]{pst-ode}[PstODE@]{silent}[true]{}%
\define@key[psset]{pst-ode}{varsteptol}{\def\ode@varsteptol{#1}}%
\def\pstODEsolve{\def\pst@par{}\pst@object{pstODEsolve}}%
\def\pstODEsolve@i#1#2#3#4#5#6#7{%
\pst@killglue%
\begingroup%
\use@par%
\def\filemode{w}%
\ifPstODE@append\def\filemode{a}\fi%
\edef\ode@ta{#3{}}%
\edef\ode@tb{#4{}}%
\edef\ode@init{#6{}}%
\edef\ode@init{\expandafter\ode@zapspace\ode@init\@nil}%
\edef\ode@arg{#7{}}%
\ifPstODE@algebraicAll%
\PstODE@algebraicTtrue%
\PstODE@algebraicICtrue%
\PstODE@algebraicOutputFormattrue%
\Pst@algebraictrue%
\fi%
\ifPstODE@algebraicOutputFormat\edef\ode@fmt{#2{}}\fi%
\pstVerb{
tx@odeDict begin
\ifPstODE@silent
/odeprint systemdict /pop get def
\else
/odeprint {0 cvs print flush} def
/odeprint load 0 256 string put
\fi
/ode@tol \ode@varsteptol\space def % rel. tolerance for step size adjustment
%process arguments
\ifPstODE@saveData /statefile (#1.dat) (\filemode) file def \fi
\ifPstODE@algebraicT
tx@Dict begin (\expandafter\ode@zapspace\ode@ta\@nil)
AlgParser cvx exec end ode@dict /tStart exch def end
tx@Dict begin (\expandafter\ode@zapspace\ode@tb\@nil)
AlgParser cvx exec end ode@dict /tEnd exch def end
\else
tx@Dict begin 1 dict begin #3 end end ode@dict /tStart exch def end
tx@Dict begin 1 dict begin #4 end end ode@dict /tEnd exch def end
\fi
ode@dict /dt tEnd tStart sub #5\space 1 sub div def end % output step size
\ifx\@empty#6\@empty\else
\ifPstODE@algebraicIC
true setglobal globaldict /ode@laststate [
tx@Dict begin (\ode@init) AlgParser cvx
exec end
] put false setglobal
\else
true setglobal
globaldict /ode@laststate [tx@Dict begin 1 dict begin #6 end end] put
false setglobal
\fi
\fi%
ode@dict /xlength ode@laststate length def end % number of equations
ode@dict /xlength1 xlength 1 add def end % number of equations plus 1
\ifPst@algebraic
/ode@rpn tx@Dict begin (\expandafter\ode@zapspace\ode@arg\@nil) AlgParser end cvx bind def
/ODESET {%system of ODEs
/x exch def /y x def tx@Dict begin ode@rpn end ode@dict xlength end array astore
} bind def
\else
/ODESET {
aload pop tx@Dict begin 4 begin #7 end end ode@dict xlength end array astore
} bind def
%ensure local scope of user defined variables in #7, from BlueBook, p. 133
/ODESET load 4 1 dict put
\fi
\ifPstODE@algebraicOutputFormat
/ode@fmtrpn tx@Dict begin (\expandafter\ode@zapspace\ode@fmt\@nil) AlgParser end cvx bind def
/formatoutput {%
ode@laststate /x exch def /y x def /t ode@dict tcur end def
tx@Dict begin ode@fmtrpn end
} bind def
\else /formatoutput {[#2] assembleresult} def \fi%
%perform ode integration
(\string\n pstODEsolve (RKF45),\string\n) odeprint
(-/+ failed/successful step; "o" output step; "!" step size underflow (stop):\string\n) odeprint
ode@dict
/tcur tStart def % current parameter t value
/tout tStart dt add def % next output t
/ddt dt def % initial integration step size
end
\ifPstODE@append\else
[
[formatoutput]
\ifPstODE@saveData dup writeresult \fi
aload pop
true setglobal
]
globaldict exch /#1 exch cvx put
false setglobal
(o) odeprint
\fi
#5\space 1 sub {
ode@laststate ODEINT [ exch aload pop true setglobal ]
globaldict exch /ode@laststate exch put false setglobal
[
#1 [formatoutput]
\ifPstODE@saveData dup writeresult \fi
aload pop
true setglobal
]
globaldict exch /#1 exch cvx put
false setglobal
} repeat (\string\n) odeprint
\ifPstODE@saveData statefile closefile \fi
end % tx@odeDict
}%
\endgroup%
\ignorespaces%
}
\def\ode@zapspace#1#2\@nil{% helper for stripping spaces from argument
\ifx#1 \relax\else#1\fi%
\ifx\@empty#2\@empty\else\ode@zapspace#2\@nil\fi%
}
%macro for saving last state vector into PS object
\def\pstODEsaveState#1{% #1: identifier
\pstVerb{
true setglobal
globaldict /#1 [ode@laststate cvx exec] cvx put
false setglobal
}%
}
%macro for restoring state vector from PS object or setting it from
%literal vector
\def\pstODEsetOrRestoreState#1{% #1: identifier or
\pstVerb{ % space separated list of numbers
true setglobal
globaldict /ode@laststate [#1] put
false setglobal
}%
}
\psset[pst-ode]{append=false,saveData=false,algebraicIC=false,algebraicT=false,
silent=false,varsteptol=1e-6,algebraicOutputFormat=false,algebraicAll=false
}
\psset{algebraic=false}
\catcode`\@=\PstAtCode\relax
%% END: pst-ode.tex
\endinput
|
