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authorKarl Berry <karl@freefriends.org>2009-10-08 18:55:37 +0000
committerKarl Berry <karl@freefriends.org>2009-10-08 18:55:37 +0000
commit691011f868f30f9ca3eb7b8e2bfd788e528b000e (patch)
tree35e20e456d20847081c28a43b6f0820578905c40 /Master/texmf-dist/doc/latex/mfpic4ode
parent64ad51ab6d8f7139855dfe80c630239f9a602e5e (diff)
mfpic4ode move .tex to runtime (luecking 08 Oct 2009 13:51:19)
git-svn-id: svn://tug.org/texlive/trunk@15692 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/mfpic4ode')
-rw-r--r--Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex207
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diff --git a/Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex b/Master/texmf-dist/doc/latex/mfpic4ode/mfpic4ode.tex
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-%%
-%% This is file `mfpic4ode.tex',
-%% generated with the docstrip utility.
-%%
-%% The original source files were:
-%%
-%% mfpic4ode.dtx (with options: `tex')
-%%
-%% This is a generated file.
-%%
-%% Copyright (C) 2007 by Robert Marik <marik@mendelu.cz>
-%%
-%% This file may be distributed and/or modified under the conditions of
-%% the LaTeX Project Public License, either version 1.2 of this license
-%% or (at your option) any later version. The latest version of this
-%% license is in:
-%%
-%% http://www.latex-project.org/lppl.txt
-%%
-%% and version 1.2 or later is part of all distributions of LaTeX version
-%% 1999/12/01 or later.
-%%
-\catcode`\@=11
-
-\newif\ifcolorODEarrow
-%%%\colorODEarrowfalse
-\colorODEarrowtrue
-
-%%% The line from one point to another
-\def\ODEline#1#2{\lines{#1,#2}}
-
-%%% The variable ODErhs is used to store the function from the right
-%%% hand side of ODE in the form y'=f(x,y). We use command
-%%% ODEdefineequation to set up this variable.
-\def\ODEdefineequation#1{\fdef{ODErhs}{x,y}{#1}}
-
-%%% Integral curve using Euler method. The step of this method is
-%%% ODEstep and the number of steps is ODEstepcount. The points are
-%%% stored in metapost variables x1,y1.
-\def\trajectory#1#2{
- \begin{connect}
- \mfsrc{x1:=#1;y1:=#2;
- for i=1 upto ODEstepcount:
- x2:=x1+ODEstep;
- y2:=y1+ODEstep*ODErhs(x1,y1);}
- \ODEline{z1}{z2}
- \mfsrc{
- if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
- endfor
- }
- \end{connect}
-}
-
-%%% Integral curve using Runge--Kutta method.
-\def\trajectoryRK#1#2{
- \begin{connect}
- \mfsrc{x1:=#1;y1:=#2;
- for i=1 upto ODEstepcount:
- k1:=ODErhs(x1,y1);
- x3:=x1+(ODEstep/2);
- y3:=y1+k1*(ODEstep/2);
- k2:=ODErhs(x3,y3);
- x2:=x1+ODEstep;
- y2:=y1+ODEstep*k2;}
- \ODEline{z1}{z2}
- \mfsrc{
- if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
- endfor
- }
- \end{connect}
-}
-%%% Integral curve using fourth order Runge--Kutta method.
-\def\trajectoryRKF#1#2{
- \begin{connect}
- \mfsrc{x1:=#1;y1:=#2;
- for i=1 upto ODEstepcount:
- k1:=ODErhs(x1,y1);
- x3:=x1+(ODEstep/2);
- y3:=y1+k1*(ODEstep/2);
- k2:=ODErhs(x3,y3);
- y4:=y1+k2*(ODEstep/2);
- k3:=ODErhs(x3,y4);
- y5:=y1+k3*(ODEstep/2);
- k4:=ODErhs(x3,y5);
- kk:=(k1+2*k2+2*k3+k4)/6;
- x2:=x1+ODEstep;
- y2:=y1+ODEstep*kk;}
- \ODEline{z1}{z2}
- \mfsrc{
- if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
- endfor
- }
- \end{connect}
-}
-\def\ODEarrow#1#2{
- \mfsrc{x1:=#1; y1:=#2;
- x3:=x1+(ODEarrowlength)/((xscale)++(ODErhs(#1,#2)*yscale));
- y3:=y1+(ODEarrowlength*ODErhs(#1,#2))/((xscale)++(ODErhs(#1,#2)*yscale));
- if y3>y1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
- }
- \ifcolorODEarrow
- \drawcolor{ODEcolorarrow} \headcolor{ODEcolorarrow}
- \fi
- \draw\arrow\lines{z1,z3}
-}
-
-\def\ODEarrows#1{\ODE@cycle@points#1;,;}
-\def\trajectories#1{\ODE@cycle@IC#1;,;}
-\def\ODE@last@point{}
-\def\ODE@cycle@points#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
- \else\ODEarrow{#1}{#2}\relax\let\next\ODE@cycle@points\fi\next}
-\def\ODE@cycle@IC#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
- \else
- \trajectoryRKF{#1}{#2}\relax\let\next\ODE@cycle@IC\fi\next}
-\mfsrc{path p,q;color ODEcolorarrow;}
-
-%%% Onedimensional autonomous systems y'=f(y) where '=d/dx
-\def\ODEharrow#1{
- \mfsrc{x1:=#1;
- if ODErhs(0,x1)>0: x3:=x1+ODEarrowlength else: x3:=x1-ODEarrowlength fi;
- if ODErhs(0,x1)*ODErhs(0,x3)<0: x1:=-100;x3:=-100 fi;
- if x3>x1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
- }
- \ifcolorODEarrow \drawcolor{ODEcolorarrow}
- \headcolor{ODEcolorarrow} \fi
- \pen{1.5pt}
- \draw\arrow\lines{(x1,0),(x3,0)}
-}
-
-\def\ODEvarrow#1{
- \mfsrc{x1:=#1;
- if ODErhs(0,#1)>0:
- x3:=x1+(ODEarrowlength/yscale) else: x3:=x1-(ODEarrowlength/yscale) fi;
- if ODErhs(0,x1)*ODErhs(0,x3)<0: x1:=-100;x3:=-100 fi;
- if x3>x1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
- }
- \ifcolorODEarrow \drawcolor{ODEcolorarrow}
- \headcolor{ODEcolorarrow} \fi
- \pen{1.5pt}
- \draw\arrow\lines{(0,x1),(0,x3)}
-}
-
-%%% Twodimensional autonomous systems x'=f(x,y), y'=g(x,y) where '=d/dt
-\def\ASdefineequations#1#2{\fdef{ASf}{x,y}{#1}\fdef{ASg}{x,y}{#2}}
-
-\def\AStrajectory#1#2{
- \begin{connect}
- \mfsrc{x1:=#1;y1:=#2;
- for i=1 upto ODEstepcount:
- x2:=x1+ODEstep*ASf(x1,y1);
- y2:=y1+ODEstep*ASg(x1,y1);}
- \ODEline{z1}{z2}
- \mfsrc{
- if ((y2>yneg) and (y2<ypos)): x1:=x2; y1:=y2 fi;
- endfor
- }
- \end{connect}
-}
-\def\ASarrow#1#2{
- \mfsrc{x1:=#1; y1:=#2;
- x3:=x1+(ODEarrowlength*ASf(#1,#2))/((ASf(#1,#2)*xscale)++(ASg(#1,#2)*yscale ));
- y3:=y1+(ODEarrowlength*ASg(#1,#2))/((ASf(#1,#2)*xscale)++(ASg(#1,#2)*yscale ));
- if y3>y1:ODEcolorarrow:=blue else: ODEcolorarrow:=red fi;
- }
- \ifcolorODEarrow
- \drawcolor{ODEcolorarrow} \headcolor{ODEcolorarrow}
- \fi
- \draw\arrow\lines{z1,z3}
-}
-
-\def\ASarrows#1{\AS@cycle@points#1;,;}
-\def\AS@cycle@points#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
- \else\ASarrow{#1}{#2}\relax\let\next\AS@cycle@points\fi\next}
-\def\AStrajectories#1{\AS@cycle@IC#1;,;}
-\def\AS@cycle@IC#1,#2;{\def\temp{#1}\ifx\temp\ODE@last@point\let\next\relax
- \else
- \AStrajectoryRKF{#1}{#2}\relax\let\next\AS@cycle@IC\fi\next}
-\def\AStrajectoryRKF#1#2{
- \begin{connect}
- \mfsrc{x1:=#1;y1:=#2;
- TIMEsteps:=abs(TIMEend/TIMEstep);
- TIME:=0;
- for i=1 upto TIMEsteps:
- k1:=ASf(x1,y1);
- l1:=ASg(x1,y1);
- k2:=ASf(x1+(TIMEstep*k1/2),y1+(TIMEstep*l1/2));
- l2:=ASg(x1+(TIMEstep*k1/2),y1+(TIMEstep*l1/2));
- k3:=ASf(x1+(TIMEstep*k2/2),y1+(TIMEstep*l2/2));
- l3:=ASg(x1+(TIMEstep*k2/2),y1+(TIMEstep*l2/2));
- k4:=ASf(x1+(TIMEstep*k3),y1+(TIMEstep*l3));
- l4:=ASg(x1+(TIMEstep*k3),y1+(TIMEstep*l3));
- k5:=((k1)/6)+((k2)/3)+((k3)/3)+((k4)/6);
- l5:=(l1/6)+(l2/3)+(l3/3)+(l4/6);
- x2:=x1+(TIMEstep*k5);
- y2:=y1+(TIMEstep*l5);}
- \ODEline{z1}{z2}
- \mfsrc{
- if ((y2>yneg) and (y2<ypos) and (x2<xpos) and (x2>xneg)): x1:=x2; y1:=y2 fi;
- endfor
- }
- \end{connect}
-}
-
-\catcode`\@12\relax
-\endinput
-%%
-%% End of file `mfpic4ode.tex'.