Gerben,
I am so happy I can contribute as a way of thanking you for all the
work that you've done for us. Thanks. Here, try this one, which uses an
RK4 routine. I just tried it out in Texshop, so I know they both
compile.
%This file creates two figures associated with the
%system x'=f(x,y), y'=g(x,y)
%1. Plots the graphs of x(t) and y(t)
%2. Plots the graph of (x(t),y(t)) in the phase plane.
%verbatimtex
%\input mtplain
%etex
%Generate standard eps
prologues:=2;
beginfig(0);
%Place RHS of x'=f(t,x,y) here
def fxy(expr t, x, y)=
(0.4-0.01*y)*x
enddef;
%Place RHS of y'=g(t,x,y) here
def gxy(expr t, x, y)=
(-0.3+0.005*x)*y
enddef;
%Declare some variables
path q, trajx, trajy;
pair L, R, B, T, xt, yt;
numeric sx[], sy[];
%Initialize clipping window
a:=0; b:=40; %left and right of viewing rectangle
c:=0; d:=150; %bottom and top of viewing rectangle
%Initialize timespan
tstart:=a;
tstop:=b;
%Initialize number of points to be plotted
N:=500;
%Calculate time increment dt for Euler's method
dt:=(tstop-tstart)/N;
%Scaling factors for horizontal and vertical axes. Note that this
produces
%an image that is 2 inches by 2 inches.
(b-a)*ux=1.75in;
(d-c)*uy=1.75in;
%Clipping boundary
q=(a,c)--(b,c)--(b,d)--(a,d)--cycle;
%Use Runge-Kutta4 to create path (t,x(t))
%Choose initial condition
t:=tstart;
x:=40;
y:=20;
trajx:=(t,x);
forever:
sx1:=fxy(t,x,y);
sy1:=gxy(t,x,y);
sx2:=fxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
sy2:=gxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
sx3:=fxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
sy3:=gxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
sx4:=fxy((t+dt),(x+dt*sx3),(y+dt*sy3));
sy4:=gxy((t+dt),(x+dt*sx3),(y+dt*sy3));
x:=x+dt*(sx1+2*sx2+2*sx3+sx4)/6;
y:=y+dt*(sy1+2*sy2+2*sy3+sy4)/6;
t:=t+dt;
trajx:=trajx..(t,x);
exitif ((t>tstop) or (t>b) or (xd));
endfor;
%Use Runge-Kutta4 to create path (t,y(t))
%Choose initial condition
t:=tstart;
x:=40;
y:=20;
trajy:=(t,y);
forever:
sx1:=fxy(t,x,y);
sy1:=gxy(t,x,y);
sx2:=fxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
sy2:=gxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
sx3:=fxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
sy3:=gxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
sx4:=fxy((t+dt),(x+dt*sx3),(y+dt*sy3));
sy4:=gxy((t+dt),(x+dt*sx3),(y+dt*sy3));
x:=x+dt*(sx1+2*sx2+2*sx3+sx4)/6;
y:=y+dt*(sy1+2*sy2+2*sy3+sy4)/6;
t:=t+dt;
trajy:=trajy..(t,y);
exitif ((t>tstop) or (t>b) or (yd));
endfor;
%Draw the paths x(t) and y(t) and clip them to bounding box
draw trajx xscaled ux yscaled uy withcolor red;
draw trajy xscaled ux yscaled uy withcolor red dashed evenly;
clip currentpicture to (q xscaled ux yscaled uy);
%Label graph x(t) and initial condition
len:= 0.65*(length trajx);
xt:=point len of trajx;
label.urt(btex $\scriptstyle x(t)$ etex, (xt xscaled ux yscaled uy));
%Label graph y(t) and initial condition
len:= 0.5*(length trajy);
yt:=point len of trajy;
label.lrt(btex $\scriptstyle y(t)$ etex, (yt xscaled ux yscaled uy));
%Initialize left and right endpoints on time-axis
L=(a*ux,0);R=(b*ux,0);
%Draw and label t-axis
drawarrow L--R;
label.rt(btex $\scriptstyle t$ etex,(b*ux,0));
%Initialize bottom and top endpoints on time-axis
B=(0,c*uy);T=(0,d*uy);
%Draw and label vertical axis
drawarrow B--T;
label.lft(btex $\scriptstyle 0$ etex, B);
label.lft(btex $\scriptstyle 150$ etex, T);
endfig;
beginfig(2);
%Make some variables local
save ux, uy;
%Place RHS of x'=f(t,x,y) here
def fxy(expr t, x, y)=
(0.4-0.01*y)*x
enddef;
%Place RHS of y'=g(t,x,y) here
def gxy(expr t, x, y)=
(-0.3+0.005*x)*y
enddef;
%Declare some variables
path q, trajxy;
pair L, R, B, T;
%Initialize clipping window
a:=0; b:=150; %left and right of viewing rectangle
c:=0; d:=100; %bottom and top of viewing rectangle
%Initialize timespan
tstart:=a;
tstop:=b;
%Initialize number of points to be plotted
N:=500;
%Calculate time increment dt for Euler's method
dt:=(tstop-tstart)/N;
%Scaling factors for horizontal and vertical axes. Note that this
produces
%an image that is 2 inches by 2 inches.
(b-a)*ux=1.75in;
(d-c)*uy=1.75in;
%Clipping boundary
q=(a,c)--(b,c)--(b,d)--(a,d)--cycle;
%Use Runge-Kutta4 to create path (x(t),y(t))
%Choose initial condition
t:=tstart;
x:=40;
y:=20;
trajxy:=(x,y);
forever:
sx1:=fxy(t,x,y);
sy1:=gxy(t,x,y);
sx2:=fxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
sy2:=gxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
sx3:=fxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
sy3:=gxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
sx4:=fxy((t+dt),(x+dt*sx3),(y+dt*sy3));
sy4:=gxy((t+dt),(x+dt*sx3),(y+dt*sy3));
x:=x+dt*(sx1+2*sx2+2*sx3+sx4)/6;
y:=y+dt*(sy1+2*sy2+2*sy3+sy4)/6;
t:=t+dt;
trajxy:=trajxy..(x,y);
exitif ((t>tstop) or (t>b) or (xb) or (yd));
endfor;
%Draw the paths x(t) and y(t) and clip them to bounding box
draw trajxy xscaled ux yscaled uy withcolor red;
clip currentpicture to (q xscaled ux yscaled uy);
%Initialize left and right endpoints on x-axis
L=(a*ux,0);R=(b*ux,0);
%Draw and label x-axis
drawarrow L--R;
label.rt(btex $\scriptstyle x$ etex,(b*ux,0));
label.bot(btex $\scriptstyle 0$ etex,L);
label.bot(btex $\scriptstyle 150$ etex,R);
%Initialize bottom and top endpoints on y-axis
B=(0,c*uy);T=(0,d*uy);
%Draw and label vertical axis
drawarrow B--T;
label.rt(btex $\scriptstyle y$ etex,(0,d*uy));
label.lft(btex $\scriptstyle 0$ etex, B);
label.lft(btex $\scriptstyle 100$ etex, T);
endfig;
end;
On Mar 26, 2005, at 3:19 PM, Gerben Wierda wrote:
I am trying to learn metapost/fun, inline in ConTeXt source. Some
basic things are clear, but now the issue is metapost itself.
For instance, I would like to plot a Fourier approximation of a block
function.
For instance, I would like to plot a gaussian spread.
I am looking for examples on how to do this. I need to do a bit of
programming here and these are my initial projects.
Thanks in advance,
G
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