How to plot a complicated function

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Atom
Atom on 15 Apr 2013
How to plot a complicated equation
-(r * x / K) + (alpha ^ 2 * (1 - c) ^ 2 * x * y / (1 + alpha * h * (1 - c) * x) ^ 2 * h) + d - d * exp(-2 * tau)=0
where x=d /(alpha*(-theta + d*h)*(-1 + c)); y=r*(K-x)*(-1-alpha*h*x+alpha*h*x*c)/(-1 + c)*K*alpha;
The other parameter values are: r=3.3;K=898;alpha=0.045;d=1.06;h=0.0437;theta=0.215;
I have to plot a tau vs c curve such that tau is varying from 0 to 1.6 & c is varying from 0 to .9. I have used the following code
r=3.3;K=898;alpha=0.045;d=1.06;h=0.0437;theta=0.215;
x=d /(alpha*(-theta + d*h) / (-1 + c));
y=r*(K-x)*(-1-alpha*h*x+alpha*h*x*c)/(-1 + c)*K*alpha;
yourfun=@(tau,c) -(r * x / K) + (alpha ^ 2 * (1 - c) ^ 2 * x * y / (1 + alpha * h * (1 - c) * x) ^ 2 * h) + d - d * exp(-2 * tau)
plot(yourfun)
I am getting a problem here and please help me to solve it, please.

Accepted Answer

Ahmed A. Selman
Ahmed A. Selman on 15 Apr 2013
It is the same code you wrote, only add loops over c and tau, and use the function (ezplot) to plot a function handle. And DO NOT use (plot) command to plot functions. So try this
clc
clear
close all
r=3.3;
K=898;
alpha=0.045;
d=1.06;
h=0.0437;
theta=0.215;
for c=0:0.1:0.9
for tau=0:0.1:0.6
x=d /(alpha*(-theta + d*h) / (-1 + c));
y=r*(K-x)*(-1-alpha*h*x+alpha*h*x*c)/(-1 + c)*K*alpha;
yourfun=@(tau,c) -(r * x / K) + (alpha ^ 2 * (1 - c) ^ 2 * x * y / ...
(1 + alpha * h * (1 - c) * x) ^ 2 * h) + d - d * exp(-2 * tau);
ezplot(yourfun)
title( {'\tau is ';num2str(tau);'c is ';num2str(c)} )
pause(0.01)
end
end
  3 Comments
Ahmed A. Selman
Ahmed A. Selman on 15 Apr 2013
@Youssef, yes it is true.
@Pallav, I've tried vectorizing the function, it generates an error (sizes do not match). You may try specifying similar size of c and tau, and use vectors instead of for..end loops. If the warning bothers you, then add:
warning off % at the beginning of the code
warning on % at the end of the code.
Regards.

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More Answers (1)

Youssef  Khmou
Youssef Khmou on 15 Apr 2013
Edited: Youssef Khmou on 15 Apr 2013
hi,
the vector x depends on the value c too, same as y , so they are also anonymous functions, in this case you have three anonymous functions with hierarchy yourfun[x(c),y(c),tau] , yourfun is built on tau, x and y and x,y are built on c , you have to make three functions, and when you try to plot function, you wont see a result because you are giving only scalar values like yourfun(4,5) that is only a point in 2d space , to get the result you need to supply two vectors c and tau and they must be of same length :
r=3.3;
K=898;
alpha=0.045;
d=1.06;
h=0.0437;
theta=0.215;
x=@(c) d./(alpha.*(-theta+d*h)./(-1+c));
y=@(c) r*(K-x(c)).*(-1-alpha*h*x(c)+alpha*h*x(c).*c)./(-1+c)*K*alpha;
yourfun=@(tau,c) -(r.*x(c)./K)+(alpha.^2.*(1-c).^2.*x(c).*y(c)./(1+alpha.*h.*(1-c).*x(c)).^2*h)+d-d.*exp(-2*tau)
tau=(0:0.1:1);
c=linspace(0,pi,length(tau));
F=yourfun(tau,c);
plot(F), grid on
figure,plot3(tau,c,F), grid on,view(-12,38)

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