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how to evaluate a symbolic function in matlab
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Hi,
I am trying to automate my code to get the derivative of a function an evaluate that in given points. For example,
syms x
func=cos((pi*x)^4);
RHS=diff(func,x,2);
% RHS will be ==> - 16*pi^8*x^6*cos(pi^4*x^4) - 12*pi^4*x^2*sin(pi^4*x^4)
x=[ -1
-0.978147600733806
-0.913545457642601
-0.809016994374947
-0.669130606358858
-0.5
-0.309016994374947
-0.104528463267653
0.104528463267653
0.309016994374947
0.5
0.669130606358858
0.809016994374947
0.913545457642601
0.978147600733806
1]
and I want RHS and Func in those z values as a vector.
I appreciate the help. Thank you.
0 Comments
Answers (4)
Youssef Khmou
on 11 Feb 2013
hi, you can use function_handle :
func=@(x) cos((pi*x).^4)
x=0:100; % example of vector x .
RHS=diff(func(x),2);
8 Comments
Youssef Khmou
on 12 Feb 2013
Edited: Youssef Khmou
on 12 Feb 2013
Well in this case you have to add diff(x) as DENOMINATOR :
Given your x :
func=@(x) x.^3;
f=x.^3;
df2=6.*x;
df2(1)=[];
d1=diff(func(x))./diff(x);
RHS=diff(d1)./diff(x(1:end-1));
figure, plot(df2), hold on, plot(RHS,'r')
legend(' numerical d²f',' diff(function_handle,2)')
you have to increase the Sample Rate in x to get better approximation .
Brian B
on 12 Feb 2013
Edited: Brian B
on 12 Feb 2013
Hi Youssef,
I'm not saying your solution is not valid. I was simply pointing out that the original question refers to symbolic calculation of an exact derivative. It is possible to evaluate the symbolic expression at any arbitrary set of points, without regard to interval size or ordering. That is what the subs command does, to which ChristianW referred. See my answer below.
regards,
Brian
Youssef Khmou
on 12 Feb 2013
Edited: Youssef Khmou
on 12 Feb 2013
Kamuran, to get better approximation you need to increase the sample rate in x and interpolate :
x=[ -1
-0.978147600733806
-0.913545457642601
-0.809016994374947
-0.669130606358858
-0.5
-0.309016994374947
-0.104528463267653
0.104528463267653
0.309016994374947
0.5
0.669130606358858
0.809016994374947
0.913545457642601
0.978147600733806
1];
x=x';
x=interp(x,5); % Example
func=@(x) x.^3;
f=x.^3;
df2=6.*x;
df2(1)=[];
d1=diff(func(x))./diff(x);
RHS=diff(d1)./diff(x(1:end-1));
figure, plot(df2), hold on, plot(RHS,'r')
legend(' numerical d²f',' diff(function_handle,2)')
Compare this result with the one given in the Comment with original x, there is an enhancement .
I hope that helps
0 Comments
Brian B
on 12 Feb 2013
syms x
func=cos((pi*x)^4);
RHS=diff(func,x,2);
xx=-1:0.1:1;
d2f = subs(RHS, xx)
2 Comments
vikas singh
on 12 Mar 2023
if I have function of two variable suppose x and t and I have to evaluate it on x=0:100:10000 and t= 0,1,5,10 15. how to do. suppose the fucnction is F(x,t)=sin(x)*exp(t)
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