Help with symbolic variables

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Tom
Tom 2014-3-7
评论： Tom 2014-3-7
Sorry, reposting this question again to see if any of you kind folk can help.
Hello,
I have the following to calculate associated legendre polynomials (in terms of angles: http://en.wikipedia.org/wiki/Associated_legendre_polynomials#Reparameterization_in_terms_of_angles)
%Calculating associated legendre polynomials %Using Rodriguez formula
syms z theta
m = 0;
l = 0;
for i = 1:10
Pl(i,:) = (inv((2^l)*factorial(l)))*diff(((z^2 - 1)^l),l);
Plm(i,:) = ((-1)^m)*((sin(theta))^m)*diff(Pl(i,:),m);
Plm(i,:) = subs(Plm(i,:), z, cos(theta));
l = l + 1;
end
I am struggling to find the way to replace the symbolic variable theta with a vector containing numerical values.
Any help would be greatly appreciated.
Tom

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Mischa Kim
Mischa Kim 2014-3-7
编辑：Mischa Kim 2014-3-7
Tom, do you mean something like
Plm_vec(i,:) = subs(Plm(i,:),{theta},{[pi/4, pi/5, pi/6]});
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Mischa Kim
Mischa Kim 2014-3-7
Copy-paste-execute the code below in the MATLAB command window:
clear all
syms z theta
m = 0;
l = 0;
for i = 1:10
Pl(i,:) = (inv((2^l)*factorial(l)))*diff(((z^2 - 1)^l),l);
Plm(i,:) = ((-1)^m)*((sin(theta))^m)*diff(Pl(i,:),m);
Plm(i,:) = subs(Plm(i,:), z, cos(theta)); l = l + 1;
Plm_vec(i,:) = subs(Plm(i,:),{theta}, {[pi/4, pi/5, pi/6]});
end
disp(Plm_vec)
you should get a 10-by-3 array of values. And, yes, you can evaluate outside the loop. E.g., following the loop you could do
subs(Plm(3),{theta},[0:0.1:0.5])
Tom
Tom 2014-3-7
Perfect, thanks a lot!
Sorry to keep bothering you with silly questions. But could you also explain why I am unable to use cosd and sind in the symbolic calculations?

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