Help with symbolic variables

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

Answer 1

[Mischa Kim]

Tom, do you mean something like

 Plm_vec(i,:) = subs(Plm(i,:),{theta},{[pi/4, pi/5, pi/6]});

[Tom]

I think that's along the right lines, Mischa.

If you run the code, the first few results are:

Plm(1,:) = 1

Plm(2,:) = cos(theta)

Plm(3,:) = (3*cos(theta)^2)/2 - 1/2

Later on in the program I want to substitute'theta' in these results with vectors containing numerical values.

Do you see what I mean?

[Mischa Kim]

Sure. Just add my code line as the last command in your for -loop. You should get 3 values for each row of Plm.

[Tom]

Oh I see. That actually just returns a single value...?

But also is it not possible to utilise the results outside of the for loop? As that is ideally what I would like.

Thanks for your help.

[Tom]

Sorry you're right, there are 3 values for each line.

[Mischa Kim]

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]

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?