How to assemble coefficient matrix?

http://postimg.org/image/ap6j4tv0r/

I am trying to assemble a N x N matrix for IC as shown above. I have vectors for ao(theta), c(theta), and thetal. I am trying to figure out how to assemble the IC matrix from these vectors using the equation above. From there I need to solve for the A vector values.

[Christopher]

I believe the repmat command can be used to assemble this matrix, but I cannot figure out how I would write this out to generate the n x n IC matrix.

Thanks

Answer 1

[Roger Stafford]

I'll assume you have a0, c, and theta as column vectors of corresponding elements and of length N.

 IC = bsxfun(@plus,4*b./(a0.*c),(1./sin(theta))*(1:N)).*sin(theta*(1:N));

Of course it is much easier to write nested for loops:

 IC = zeros(N);
 for l = 1:N
   for m = 1:N
     IC(l,m) = (4*b/a(l)/c(l)+m/sin(theta(l)))*sin(m*theta(l));
   end
 end

Note: You ought to use something other than lowercase l for your index. It is too easily confused with the numeral 1.

[Christopher]

Thank you Roger

One question though, what purpose does the IC=zeros(N) line serve?

Thanks again

[Roger Stafford]

Doing the initial 'zeros' preallocates memory for the IC array all at once rather than increasing it piecemeal in the for-loops. For large arrays the latter can slow down the execution of code greatly. This does not apply to vectorized code such as in the first method above using 'bsxfun' since these matlab functions do their own preallocation.