Matlab vectorizing equations and matrix multiplication - matlab

Question

I have a program that currently uses a for loop to iterate through a set of functions. I've tried using parfor but that only works on the university's version of Matlab. I'd like to vectorize the handling of this so that a for loop isn't necessary. The equations I'm using basically call different types of Bessel functions and are contained in separate functions.
Here's what I'm trying to do:
For each value of m, build a vector of matrix elements for each required matrix. Then build each full matrix. I think this is working correctly.
Where it's throwing an error is on the final matrix multiplication... even if I just multiply the left 2x2 by the middle 2x2 I get the dreaded error:
??? Error using ==> mtimes
Inner matrix dimensions must agree.
Error in ==> #(m)CL(m)*CM(m)*CR(m)
% Vector for summation. 1 row, 301 columns with data from 0->300
m_max=301;
m=[0:m_max-1];
% Build the 300 elements for the left 2x2 matrix.
CL_11=#(m) H1(m,alpha1);
CL_12=#(m) H2(m,alpha1);
CL_21=#(m) n1*dH1(m,alpha1);
CL_22=#(m) n1*dH2(m,alpha1);
% Build the 300 elements for the middle 2x2 matrix.
CM_11=#(m) n1*dH2(m,alpha2);
CM_12=#(m) -1*H2(m,alpha2);
CM_21=#(m) -1*n1*dH1(m,alpha2);
CM_22=#(m) H1(m,alpha2);
% Build the 300 elements for the right 2x1 matrix.
CR_11=#(m) J(m,alpha3);
CR_21=#(m) n2*dJ(m,alpha3);
% Build the left (CL), middle (CM) and right (CR) matrices.
CL=#(m) [CL_11(m) CL_12(m);CL_21(m) CL_22(m)];
CM=#(m) [CM_11(m) CM_12(m);CM_21(m) CM_22(m)];
CR=#(m) [CR_11(m);CR_21(m)];
% Build the vector containing the products of each triplet of
% matrices.
C=#(m) CL(m)*CM(m)*CR(m);
cl=CL(m)
cm=CM(m)
cr=CR(m)
c=CL(m)*CM(m)*CR(m)
If you have any suggestions or recommendations, I'd greatly appreciate it! I'm still a newbie with Matlab and am trying to develop a higher level of ability with use of matrices and vectors.
Thanks!!

Answer 1

Your matrices are not 2x2. When you do CL_11(m) with m a 1x300 vector, CL_11(m) will be 1x300 as well. Thus CL(m) is 2x301. To get around this, you have to calculate the matrices one-by-one. There are two approaches here.
c=arrayfun(C,m,'UniformOutput',false)
will return a cell array, and so c{1} corresponds to m(1), c{2} to m(2), etc.
On the other hand, you can do
for i=1:m_max
c(:,:,i)=C(m(i));
end
and then c(:,:,i) corresponds to m(1), etc.
I'm not sure which version will be faster, but you can test it easily enough with your code.

Answer 2

If you go through the symbolic toolbox you can construct a function that is easier to handle.
%% symbolic
CL = sym('CL',[2,2])
CM = sym('CM',[2,2])
CR = sym('CR',[2,1])
r = CL*CM*CR
f = matlabFunction(r)
%% use some simple functions so it can be calculated as example
CL_11=#(m) m+1;
CL_12=#(m) m;
CL_21=#(m) m-1;
CL_22=#(m) m+2;
CM_11=#(m) m;
CM_12=#(m) m;
CM_21=#(m) 2*m;
CM_22=#(m) 2*m;
CR_11=#(m) m;
CR_21=#(m) 1-m;
%% here the substitution happens:
fh = #(m) f(CL_11(m),CL_12(m),CL_21(m),CL_22(m),CM_11(m),CM_12(m),CM_21(m),CM_22(m),CR_11(m),CR_21(m))
Out of interest I did a small speed test:
N=1e5;
v = 1:N;
tic
% .... insert symbolic stuff from above
r1 = fh(v);
t1=toc % gives 0.0842s for me
vs
CL=#(m) [CL_11(m) CL_12(m);CL_21(m) CL_22(m)];
CM=#(m) [CM_11(m) CM_12(m);CM_21(m) CM_22(m)];
CR=#(m) [CR_11(m);CR_21(m)];
C=#(m) CL(m)*CM(m)*CR(m);
tic
r2 =arrayfun(C,v,'UniformOutput',false);
t2=toc % gives 7.6874s for me
and
tic
r3 = nan(2,N);
for i=1:N
r3(:,i)=C(v(i));
end
t3=toc % 8.1503s for me