Loop these vectors into an array?

I have a function that needs to be integrated.

int = @(x)(1+0.25*sin((P/5)*x*sin(AngRad)+(P/4))).*exp(-1i*2.*x.*cos(AngRad).*K(1));
q01 = integral(int,-L/2,L/2,'ArrayValued',true);

int = @(x)(1+0.25*sin((P/5)*x*sin(AngRad)+(P/4))).*exp(-1i*2.*x.*cos(AngRad).*K(2));
q02 = integral(int,-L/2,L/2,'ArrayValued',true);

%this goes on 35 more times

The value "P" is pi just with more digits, "AngRad" is a 721x1 vector of angles 0-360 degrees in radians, and "K" is originally a 37x1 vector of wave numbers. My goal is to find a way to loop (or some other way) the function and the integral so that I don't have to have 37 different "q01" to form my ultimate matrix which is a 721x37 matrix, a combination of the AngRad and K vectors. How and what is the best way to go about this and save computation time?

Answer 1

[Star Strider]

I would just index it into a loop:

intfcn = @(x,Kv)(1+0.25*sin((P/5)*x*sin(AngRad)+(P/4))).*exp(-1i*2.*x.*cos(AngRad).*Kv);
for k1 = 1:37
    q(:,k1) = integral(@(x)intfcn(x,K(k1)), -L/2,L/2, 'ArrayValued',true);
end

This is UNTESTED CODE (since I can’t test it), but should produce the matrix ‘q’ that you want. It changes your ‘intfcn’ function slightly (I changed its name because int is the Symbolic Math Toolbox integral function, and ‘overshadowing’ built-in MATLAB functions is to be avoided), but you also don’t have to re-define it in the loop each time, so it should be a bit more efficient as well.

[Sean Raffetto]

This loop does work, even though it's outputting the wrong matrix values. Thank you.

[Star Strider]

My pleasure!

I’m not quite certain what function you’re integrating (so I’m not certain how much this will help), but when in doubt, vectorise everything as a first step, unless you want matrix — rather than array — operations:

intfcn = @(x,Kv) (1+0.25.*sin((P/5)*x.*sin(AngRad)+(P/4))).*exp(-1i*2*x.*cos(AngRad).*Kv);

Answer 2

[Walter Roberson]

tic;
P = 3.14159265358979323846264338328;
AngRad = linspace(0,2*pi,721);
K = round(linspace(380,650,37));
L = sqrt(1/5);      %for lack of better value

[RadR, KR] = ndgrid(AngRad, K);
int = @(x)  (1+0.25.*sin((P/5).*x.*sin(RadR)).*(exp(-1i.*2.*x.*cos(RadR).*KR)));
q = integral(int, -L/2,L/2, 'ArrayValued', true);
toc
size(q)

Elapsed time is 1.986690 seconds.

ans =

     721    37