How to speed up iterating a large data in a nested loop ?

%example 
a=1x1000;
b=1x1000;
for i=1:length(a)
    for j 1:length(b)
        x(i,j)=cos(a(i));
        y(i,j)=sin(b(j));
    end
end

Thank you and appreciate!

Answer 1

[Image Analyst]

Try this:

% Create sample data.
% numPoints = 500;
a = pi * rand(1, numPoints);
b = pi * rand(1, numPoints);
% Create x and y
x = repmat(cos(a(:)), [1, numPoints]);
y = repmat(sin(b), [numPoints, 1]);
% Display the x and y matrices:
cmap = jet(256);
subplot(2, 1, 1);
imshow(x, [], 'Colormap', cmap);
colorbar;
title('x', 'FontSize', 20);
subplot(2, 1, 2);
imshow(y, [], 'Colormap', cmap);
colorbar;
title('y', 'FontSize', 20);

[HN]

Image Analyst , Actually the code in the original quesion has been just example not a real issue. In the actual problem, the input cannot be moidified as you put it in the answer. Below is the actual problem and the computation time is quite long. Can it be still improved ?

Thank you .

th_int  =1X1000  % value cannot be changed  
psi_int = 1X1000 % value cannot be changed  
phi_int = 1X1000 % value cannot be changed  
for k=1: length(th_int)
    for j=1:length(th_int)
        th(j) = th_int(j);
        psi(k) = psi_int(k);
        phi(j) =phi_int(j);
        R=Rot('z',th(j))*Rot('y',psi(k))*Rot('x',phi(j)); % rotation matrix    
        p=[Pose(1,k); Pose(2,k);Pose(3,k)]; 
        
        a1(:,k)=R*[rp;0;0];
        a2(:,k)=R*[rp*cos(alpha);rp*sin(alpha);0];
        a3(:,k)=R*[rp*cos(beta);rp*sin(beta);0];
        
        r1=p+R*[rp;0;0];
        r2=p+R*[rp*cos(alpha);rp*sin(alpha);0];
        r3=p+R*[rp*cos(beta);rp*sin(beta);0];
        
        g1=inv(Rot('z',0))*r1;
        g2=inv(Rot('z',alpha))*r2;
        g3=inv(Rot('z',beta))*r3;
        
        
        
        b1(k)=g1(1)+sqrt(L^2-g1(3)^2);
        b2(k)=g2(1)+sqrt(L^2-g2(3)^2);
        b3(k)=g3(1)+sqrt(L^2-g3(3)^2);
        
        % passive koint value
        sin_th21=(g1(1)-b1(k))/L;
        cos_th21=g1(3)/L;
        th21(k)=atan2(sin_th21,cos_th21);
        
        sin_th22=(g2(1)-b2(k))/L;
        cos_th22=g2(3)/L;
        th22(k)=atan2(sin_th22,cos_th22);
        
        sin_th23=(g3(1)-b3(k))/L;
        cos_th23=g3(3)/L;
        th23(k)=atan2(sin_th23,cos_th23);
        
        %%   
        pr1(k)=norm(r1-p); % radius 1
        pr2(k)=norm(r3-p); % radius 2
        pr3(k)=norm(r3-p);  % radius 3

        r12(k)=norm(r1-r2);
        r23(k)=norm(r3-r2);
        r31(k)=norm(r3-r1);
        
        p11=Rot('z',0)*[b1(k)*1000;0;0];         
        p12=Rot('z',2*pi/3)*[b2(k)*1000;0;0]; 
        p13=Rot('z',4*pi/3)*[b3(k)*1000;0;0];
        
        L1(k)=norm(r1-[b1(k);0;0]);
        L2(k)=norm(r2-Rot('z',2*pi/3)*[b2(k);0;0]);
        L3(k)=norm(r3-Rot('z',4*pi/3)*[b3(k);0;0]);   
        
        o=[0;0;0];
        figure(1)
        clf;
        hold on
        drawVector([o,p11],'b2*');
        drawVector([o,p12],'b2*');
        drawVector([o,p13],'b2*');
        
        drawLine([p11,r1*1000],'b2*');
        drawLine([p12,r2*1000],'b2*');
        drawLine([p13,r3*1000],'b2*');
        
        drawLine([o,[1707;0;0]],'k');
        drawLine([o,Rot('z',2*pi/3)*[1707;0;0]],'k--');
        drawLine([o,Rot('z',-2*pi/3)*[1707;0;0]],'k--');   %beta(j)
        
        drawLine([r1*1000 r2*1000]);
        drawLine([r2*1000 r3*1000]);
        drawLine([r3*1000 r1*1000]);
        
        xlim ([-2000 2000]);
        ylim ([-2000 2000]);
        zlim ([-250 1000]);
        axis square;
        hold on;
        pause(0.01)
        
        
        Rx(k,j)=(th(j));
        Ry(k,j)=(psi(k));
        Rz(k,j)=(phi(k));
        XX(k,j)=p(1);
        YY(k,j)=p(2);
        ZZ(k,j)=p(3);
            
    end 
end 

[Image Analyst]

If things depend on only k, and not j, then put them between the k and j loop, not inside the j loop.