how to Improve the speed matlab - matlab

Question

This is my matlab code. It runs too slow and I had no clue how to improve it.
Could you help me to improve the speed?
What I would like to do is to create some random points and then remove the random points to make them similar to my target points.
syms Dx Dy p q;
a = 0;
num = 10;
x = rand(1,num);
y = rand(1,num);
figure(1)
scatter(x,y,'.','g')
%num_x = xlsread('F:\bin\test_2');% num 1024
%figure(2)
%scatter(num_x(:,1),num_x(:,2),'.','r');
q = 0;
num_q = 10;
x_q = randn(1,num_q);
y_q = randn(1,num_q);
%figure(2)
hold on;
scatter(x_q,y_q,'.','r')
for i = 1:num_q;
for j = 1:num_q;
qx(i,j) = x_q(i) - x_q(j);
qy(i,j) = y_q(i) - y_q(j);
%qx(i,j) = num_x(i,1) - num_x(j,1);
%qy(i,j) = num_x(i,2) - num_x(j,2);
%d~(s(i),s(j))
if ((qx(i,j))^2+(qy(i,j)^2))> 0.01 % find neighbours
qx(i,j) = 0;
qy(i,j) = 0;
end
end
end
for i = 1:num_q;
for j = 1:num_q;
if qx(i,j)>0&&qy(i,j)>0
q = q + exp(-(((Dx - qx(i,j))^2)+((Dy - qy(i,j))^2))/4);%exp(-(((Dx - qx(i,j))^2)+((Dy - qy(i,j))^2))/4);
end
end
end
%I = ones(num,num); % I(s) should from a grayscale image
%r = 1./sqrt(I);
for s = 1:100;
for i = 1:num;
for j = 1:num;
dx(i,j) = x(i) - x(j);
dy(i,j) = y(i) - y(j);
%d~(s(i),s(j))
if ((dx(i,j))^2+(dy(i,j)^2))> 0.05 % delta p, find neighbours
dx(i,j) = 0;
dy(i,j) = 0;
end
end
end
p = 0;
for i = 1:num;
for j = 1:num;
if dx(i,j)>0&&dy(i,j)>0
p = p + exp(-(((Dx - dx(i,j))^2)+((Dy - dy(i,j))^2))/4);
end
end
end
p = p - q;
sum = 0;
for i = 1:num;
for j = 1:num;
if dx(i,j)>0&&dy(i,j)>0;
kx(i,j) = (1/2)*(Dx-dx(i,j))*exp((-(Dx-dx(i,j))^2+(Dy-dy(i,j))^2)/4);
ky(i,j) = (1/2)*(Dy-dy(i,j))*exp((-(Dx-dx(i,j))^2+(Dy-dy(i,j))^2)/4);
end
end
end
sum_x = ones(1,num);% 1行N列0矩阵
sum_y = ones(1,num);
%fx = zeros(1,num);
for i = 1:num;
for j = 1:num;
if dx(i,j)>0&&dy(i,j)>0;
fx(i) = p*kx(i,j);% j is neighbour to i
fy(i) = p*ky(i,j);
%fx(i) = matlabFunction(fx(i));
%fy(i) = matlabFunction(fy(i));
%P =quad2d(#(Dx,Dy) fx,0,0.01,0,0.01);
%fx =quad(#(Dx) fx,0,0.01);
%fx(i) =quad(#(Dy) fx(i),0,0.01);
%Q =quad2d(#(Dx,Dy) fy,0,0.01,0,0.01);
fx(i) = double(int(int(fx(i),Dx,0,0.01),Dy,0,0.01));
fy(i) = double(int(int(fy(i),Dx,0,0.01),Dy,0,0.01));
%fx(i) = vpa(p*kx(i,j));
%fy(i) = vpa(p*ky(i,j));
%fx(i) = dblquad(#(Dx,Dy)fx(i),0,0.01,0,0.01);
%fy(i) = dblquad(#(Dx,Dy)fy(i),0,0.01,0,0.01);
sum_x(i) = sum_x(i) + fx(i);
sum_y(i) = sum_y(i) + fy(i);
end
end
end
for i = 1:num;
sum_x = 4.*sum_x./num;
sum_y = 4.*sum_y./num;
x(i) = x(i) - 0.05*sum_x(i);
y(i) = y(i) - 0.05*sum_y(i);
end
a = a+1
end
hold on;
scatter(x,y,'.','b')

Answer 1

The fast version of your loop should be something like:
qx = bsxfun(#minus, x_q.', x_q);
qy = bsxfun(#minus, y_q.', y_q);
il = (qx.^2 + qy.^2 >= 0.01);
qx(il) = 0;
qy(il) = 0;
il = qx>0 && qy>0;
q = sum(exp(-((Dx-qx(il)).^2 + (Dy-qy(il)).^2)/4));
%// etc. for vectorization of the inner loops