3D / 4D Matrix manipulation - arrays

Question

I often struggle with slow Matlab processing due to high numbers of for loops.
Maybe you can help me with this example, which would help me in other cases as well: Is it possible to completely transfer it to matrices?
R = [1 2 3; 1 2 3; 1 2 3];
u1 = 200; u2 = 300; v1 = 100; v2 = 222; w1 = 123; w2 = 312;
px = 20; py = 30; pz = 25;
a = 20; b = 30; c = 25;
Ellipse = zeros(500,600,500)
for i=u1:u2
for j=v1:v2
for k=w1:w2
x=[i-px;j-py;k-pz];
x=R*x;
if (x(1)/a)^2+(x(2)/b)^2+(x(3)/c)^2<1
Ellipse(i,j,k)=1;
end
end
end
end

Answer 1

Here's one approach that runs about 2 orders of magnitude faster
R = [1 2 3; 1 2 3; 1 2 3];
u1 = 200; u2 = 300; v1 = 100; v2 = 222; w1 = 123; w2 = 312;
px = 20; py = 30; pz = 25;
a = 20; b = 30; c = 25;
Ellipse = zeros(500,600,500);
% Create mesh of points to process
vx = (u1:u2) - px;
vy = (v1:v2) - py;
vz = (w1:w2) - pz;
[X,Y,Z] = meshgrid(vx, vy, vz);
% Compute R*x
V = [X(:)'; Y(:)'; Z(:)'];
V = R * V;
% Divide by ellipse axes
M = diag([1/a, 1/b, 1/c]);
V = M * V;
% Determine if norm criteria is met
index = norm(V') < 1;
Ellipse(X(index), Y(index), Z(index)) = 1;
Agree with #Dan, a smaller working example would make it easier to test.

Answer 2

If you are doing more than simple mathematical operations matrices can be tricky.
Here you can (should) reduce the size of Ellipse because you are not using most of its entries.
All you need is (101,123,190) and things will be much faster, especially the way you are accessing the matrix entries, remember MATLAB will eventually store the matrix as just an array.

Answer 3

#dpmcmlxxvi Thank you very much for the answer. At first, sorry for the large example. I used your answer with some modification as norm(XY) did not work for me.(smaller example and valueas adapted to run properly)
R = [1 2 3; 1 2 3; 1 2 3];
u1 = 50; u2 = 90; v1 = 20; v2 = 50; w1 = 30; w2 = 60;
px = 60; py = 25; pz = 50;
a = 10; b = 20; c = 15;
Ellipse = zeros(100,200,100);
% Create mesh of points to process
vx = (u1:u2) - px;
vy = (v1:v2) - py;
vz = (w1:w2) - pz;
[X,Y,Z] = meshgrid(vx, vy, vz);
% Compute R*x
V = [X(:)'; Y(:)'; Z(:)'];
V = R * V;
% Divide by ellipse axes
M = diag([1/a, 1/b, 1/c]);
V = M * V;
% Apply criteria
Vsq = V.*V;
crit = Vsq(1,:)+Vsq(2,:)+Vsq(3,:);
% Look for indices in the meshgrid fullfilling criteria
xe = X(find(crit<1));
ye = Y(find(crit<1));
ze = Z(find(crit<1));
xi = ceil(abs(xe+px));
yi = ceil(abs(ye+py));
zi = ceil(abs(ze+pz));
% Set values at correpsonding indices to 1
linind = sub2ind(size(Ellipse),xi,yi,zi);
Ellipse(linind) = 1;
It works fine and all for loops have been removed.