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# Efficient code writing...

Asked by Daniel on 16 Nov 2011

Hi all. First time posting here, hope I can get some nice ideas. I have 3 large matrices (of equal size), representing the x,y and z coordinates of points. So say my matrices are 200 by 200, it means they are representing 200x200 points. Now, I want to apply this transformation matrix to each point, so that I get some linear combination of the point being transformed. Of course, I know I could opt for a loop where I update the indices of my matrices and each time apply the transformation. But I'd like to know how I can do this more efficiently... I know matlab works better using vectorisation, so I am thinking along the lines of using structures or something... Any ideas?

Thanks. Dan

Jan Simon on 16 Nov 2011

What does "aply this transformation matrix to each point" exactly mean?

Daniel on 16 Nov 2011

@ Naz & Jan
Sorry I wasn't too clear.
To be exact, the 3 matrices I mention are x,y and z - each with 200 by 200 elements. the (1,1) entry in the matrices represents a certain point say vertex 1, the (1,2) represents vertex 2 etc...
So vertex 1, has coordinates [x(1,1),y(1,1),z(1,1)],
vertex 2, has coordinates [x(1,2),y(1,2),z(1,2)] etc etc...

Now I need to transform the points in these matrices into another coordinate system. I do this transformation using a simple 3x3 matrix (say its called M), which gives me my new coordinates.
So new coordinates of vertex1 = M*(x(1,1),y(1,1),z(1,1)) etc..
But as I said, the 3 matrices contain the different coordinates...

You can look at it anther way..
If you sort of draw a 3Dimensional matrix with the x,y,z insterted into the 3rd dimension, maybe you can visualise better what i mean -
for instance, the new 3D matrix CS will be:
CS(:,:,1)=x;
CS(:,:,1)=y;
CS(:,:,1)=z;
Then each vertex1 would here be CS(1,1,:)...
So in terms of this, the transformation needs to be applied like
M*CS(1,1,:) - but I was asking whether I can do this for all points, rather than cycle through CS using a loop...
did I confuse you more??

Daniel on 16 Nov 2011

Sorry I meant to write,

CS(:,:,1)=x;
CS(:,:,2)=y;
CS(:,:,3)=z;

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Answer by Andrei Bobrov on 16 Nov 2011

variant

```C = cat(3,x, y, z);
s = size(C);
Cout = permute(reshape(M*reshape(permute(C,[3 2 1]),s(3),[]),s(3),s(2),[]),[3 2 1]);
```

variant 2

```Cout2 = C;
for i1 = 1:size(C,2)
Cout2(:,i1,:) = (M*squeeze(C(:,i1,:)).').';
end
```

Answer by Sean de Wolski on 16 Nov 2011

A well written for-loop should be pretty fast. I would recommend doing that. make sure to preallocate your matrix of transformations to be equal to its final size.