Can we use implicit array expansion across = sign?

I recently started to port some of my MATLAB scripts to numpy/python and found a difference between MATLAB implicit array expansion and numpy/python broadcasting.

Here's my working python code:

# >>>>> calculate COORD (use broadcast)

coord = np.zeros((ny+1, nx+1, 6))
coord[:, :, [0, 3]] = x0 - dx/2 + dx*np.arange(nx+1).reshape([1, -1, 1])
coord[:, :, [1, 4]] = y0 - dy/2 + dy*np.arange(ny+1).reshape([-1, 1, 1])
coord[:, :, [2, 5]] = z0 - dz/2 + dz*np.array([0, nz+1]).reshape([1, 1, 2])

Here's my equivalent MATLAB code:

coord=zeros(6,nx+1,ny+1);
coord([1 4],:,:)=x0-dx/2+dx*repmat(reshape((0:nx),1,[],1),[2 1 ny+1]);
coord([2 5],:,:)=y0-dy/2+dy*repmat(reshape((0:ny),1,1,[]),[2 nx+1 1]);
coord([3 6],:,:)=z0-dz/2+dz*repmat(reshape([0,nz],[],1,1),[1 nx+1 ny+1]);

So, in the spirit of increasing my MATLAB skills, two questions:

1/ Is there a way to coax MATLAB to perform implicit array expansion across the "=" sign, to match the simplicity of the numpy/python broadcast calculation?

2/ Does it matter? Is the memory overhead in using repmat irrelevant?

My thanks in advance, for advice!

Mike

Answer 1

[Matt J]

2/ Does it matter? Is the memory overhead in using repmat irrelevant?

It could matter. Most people would probably not bother to optimize it, but you could use a for-loop instead of repmat, e.g.,

tmp=x0-dx/2+dx*(0:nx);
for i=[1,4],  coord(i,:)=tmp;  end

This should have no memory allocation overhead.

1/ Is there a way to coax MATLAB to perform implicit array expansion across the "=" sign, to match the simplicity of the numpy/python broadcast calculation?

No, unfortunately. But as shown above, you can avoid reshape() in this case.

[Mike]

Can you clarify how this solution is intended to work?

for i=[1,4], coord(i,:)=tmp; end

Since coord is a 3d (not 2d) array, I get a mis-match in array dimensions.

[Matt J]

Whoops. You're right. I guess it should be this instead,

[nx,ny,x0,dx]=deal(7,1,0,2);
coord=zeros(6,nx+1,ny+1);

tmp=x0-dx/2+dx*(0:nx);
for j=1:numel(tmp),  coord([1,4],j,:)=tmp(j);  end

coord

coord = 
coord(:,:,1) =

    -1     1     3     5     7     9    11    13
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
    -1     1     3     5     7     9    11    13
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0


coord(:,:,2) =

    -1     1     3     5     7     9    11    13
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
    -1     1     3     5     7     9    11    13
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0

[Mike]

Thanks for the quick answer & revision!

Yes, MATLAB lets us do Mx...xN to 1 implicit expansion across an "=" sign, which is what I was hoping could be generalized to compatible arrays.

I was really trying to avoid the use of repmat not of reshape. As I understand it, reshape only changes the internal header information for an array, not the data itself, so it should be a fast operation. Can you advise on that?

[Matt J]

Reshape indeed has negligible, purely header-editiing overhead. I was just suggesting that omitting it could save typing. My original answer works if you were attempting to broadcast over only 1 dimension, e.g.

[nx,ny,x0,dx]=deal(7,1,0,2);
coord=zeros(6,nx+1,ny+1);

tmp=rand(1,8,2);
for i=[1,4],  coord(i,:)=tmp(:);  end

coord

coord = 
coord(:,:,1) =

    0.7961    0.7052    0.0838    0.2383    0.7550    0.6899    0.8388    0.9313
         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0
    0.7961    0.7052    0.0838    0.2383    0.7550    0.6899    0.8388    0.9313
         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0


coord(:,:,2) =

    0.3888    0.4559    0.0947    0.1061    0.5516    0.0825    0.3129    0.3639
         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0
    0.3888    0.4559    0.0947    0.1061    0.5516    0.0825    0.3129    0.3639
         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0

[Mike]

Now that’s interesting (= unexpected). Thanks for the advice and quick assistance!

[Matt J]

You're quite welcome, but if this resolves your question, please Accept-click the answer.