Mathematica permutes indices when reading Matlab files

Question

I wrote the following Matlab script:

A=reshape(1:(3*4*5),[3,4,5]);
size(A)
save('A.mat','A');

B=reshape(1:(7*8),[7,8]);
size(B)
save('B.mat','B');

C=reshape(1:(2*3*4*5),[2,3,4,5]);
size(C)
save('C.mat','C');

and it ouput

ans =
     3     4     5
ans =
     7     8
ans =
     2     3     4     5

which shows that indices go increasing.

Then I read these tensors with Mathematica:

In[20]:= mat = Import["A.mat", "LabeledData"];
In[15]:= Dimensions["A" /. mat]
Out[15]= {5, 3, 4}
In[21]:= mat = Import["B.mat", "LabeledData"];
In[17]:= Dimensions["B" /. mat]
Out[17]= {7, 8}
In[22]:= mat = Import["C.mat", "LabeledData"];
In[23]:= Dimensions["C" /. mat]
Out[23]= {5, 4, 2, 3}

which shows that first two Matlab indices go to tail in the same order and remaining indices go from the beginning in reverse order.

Is this behaviour by design or by bug? Can I read somewhere about exact rules of index transposing during import?

I see no word about it here.

Answer 1

My personal opinion is that this is a bug.

Our MATLink package handles this well.

In[1]:= << MATLink`

In[2]:= OpenMATLAB[]

In[3]:= MEvaluate[
 "a=reshape(1:(3*4*5), [3,4,5]);
 size(a)"]

Out[3]= ">> 
ans =

     3     4     5

"

In[5]:= Dimensions@MGet["a"]

Out[5]= {3, 4, 5}

---

Update:

I looked at the implementation of the MAT5 file importer. It is written in pure Mathematica. The relevant section is this:

It gives the impression that this is done quite deliberately. Therefore I no longer think that it is a bug, but I do not know why it is done this way.

If you want to transfer data to/from MATLAB, and have both Mathematica and MATLAB installed on the same computer, I still recommend using MATLink.

Answer 2

as a workaround use hdf5

A=reshape(1:(3*4*5),[3,4,5]);
h5create('xyz.hdf5','/A',[3,4,5])
h5write('xyz.hdf5','/A',A)

mathematica

a=Import["xyz.hdf5", "Data"][[1]] 

this is fully reverse indexed..

Dimensions[a] 

{5,4,3}

reverse the index order to be matlab-like:

a = Transpose[a, Reverse@Range@ArrayDepth@a]];
Dimensions[a] 

{3,4,5}