Add transpose function

[EmilyBourne]

Implement the transpose function. In fortran when used as a temporary variable the transpose function is used. When the variable is saved, the ordering is used to ensure pointers are created. In C the function is handled through unravelling or with a new function transpose_alias_assign.

The transpose function is also used to implement the ndarray property .T and method .transpose()

Related to #806 and #458

[EmilyBourne]

Fortran's transpose function only works for 2D arrays, so I expect that reshape should be used instead of transpose...

Fixed 018c0a1

[yguclu]

@yguclu

Indeed I am puzzled by the fact that the 3D test works... We need to understand what is going on there!

It is strange. gfortran doesn't specify what happens if you pass something that is not 3d, so maybe they have implemented this to be helpful?

Possibly. Do you have access to an Intel or PGI compiler? At least one of them should raise an error...

[EmilyBourne]

@EmilyBourne How do you handle the case of Numpy arrays with rank > 2? Fortran's transpose function only works for 2D arrays, so I expect that reshape should be used instead of transpose...

Hmm, it seems the tests are passing as there is no transpose required in most cases, it just changes the order of the resulting array. And in the case of an expression the transpose is often unrolled anyway. I have added a test case to force the use of the transpose function and it seems that the transpose is not correctly managed

[yguclu]

Hmm, it seems the tests are passing as there is no transpose required in most cases, it just changes the order of the resulting array. And in the case of an expression the transpose is often unrolled anyway. I have added a test case to force the use of the transpose function and it seems that the transpose is not correctly managed

Thanks for looking into this, that makes a lot of sense! I am afraid that this PR will need a bit more work then, so it may be worth checking a couple of other things:

• Do you handle the method a.transpose() in addition to the property a.T?
• Can the user pass the *axes parameters to the function and method as described here?

[EmilyBourne]

Do you handle the method a.transpose() in addition to the property a.T?

No, I will add this

Can the user pass the *axes parameters to the function and method?

No, I wanted to add this, but in python I believe it is possible to do this without necessarily allocating memory. This is not possible in Fortran unless we change all our element-wise access methods to carry axes instead of order (with order='C' equivalent to (0,1,2,3,...) and order='F' equivalent to (rank-1,rank-2,,...) ) so I thought it was probably complicated enough to leave for another PR.

[yguclu]

Can the user pass the *axes parameters to the function and method?

No, I wanted to add this, but in python I believe it is possible to do this without necessarily allocating memory. This is not possible in Fortran unless we change all our element-wise access methods to carry axes instead of order (with order='C' equivalent to (0,1,2,3,...) and order='F' equivalent to (rank-1,rank-2,,...) ) so I thought it was probably complicated enough to leave for another PR.

I thought that even in Numpy a new array was created in all cases where it is not sufficient to change the ordering... I am going to check this.

[EmilyBourne]

I thought that even in Numpy a new array was created in all cases where it is not sufficient to change the ordering... I am going to check this.

No, as long as it can be handled by modifying the steps array numpy (and c for us) does not need to create a new array. E.g:

> import numpy as np
> x = np.random.randint(50, size=(3,2,4))
> y=x.transpose((1,2,0))
> y.flags
  C_CONTIGUOUS : False
  F_CONTIGUOUS : False
  OWNDATA : False
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
  UPDATEIFCOPY : False

[yguclu]

I thought that even in Numpy a new array was created in all cases where it is not sufficient to change the ordering... I am going to check this.

No, as long as it can be handled by modifying the steps array numpy (and c for us) does not need to create a new array. E.g:

> import numpy as np
> x = np.random.randint(50, size=(3,2,4))
> y=x.transpose((1,2,0))
> y.flags
  C_CONTIGUOUS : False
  F_CONTIGUOUS : False
  OWNDATA : False
  WRITEABLE : True
  ALIGNED : True
  WRITEBACKIFCOPY : False
  UPDATEIFCOPY : False

You're right. Upon calling transpose Numpy recomputes the strides and stores them in the array struct.

[yguclu]

For now I suggest to add the transpose method, and raise a neat error if the user passes the *axes parameters.

[EmilyBourne]

For now I suggest to add the transpose method, and raise a neat error if the user passes the *axes parameters.

Done. Should I open an issue for the *axes parameter?

[yguclu]

@EmilyBourne I think the PR description should be expanded a bit (the method transpose and the property T should be mentioned). After that this can be merged.