transpose degree n matrices

[Alex-Jordan]

This builds on #1216 (which builds on #1215). If #1216 is updated following feedback, I will update here too. Once #1216 is merged, this diff should be more manageable.

In addition to changes from #1216, this has:

• a slice method for a Matrix object. This produces a degree (n-1) Matrix from a degree n Matrix. You specify an index and a value for that index, and it produces the degree (n-1) Matrix that is thereby defined. This is currently only used as a helper for the update to transpose. It is similar to row and column methods, but more general. And always produces something of the next lower degree.
• to transpose a degree n Matrix, the word "transpose" is perhaps a misnomer. Instead you have some permutation of the index dimensions in mind. For the usual transpose of a degree 2 matrix, this is just the permutation (12). For a degree n matrix, you might want to permute the indices in a different way. Doing this once can make it more efficient to repeatedly access data in the Matrix, depending on the scenario. So now you can transpose a degree n Matrix. If you don't specify a permutation, the default is to just swap the last two indices. This will look like a regular transposition on each of the degree 2 matrices in the frontal slice. Otherwise, for the permutation you may specify a cycle in the form of an array reference, or a product of cycles in the form of an array reference of array references.

This is the last of the updates I wanted to do before adding new methods for setting elements, removing columns and rows and a submatrix that @pstaabp has in #1076. We should make sure new tools work with degree n Matrix objects as we add them. Unless it is for sure only appropriate for degree 2 matrices.

[pstaabp]

Looks good, but we should bring the test suite in soon. There was one in my branch that probably works for a lot of this, but should be update.

Although I'm guessing you have a number of problems that you've been testing with, it's more efficient to have the test suite.

I can get it working with this branch and put in a PR to this if you'd like.

[drgrice1]

I haven't tested this at all yet, but I see some code changes that are needed. Some things that perlcritic pointed out.

[drgrice1]

I think this generally looks good aside from the comments I made.

[drgrice1]

I think this could use some clarification as to what this really means. What do index and value mean in this context?

[Alex-Jordan]

I tried to do better here. I will push and you can see. Imagine a 5x7x9 matrix. Entry positions are defined by three indices i,j,k. The first index, second index, and third index. So "index" here would be 1, 2, or 3. Say it is 3. Then a value for that index can be 1, 2, ..., or 9. Take a look and see if what I changed to is OK or can be improved upon.

[drgrice1]

I think what you changed it to is better. What you said here really is what really worked for me though. Perhaps adding an example like that to the POD would better. Terminology with these "tensor" things can get confusing!

[Alex-Jordan]

OK, I put something like that in the POD.

[pstaabp]

The code at the end of this can be made with C<<$M->slice(2,3)>>, a bit easier than the notation.

[drgrice1]

That actually needs to be C<< $M->slice(2, 3) >>. There must be spaces after << and before >>.

[pstaabp]

Good point.