Fix incorrect QR/QL/LU decomposition and TRANSPOSE!

[shamazmazum]

These functions returned incorrect values and could even crash lisp when working with row-major matrices.

Fixes #217

[shamazmazum]

I am sorry that transpose! is not inplace now, but it's correct which is more important

[shamazmazum]

I was thinking about matrix transposition. It seems it's not needed at all.

E.g. for QR decomposition you can do A^T = R^T Q^T and obtain A^T, R^T and Q^T by simply swapping dimensions and changing :row-major to :column-major. Matrix-matrix multiplication also has :transa and :transb flags to avoid transposition.

I guess, maybe you can merge this PR as a quick fix and then I can eliminate transposition in the next PR.

P.S. Inplace transposition of MxN matrices with M/=N is not trivial. I won't do this :)

[shamazmazum]

I've tried to eliminate transposition in SVD decomposition. This works as follows:

• If m is in column-major format, proceed as usual
• If m is in row-major format:
  • fast-transpose it (create a new matrix with the same storage, layout changed to :column-major and dimensions reversed):
    m' = fast-transpose m
  • Obtain vt' s u' = lapack-svd m'
  • Calculate vt = fast-transpose vt' and u = fast-transpose u'
  • Return u, s, vt.

The outcome of this is that svd returns different (but correct) results for the same matrices in row-major and in column-major formats (the difference is in signs of elements in u and vt matrices).

All said is true for other non-unique decompositions (e.g. for eigenvalue decomposition: if there are many eigenvalues with the same absolute value, they may appear in different order).

Can this be allowed in magicl? If yes, there is no need to transpose anything.