Example,
Compute the qr factorization of a matrix.
Factor the matrix `a` as `qr`, where `q` is orthonormal
(:math:`dot( q_{:,i}, q_{:,j}) = \delta_{ij}`, the Kronecker delta) and
`r` is upper-triangular.
Arrggghhhh... Totally. Unreadable. Why not say the columns of q are orthonormal vectors and r is upper triangular? The math tutorial should go in the notes, if anywhere. Might mention that this is a 'thin' factorization (Golub). Let me propose a rule: no math markup in the summary, ever.
Parameters
----------
a : array_like, shape (M, N)
Matrix to be factored.
mode : {'full', 'r', 'economic'}
Specifies the information to be returned. 'full' is the default.
mode='r' returns a "true" `r`, while 'economic' returns a "polluted"
`r` (albeit slightly faster; see Returns below).
Oh, come now, "true", "polluted"? Sounds a bit political... Actually, 'economic' contains info on the Householder reflections. In any case, why mention it at all, just refer to the return documentation. And wouldn't values be a better word than information?
Returns
-------
* If mode = 'full':
* q : ndarray of float or complex, shape (M, K)
* r : ndarray of float or complex, shape (K, N)
Size K = min(M, N)
* If mode = 'r':
* r : ndarray of float or complex, shape (K, N)
* If mode = 'economic':
* a2 : ndarray of float or complex, shape (M, N)
The diagonal and the upper triangle of a2 contains r,
while the rest of the matrix is undefined.
WTF? I'm seeing stars.
I may be old and crotchety, and I don't mean to be mean to the folks who have done the hard work to bring the docstring to its current state, but I think things have gotten out of hand.
Chuck