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