On Sat, Mar 20, 2010 at 2:00 PM, Charles R Harris
<
charlesr.harris@gmail.com> wrote:
> 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.