[Numpy-discussion] Proposal for matrix_rank function in numpy
Bruce Southey
bsouthey@gmail....
Tue Dec 15 12:39:11 CST 2009
On 12/15/2009 11:12 AM, josef.pktd@gmail.com wrote:
> On Tue, Dec 15, 2009 at 12:01 PM, Matthew Brett<matthew.brett@gmail.com> wrote:
>
>> Hi,
>>
>> Following on from the occasional discussion on the list, can I propose
>> a small matrix_rank function for inclusion in numpy/linalg?
>>
>> I suggest it because it seems rather a basic need for linear algebra,
>> and it's very small and simple...
>>
>> I've appended an implementation with some doctests in the hope that it
>> will be acceptable,
>>
>> Robert - I hope you don't mind me quoting you in the notes.
>>
>> Thanks a lot,
>>
>> Matthew
>>
>>
>> def matrix_rank(M, tol=None):
>> ''' Return rank of matrix using SVD method
>>
>> Rank of the array is the number of SVD singular values of the
>> array that are greater than `tol`.
>>
>> Parameters
>> ----------
>> M : array-like
>> array of<=2 dimensions
>> tol : {None, float}
>> threshold below which SVD values are considered zero. If `tol`
>> is None, and `S` is an array with singular values for `M`, and
>> `eps` is the epsilon value for datatype of `S`, then `tol` set
>> to ``S.max() * eps``.
>>
>> Examples
>> --------
>> >>> matrix_rank(np.eye(4)) # Full rank matrix
>> 4
>> >>> matrix_rank(np.c_[np.eye(4),np.eye(4)]) # Rank deficient matrix
>> 4
>> >>> matrix_rank(np.zeros((4,4))) # All zeros - zero rank
>> 0
>> >>> matrix_rank(np.ones((4,))) # 1 dimension - rank 1 unless all 0
>> 1
>> >>> matrix_rank(np.zeros((4,)))
>> 0
>> >>> matrix_rank([1]) # accepts array-like
>> 1
>>
>> Notes
>> -----
>> Golub and van Loan define "numerical rank deficiency" as using
>> tol=eps*S[0] (note that S[0] is the maximum singular value and thus
>> the 2-norm of the matrix). There really is not one definition, much
>> like there isn't a single definition of the norm of a matrix. For
>> example, if your data come from uncertain measurements with
>> uncertainties greater than floating point epsilon, choosing a
>> tolerance of about the uncertainty is probably a better idea (the
>> tolerance may be absolute if the uncertainties are absolute rather
>> than relative, even). When floating point roundoff is your concern,
>> then "numerical rank deficiency" is a better concept, but exactly
>> what the relevant measure of the tolerance is depends on the
>> operations you intend to do with your matrix. [RK, numpy mailing
>> list]
>>
>> References
>> ----------
>> Matrix Computations by Golub and van Loan
>> '''
>> M = np.asarray(M)
>> if M.ndim> 2:
>> raise TypeError('array should have 2 or fewer dimensions')
>> if M.ndim< 2:
>> return int(not np.all(M==0))
>> S = npl.svd(M, compute_uv=False)
>> if tol is None:
>> tol = S.max() * np.finfo(S.dtype).eps
>> return np.sum(S> tol)
>> _______________________________________________
>> NumPy-Discussion mailing list
>> NumPy-Discussion@scipy.org
>> http://mail.scipy.org/mailman/listinfo/numpy-discussion
>>
>>
> This was missing from numpy compared to matlab and gauss.
>
> If we put it in linalg next to np.linalg.cond, then we could shorten
> the name to `rank`, since the meaning of np.linalg.rank should be
> pretty obvious.
>
> Josef
> _______________________________________________
>
+1 for the function but we can not shorten the name because of existing
numpy.rank() function.
Bruce
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