Hi, Is it reasonable to summarize that, to avoid confusion, we keep 'matrix_rank' as the name?
I've edited as Robert suggested, attempting to adopt a more suitable tone in the docstring... 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 >>> I=np.eye(4); I[-1,-1] = 0. # rank deficient matrix >>> matrix_rank(I) 3 >>> 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 [1]_ define "numerical rank deficiency" as using tol=eps*S[0] (where S[0] is the maximum singular value and thus the 2-norm of the matrix). This is one definition of rank deficiency, and the one we use here. When floating point roundoff is the main concern, then "numerical rank deficiency" is a reasonable choice. In some cases you may prefer other definitions. The most useful measure of the tolerance depends on the operations you intend to use on your matrix. For example, if your data come from uncertain measurements with uncertainties greater than floating point epsilon, choosing a tolerance near that uncertainty may be preferable. The tolerance may be absolute if the uncertainties are absolute rather than relative. References ---------- .. [1] G. H. Golub and C. F. Van Loan, _Matrix Computations_. Baltimore: Johns Hopkins University Press, 1996. ''' 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