Re: [Numpy-discussion] Linear algebra functions on empty arrays
On Mon, Sep 15, 2014 at 5:48 AM, Sebastian Berg wrote: > Hey all, > > for https://github.com/numpy/numpy/pull/3861/files I would like to allow > 0-sized dimensions for generalized ufuncs, meaning that the gufunc has > to be able to handle this, but also that it *can* handle it at all. > However lapack does not support this, so it needs some explicit fixing. > Also some of the linalg functions currently explicitly allow and others > explicitly disallow empty arrays. > > For example the QR and eigvals does not allow it, but on the other hand > solve explicitly does (most probably never did, simply because lapack > does not). So I am wondering if there is some convention for this, or > what convention we should implement. What does an empty square matrix/array look like? np.linalg.solve can have empty rhs, but shape of empty lhs, `a`, is ? If I do a QR(arr) with arr.shape=(0, 5), what is R supposed to be ? I just wrote some loops over linalg.qr, but I always initialized explicitly. I didn't manage to figure out how empty arrays would be useful. If an empty square matrix can only only be of shape (0, 0), then it's no use (in my applications). Josef > > Regards, > > Sebastian > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Linear algebra functions on empty arrays
On Mo, 2014-09-15 at 07:07 -0400, josef.p...@gmail.com wrote: > On Mon, Sep 15, 2014 at 5:48 AM, Sebastian Berg > wrote: > > Hey all, > > > > for https://github.com/numpy/numpy/pull/3861/files I would like to allow > > 0-sized dimensions for generalized ufuncs, meaning that the gufunc has > > to be able to handle this, but also that it *can* handle it at all. > > However lapack does not support this, so it needs some explicit fixing. > > Also some of the linalg functions currently explicitly allow and others > > explicitly disallow empty arrays. > > > > For example the QR and eigvals does not allow it, but on the other hand > > solve explicitly does (most probably never did, simply because lapack > > does not). So I am wondering if there is some convention for this, or > > what convention we should implement. > > What does an empty square matrix/array look like? > > np.linalg.solve can have empty rhs, but shape of empty lhs, `a`, is ? > > If I do a QR(arr) with arr.shape=(0, 5), what is R supposed to be ? > QR may be more difficult since R may itself could not be empty, begging the question if you want to error out or fill it sensibly. Cholesky would require (0, 0) for example and for eigenvalues it would somewhat make sense too, the (0, 0) matrix has 0 eigenvalues. I did not go through them all, but I would like to figure out whether we should aim to generally allow it, or maybe just allow it for some special ones. - Sebastian > > I just wrote some loops over linalg.qr, but I always initialized explicitly. > > I didn't manage to figure out how empty arrays would be useful. > > If an empty square matrix can only only be of shape (0, 0), then it's > no use (in my applications). > > > Josef > > > > > > Regards, > > > > Sebastian > > > > ___ > > NumPy-Discussion mailing list > > NumPy-Discussion@scipy.org > > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > signature.asc Description: This is a digitally signed message part ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Linear algebra functions on empty arrays
On Mon, Sep 15, 2014 at 7:26 AM, Sebastian Berg wrote: > On Mo, 2014-09-15 at 07:07 -0400, josef.p...@gmail.com wrote: >> On Mon, Sep 15, 2014 at 5:48 AM, Sebastian Berg >> wrote: >> > Hey all, >> > >> > for https://github.com/numpy/numpy/pull/3861/files I would like to allow >> > 0-sized dimensions for generalized ufuncs, meaning that the gufunc has >> > to be able to handle this, but also that it *can* handle it at all. >> > However lapack does not support this, so it needs some explicit fixing. >> > Also some of the linalg functions currently explicitly allow and others >> > explicitly disallow empty arrays. >> > >> > For example the QR and eigvals does not allow it, but on the other hand >> > solve explicitly does (most probably never did, simply because lapack >> > does not). So I am wondering if there is some convention for this, or >> > what convention we should implement. >> >> What does an empty square matrix/array look like? >> >> np.linalg.solve can have empty rhs, but shape of empty lhs, `a`, is ? >> >> If I do a QR(arr) with arr.shape=(0, 5), what is R supposed to be ? >> > > QR may be more difficult since R may itself could not be empty, begging > the question if you want to error out or fill it sensibly. I shouldn't have tried it again (I got this a few times last week): >>> ze = np.ones((z.shape[1], 0)) >>> np.linalg.qr(ze) ** On entry to DGEQRF parameter number 7 had an illegal value crash z.shape[1] is 3 >>> np.__version__ '1.6.1' I think, I would prefer an exception if the output would require a empty square matrix with shape > (0, 0) I don't see any useful fill value. > Cholesky would require (0, 0) for example and for eigenvalues it would > somewhat make sense too, the (0, 0) matrix has 0 eigenvalues. > I did not go through them all, but I would like to figure out whether we > should aim to generally allow it, or maybe just allow it for some > special ones. If the return square array has shape (0, 0), then it would make sense, but I haven't run into a case for it yet. np.cholesky(np.ones((0, 0))) ? (I didn't try since my interpreter is crashed. :) Josef > > - Sebastian > >> >> I just wrote some loops over linalg.qr, but I always initialized explicitly. >> >> I didn't manage to figure out how empty arrays would be useful. >> >> If an empty square matrix can only only be of shape (0, 0), then it's >> no use (in my applications). >> >> >> Josef >> >> >> > >> > Regards, >> > >> > Sebastian >> > >> > ___ >> > NumPy-Discussion mailing list >> > NumPy-Discussion@scipy.org >> > http://mail.scipy.org/mailman/listinfo/numpy-discussion >> > >> ___ >> NumPy-Discussion mailing list >> NumPy-Discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion >> > > > ___ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Linear algebra functions on empty arrays
On 15 Sep 2014 05:49, "Sebastian Berg" wrote: > For example the QR and eigvals does not allow it, but on the other hand > solve explicitly does (most probably never did, simply because lapack > does not). So I am wondering if there is some convention for this, or > what convention we should implement. To me the obvious convention would be that whenever there's a unique obvious answer that satisfies the operation's invariants, then we should prefer to implement it (though possibly with low priority), even if this means papering over lapack edge cases. This is consistent with how e.g. we already define sum([]) and prod([]) and empty matrix products, etc. Of course this requires some thinking... e.g. the empty matrix is a null matrix, b/c given empty_vec = np.ones((0,)) empty_mat = np.ones((0, 0)) then we have empty_vec @ empty_mat @ empty_vec = empty_vec @ empty_vec = sum([]) = 0 and therefore empty_mat is not positive definite. np.linalg.cholesky raises an error on non-positive-definite matrices in general (e.g. try np.linalg.cholesky(np.zeros((1, 1, so I guess cholesky shouldn't handle empty matrices. For eigvals, I guess empty_mat @ empty_vec = empty_vec, meaning that empty_vec is a arguably an eigenvector with some indeterminate eigenvalue? Or maybe the fact that scalar * empty_vec = empty_vec for ever scalar means that empty_vec should be counted as a zero vector, and thus be ineligible to be an eigenvector. Saying that the empty matrix has zero eigenvectors or eigenvalues seems pretty intuitive. I don't see any trouble with defining qr for empty matrices either. -n ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
