On Fri, Aug 26, 2011 at 2:57 PM, Charles R Harris <charlesr.har...@gmail.com> wrote: > > > On Fri, Aug 26, 2011 at 12:38 PM, Mark Janikas <mjani...@esri.com> wrote: >> >> Charles! That looks like it could be a winner! It looks like you always >> choose the last column of the U matrix and ID the columns that have the same >> values? It works when I add extra columns as well! BTW, sorry for my lack >> of knowledge… but what was the point of the dot multiply at the end? That >> they add up to essentially zero, indicating singularity? Thanks so much! > > The indicator of collinearity is the singular value in d, the corresponding > column in u represent the linear combination of rows that are ~0, the > corresponding row in v represents the linear combination of columns that are > ~0. If you have several combinations that are ~0, of course you can add them > together and get another. Basically, if you take the rows in v corresponding > to small singular values, you get a basis for the for the null space of the > matrix, the corresponding columns in u are a basis for the orthogonal > complement of the range of the matrix. If that is getting a bit technical > you can just play around with things.
Interpretation is a bit difficult if there are more than one zero eigenvalues >>> zt2 = np.vstack((zt, zt[2,:] + zt[3,:])) >>> zt2 array([[ 1. , 1. , 1. , 1. , 1. ], [ 0.25, 0.1 , 0.2 , 0.25, 0.5 ], [ 0.75, 0.9 , 0.8 , 0.75, 0.5 ], [ 3. , 8. , 0. , 5. , 0. ], [ 3.75, 8.9 , 0.8 , 5.75, 0.5 ]]) >>> u,d,v = np.linalg.svd(zt2) >>> d array([ 1.51561431e+01, 1.91327688e+00, 3.25113875e-01, 1.05664844e-15, 5.29054218e-16]) >>> u[:,-2:] array([[ 0.59948553, -0.12496837], [-0.59948553, 0.12496837], [-0.51747833, -0.48188813], [ 0.0820072 , -0.60685651], [-0.0820072 , 0.60685651]]) Josef > > <snip> > > Chuck > > _______________________________________________ > 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