cjekel
commented
4 years ago Something interesting to note. If you happen to extrapolate beyond the largest data point, by even just one point, I think you'll end up with something like
Ad = np.array([[ 1., 2., 0.],
[ 1., 4., 0.],
[ 1., 6., 0.],
[ 1., 7., 0.],
[ 1., 8., 0.],
[ 1., 9., 0.],
[ 1., 11., 0.],
[ 1., 12., 0.],
[ 1., 16., 0.],
[ 1., 18., 0.],
[ 1., 19., 0.],
[ 1., 20., 0.],
[ 1., 21., 0.],
[ 1., 22., 0.],
[ 1., 23., 0.],
[ 1., 24., 1.]])which should be invertible. Perhaps the regression matrix should be created using
A_list.append(np.where(x => self.fit_breaks[i+1],
x - self.fit_breaks[i+1],
0.0))instead of
A_list.append(np.where(x > self.fit_breaks[i+1],
x - self.fit_breaks[i+1],
0.0))? I believe that would avoid the last column being all zero. Not sure if that will end up breaking many things...
I'm pretty sure this has come up before. A PR is welcome!
How about adding inv_solver keyword to prediction_variance(), with choices of 'inv', 'pinv', or 'pinv2'? I think I want to keep the default to 'inv' since that wouldn't change anything. Feel free to add a note in the docstring.
Could even add our own method to catch the LinAlgError methods and try another method. The order of such could be something like inv > pinv > pinv2, which would be fine as the default since it won't break any existing behavior.
Thanks for creating the issue, with an easy to reproduce case!
When I use this method https://github.com/cjekel/piecewise_linear_fit_py/blob/master/pwlf/pwlf.py#L1240 it provides the "LinAlgError: Singular matrix" too often. When debugging, I see that the Ad matrix calculated in here: https://github.com/cjekel/piecewise_linear_fit_py/blob/master/pwlf/pwlf.py#L1304 has the last column is all 0, such as: (Pdb) p Ad array([[ 1., 2., 0.], [ 1., 4., 0.], [ 1., 6., 0.], [ 1., 7., 0.], [ 1., 8., 0.], [ 1., 9., 0.], [ 1., 11., 0.], [ 1., 12., 0.], [ 1., 16., 0.], [ 1., 18., 0.], [ 1., 19., 0.], [ 1., 20., 0.], [ 1., 21., 0.], [ 1., 22., 0.], [ 1., 23., 0.]]) so: (Pdb) np.dot(Ad.T, Ad) array([[ 15., 198., 0.], [ 198., 3310., 0.], [ 0., 0., 0.]]) and then https://github.com/cjekel/piecewise_linear_fit_py/blob/master/pwlf/pwlf.py#L1323 will throw the error. Have you consider using pinv instead of inv here, which still provides a good pseudo inverse matrix to use later? (Pdb) linalg.pinv(np.dot(Ad.T, Ad)) array([[ 0.3168677 , -0.01895462, 0. ], [-0.01895462, 0.00143596, 0. ], [ 0. , 0. , 0. ]]) I can make a PR if you see it helpful