weighted norm minimization

[narges-mhm]

I have a problem with using weighted-l2. In fact, according to the docs, the dimension of w should be the same as the dimension of y while I get a dimension error. I need to know whether you have tried the weighted ones. The error is exactly in the same part as it is mentioned:
Nati: I've checked this code the use of 'y' seems correct

[nperraud]

Yes this has been tested here:

pyunlocbox/pyunlocbox/tests/test_functions.py

Line 116 in d0bd39b

f = functions.norm_l2(A=L, tight=False, y=np.array([1, 2, 3, 4]),

Nati: I've checked this code the use of 'y' seems correct this is actually in the norm_l1

I have added some test in the norm_l1 and did not found any bugs... See this PR: #21

[narges-mhm]

Thanks for your response but the error still persists. Suppose A is M*N (where M>N) and consequently x dim would be Nx1 and w&y are Mx1. In this case:
class norm_l2:
def _prox:
if self.tight:
sol = x + 2. * gamma * self.At(self.y() * self.w2)
sol /= 1. + 2. * gamma * self.nu * self.w2

from the first line sol is Nx1 and in the second line, sol is going to be divide by w which is Mx1. And that is why I get dimension error.

[nperraud]

Could you simply make a simple example with an error?

[narges-mhm]

https://user-images.githubusercontent.com/61758751/75893435-cbc64100-5e00-11ea-93f4-f3ffdb82c405.JPG

This is an error for norm_l2 and tight=True.

[nperraud]

Please copy the code here so I can try it. It is more efficient thant recopying everything from your image.

[narges-mhm]

import numpy as np
from pyunlocbox import functions, solvers

w=np.array([1,2,2,1])
A=np.random.normal(size=(4,3))
x=np.array([1,-1,1])
y=A@x
f1=functions.norm_l2(A=A,y=y,w=w,tight=True)
f2=functions.dummy()
step= 0.5 / np.linalg.norm(A, ord=2)**2
x1=np.array([.2,.2,.2])
solver2= solvers.generalized_forward_backward(step=step*0.1)
ret2= solvers.solve([f1,f2], x1, solver2, rtol=1e-6, maxit=1000)
objective2= np.array(ret2['objective'])

[nperraud]

Sorry for my late reply. I was able to reproduce the problem.

One thing that see is that you are using tight=True, which is not correct in your example. Indeed A is not a tight operator. If ignore this, the proximal solution for a tight operator requires a constant weight to be valid. Hence, if tight=True, then w should be a scalar. To solve this problem, you can simply set tight=False in your code.

i will add a check for this in the code such that one cannot define a function with multiple weights and a tight operator.