# Source code for pygsp.optimization

# -*- coding: utf-8 -*-

r"""
The :mod:pygsp.optimization module provides tools for convex optimization on
graphs.
"""

from pygsp import utils

logger = utils.build_logger(__name__)

[docs]def prox_tv(x, gamma, G, A=None, At=None, nu=1, tol=10e-4, maxit=200, use_matrix=True):
r"""
Total Variation proximal operator for graphs.

This function computes the TV proximal operator for graphs. The TV norm
is the one norm of the gradient. The gradient is defined in the
function :meth:pygsp.graphs.Graph.grad.
This function requires the PyUNLocBoX to be executed.

This function solves:

:math:sol = \min_{z} \frac{1}{2} \|x - z\|_2^2 + \gamma  \|x\|_{TV}

Parameters
----------
x: int
Input signal
gamma: ndarray
Regularization parameter
G: graph object
Graphs structure
A: lambda function
Forward operator, this parameter allows to solve the following problem:
:math:sol = \min_{z} \frac{1}{2} \|x - z\|_2^2 + \gamma  \| A x\|_{TV}
(default = Id)
At: lambda function
nu: float
Bound on the norm of the operator (default = 1)
tol: float
Stops criterion for the loop. The algorithm will stop if :
:math:\frac{n(t) - n(t - 1)} {n(t)} < tol
where :math:n(t) = f(x) + 0.5 \|x-y\|_2^2 is the objective function at iteration :math:t
(default = :math:10e-4)
maxit: int
Maximum iteration. (default = 200)
use_matrix: bool
If a matrix should be used. (default = True)

Returns
-------
sol: solution

Examples
--------

"""
if A is None:
def A(x):
return x
if At is None:
def At(x):
return x

tight = 0
l1_nu = 2 * G.lmax * nu

if use_matrix:
def l1_a(x):
return G.Diff * A(x)

def l1_at(x):
return G.Diff * At(D.T * x)
else:
def l1_a(x):