# Source code for cr.sparse._src.fom.l1rls

# Copyright 2021 CR-Suite Development Team
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# Licensed under the Apache License, Version 2.0 (the "License");
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# https://www.apache.org/licenses/LICENSE-2.0
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from jax import jit
import cr.sparse.opt as opt
from .util import matrix_affine_func
from .fom import fom
from .defs import FomOptions
[docs]def l1rls(A, b, lambda_, x0, options: FomOptions = FomOptions()):
r"""Solver for l1 regulated least square problem
Args:
A (cr.sparse.lop.Operator): A linear operator
b (jax.numpy.ndarray): The measurements :math:`b \approx A x`
lambda_ (float): The regularization parameter for the l1 term
x0 (jax.numpy.ndarray): Initial guess for solution vector
options (FomOptions): Options for configuring the algorithm
Returns:
FomState: Solution of the optimization problem
The l1 regularized least square problem is defined as:
.. math::
\text{minimize} \frac{1}{2} \| A x - b \|_2^2 + \lambda \| x \|_1
Sometimes, this is also called LASSO in literature.
"""
f = opt.smooth_quad_matrix()
h = opt.prox_l1(lambda_)
return fom(f, h, A, -b, x0, options)
l1rls_jit = jit(l1rls, static_argnums=(0, 4))