# Source code for cr.sparse._src.opt.proximal_ops.basic

# Copyright 2021 CR-Suite Development Team
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

from jax import jit, lax

import jax.numpy as jnp
import cr.nimble as cnb

from .prox import build, build3

[docs]def prox_zero():
r"""Returns a prox-capable wrapper for the function  :math:f(x)=0

Returns:
ProxCapable: A prox-capable function

The function :math:f(x)=0 is the indicator function for the vector space :math:\RR^n.

The proximal operator

.. math::

p_f(x, t) = \text{arg} \min_{z \in \RR^n} f(x) + \frac{1}{2t} \| z - x \|_2^2

reduces to:

.. math::

p_f(x, t) = \text{arg} \min_{z \in \RR^n} \frac{1}{2t} \| z - x \|_2^2 = x

"""

@jit
def func(x):
return 0.

@jit
def proximal_op(x, t):
x = jnp.asarray(x)
x = cnb.promote_arg_dtypes(x)
return x

@jit
def prox_vec_val(x, t):
x = jnp.asarray(x)
x = cnb.promote_arg_dtypes(x)
return x, 0.

return build3(func, proximal_op, prox_vec_val)