# Source code for pyproximal.projection.AffineSet

from scipy.sparse.linalg import lsqr as sp_lsqr
from scipy.sparse.linalg import cg as sp_cg
from pylops.optimization.basic import cg, lsqr
from pylops.utils.backend import get_array_module, get_module_name

[docs]class AffineSetProj():
r"""Affine set projection.

Parameters
----------
Op : :obj:pylops.LinearOperator
Linear operator
b : :obj:numpy.ndarray
Data vector
niter : :obj:int
Number of iterations of iterative scheme used to compute the projection.

Notes
-----
Given an Affine set defined as:

.. math::

\{ \mathbf{x} : \mathbf{Opx}=\mathbf{b} \}

its orthogonal projection is:

.. math::

P_{\{\mathbf{y}:\mathbf{Opy}=\mathbf{b}\}} (\mathbf{x}) = \mathbf{x} -
\mathbf{Op}^H(\mathbf{Op}\mathbf{Op}^H)^{-1}(\mathbf{Opx}-\mathbf{b})

Note the this is the proximal operator of the corresponding
indicator function :math:I_{\{\mathbf{Opx}=\mathbf{b}\}}

"""
def __init__(self, Op, b, niter):
self.Op = Op
self.b = b
self.niter = niter

def __call__(self, x):
if get_module_name(get_array_module(x)) == 'numpy':
inv = sp_cg(self.Op * self.Op.H, self.Op * x - self.b, maxiter=self.niter)[0]
else:
inv = cg(self.Op * self.Op.H, self.Op * x - self.b, niter=self.niter)[0]
y = x - self.Op.H * inv.ravel() # currently ravel is added to ensure that the output is always a vector
return y