# Source code for cvxpy.atoms.affine.conv

"""

This file is part of CVXPY.

CVXPY is free software: you can redistribute it and/or modify
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

CVXPY is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with CVXPY.  If not, see <http://www.gnu.org/licenses/>.
"""

from cvxpy.atoms.affine.affine_atom import AffAtom
import cvxpy.utilities as u
import cvxpy.interface as intf
import cvxpy.lin_ops.lin_utils as lu
import numpy as np

[docs]class conv(AffAtom):
""" 1D discrete convolution of two vectors.

The discrete convolution :math:c of vectors :math:a and :math:b of
lengths :math:n and :math:m, respectively, is a length-:math:(n+m-1)
vector where

.. math::

c_k = \\sum_{i+j=k} a_ib_j, \quad k=0, \ldots, n+m-2.

Parameters
----------
lh_expr : Constant
A constant 1D vector or a 2D column vector.
rh_expr : Expression
A 1D vector or a 2D column vector.
"""
# TODO work with right hand constant.

def __init__(self, lh_expr, rh_expr):
super(conv, self).__init__(lh_expr, rh_expr)

@AffAtom.numpy_numeric
def numeric(self, values):
"""Convolve the two values.
"""
# Convert values to 1D.
values = list(map(intf.from_2D_to_1D, values))
return np.convolve(values[0], values[1])

def validate_arguments(self):
"""Checks that both arguments are vectors, and the first is constant.
"""
if not self.args[0].is_vector() or not self.args[1].is_vector():
raise ValueError("The arguments to conv must resolve to vectors.")
if not self.args[0].is_constant():
raise ValueError("The first argument to conv must be constant.")

def shape_from_args(self):
"""The sum of the argument dimensions - 1.
"""
lh_length = self.args[0].shape[0]
rh_length = self.args[1].shape[0]
return (lh_length + rh_length - 1, 1)

def sign_from_args(self):
"""Same as times.
"""
return u.sign.mul_sign(self.args[0], self.args[1])

def is_incr(self, idx):
"""Is the composition non-decreasing in argument idx?
"""
return self.args[0].is_nonneg()

def is_decr(self, idx):
"""Is the composition non-increasing in argument idx?
"""
return self.args[0].is_nonpos()

@staticmethod
def graph_implementation(arg_objs, shape, data=None):
"""Convolve two vectors.

Parameters
----------
arg_objs : list
LinExpr for each argument.
shape : tuple
The shape of the resulting expression.
data :
Additional data required by the atom.

Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
return (lu.conv(arg_objs[0], arg_objs[1], shape), [])