# Source code for cvxpy.atoms.total_variation

"""
Copyright 2013 Steven Diamond

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

from cvxpy.expressions.expression import Expression
from cvxpy.atoms.norm import norm
from cvxpy.atoms.affine.vstack import vstack
from cvxpy.atoms.affine.sum import sum
from cvxpy.atoms.affine.reshape import reshape

[docs]def tv(value, *args):
"""Total variation of a vector, matrix, or list of matrices.

Uses L1 norm of discrete gradients for vectors and
L2 norm of discrete gradients for matrices.

Parameters
----------
value : Expression or numeric constant
The value to take the total variation of.
args : Matrix constants/expressions
Additional matrices extending the third dimension of value.

Returns
-------
Expression
An Expression representing the total variation.
"""
value = Expression.cast_to_const(value)
if value.ndim == 0:
raise ValueError("tv cannot take a scalar argument.")
# L1 norm for vectors.
elif value.ndim == 1:
return norm(value[1:] - value[0:value.shape-1], 1)
# L2 norm for matrices.
else:
rows, cols = value.shape
args = map(Expression.cast_to_const, args)
values = [value] + list(args)
diffs = []
for mat in values:
diffs += [
mat[0:rows-1, 1:cols] - mat[0:rows-1, 0:cols-1],
mat[1:rows, 0:cols-1] - mat[0:rows-1, 0:cols-1],
]
length = diffs.shape*diffs.shape
stacked = vstack([reshape(diff, (1, length)) for diff in diffs])
return sum(norm(stacked, p=2, axis=0))