# Source code for cvxpy.atoms.affine.cumsum

"""

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 cvxpy.atoms.axis_atom import AxisAtom
from cvxpy.atoms.affine.affine_atom import AffAtom
from cvxpy.atoms.affine.binary_operators import MulExpression
from cvxpy.expressions.variable import Variable
import cvxpy.lin_ops.lin_utils as lu
import numpy as np
import scipy.sparse as sp

def get_diff_mat(dim, axis):
"""Return a sparse matrix representation of first order difference operator.

Parameters
----------
dim : int
The length of the matrix dimensions.
axis : int
The axis to take the difference along.

Returns
-------
SciPy CSC matrix
A square matrix representing first order difference.
"""
# Construct a sparse matrix representation.
val_arr = []
row_arr = []
col_arr = []
for i in range(dim):
val_arr.append(1.)
row_arr.append(i)
col_arr.append(i)
if i > 0:
val_arr.append(-1.)
row_arr.append(i)
col_arr.append(i-1)

mat = sp.csc_matrix((val_arr, (row_arr, col_arr)),
(dim, dim))
if axis == 0:
return mat
else:
return mat.T

[docs]class cumsum(AffAtom, AxisAtom):
"""Cumulative sum.

Attributes
----------
expr : CVXPY expression
The expression being summed.
axis : int
The axis to sum across if 2D.
"""
def __init__(self, expr, axis=0):
super(cumsum, self).__init__(expr, axis)

@AffAtom.numpy_numeric
def numeric(self, values):
"""Convolve the two values.
"""
return np.cumsum(values[0], axis=self.axis)

def shape_from_args(self):
"""The same as the input.
"""
return self.args[0].shape

"""Gives the (sub/super)gradient of the atom w.r.t. each argument.

Matrix expressions are vectorized, so the gradient is a matrix.

Args:
values: A list of numeric values for the arguments.

Returns:
A list of SciPy CSC sparse matrices or None.
"""
# TODO inefficient
dim = values[0].shape[self.axis]
mat = np.zeros((dim, dim))
for i in range(dim):
for j in range(i+1):
mat[i, j] = 1
var = Variable(self.args[0].shape)
if self.axis == 0:
else:

def get_data(self):
"""Returns the axis being summed.
"""
return [self.axis]

@staticmethod
def graph_implementation(arg_objs, shape, data=None):
"""Cumulative sum via difference matrix.

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)
"""
# Implicit O(n) definition:
# X = Y[:1,:] - Y[1:,:]
Y = lu.create_var(shape)
axis = data[0]
dim = shape[axis]
diff_mat = get_diff_mat(dim, axis)
diff_mat = lu.create_const(diff_mat, (dim, dim), sparse=True)
if axis == 0:
diff = lu.mul_expr(diff_mat, Y)
else:
diff = lu.rmul_expr(Y, diff_mat)
return (Y, [lu.create_eq(arg_objs[0], diff)])