text: """
  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.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
  
  
  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
  
      def _grad(self, values):
          """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:
              grad = MulExpression(mat, var)._grad(values)[1]
          else:
              grad = MulExpression(var, mat.T)._grad(values)[0]
          return [grad]
  
      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)])
  