code: """
  Copyright 2017 Robin Verschueren
  
  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.
  """
  
  import numpy as np
  import scipy.sparse as sp
  
  from cvxpy.atoms.affine.add_expr import AddExpression
  from cvxpy.atoms.affine.binary_operators import MulExpression
  from cvxpy.atoms.quad_form import QuadForm
  from cvxpy.constraints import NonPos, Zero
  from cvxpy.problems.objective import Minimize
  from cvxpy.reductions import InverseData
  from cvxpy.reductions.solvers.conic_solvers.conic_solver import ConicSolver
  from cvxpy.reductions.solvers.solver import Solver
  from cvxpy.reductions.utilities import are_args_affine
  import cvxpy.settings as s
  
  
  def is_stuffed_qp_objective(objective):
      """QPSolver requires objectives to be stuffed in the following way.
      """
      expr = objective.expr
      return (type(expr) == AddExpression
              and len(expr.args) == 2
              and type(expr.args[0]) == QuadForm
              and type(expr.args[1]) == MulExpression
              and expr.args[1].is_affine())
  
  
  class QpSolver(Solver):
      """
      A QP solver interface.
      """
  
      def accepts(self, problem):
          return (type(problem.objective) == Minimize
                  and is_stuffed_qp_objective(problem.objective)
                  and all(type(c) == Zero or type(c) == NonPos
                          for c in problem.constraints)
                  and are_args_affine(problem.constraints))
  
      def apply(self, problem):
          """
          Construct QP problem data stored in a dictionary.
          The QP has the following form
  
              minimize      1/2 x' P x + q' x
              subject to    A x =  b
                            F x <= g
  
          """
          inverse_data = InverseData(problem)
  
          obj = problem.objective
          # quadratic part of objective is x.T * P * x but solvers expect
          # 0.5*x.T * P * x.
          P = 2*obj.expr.args[0].args[1].value
          q = obj.expr.args[1].args[0].value.flatten()
  
          # Get number of variables
          n = problem.size_metrics.num_scalar_variables
  
          # TODO(akshayka): This dependence on ConicSolver is hacky; something
          # should change here.
          eq_cons = [c for c in problem.constraints if type(c) == Zero]
          if eq_cons:
              eq_coeffs = list(zip(*[ConicSolver.get_coeff_offset(con.expr)
                                     for con in eq_cons]))
              A = sp.vstack(eq_coeffs[0])
              b = - np.concatenate(eq_coeffs[1])
          else:
              A, b = sp.csr_matrix((0, n)), -np.array([])
  
          ineq_cons = [c for c in problem.constraints if type(c) == NonPos]
          if ineq_cons:
              ineq_coeffs = list(zip(*[ConicSolver.get_coeff_offset(con.expr)
                                       for con in ineq_cons]))
              F = sp.vstack(ineq_coeffs[0])
              g = - np.concatenate(ineq_coeffs[1])
          else:
              F, g = sp.csr_matrix((0, n)), -np.array([])
  
          # Create dictionary with problem data
          variables = problem.variables()[0]
          data = {}
          data[s.P] = sp.csc_matrix(P)
          data[s.Q] = q
          data[s.A] = sp.csc_matrix(A)
          data[s.B] = b
          data[s.F] = sp.csc_matrix(F)
          data[s.G] = g
          data[s.BOOL_IDX] = [t[0] for t in variables.boolean_idx]
          data[s.INT_IDX] = [t[0] for t in variables.integer_idx]
          data['n_var'] = n
          data['n_eq'] = A.shape[0]
          data['n_ineq'] = F.shape[0]
  
          inverse_data.sorted_constraints = ineq_cons + eq_cons
  
          # Add information about integer variables
          inverse_data.is_mip = \
              len(data[s.BOOL_IDX]) > 0 or len(data[s.INT_IDX]) > 0
  
          return data, inverse_data
  
apis: scipy.sparse.csc_matrix scipy.sparse.csr_matrix numpy.array numpy.concatenate scipy.sparse.vstack