# Copyright 2011 Hakan Kjellerstrand hakank@bonetmail.com
#
# 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.

"""

  Least square optimization problem in Google or-tools.

  Solving a fourth grade least square equation.

  From the Swedish book 'Optimeringslara' [Optimization Theory],
  page 286f.

  This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
  Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
"""

import sys
from ortools.linear_solver import pywraplp

def main(sol = 'GLPK'):

  # Create the solver.

  # using GLPK
  if sol == 'GLPK':
    solver = pywraplp.Solver('CoinsGridGLPK',
                             pywraplp.Solver.GLPK_LINEAR_PROGRAMMING)
  else:
    # Using CLP
    solver = pywraplp.Solver('CoinsGridCLP',
                             pywraplp.Solver.CLP_LINEAR_PROGRAMMING)


  # data
  # number of points
  num = 14

  # temperature
  t = [20, 30, 80,125,175,225,275,325,360,420,495,540,630,700]

  # percentage gas
  F = [0.0,5.8,14.7,31.6,43.2,58.3,78.4,89.4,96.4,99.1,99.5,99.9,100.0,100.0]

  p = 4

  #
  # declare variables
  #
  a = [solver.NumVar(-100, 100, 'a[%i]' % i ) for i in range(p + 1)]

  # to minimize
  z = solver.Sum([(F[i] -
                   (sum([a[j]*t[i]**j for j in range(p+1)])))
                  for i in range(num)])

  #
  # constraints
  #
  solver.Add(solver.Sum([20**i*a[i] for i in range(p+1)]) == 0)

  solver.Add( (a[0] + sum([700.0**j*a[j]
                           for j in range(1,p+1)])) == 100.0)

  for i in range(num):
    solver.Add(solver.Sum([j*a[j]*t[i]**(j-1)
                           for j in range(p+1)])  >= 0)

  objective = solver.Minimize(z)

  solver.Solve()

  print
  print 'z = ', solver.Objective().Value()
  for i in range(p + 1):
    print a[i].SolutionValue(),
  print


if __name__ == '__main__':

  sol = 'GLPK'
  if len(sys.argv) > 1:
    sol = sys.argv[1]
    if sol != 'GLPK' and sol != 'CBC':
      print 'Solver must be either GLPK or CBC'
      sys.exit(1)

  main(sol)