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least_square

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/least_square.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/least_square.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python

%pip install ortools

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 ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

python

import sys
from ortools.linear_solver import pywraplp


def main(sol='CBC'):

  # Create the solver.
  solver = pywraplp.Solver.CreateSolver(sol)
  if not solver:
    return

  # 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(), end=' ')
  print()



sol = 'CBC'
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)