optimizer.py
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	#!/usr/bin/env python3
	# -- coding: utf-8 --
	"""
	Created on Thu Oct 10 10:19:11 2019
	Authors: Omid Ashtari and Armand Sieber
	Description: Scripts intended to minimize a quadratic function using scipy.optimize built-in function.
	The function to minimize is defined as S(X)= X'AX - X'B, with X = [x, y], X' the transform of X
	A is a 2x2 matrix and B 2X1 vector
	"""

	import numpy as np
	import sys
	from scipy.optimize import minimize
	import post_processing

	def objective(X, *args): #objective function to be minimized
	A = args[0]
	B = args[1].T
	S = np.dot(X.T, np.dot(A, X)) - np.dot(X.T, B)
	return S

	def reporter(X_r):
	global X_int
	X_int = np.vstack([X_int, X_r])
	return 0

	# Import minimization method
	if len(sys.argv) < 2:
	print('Solver method missing. Default method implemented --> CG')
	method = 'CG'
	else:
	method = sys.argv[1]

	available_methods = ('Nelder-Mead', 'Powell', 'CG', 'BFGS', 'L-BFGS-B', 'TNC', 'SLSQP')

	if method in available_methods: # test availibility of user inputs
	print('Minimzation performed with the %s solver' % method)
	else:
	sys.exit('Minimization method missing or not available!')

	# Parameters of the function to minimize
	A = np.array([[4, 0], [1, 3]])
	B = np.array([0, 1])

	# Minimization process
	X0 = np.array([3, 2]) #initial guess
	X_int = X0 #stores solution at each step
	solution = minimize(objective, X0, args = (A, B), method = method, callback = reporter,options = {'maxiter':100})
	print(solution)
	print(X_int)

	# Post-processing
	post_processing.plot_results(X_int, A, B, method)