R9490/exercise_1.py
ba5fdc1fc5d8master

exercise_1.py
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			"""
			EXERCISE 1
			Find the minimizer of a scalar function of 2 variables.

			"""

			import numpy as np
			import plot
			import optimizer

			# The function to be minimized
			def f(x):
			# x can be an array of coordinate [x1, y1]
			A = np.array([[4., 0.], [1., 3.]])
			b = np.array([0., 1.])
			# f(x)=xAx-bx
			Ax = np.einsum('ik,k->i', A, x)
			return np.einsum('i,i->', x, Ax) - np.einsum('i,i->', x, b)

			# methods : e.g. "CG" or "BFGS"
			method = 'BFGS'

			# initial guess :
			x0 = np.array([3., 3.])

			# exit tolerance for the method :
			tol = 1e-9

			# call the optimizer function :
			minimizer, resultINFO, points = optimizer.optimizer(f, method, x0, tol)

			# Print the results :
			print("_________________________________________")
			print("Find the minimizer of a scalar function of 2 variables using the method: "+method)
			print(resultINFO.message)
			print(" solution x,y : "+repr(resultINFO.x))
			print(" number of iterations : "+repr(resultINFO.nit))
			print(" value of the function at the minimizer : "+repr(f(resultINFO.x)))

			plot.plotminimizer(f, points, method)