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main.py
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Mon, Feb 24, 08:00

main.py
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#!/usr/bin/env python3
from conjugate_gradient import solve as cgSolve
from optimizer import solve as scipySolve
from optimizer import plot
import numpy as np
import argparse
################################################################
# definitions of the quadratic form
################################################################
A = np.array([[4, 1], [1, 3]])
b = np.array([1, 2])
c = 6
def func(X):
"functor calculation of the quadratic form"
# makes a long array of shape [:, 2]
X = np.array(X).flatten()
X = X.reshape((X.shape[0]//2, 2))
# computes the quadratic form
res = 0.5*np.einsum('ai,ij,aj->a', X, A, X)
res -= np.einsum('i,ai->a', b, X) + c
return res
def jac(x):
return A.dot(x) - b
def hess(x):
return A
################################################################
# generic optimization program
################################################################
def optimize(method='cg'):
tol = 1e-6
x0 = np.array([2, 1])
if method == 'BFGS':
optimizer = scipySolve
elif method == 'cg':
optimizer = cgSolve
else:
raise RuntimeError('unknown solve method: ' + str(method))
iterations = []
iterations.append(x0)
res = optimizer(
func, x0, tol=tol, jac=jac, hess=hess,
callback=lambda Xi: iterations.append(Xi))
print('Method: ', method, ' Solution :', res)
plot(func, iterations, method)
################################################################
# main function: parsing of program arguments
################################################################
if __name__ == '__main__':
parser = argparse.ArgumentParser(
description='Optimization exercise in python')
parser.add_argument(
'-m', '--method', type=str,
help=('Specify the method to use for the optimization.'
' Can be cg/BFGS'), default='cg')
args = parser.parse_args()
optimize(args.method)

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