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R9316/exercises/week4/conjugate_gradient/sources-solution/optimizer.py
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optimizer.py
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#!/usr/bin/env python3
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from conjugate_gradient import solve as cgSolve
from scipy.optimize import minimize as scipySolve
def plotFunction(func, iterations, title):
'Plotting function for plane and iterations'
x = np.linspace(-3, 3, 100)
y = np.linspace(-3, 3, 100)
x, y = np.meshgrid(x, y)
X = np.stack([x.flatten(), y.flatten()], axis=1)
z = func(X).reshape((100, 100))
xy = np.array(iterations)
zs = func(xy)
fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(x, y, z, linewidth=0, antialiased=True,
cmap=plt.cm.viridis, alpha=0.2)
ax.contour(x, y, z, 10, colors="k", linestyles="solid")
ax.plot(xy[:, 0], xy[:, 1], zs, 'ro--')
ax.grid(False)
ax.view_init(elev=62., azim=143)
ax.set_title(title)
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.show()
################################################################
# generic optimization program
################################################################
def optimize(method='cg', plot=False, func=None, **kwargs):
if func is None:
raise RuntimeError('Need a function to optimize')
tol = 1e-6
x0 = np.array([2, 2])
if method == 'BFGS':
optimizer = scipySolve
if 'hess' in kwargs:
del kwargs['hess']
elif method == 'cg':
optimizer = cgSolve
else:
raise RuntimeError('unknown solve method: ' + str(method))
iterations = []
iterations.append(x0)
res = optimizer(
func, x0, tol=tol, callback=lambda Xi: iterations.append(Xi),
**kwargs)
print('Method: ', method, ' Solution :', res)
if plot is True:
plotFunction(func, iterations, method)
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