def test_sd_p(self):
x = np.array([[0], [0], [0], [0], [0], [0]])
x_opt = opt.steepest_descent(self.p, x, tol=1e-6)
print('sd')
print(x_opt)
print(self.x_opt)
print()
self.assertTrue(np.linalg.norm(x_opt - self.x_opt) < 1e-3)
def test_sd(self):
P = np.array([[1, 0, 0], [0, 2, 0], [0, 0, 4]])
v = lambda x: 0.5 * x.T @ P @ x
del_v = lambda x: x.T @ P
p = opt.Problem(v, del_v)
x = np.array([[1], [1], [1]])
x_opt = np.array([[0], [0], [0]])
x_sd = opt.steepest_descent(p, x)
self.assertTrue(np.linalg.norm(x_sd - x_opt) < 1e-6)
def test_sd(self):
x = np.array([[0], [0], [0], [0], [0], [0]])
start = time.time()
x_opt = opt.steepest_descent(self.p, x, tol=1e-6, hist=True)
end = time.time()
g = np.array(
[np.linalg.norm(self.p.grad(x_opt[i])) for i in range(len(x_opt))])
fig = plt.figure()
plt.plot(np.arange(len(x_opt)), g)
plt.xlabel('Iteration')
plt.ylabel('Norm of Gradient')
fig.savefig('./fig/sd-pA.eps', format='eps')
print('\nProblem A, Steepest Descent')
print('arg min v(x) =\n', x_opt[-1])
print('time =\n', end - start, 's')
def test_sd(self):
# Pick initial value
x = np.array([[0], [0], [0], [0], [0], [0]])
start = time.time()
# Run steepest descent with history turned on (get x at each iteration)
x_opt = opt.steepest_descent(self.p, x, hist=True)
end = time.time()
# Calculate gradient at each iteration
g = np.array(
[np.linalg.norm(self.p.grad(x_opt[i])) for i in range(len(x_opt))])
# Plot gradient and save figure
fig = plt.figure()
plt.plot(np.arange(len(x_opt)), g)
plt.xlabel('Iteration')
plt.ylabel('Norm of Gradient')
fig.savefig('./fig/sd-pA-grad.eps', format='eps')
# Print out stats
print('\nProblem A, Steepest Descent (Exact Gradient)')
print('arg min v(x) =\n', x_opt[-1])
print('time =\n', end - start, 's')
def test_sd(self):
x = np.array([[10], [10]])
x_opt = opt.steepest_descent(self.p, x, tol=1e-4)
self.assertTrue(np.linalg.norm(x_opt - self.x_opt) < 1e-3)
