def test_gradient_descent_optimizer_multivar(self, tol):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multivariate functions."""
stepsize = 0.1
sgd_opt = GradientDescentOptimizer(stepsize)
multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_**2 for x_ in x]),
]
grad_multi_funcs = [
lambda x: (np.array([np.cos(x[0]), -np.sin(x[1])]), ),
lambda x: (np.array([
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1])**2),
]), ),
lambda x: (np.array([2 * x_ for x_ in x]), ),
]
x_vals = np.linspace(-10, 10, 16, endpoint=False)
for gradf, f in zip(grad_multi_funcs, multivariate_funcs):
for jdx in range(len(x_vals[:-1])):
x_vec = x_vals[jdx:jdx + 2]
x_new = sgd_opt.step(f, x_vec)
x_correct = x_vec - gradf(x_vec)[0] * stepsize
assert np.allclose(x_new, x_correct, atol=tol)
def setUp(self):
self.sgd_opt = GradientDescentOptimizer(stepsize)
self.mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
self.nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
self.adag_opt = AdagradOptimizer(stepsize)
self.rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
self.adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
self.fnames = ['test_function_1', 'test_function_2', 'test_function_3']
self.univariate_funcs = [
np.sin, lambda x: np.exp(x / 10.), lambda x: x**2
]
self.grad_uni_fns = [
np.cos, lambda x: np.exp(x / 10.) / 10., lambda x: 2 * x
]
self.multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_**2 for x_ in x])
]
self.grad_multi_funcs = [
lambda x: np.array([np.cos(x[0]), -np.sin(x[1])]),
lambda x: np.array([
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1])**2)
]), lambda x: np.array([2 * x_ for x_ in x])
]
self.mvar_mdim_funcs = [
lambda x: np.sin(x[0, 0]) + np.cos(x[1, 0]) - np.sin(x[0, 1]) + x[
1, 1], lambda x: np.exp(x[0, 0] / 3) * np.tanh(x[0, 1]),
lambda x: np.sum([x_[0]**2 for x_ in x])
]
self.grad_mvar_mdim_funcs = [
lambda x: np.array([[np.cos(x[0, 0]), -np.cos(x[0, 1])],
[-np.sin(x[1, 0]), 1.]]),
lambda x: np.array([[
np.exp(x[0, 0] / 3) / 3 * np.tanh(x[0, 1]),
np.exp(x[0, 0] / 3) * (1 - np.tanh(x[0, 1])**2)
], [0., 0.]]), lambda x: np.array([[2 * x_[0], 0.] for x_ in x])
]
self.class_fun = class_fun
self.quant_fun = quant_fun
self.hybrid_fun = hybrid_fun
self.hybrid_fun_nested = hybrid_fun_nested
self.hybrid_fun_flat = hybrid_fun_flat
self.hybrid_fun_mdarr = hybrid_fun_mdarr
self.hybrid_fun_mdlist = hybrid_fun_mdlist
self.mixed_list = [(0.2, 0.3), np.array([0.4, 0.2, 0.4]), 0.1]
self.mixed_tuple = (np.array([0.2, 0.3]), [0.4, 0.2, 0.4], 0.1)
self.nested_list = [[[0.2], 0.3], [0.1, [0.4]], -0.1]
self.flat_list = [0.2, 0.3, 0.1, 0.4, -0.1]
self.multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
self.multid_list = [[0.1, 0.2], [-0.1, -0.4]]
def test_apply_grad(self, grad, args, tol):
"""
Test that a gradient step can be applied correctly to a set of parameters.
"""
stepsize = 0.1
sgd_opt = GradientDescentOptimizer(stepsize)
grad, args = np.array(grad), np.array(args, requires_grad=True)
res = sgd_opt.apply_grad(grad, args)
expected = args - stepsize * grad
assert np.allclose(res, expected, atol=tol)
def getCost(var):
iimport pennylane as qml
from pennylane import numpy as np
from pennylane.optimize import GradientDescentOptimizer
dev = qml.device('default.qubit', wires=2)
def GetAnsatz():
qml.Rot(0.3, 1.8, 5.4, wires=1)
qml.RX(-0.5, wires=0)
qml.RY( 0.5, wires=1)
qml.CNOT(wires=[0, 1])
@qml.qnode(dev)
def getCircuitX():
GetAnsatz()
return qml.expval.PauliX(1)
@qml.qnode(dev)
def getCircuitY():
GetAnsatz()
return qml.expval.PauliY(1)
def getCost(var):
expX = getCircuitX()
expY = getCircuitY()
return (var[0] * expX + var[1] * expY) ** 2
optimizer = GradientDescentOptimizer(0.5)
variables = [0.3, 2.5]
variables_gd = [variables]
num_iterations = 20
for i in range(num_iterations):
variables = optimizer.step(getCost, variables)
variables_gd.append(variables)
print('Cost - step {:5d}: {: .7f} | Variable values: [{: .5f},{: .5f}]'
.format(i+1, getCost(variables), variables[0], variables[1]) )
def test_step_and_cost_supplied_grad(self, args):
"""Test that returned cost is correct if gradient function is supplied"""
stepsize = 0.1
sgd_opt = GradientDescentOptimizer(stepsize)
univariate_funcs = [np.sin, lambda x: np.exp(x / 10.0), lambda x: x**2]
grad_uni_fns = [
lambda x: (np.cos(x), ),
lambda x: (np.exp(x / 10.0) / 10.0, ),
lambda x: (2 * x, ),
]
for gradf, f in zip(grad_uni_fns, univariate_funcs):
_, res = sgd_opt.step_and_cost(f, args, grad_fn=gradf)
expected = f(args)
assert np.all(res == expected)
class GradientOptimizer(object):
def __init__(self, cost, step_size):
self.cost = cost
self.optimizer = GradientDescentOptimizer(step_size)
def optimize(self, **kwargs):
params = kwargs.get("params", None)
steps = kwargs.get("steps", None)
# Validate the cost function parameters
if params is None:
raise ValueError(
"Excepted 'params' passed as a keyword argument to be used by the cost function."
)
if isinstance(params, list) == False:
raise ValueError(
"The 'params' keyword argument must be a list of parameters to be passed to the cost function."
)
# Make sure we were given the number of steps unti convergence
if steps is None:
raise ValueError(
"Excepted 'steps' to be passed a keyword argument for the number of steps the optimizer is to take towards convergence."
)
# Run the optmizer for the given number of steps
for i in range(steps):
params = self.optimizer.step(self.cost, params)
return self.cost(params)
class A:
sgd_opt = GradientDescentOptimizer(stepsize)
mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
adag_opt = AdagradOptimizer(stepsize)
rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
def test_gradient_descent_optimizer_usergrad(self, x_start, tol):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
using user-provided gradients."""
stepsize = 0.1
sgd_opt = GradientDescentOptimizer(stepsize)
univariate_funcs = [np.sin, lambda x: np.exp(x / 10.0), lambda x: x**2]
grad_uni_fns = [
lambda x: (np.cos(x), ),
lambda x: (np.exp(x / 10.0) / 10.0, ),
lambda x: (2 * x, ),
]
for gradf, f in zip(grad_uni_fns[::-1], univariate_funcs):
x_new = sgd_opt.step(f, x_start, grad_fn=gradf)
x_correct = x_start - gradf(x_start)[0] * stepsize
assert np.allclose(x_new, x_correct, atol=tol)
def test_step_and_cost_autograd_sgd_single_multid_input(self):
"""Test that the correct cost is returned via the step_and_cost method for the
gradient-descent optimizer"""
stepsize = 0.1
sgd_opt = GradientDescentOptimizer(stepsize)
multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
@qml.qnode(qml.device("default.qubit", wires=1))
def quant_fun_mdarr(var):
qml.RX(var[0, 1], wires=[0])
qml.RY(var[1, 0], wires=[0])
qml.RY(var[1, 1], wires=[0])
return qml.expval(qml.PauliZ(0))
_, res = sgd_opt.step_and_cost(quant_fun_mdarr, multid_array)
expected = quant_fun_mdarr(multid_array)
assert np.all(res == expected)
def test_step_and_cost_autograd_sgd_multiple_inputs(self):
"""Test that the correct cost is returned via the step_and_cost method for the
gradient-descent optimizer"""
stepsize = 0.1
sgd_opt = GradientDescentOptimizer(stepsize)
@qml.qnode(qml.device("default.qubit", wires=1))
def quant_fun(*variables):
qml.RX(variables[0][1], wires=[0])
qml.RY(variables[1][2], wires=[0])
qml.RY(variables[2], wires=[0])
return qml.expval(qml.PauliZ(0))
inputs = [
np.array((0.2, 0.3), requires_grad=True),
np.array([0.4, 0.2, 0.4], requires_grad=True),
np.array(0.1, requires_grad=True),
]
_, res = sgd_opt.step_and_cost(quant_fun, *inputs)
expected = quant_fun(*inputs)
assert np.all(res == expected)
def test_gradient_descent_optimizer_multivar_multidim(self, tol):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multivariate functions and with higher dimensional inputs."""
stepsize = 0.1
sgd_opt = GradientDescentOptimizer(stepsize)
mvar_mdim_funcs = [
lambda x: np.sin(x[0, 0]) + np.cos(x[1, 0]) - np.sin(x[0, 1]) + x[
1, 1],
lambda x: np.exp(x[0, 0] / 3) * np.tanh(x[0, 1]),
lambda x: np.sum([x_[0]**2 for x_ in x]),
]
grad_mvar_mdim_funcs = [
lambda x: (np.array([[np.cos(x[0, 0]), -np.cos(x[0, 1])],
[-np.sin(x[1, 0]), 1.0]]), ),
lambda x: (np.array([
[
np.exp(x[0, 0] / 3) / 3 * np.tanh(x[0, 1]),
np.exp(x[0, 0] / 3) * (1 - np.tanh(x[0, 1])**2),
],
[0.0, 0.0],
]), ),
lambda x: (np.array([[2 * x_[0], 0.0] for x_ in x]), ),
]
x_vals = np.linspace(-10, 10, 16, endpoint=False)
for gradf, f in zip(grad_mvar_mdim_funcs, mvar_mdim_funcs):
for jdx in range(len(x_vals[:-3])):
x_vec = x_vals[jdx:jdx + 4]
x_vec_multidim = np.reshape(x_vec, (2, 2))
x_new = sgd_opt.step(f, x_vec_multidim)
x_correct = x_vec_multidim - gradf(
x_vec_multidim)[0] * stepsize
x_new_flat = x_new.flatten()
x_correct_flat = x_correct.flatten()
assert np.allclose(x_new_flat, x_correct_flat, atol=tol)
def test_private_stepsize(self):
"""
Tests whether it is possible to get and set ``stepsize`` using ``_stepsize``
and whether a ``UserWarning`` is raised while doing so.
"""
eta = 0.5
opt = GradientDescentOptimizer(eta)
assert opt._stepsize == eta
with pytest.warns(
UserWarning,
match=
"'_stepsize' is deprecated. Please use 'stepsize' instead."):
opt._stepsize
eta2 = 0.1
opt._stepsize = eta2
assert opt.stepsize == eta2
with pytest.warns(
UserWarning,
match=
"'_stepsize' is deprecated. Please use 'stepsize' instead."):
opt._stepsize = eta2
def opt(opt_name):
stepsize, gamma, delta = 0.1, 0.5, 0.8
if opt_name == "gd":
return GradientDescentOptimizer(stepsize)
if opt_name == "nest":
return NesterovMomentumOptimizer(stepsize, momentum=gamma)
if opt_name == "moment":
return MomentumOptimizer(stepsize, momentum=gamma)
if opt_name == "ada":
return AdagradOptimizer(stepsize)
if opt_name == "rms":
return RMSPropOptimizer(stepsize, decay=gamma)
if opt_name == "adam":
return AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
def test_update_stepsize(self):
"""
Tests whether the stepsize value is updated correctly and whether a ``UserWarning``
is raised when the ``update_stepsize`` method is used.
"""
eta = 0.5
opt = GradientDescentOptimizer(eta)
assert opt.stepsize == eta
eta2 = 0.1
opt.update_stepsize(eta2)
assert opt.stepsize == eta2
with pytest.warns(
UserWarning,
match=
"'update_stepsize' is deprecated. Stepsize value can be updated using "
"the 'stepsize' attribute.",
):
opt.update_stepsize(eta)
import pennylane as qml
from pennylane.optimize import GradientDescentOptimizer
# Create device
dev = qml.device('default.qubit', wires=1)
# Quantum node
@qml.qnode(dev)
def circuit1(var):
qml.RX(var[0], wires=0)
qml.RY(var[1], wires=0)
return qml.expval(qml.PauliZ(0))
# Create optimizer
opt = GradientDescentOptimizer(0.25)
# Optimize circuit output
var = [0.5, 0.2]
for it in range(30):
var = opt.step(circuit1, var)
print("Step {}: cost: {}".format(it, circuit1(var)))
assert opt._stepsize == eta
eta2 = 0.1
opt.update_stepsize(eta2)
assert opt._stepsize == eta2
def reset(opt):
if getattr(opt, "reset", None):
opt.reset()
@pytest.mark.parametrize(
"opt, opt_name",
[
(GradientDescentOptimizer(stepsize), "gd"),
(MomentumOptimizer(stepsize, momentum=gamma), "moment"),
(NesterovMomentumOptimizer(stepsize, momentum=gamma), "nest"),
(AdagradOptimizer(stepsize), "ada"),
(RMSPropOptimizer(stepsize, decay=gamma), "rms"),
(AdamOptimizer(stepsize, beta1=gamma, beta2=delta), "adam"),
(RotosolveOptimizer(), "roto"),
],
)
class TestOverOpts:
"""Tests keywords, multiple arguements, and non-training arguments in relevent optimizers"""
def test_kwargs(self, mocker, opt, opt_name, tol):
"""Test that the keywords get passed and alter the function"""
class func_wrapper:
@staticmethod
def func(x, c=1.0):
gen_weights: variables of the generator
"""
return -prob_fake_true(gen_weights, disc_weights)
# Fix the angles with which the true data is generated
phi = np.pi / 6
theta = np.pi / 2
omega = np.pi / 7
# Initialize the other variables
np.random.seed(0)
eps = 1e-2
gen_weights = np.array([np.pi] + [0] * 8) + np.random.normal(scale=eps, size=[9])
disc_weights = np.random.normal(size=[9])
opt = GradientDescentOptimizer(0.1)
print("Training the discriminator.")
for it in range(50):
disc_weights = opt.step(disc_cost, disc_weights)
cost = disc_cost(disc_weights)
if it % 5 == 0:
print("Step {}: cost = {}".format(it+1, cost))
print("Probability for the discriminator to classify real data correctly: ", prob_real_true(disc_weights))
print("Probability for the discriminator to classify fake data as real: ", prob_fake_true(gen_weights, disc_weights))
print("Training the generator.")
# train generator
for it in range(200):
gen_weights = opt.step(gen_cost, gen_weights)
#test it for [1,-1,-1] spin configuration. Total energy for this ising model should be
#H = -1(J1*s1*s2 + J2*s2*s3) = -1 (1*1*-1 + -1*-1*-1) = 2
#t1=np.array([0, np.pi, 0])
#t2=np.array([0,np.pi ,0])
t1 = np.pi * (np.random.ranf(3))
t2 = np.pi * (np.random.ranf(3))
var_init = np.array([t1, t2])
cost_init = cost(var_init)
print(var_init)
print(cost_init)
#Now we optimize using pennylane numpy gradient descent optimizer
gd = GradientDescentOptimizer(0.4)
var = var_init
var_gd = [var]
cost_gd = [cost_init]
for it in range(100):
var = gd.step(cost, var)
if (it + 1) % 5 == 0:
var_gd.append(var)
cost_gd.append(cost(var))
print('Energy after step {:5d}: {: .7f} | Angles: {}'.format(
it + 1, cost(var), var))
#As expected the minimum energy is -2 for the spin configuration [1,1,-1]
def __init__(self, cost, step_size):
self.cost = cost
self.optimizer = GradientDescentOptimizer(step_size)
def objective(var):
"""Cost function to be minimized.
Args:
var (array[float]): array of variables
Returns:
float: output of variational circuit
"""
return circuit(var)
var_init = np.array([-0.011, -0.012])
gd = GradientDescentOptimizer(0.4)
var = var_init
var_gd = [var]
for it in range(100):
var = gd.step(objective, var)
if (it + 1) % 5 == 0:
var_gd.append(var)
print('Objective after step {:5d}: {: .7f} | Angles: {}'.format(
it + 1, objective(var), var))
ada = AdagradOptimizer(0.4)
var = var_init
class BasicTest(BaseTest):
"""Basic optimizer tests.
"""
def setUp(self):
self.sgd_opt = GradientDescentOptimizer(stepsize)
self.mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
self.nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
self.adag_opt = AdagradOptimizer(stepsize)
self.rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
self.adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
self.fnames = ['test_function_1', 'test_function_2', 'test_function_3']
self.univariate_funcs = [
np.sin, lambda x: np.exp(x / 10.), lambda x: x**2
]
self.grad_uni_fns = [
np.cos, lambda x: np.exp(x / 10.) / 10., lambda x: 2 * x
]
self.multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_**2 for x_ in x])
]
self.grad_multi_funcs = [
lambda x: np.array([np.cos(x[0]), -np.sin(x[1])]),
lambda x: np.array([
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1])**2)
]), lambda x: np.array([2 * x_ for x_ in x])
]
self.mvar_mdim_funcs = [
lambda x: np.sin(x[0, 0]) + np.cos(x[1, 0]) - np.sin(x[0, 1]) + x[
1, 1], lambda x: np.exp(x[0, 0] / 3) * np.tanh(x[0, 1]),
lambda x: np.sum([x_[0]**2 for x_ in x])
]
self.grad_mvar_mdim_funcs = [
lambda x: np.array([[np.cos(x[0, 0]), -np.cos(x[0, 1])],
[-np.sin(x[1, 0]), 1.]]),
lambda x: np.array([[
np.exp(x[0, 0] / 3) / 3 * np.tanh(x[0, 1]),
np.exp(x[0, 0] / 3) * (1 - np.tanh(x[0, 1])**2)
], [0., 0.]]), lambda x: np.array([[2 * x_[0], 0.] for x_ in x])
]
self.class_fun = class_fun
self.quant_fun = quant_fun
self.hybrid_fun = hybrid_fun
self.hybrid_fun_nested = hybrid_fun_nested
self.hybrid_fun_flat = hybrid_fun_flat
self.hybrid_fun_mdarr = hybrid_fun_mdarr
self.hybrid_fun_mdlist = hybrid_fun_mdlist
self.mixed_list = [(0.2, 0.3), np.array([0.4, 0.2, 0.4]), 0.1]
self.mixed_tuple = (np.array([0.2, 0.3]), [0.4, 0.2, 0.4], 0.1)
self.nested_list = [[[0.2], 0.3], [0.1, [0.4]], -0.1]
self.flat_list = [0.2, 0.3, 0.1, 0.4, -0.1]
self.multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
self.multid_list = [[0.1, 0.2], [-0.1, -0.4]]
def test_mixed_inputs_for_hybrid_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for hybrid optimization tasks."""
self.logTestName()
hybrid_list = self.sgd_opt.step(self.hybrid_fun, self.mixed_list)
hybrid_tuple = self.sgd_opt.step(self.hybrid_fun, self.mixed_tuple)
self.assertAllAlmostEqual(hybrid_list[0],
hybrid_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[1],
hybrid_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[2],
hybrid_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_classical_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely classical optimization tasks."""
self.logTestName()
class_list = self.sgd_opt.step(self.class_fun, self.mixed_list)
class_tuple = self.sgd_opt.step(self.class_fun, self.mixed_tuple)
self.assertAllAlmostEqual(class_list[0],
class_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(class_list[1],
class_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(class_list[2],
class_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_quantum_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely quantum optimization tasks."""
self.logTestName()
quant_list = self.sgd_opt.step(self.quant_fun, self.mixed_list)
quant_tuple = self.sgd_opt.step(self.quant_fun, self.mixed_tuple)
self.assertAllAlmostEqual(quant_list[0],
quant_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[1],
quant_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[2],
quant_tuple[2],
delta=self.tol)
def test_nested_and_flat_returns_same_update(self):
"""Tests that gradient descent optimizer has the same output for
nested and flat lists."""
self.logTestName()
nested = self.sgd_opt.step(self.hybrid_fun_nested, self.nested_list)
flat = self.sgd_opt.step(self.hybrid_fun_flat, self.flat_list)
self.assertAllAlmostEqual(flat, list(_flatten(nested)), delta=self.tol)
def test_array_and_list_return_same_update(self):
"""Tests that gradient descent optimizer has the same output for
lists and arrays."""
self.logTestName()
array = self.sgd_opt.step(self.hybrid_fun_mdarr, self.multid_array)
list = self.sgd_opt.step(self.hybrid_fun_mdlist, self.multid_list)
self.assertAllAlmostEqual(array, list, delta=self.tol)
def test_gradient_descent_optimizer_univar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
x_vec = x_vals[jdx:jdx + 2]
x_new = self.sgd_opt.step(f, x_vec)
x_correct = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar_multidim(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions and with higher dimensional inputs."""
self.logTestName()
for gradf, f, name in zip(self.grad_mvar_mdim_funcs,
self.mvar_mdim_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-3])):
x_vec = x_vals[jdx:jdx + 4]
x_vec_multidim = np.reshape(x_vec, (2, 2))
x_new = self.sgd_opt.step(f, x_vec_multidim)
x_correct = x_vec_multidim - gradf(
x_vec_multidim) * stepsize
x_new_flat = x_new.flatten()
x_correct_flat = x_correct.flatten()
self.assertAllAlmostEqual(x_new_flat,
x_correct_flat,
delta=self.tol)
def test_gradient_descent_optimizer_usergrad(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start, grad_fn=gradf)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_momentum_optimizer_univar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.mom_opt.reset()
x_onestep = self.mom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_momentum_optimizer_multivar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.mom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.mom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_univar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_multivar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.nesmom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.nesmom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_usergrad(self):
"""Tests that nesterov momentum optimizer takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start, grad_fn=gradf)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f,
x_onestep,
grad_fn=gradf)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_univar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adag_opt.reset()
x_onestep = self.adag_opt.step(f, x_start)
past_grads = gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_start) * gradf(x_start) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_multivar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adag_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adag_opt.step(f, x_vec)
past_grads = gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_vec) * gradf(x_vec) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_univar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.rms_opt.reset()
x_onestep = self.rms_opt.step(f, x_start)
past_grads = (1 - gamma) * gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_start)*gradf(x_start) \
+ (1 - gamma) * gradf(x_onestep)*gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_multivar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.rms_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.rms_opt.step(f, x_vec)
past_grads = (1 - gamma) * gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_vec) * gradf(x_vec) \
+ (1 - gamma) * gradf(x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_univar(self):
"""Tests that adam optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adam_opt.reset()
x_onestep = self.adam_opt.step(f, x_start)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_start)
secondmoment = gradf(x_start) * gradf(x_start)
x_onestep_target = x_start - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_start) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_start) * gradf(x_start) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_multivar(self):
"""Tests that adam optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adam_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adam_opt.step(f, x_vec)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_vec)
secondmoment = gradf(x_vec) * gradf(x_vec)
x_onestep_target = x_vec - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_vec) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_vec) * gradf(x_vec) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
return qml.expval.MeanPhoton(0)
def objective(var):
"""Objective to minimize.
Args:
var (array[float]): array containing the variables
Returns:
output of the variational circuit
"""
return circuit(var)
opt = GradientDescentOptimizer(stepsize=0.1)
var_init = np.array([0.01, 0.01])
var = var_init
var_gd = []
for iteration in range(100):
var = opt.step(objective, var)
var_gd.append(var)
if iteration % 10 == 0:
print('Cost after step {:3d}: {:0.7f} | Variables [{:0.7f}, {:0.7f}]'
''.format(iteration, objective(var), var[0], var[1]))
def cost(var):
"""Cost function to be minimized.
Args:
var (list[float]): list of variables
Returns:
float: square of linear combination of the expectations
"""
expX = circuit_X()
expY = circuit_Y()
return (var[0] * expX + var[1] * expY)**2
# optimizer
opt = GradientDescentOptimizer(0.5)
# minimize the cost
var = [0.3, 2.5]
var_gd = [var]
for it in range(20):
var = opt.step(cost, var)
var_gd.append(var)
print(
'Cost after step {:5d}: {: .7f} | Variables: [{: .5f},{: .5f}]'.format(
it + 1, cost(var), var[0], var[1]))
