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Algorithms.py
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Algorithms.py
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# -*- coding:utf-8 -*-
"""
@author:Xu Jingyi
@file:Algorithms.py
@time:2018/11/914:38
Algorithms:
GD_PR: Gradient Descent Phase Retrieval (Wirtinger Flow)
N_PR: Newton Phase Retrieval
GN_PR: Gaussian Newton Phase Retrieval
SP_PR: Subspace Pursuit Phase Retrieval
HTP_PR: Hard Thresholding Pursuit Phase Retrieval
IHT_PR: Iterative Hard Thresholding Phase Retrieval
OMP_PR: Orthogonal Matching Pursuit Phase Retrieval
"""
import numpy as np
import Initialization
import Projection
class PhaseRetrieval(object):
def __init__(self, x, A, y, z, param):
self.x = x
self.A = A
self.y = y
self.z = z
self.m, self.n = A.shape
self.param = param
# self.loss_func = Projection.LossFunction(self.x, A, y, z, param)
def select_initialization(self, initializer):
init_object = Initialization.Initialization(self.A, self.z, self.param.k, self.param.data_type,
self.param.isComplex)
if initializer in ['init_random', 'init_constant', 'init_spectral', 'init_optimal_spectral']:
init_func = getattr(init_object, initializer)
return init_func
else:
print('There is no such initializer %s' % initializer)
def select_step_chooser(self, step_chooser):
step_object = Projection.StepChooser(self.param.k, self.param.step_value)
if step_chooser in ['backtracking_line_search', 'constant_step']:
step_chooser_func = getattr(step_object, step_chooser)
return step_chooser_func
else:
print('There is no such step_chooser %s' % step_chooser)
def select_projection_method(self, projection, support):
projection_object = Projection.ProjectionMethod(support, self.x, self.A, self.y, self.z, self.param)
if projection in ['gradient_descent', 'newton', 'gauss_newton', 'steepest_descent', 'coordinate_descent']:
projection_func = getattr(projection_object, projection)
return projection_func
else:
print('There is no such projection method %s' % projection)
class GD_PR(PhaseRetrieval):
def __init__(self, x, A, y, z, param):
PhaseRetrieval.__init__(self, x, A, y, z, param)
def solver(self):
init_func = self.select_initialization(self.param.initializer)
step_func = self.select_step_chooser(self.param.step_chooser)
# projection_func = self.select_projection_method(self.param.projection, np.array(range(self.n)))
projection_object = Projection.ProjectionMethod(np.array(range(self.n)), self.x, self.A, self.y, self.z,
self.param)
x0 = init_func()
x_hat, recon_error, meas_error, iteration, success = projection_object.gradient_descent(x0, step_func,
truncated=True)
return recon_error, meas_error, iteration, success
class N_PR(PhaseRetrieval):
def __init__(self, x, A, y, z, param):
PhaseRetrieval.__init__(self, x, A, y, z, param)
def solver(self):
init_func = self.select_initialization(self.param.initializer)
step_func = self.select_step_chooser(self.param.step_chooser)
# projection_func = self.select_projection_method(self.param.projection, np.array(range(self.n)))
projection_object = Projection.ProjectionMethod(np.array(range(self.n)), self.x, self.A, self.y, self.z,
self.param)
x0 = init_func()
x_hat, recon_error, meas_error, iteration, success = projection_object.newton(x0, step_func, truncated=True)
return recon_error, meas_error, iteration, success
class GN_PR(PhaseRetrieval):
def __init__(self, x, A, y, z, param):
PhaseRetrieval.__init__(self, x, A, y, z, param)
def solver(self):
init_func = self.select_initialization(self.param.initializer)
step_func = self.select_step_chooser(self.param.step_chooser)
# projection_func = self.select_projection_method(self.param.projection, np.array(range(self.n)))
projection_object = Projection.ProjectionMethod(np.array(range(self.n)), self.x, self.A, self.y, self.z,
self.param)
x0 = init_func()
x_hat, recon_error, meas_error, iteration, success = projection_object.gauss_newton(x0, step_func,
truncated=True)
return recon_error, meas_error, iteration, success
class SP_PR(PhaseRetrieval):
def __init__(self, x, A, y, z, param):
PhaseRetrieval.__init__(self, x, A, y, z, param)
def get_projection(self, support, x0, step_func, truncated):
projection_func = self.select_projection_method(self.param.projection, support)
x_hat, recon_error, meas_error, iteration, success = projection_func(x0, step_func, truncated)
return x_hat, recon_error, meas_error, iteration, success
def gradient_f(self, x_hat):
z_hat = self.A.dot(x_hat) ** 2
b = z_hat - self.z
grad = 2 / len(self.A) * np.dot(np.dot(self.A.transpose(), b * self.A), x_hat)
return grad
def solver(self):
init_func = self.select_initialization(self.param.initializer)
step_func = self.select_step_chooser(self.param.step_chooser)
x0 = init_func()
grad = self.gradient_f(x0)
sort_grad_index = np.argsort(-abs(grad), axis=0)
T0 = sort_grad_index[0:self.param.k, :].reshape(self.param.k)
x0, recon_error, meas_error, iteration, success = self.get_projection(T0, x0[T0], step_func, truncated=False)
for iteration_alg in range(self.param.max_iter):
grad = self.gradient_f(x0)
sort_grad_index = np.argsort(-abs(grad), axis=0)
T1 = sort_grad_index[0:self.param.k, :].reshape(self.param.k)
T_tilde = np.union1d(T0, T1)
x_tilde, recon_error, meas_error, iteration, success = self.get_projection(T_tilde, x0[T_tilde], step_func,
truncated=False)
sort_x_index = np.argsort(-abs(x_tilde), axis=0)
T0 = sort_x_index[0:self.param.k, :].reshape(self.param.k)
x0, recon_error, meas_error, iteration, success = self.get_projection(T0, x_tilde[T0], step_func,
truncated=False)
if success:
break
return recon_error, meas_error, iteration_alg, success
class OMP_PR(PhaseRetrieval):
def __init__(self, x, A, y, z, param):
PhaseRetrieval.__init__(self, x, A, y, z, param)
def get_projection(self, support, x0, step_func, truncated):
projection_func = self.select_projection_method(self.param.projection, support)
x_hat, recon_error, meas_error, iteration, success = projection_func(x0, step_func, truncated)
return x_hat, recon_error, meas_error, iteration, success
def gradient_f(self, x_hat):
z_hat = (np.dot(self.A, x_hat) ** 2).reshape(self.m, 1)
b = z_hat - self.z
grad = 2 / len(self.A) * np.dot(np.dot(self.A.transpose(), b * self.A), x_hat)
return grad
def solver(self):
init_func = self.select_initialization(self.param.initializer)
step_func = self.select_step_chooser(self.param.step_chooser)
x0 = init_func()
index_set = []
for iteration_alg in range(self.param.k):
grad = self.gradient_f(x0)
grad[index_set] = 0
sort_grad_index = np.argsort(-abs(grad), axis=0).reshape(self.n)
index_set.append(sort_grad_index[0])
num_trial = 10
x_project = np.zeros([num_trial, self.n])
error = []
for test in range(num_trial):
if test == 0:
x_init = x0[index_set].reshape(len(index_set), 1)
else:
x_init = np.random.randn(len(index_set), 1)
x_temp, recon_error, meas_error, iteration, success = self.get_projection(index_set, x_init, step_func,
truncated=False)
x_project[test, :] = x_temp.reshape(self.n, )
error.append(meas_error)
if success:
x0 = x_project[test]
break
x0 = x_project[error.index(min(error))]
if success:
break
return recon_error, meas_error, iteration_alg, success
class OMP_PR_2(PhaseRetrieval):
def __init__(self, x, A, y, z, param):
PhaseRetrieval.__init__(self, x, A, y, z, param)
def get_projection(self, support, x0, step_func, truncated):
projection_func = self.select_projection_method(self.param.projection, support)
x_hat, recon_error, meas_error, iteration, success = projection_func(x0, step_func, truncated)
return x_hat, recon_error, meas_error, iteration, success
def gradient_f(self, x_hat):
z_hat = (np.dot(self.A, x_hat) ** 2).reshape(self.m, 1)
b = z_hat - self.z
grad = 2 / len(self.A) * np.dot(np.dot(self.A.transpose(), b * self.A), x_hat)
return grad
def solver(self):
init_func = self.select_initialization(self.param.initializer)
step_func = self.select_step_chooser(self.param.step_chooser)
x0 = init_func()
index_set = []
for iteration_alg in range(self.param.k):
grad = self.gradient_f(x0)
grad[index_set] = 0
sort_grad_index = np.argsort(-abs(grad), axis=0).reshape(self.n)
index_set.append(sort_grad_index[0:2])
num_trial = 10
x_project = np.zeros([num_trial, self.n])
error = []
for test in range(num_trial):
x_init = np.random.randn(len(index_set), 1)
x_temp, recon_error, meas_error, iteration, success = self.get_projection(index_set, x_init, step_func,
truncated=False)
x_project[test, :] = x_temp.reshape(self.n, )
error.append(meas_error)
if success:
x0 = x_project[test]
break
x0 = x_project[error.index(min(error))]
if success:
break
return recon_error, meas_error, iteration_alg, success
class HTP_PR(PhaseRetrieval):
def __init__(self, x, A, y, z, param):
PhaseRetrieval.__init__(self, x, A, y, z, param)
def get_projection(self, support, x0, step_func, truncated):
projection_func = self.select_projection_method(self.param.projection, support)
x_hat, recon_error, meas_error, iteration, success = projection_func(x0, step_func, truncated)
return x_hat, recon_error, meas_error, iteration, success
def gradient_f(self, x_hat):
z_hat = (np.dot(self.A, x_hat) ** 2).reshape(self.m, 1)
b = z_hat - self.z
grad = 2 / len(self.A) * np.dot(np.dot(self.A.transpose(), b * self.A), x_hat)
return grad
def solver(self):
init_func = self.select_initialization(self.param.initializer)
step_func = self.select_step_chooser(self.param.step_chooser)
x0 = init_func()
for iteration_alg in range(self.param.max_iter):
grad = self.gradient_f(x0)
mu = 1
# sort_index = np.argsort(-abs(x0 + mu * grad), axis=0).reshape(self.n)
sort_index = np.argsort(-abs(mu * grad), axis=0).reshape(self.n)
index_set = sort_index[0:(self.param.k)].reshape(self.param.k)
num_trial = 10
x_project = np.zeros([num_trial, self.n])
error = []
for test in range(num_trial):
# if test == 0:
# x_init = x0[index_set].reshape(len(index_set), 1)
# else:
# x_init = np.random.randn(len(index_set), 1)
x_init = np.random.randn(len(index_set), 1)
x_temp, recon_error, meas_error, iteration, success = self.get_projection(index_set, x_init, step_func,
truncated=False)
x_project[test, :] = x_temp.reshape(self.n, )
error.append(meas_error)
if success:
x0 = x_project[test]
break
x0 = x_project[error.index(min(error))]
if success:
break
return recon_error, meas_error, iteration_alg, success