def test_np_backend(self):
"""Test numpy backend."""
xp, backend = get_backend('numpy')
if backend != 'numpy' or xp != LIBRARIES['numpy']:
raise AssertionError('numpy get_backend fails!')
np_input = change_backend(self.input, 'numpy')
if (get_array_module(LIBRARIES['numpy'].ones(1)) != LIBRARIES['numpy']
or get_array_module(np_input) != LIBRARIES['numpy']):
raise AssertionError('numpy backend fails!')
def test_tf_backend(self):
"""Test tensorflow backend."""
xp, backend = get_backend('tensorflow')
if backend != 'tensorflow' or xp != LIBRARIES['tensorflow']:
raise AssertionError('tensorflow get_backend fails!')
tf_input = change_backend(self.input, 'tensorflow')
if (get_array_module(
LIBRARIES['tensorflow'].ones(1)) != LIBRARIES['tensorflow']
or get_array_module(tf_input) != LIBRARIES['tensorflow']):
raise AssertionError('tensorflow backend fails!')
def is_restart(self, z_old, x_new, x_old):
"""Check whether the algorithm needs to restart.
This method implements the checks necessary to tell whether the
algorithm needs to restart depending on the restarting strategy.
It also updates the FISTA parameters according to the restarting
strategy (namely beta and r).
Parameters
----------
z_old: numpy.ndarray
Corresponds to y_n in :cite:`liang2018`.
x_new: numpy.ndarray
Corresponds to x_{n+1} in :cite:`liang2018`.
x_old: numpy.ndarray
Corresponds to x_n in :cite:`liang2018`.
Returns
-------
bool
Whether the algorithm should restart
Notes
-----
Implements restarting and safeguarding steps in alg 4-5 o
:cite:`liang2018`
"""
xp = backend.get_array_module(x_new)
if self.restart_strategy is None:
return False
criterion = xp.vdot(z_old - x_new, x_new - x_old) >= 0
if criterion:
if 'adaptive' in self.restart_strategy:
self.r_lazy *= self.xi_restart
if self.restart_strategy in {'adaptive-ii', 'adaptive-2'}:
self._t_now = 1
if self.restart_strategy == 'greedy':
cur_delta = xp.linalg.norm(x_new - x_old)
if self._delta0 is None:
self._delta0 = self.s_greedy * cur_delta
else:
self._safeguard = cur_delta >= self._delta0
return criterion
def _check_cost(self):
"""Check cost function.
This method tests the cost function for convergence in the specified
interval of iterations using the last :math:`n` (``test_range``) cost
values.
Returns
-------
bool
Result of the convergence test
"""
# Add current cost value to the test list
self._test_list.append(self.cost)
xp = get_array_module(self.cost)
# Check if enough cost values have been collected
if len(self._test_list) == self._test_range:
# The mean of the first half of the test list
t1 = xp.mean(
xp.array(self._test_list[len(self._test_list) // 2:]),
axis=0,
)
# The mean of the second half of the test list
t2 = xp.mean(
xp.array(self._test_list[:len(self._test_list) // 2]),
axis=0,
)
# Calculate the change across the test list
if xp.around(t1, decimals=16):
cost_diff = (xp.linalg.norm(t1 - t2) / xp.linalg.norm(t1))
else:
cost_diff = 0
# Reset the test list
self._test_list = []
if self._verbose:
print(' - CONVERGENCE TEST - ')
print(' - CHANGE IN COST:', cost_diff)
print('')
# Check for convergence
return cost_diff <= self._tolerance
return False
def get_spec_rad(self, tolerance=1e-6, max_iter=20, extra_factor=1.0):
"""Get spectral radius.
This method calculates the spectral radius
Parameters
----------
tolerance : float, optional
Tolerance threshold for convergence (default is ``1e-6``)
max_iter : int, optional
Maximum number of iterations (default is ``20``)
extra_factor : float, optional
Extra multiplicative factor for calculating the spectral radius
(default is ``1.0``)
"""
# Set (or reset) values of x.
x_old = self._set_initial_x()
# Iterate until the L2 norm of x converges.
for i_elem in range(max_iter):
xp = get_array_module(x_old)
x_old_norm = xp.linalg.norm(x_old)
x_new = self._operator(x_old) / x_old_norm
x_new_norm = xp.linalg.norm(x_new)
if (xp.abs(x_new_norm - x_old_norm) < tolerance):
message = (' - Power Method converged after {0} iterations!')
if self._verbose:
print(message.format(i_elem + 1))
break
elif i_elem == max_iter - 1 and self._verbose:
message = (
' - Power Method did not converge after {0} iterations!')
print(message.format(max_iter))
xp.copyto(x_old, x_new)
self.spec_rad = x_new_norm * extra_factor
self.inv_spec_rad = 1.0 / self.spec_rad
def thresh(input_data, threshold, threshold_type='hard'):
r"""Threshold data.
This method perfoms hard or soft thresholding on the input data.
Parameters
----------
input_data : numpy.ndarray, list or tuple
Input data array
threshold : float or numpy.ndarray
Threshold level(s)
threshold_type : {'hard', 'soft'}
Type of noise to be added (default is ``'hard'``)
Returns
-------
numpy.ndarray
Thresholded data
Raises
------
ValueError
If ``threshold_type`` is not ``'hard'`` or ``'soft'``
Notes
-----
Implements one of the following two equations:
* Hard Threshold
.. math::
\mathrm{HT}_\lambda(x) =
\begin{cases}
x & \text{if } |x|\geq\lambda \\
0 & \text{otherwise}
\end{cases}
* Soft Threshold
.. math::
\mathrm{ST}_\lambda(x) =
\begin{cases}
x-\lambda\text{sign}(x) & \text{if } |x|\geq\lambda \\
0 & \text{otherwise}
\end{cases}
Examples
--------
>>> import numpy as np
>>> from modopt.signal.noise import thresh
>>> np.random.seed(1)
>>> x = np.random.randint(-9, 9, 10)
>>> x
array([-4, 2, 3, -1, 0, 2, -4, 6, -9, 7])
>>> thresh(x, 4)
array([-4, 0, 0, 0, 0, 0, -4, 6, -9, 7])
>>> import numpy as np
>>> from modopt.signal.noise import thresh
>>> np.random.seed(1)
>>> x = np.random.ranf((3, 3))
>>> x
array([[4.17022005e-01, 7.20324493e-01, 1.14374817e-04],
[3.02332573e-01, 1.46755891e-01, 9.23385948e-02],
[1.86260211e-01, 3.45560727e-01, 3.96767474e-01]])
>>> thresh(x, 0.2, threshold_type='soft')
array([[0.217022 , 0.52032449, 0. ],
[0.10233257, 0. , 0. ],
[0. , 0.14556073, 0.19676747]])
"""
xp = get_array_module(input_data)
input_data = xp.array(input_data)
if threshold_type not in {'hard', 'soft'}:
raise ValueError(
'Invalid threshold type. Options are "hard" or "soft"',
)
if threshold_type == 'soft':
denominator = xp.maximum(xp.finfo(np.float64).eps, xp.abs(input_data))
max_value = xp.maximum((1.0 - threshold / denominator), 0)
return xp.around(max_value * input_data, decimals=15)
return input_data * (xp.abs(input_data) >= threshold)