def _ifftc(input, oshape=None, axes=None, norm='ortho'):
ndim = input.ndim
axes = util._normalize_axes(axes, ndim)
xp = backend.get_array_module(input)
if oshape is None:
oshape = input.shape
tmp = util.resize(input, oshape)
tmp = xp.fft.ifftshift(tmp, axes=axes)
tmp = xp.fft.ifftn(tmp, axes=axes, norm=norm)
output = xp.fft.fftshift(tmp, axes=axes)
return output
def _ifftc(input, oshape=None, axes=None, norm='ortho'):
ndim = input.ndim
axes = util._normalize_axes(axes, ndim)
device = backend.get_device(input)
xp = device.xp
if oshape is None:
oshape = input.shape
with device:
tmp = util.resize(input, oshape)
tmp = xp.fft.ifftshift(tmp, axes=axes)
tmp = xp.fft.ifftn(tmp, axes=axes, norm=norm)
output = xp.fft.fftshift(tmp, axes=axes)
return output
def Gradient(ishape, axes=None):
"""Linear operator that computes numerical gradient.
Args:
ishape (tuple of ints): Input shape.
"""
I = Identity(ishape)
axes = util._normalize_axes(axes, len(ishape))
ndim = len(ishape)
G = Vstack([
I - Circshift(ishape, [0] * i + [1] + [0] * (ndim - i - 1))
for i in range(ndim)
])
G.repr_str = 'Gradient'
return G
def FiniteDifference(ishape, axes=None):
"""Linear operator that computes finite difference gradient.
Args:
ishape (tuple of ints): Input shape.
"""
I = Identity(ishape)
axes = util._normalize_axes(axes, len(ishape))
ndim = len(ishape)
linops = []
for i in range(ndim):
D = I - Circshift(ishape, [0] * i + [1] + [0] * (ndim - i - 1))
R = Reshape([1] + list(ishape), ishape)
linops.append(R * D)
G = Vstack(linops, axis=0)
return G
def l2_proj(eps, input, axes=None):
"""Projection onto L2 ball.
Args:
eps (float, or array): L2 ball scaling.
input (array)
Returns:
array: Result.
"""
axes = util._normalize_axes(axes, input.ndim)
xp = backend.get_array_module(input)
norm = xp.sum(xp.abs(input)**2, axis=axes, keepdims=True)**0.5
mask = norm < eps
output = mask * input + (1 - mask) * (eps * input / (norm + mask))
return output
def FiniteDifference(ishape, axes=None):
"""Linear operator that computes finite difference gradient.
Args:
ishape (tuple of ints): Input shape.
axes (tuple or list): Axes to circularly shift. All axes are used if
None.
"""
I = Identity(ishape)
ndim = len(ishape)
axes = util._normalize_axes(axes, ndim)
linops = []
for i in axes:
D = I - Circshift(ishape, [1], axes=[i])
R = Reshape([1] + list(ishape), ishape)
linops.append(R * D)
G = Vstack(linops, axis=0)
return G
def elitist_thresh(lamda, input, axes=None):
"""Elitist threshold.
Solves for
:math::
\text{argmin}_x \| x - y \|_2^2 + \lambda \| x \|_1^2
Args:
lamda (float, or array): Threshold parameter.
input (array): Input array.
axes (None or tuple of ints): Axes to perform threshold.
Returns:
array: Result.
References:
Kowalski, M. 2009. Sparse regression using mixed norms.
"""
shape = input.shape
axes = util._normalize_axes(axes, input.ndim)
remain_axes = tuple(set(range(input.ndim)) - set(axes))
length = util.prod([shape[a] for a in axes])
batch = input.size // length
input = input.transpose(remain_axes + axes)
input = input.reshape([batch, length])
thresh = find_elitist_thresh(lamda, input)
output = soft_thresh(thresh, input)
output = output.reshape([shape[a] for a in remain_axes + axes])
output = output.transpose(np.argsort(remain_axes + axes))
return output
