Commit f6d28ab7 authored by Martin Reinecke's avatar Martin Reinecke

Merge branch 'working_on_demos' into 'NIFTy_4'

Working on demos

See merge request ift/NIFTy!260
parents ec50fcc0 087530b0
Pipeline #29816 passed with stages
in 12 minutes and 39 seconds
import numpy as np
import nifty4 as ift
# TODO: MAKE RESPONSE MPI COMPATIBLE OR USE LOS RESPONSE INSTEAD
class CustomResponse(ift.LinearOperator):
"""
A custom operator that measures a specific points`
An operator that is a delta measurement at certain points
"""
def __init__(self, domain, data_points):
self._domain = ift.DomainTuple.make(domain)
self._points = data_points
data_shape = ift.Field.full(domain, 0.).to_global_data()[data_points]\
.shape
self._target = ift.DomainTuple.make(ift.UnstructuredDomain(data_shape))
def _times(self, x):
d = np.zeros(self._target.shape, dtype=np.float64)
d += x.to_global_data()[self._points]
return ift.from_global_data(self._target, d)
def _adjoint_times(self, d):
x = np.zeros(self._domain.shape, dtype=np.float64)
x[self._points] += d.to_global_data()
return ift.from_global_data(self._domain, x)
@property
def domain(self):
return self._domain
@property
def target(self):
return self._target
def apply(self, x, mode):
self._check_input(x, mode)
return self._times(x) if mode == self.TIMES else self._adjoint_times(x)
@property
def capability(self):
return self.TIMES | self.ADJOINT_TIMES
if __name__ == "__main__":
np.random.seed(43)
# Set up physical constants
# Total length of interval or volume the field lives on, e.g. in meters
L = 2.
# Typical distance over which the field is correlated (in same unit as L)
correlation_length = 0.3
# Variance of field in position space sqrt(<|s_x|^2>) (in same unit as s)
field_variance = 2.
# Smoothing length of response (in same unit as L)
response_sigma = 0.01
# typical noise amplitude of the measurement
noise_level = 0.
# Define resolution (pixels per dimension)
N_pixels = 256
# Set up derived constants
k_0 = 1./correlation_length
# defining a power spectrum with the right correlation length
# we later set the field variance to the desired value
unscaled_pow_spec = (lambda k: 1. / (1 + k/k_0) ** 4)
pixel_width = L/N_pixels
# Set up the geometry
s_space = ift.RGSpace([N_pixels, N_pixels], distances=pixel_width)
h_space = s_space.get_default_codomain()
s_var = ift.get_signal_variance(unscaled_pow_spec, h_space)
pow_spec = (lambda k: unscaled_pow_spec(k)/s_var*field_variance**2)
HT = ift.HarmonicTransformOperator(h_space, s_space)
# Create mock data
Sh = ift.create_power_operator(h_space, power_spectrum=pow_spec)
sh = Sh.draw_sample()
Rx = CustomResponse(s_space, [np.arange(0, N_pixels, 5)[:, np.newaxis],
np.arange(0, N_pixels, 2)[np.newaxis, :]])
ift.extra.consistency_check(Rx)
a = ift.Field.from_random('normal', s_space)
b = ift.Field.from_random('normal', Rx.target)
R = Rx * HT
noiseless_data = R(sh)
N = ift.ScalingOperator(noise_level**2, R.target)
n = N.draw_sample()
d = noiseless_data + n
# Wiener filter
IC = ift.GradientNormController(name="inverter", iteration_limit=1000,
tol_abs_gradnorm=0.0001)
inverter = ift.ConjugateGradient(controller=IC)
# setting up measurement precision matrix M
M = (ift.SandwichOperator.make(R.adjoint, Sh) + N)
M = ift.InversionEnabler(M, inverter)
m = Sh(R.adjoint(M.inverse_times(d)))
# Plotting
backprojection = Rx.adjoint(d)
reweighted_backprojection = (backprojection / backprojection.max() *
HT(sh).max())
zmax = max(HT(sh).max(), reweighted_backprojection.max(), HT(m).max())
zmin = min(HT(sh).min(), reweighted_backprojection.min(), HT(m).min())
plotdict = {"colormap": "Planck-like", "zmax": zmax, "zmin": zmin}
ift.plot(HT(sh), name="mock_signal.png", **plotdict)
ift.plot(backprojection, name="backprojected_data.png", **plotdict)
ift.plot(HT(m), name="reconstruction.png", **plotdict)
import numpy as np
import nifty4 as ift
if __name__ == "__main__":
np.random.seed(43)
# Set up physical constants
......@@ -12,21 +13,25 @@ if __name__ == "__main__":
field_variance = 2.
# Smoothing length of response (in same unit as L)
response_sigma = 0.01
# typical noise amplitude of the measurement
noise_level = 1.
# Define resolution (pixels per dimension)
N_pixels = 256
# Set up derived constants
k_0 = 1./correlation_length
# Note that field_variance**2 = a*k_0/4. for this analytic form of power
# spectrum
a = field_variance**2/k_0*4.
pow_spec = (lambda k: a / (1 + k/k_0) ** 4)
#defining a power spectrum with the right correlation length
#we later set the field variance to the desired value
unscaled_pow_spec = (lambda k: 1. / (1 + k/k_0) ** 4)
pixel_width = L/N_pixels
# Set up the geometry
s_space = ift.RGSpace([N_pixels, N_pixels], distances=pixel_width)
h_space = s_space.get_default_codomain()
s_var = ift.get_signal_variance(unscaled_pow_spec, h_space)
pow_spec = (lambda k: unscaled_pow_spec(k)/s_var*field_variance**2)
HT = ift.HarmonicTransformOperator(h_space, s_space)
# Create mock data
......@@ -36,11 +41,8 @@ if __name__ == "__main__":
R = HT*ift.create_harmonic_smoothing_operator((h_space,), 0,
response_sigma)
noiseless_data = R(sh)
signal_to_noise = 1.
noise_amplitude = noiseless_data.val.std()/signal_to_noise
N = ift.ScalingOperator(noise_amplitude**2, s_space)
N = ift.ScalingOperator(noise_level**2, s_space)
n = N.draw_sample()
d = noiseless_data + n
......
......@@ -31,7 +31,8 @@ from .logger import logger
__all__ = ['PS_field', 'power_analyze', 'create_power_operator',
'create_harmonic_smoothing_operator', 'from_random',
'full', 'empty', 'from_global_data', 'from_local_data',
'makeDomain', 'sqrt', 'exp', 'log', 'tanh', 'conjugate']
'makeDomain', 'sqrt', 'exp', 'log', 'tanh', 'conjugate',
'get_signal_variance']
def PS_field(pspace, func):
......@@ -41,6 +42,34 @@ def PS_field(pspace, func):
return Field(pspace, val=data)
def get_signal_variance(spec, space):
"""
Computes how much a field with a given power spectrum will vary in space
This is a small helper function that computes how the expected variance
of a harmonically transformed sample of this power spectrum.
Parameters
---------
spec: method
a method that takes one k-value and returns the power spectrum at that
location
space: PowerSpace or any harmonic Domain
If this function is given a harmonic domain, it creates the naturally
binned PowerSpace to that domain.
The field, for which the signal variance is then computed, is assumed
to have this PowerSpace as naturally binned PowerSpace
"""
if space.harmonic:
space = PowerSpace(space)
if not isinstance(space, PowerSpace):
raise ValueError(
"space must be either a harmonic space or Power space.")
field = PS_field(space, spec)
dist = PowerDistributor(space.harmonic_partner, space)
k_field = dist(field)
return k_field.weight(2).sum()
def _single_power_analyze(field, idx, binbounds):
power_domain = PowerSpace(field.domain[idx], binbounds)
pd = PowerDistributor(field.domain, power_domain, idx)
......
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