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Commit ae697a00 authored by Jakob Knollmueller's avatar Jakob Knollmueller
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remove all old demos, GN prototype in

parent 67e96903
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demos/critical_filtering.py deleted 100644 → 0
View file @ 67e96903
import nifty5 as ift
from nifty5.library.nonlinearities import Linear, Tanh, Exponential
import numpy as np
np.random.seed(42)
def adjust_zero_mode(m0, t0):
mtmp = m0.to_global_data().copy()
zero_position = len(m0.shape)*(0,)
zero_mode = mtmp[zero_position]
mtmp[zero_position] = zero_mode / abs(zero_mode)
ttmp = t0.to_global_data().copy()
ttmp[0] += 2 * np.log(abs(zero_mode))
return (ift.Field.from_global_data(m0.domain, mtmp),
ift.Field.from_global_data(t0.domain, ttmp))
if __name__ == "__main__":
noise_level = 1.
p_spec = (lambda k: (.5 / (k + 1) ** 3))
nonlinearity = Linear()
# Set up position space
s_space = ift.RGSpace((128, 128))
h_space = s_space.get_default_codomain()
# Define harmonic transformation and associated harmonic space
HT = ift.HarmonicTransformOperator(h_space, target=s_space)
# Setting up power space
p_space = ift.PowerSpace(h_space,
binbounds=ift.PowerSpace.useful_binbounds(
h_space, logarithmic=True))
# Choosing the prior correlation structure and defining
# correlation operator
p = ift.PS_field(p_space, p_spec)
log_p = ift.log(p)
S = ift.create_power_operator(h_space, power_spectrum=lambda k: 1e-5)
# Drawing a sample sh from the prior distribution in harmonic space
sh = S.draw_sample()
# Choosing the measurement instrument
# Instrument = SmoothingOperator(s_space, sigma=0.01)
mask = np.ones(s_space.shape)
# mask[6000:8000] = 0.
mask[30:70, 30:70] = 0.
mask = ift.Field.from_global_data(s_space, mask)
MaskOperator = ift.DiagonalOperator(mask)
R = ift.GeometryRemover(s_space)
R = R*MaskOperator
# R = R*HT
# R = R * ift.create_harmonic_smoothing_operator((harmonic_space,), 0,
# response_sigma)
MeasurementOperator = R
d_space = MeasurementOperator.target
Distributor = ift.PowerDistributor(target=h_space, power_space=p_space)
power = Distributor(ift.exp(0.5*log_p))
# Creating the mock data
true_sky = nonlinearity(HT(power*sh))
noiseless_data = MeasurementOperator(true_sky)
noise_amplitude = noiseless_data.val.std()*noise_level
N = ift.ScalingOperator(noise_amplitude**2, d_space)
n = N.draw_sample()
# Creating the mock data
d = noiseless_data + n
m0 = ift.full(h_space, 1e-7)
t0 = ift.full(p_space, -4.)
power0 = Distributor.times(ift.exp(0.5 * t0))
plotdict = {"colormap": "Planck-like"}
zmin = true_sky.min()
zmax = true_sky.max()
ift.plot(true_sky, title="True sky", name="true_sky.png", **plotdict)
ift.plot(MeasurementOperator.adjoint_times(d), title="Data",
name="data.png", **plotdict)
IC1 = ift.GradientNormController(name="IC1", iteration_limit=100,
tol_abs_gradnorm=1e-3)
LS = ift.LineSearchStrongWolfe(c2=0.02)
minimizer = ift.RelaxedNewton(IC1, line_searcher=LS)
IC = ift.GradientNormController(iteration_limit=500,
tol_abs_gradnorm=1e-3)
for i in range(20):
power0 = Distributor(ift.exp(0.5*t0))
map0_energy = ift.library.NonlinearWienerFilterEnergy(
m0, d, MeasurementOperator, nonlinearity, HT, power0, N, S, IC)
# Minimization with chosen minimizer
map0_energy, convergence = minimizer(map0_energy)
m0 = map0_energy.position
# Updating parameters for correlation structure reconstruction
D0 = map0_energy.curvature
# Initializing the power energy with updated parameters
power0_energy = ift.library.NonlinearPowerEnergy(
position=t0, d=d, N=N, xi=m0, D=D0, ht=HT,
Instrument=MeasurementOperator, nonlinearity=nonlinearity,
Distributor=Distributor, sigma=1., samples=2,
iteration_controller=IC)
power0_energy = minimizer(power0_energy)[0]
# Setting new power spectrum
t0 = power0_energy.position
# break degeneracy between amplitude and excitation by setting
# excitation monopole to 1
m0, t0 = adjust_zero_mode(m0, t0)
ift.plot(nonlinearity(HT(power0*m0)), title="Reconstructed sky",
name="reconstructed_sky.png", zmin=zmin, zmax=zmax, **plotdict)
ymin = np.min(p.to_global_data())
ift.plot([ift.exp(t0), p], title="Power spectra",
name="ps.png", ymin=ymin, **plotdict)
demos/getting_started_1.py 0 → 100644
View file @ ae697a00
import nifty5 as ift
import numpy as np
from global_newton.models_other.apply_data import ApplyData
from global_newton.models_energy.hamiltonian import Hamiltonian
from nifty5.library.unit_log_gauss import UnitLogGauss
if __name__ == '__main__':
# s_space = ift.RGSpace([1024])
s_space = ift.RGSpace([128,128])
# s_space = ift.HPSpace(64)
h_space = s_space.get_default_codomain()
total_domain = ift.MultiDomain.make({'xi': h_space})
HT = ift.HarmonicTransformOperator(h_space, s_space)
def sqrtpspec(k):
return 16. / (20.+k**2)
GR = ift.GeometryRemover(s_space)
d_space = GR.target
B = ift.FFTSmoothingOperator(s_space,0.1)
mask = np.ones(s_space.shape)
mask[64:89,76:100] = 0.
mask = ift.Field(s_space,val=mask)
Mask = ift.DiagonalOperator(mask)
R = GR * Mask * B
noise = 1.
N = ift.ScalingOperator(noise, d_space)
p_space = ift.PowerSpace(h_space)
pd = ift.PowerDistributor(h_space, p_space)
position = ift.from_random('normal', total_domain)
xi = ift.Variable(position)['xi']
a = ift.Constant(position, ift.PS_field(p_space, sqrtpspec))
A = pd(a)
s_h = A * xi
s = HT(s_h)
Rs = R(s)
MOCK_POSITION = ift.from_random('normal',total_domain)
data = Rs.at(MOCK_POSITION).value + N.draw_sample()
NWR = ApplyData(data, ift.Field(d_space,val=noise), Rs)
INITIAL_POSITION = ift.from_random('normal',total_domain)
likelihood = UnitLogGauss(INITIAL_POSITION, NWR)
IC = ift.GradientNormController(iteration_limit=500, tol_abs_gradnorm=1e-3)
inverter = ift.ConjugateGradient(controller=IC)
IC2 = ift.GradientNormController(name='Newton', iteration_limit=15)
minimizer = ift.RelaxedNewton(IC2)
H = Hamiltonian(likelihood, inverter)
H, convergence = minimizer(H)
result = s.at(H.position).value
demos/nonlinear_critical_filter.py deleted 100644 → 0
View file @ 67e96903
import nifty5 as ift
from nifty5.library.nonlinearities import Exponential
import numpy as np
np.random.seed(42)
def adjust_zero_mode(m0, t0):
mtmp = m0.to_global_data().copy()
zero_position = len(m0.shape)*(0,)
zero_mode = mtmp[zero_position]
mtmp[zero_position] = zero_mode / abs(zero_mode)
ttmp = t0.to_global_data().copy()
ttmp[0] += 2 * np.log(abs(zero_mode))
return (ift.Field.from_global_data(m0.domain, mtmp),
ift.Field.from_global_data(t0.domain, ttmp))
if __name__ == "__main__":
noise_level = 1.
p_spec = (lambda k: (1. / (k + 1) ** 2))
# nonlinearity = Linear()
nonlinearity = Exponential()
# Set up position space
# s_space = ift.RGSpace([1024])
s_space = ift.HPSpace(32)
h_space = s_space.get_default_codomain()
# Define harmonic transformation and associated harmonic space
HT = ift.HarmonicTransformOperator(h_space, target=s_space)
# Setting up power space
p_space = ift.PowerSpace(h_space,
binbounds=ift.PowerSpace.useful_binbounds(
h_space, logarithmic=True))
# Choosing the prior correlation structure and defining
# correlation operator
p = ift.PS_field(p_space, p_spec)
log_p = ift.log(p)
S = ift.create_power_operator(h_space, lambda k: 1.)
# Drawing a sample sh from the prior distribution in harmonic space
sh = S.draw_sample()
# Choosing the measurement instrument
# Instrument = SmoothingOperator(s_space, sigma=0.01)
mask = np.ones(s_space.shape)
mask[6000:8000] = 0.
mask = ift.Field.from_global_data(s_space, mask)
MaskOperator = ift.DiagonalOperator(mask)
R = ift.GeometryRemover(s_space)
R = R*MaskOperator
# R = R*HT
# R = R * ift.create_harmonic_smoothing_operator((harmonic_space,), 0,
# response_sigma)
MeasurementOperator = R
d_space = MeasurementOperator.target
Distributor = ift.PowerDistributor(target=h_space, power_space=p_space)
power = Distributor(ift.exp(0.5*log_p))
# Creating the mock data
true_sky = nonlinearity(HT(power*sh))
noiseless_data = MeasurementOperator(true_sky)
noise_amplitude = noiseless_data.val.std()*noise_level
N = ift.ScalingOperator(noise_amplitude**2, d_space)
n = N.draw_sample()
# Creating the mock data
d = noiseless_data + n
m0 = ift.full(h_space, 1e-7)
t0 = ift.full(p_space, -4.)
power0 = Distributor.times(ift.exp(0.5 * t0))
IC1 = ift.GradientNormController(name="IC1", iteration_limit=100,
tol_abs_gradnorm=1e-3)
LS = ift.LineSearchStrongWolfe(c2=0.02)
minimizer = ift.RelaxedNewton(IC1, line_searcher=LS)
IC = ift.GradientNormController(iteration_limit=500,
tol_abs_gradnorm=1e-3)
for i in range(20):
power0 = Distributor(ift.exp(0.5*t0))
map0_energy = ift.library.NonlinearWienerFilterEnergy(
m0, d, MeasurementOperator, nonlinearity, HT, power0, N, S, IC)
# Minimization with chosen minimizer
map0_energy, convergence = minimizer(map0_energy)
m0 = map0_energy.position
# Updating parameters for correlation structure reconstruction
D0 = map0_energy.curvature
# Initializing the power energy with updated parameters
power0_energy = ift.library.NonlinearPowerEnergy(
position=t0, d=d, N=N, xi=m0, D=D0, ht=HT,
Instrument=MeasurementOperator, nonlinearity=nonlinearity,
Distributor=Distributor, sigma=1., samples=2, iteration_controller=IC)
power0_energy = minimizer(power0_energy)[0]
# Setting new power spectrum
t0 = power0_energy.position
# break degeneracy between amplitude and excitation by setting
# excitation monopole to 1
m0, t0 = adjust_zero_mode(m0, t0)
plotdict = {"colormap": "Planck-like"}
ift.plot(true_sky, name="true_sky.png", **plotdict)
ift.plot(nonlinearity(HT(power0*m0)),
name="reconstructed_sky.png", **plotdict)
ift.plot(MeasurementOperator.adjoint_times(d), name="data.png", **plotdict)
ift.plot([ift.exp(t0), p], name="ps.png")
demos/nonlinear_wiener_filter.py deleted 100644 → 0
View file @ 67e96903
import nifty5 as ift
from nifty5.library.nonlinearities import Linear, Exponential, Tanh
import numpy as np
np.random.seed(20)
if __name__ == "__main__":
noise_level = 0.3
correlation_length = 0.1
p_spec = lambda k: (1. / (k*correlation_length + 1) ** 4)
nonlinearity = Tanh()
# nonlinearity = Linear()
# nonlinearity = Exponential()
# Set up position space
s_space = ift.RGSpace(1024)
h_space = s_space.get_default_codomain()
# Define harmonic transformation and associated harmonic space
HT = ift.HarmonicTransformOperator(h_space, target=s_space)
S = ift.ScalingOperator(1., h_space)
# Drawing a sample sh from the prior distribution in harmonic space
sh = S.draw_sample()
# Choosing the measurement instrument
# Instrument = SmoothingOperator(s_space, sigma=0.01)
mask = np.ones(s_space.shape)
mask[600:800] = 0.
mask = ift.Field.from_global_data(s_space, mask)
R = ift.GeometryRemover(s_space) * ift.DiagonalOperator(mask)
d_space = R.target
p_op = ift.create_power_operator(h_space, p_spec)
power = ift.sqrt(p_op(ift.full(h_space, 1.)))
# Creating the mock data
true_sky = nonlinearity(HT(power*sh))
noiseless_data = R(true_sky)
noise_amplitude = noiseless_data.val.std()*noise_level
N = ift.ScalingOperator(noise_amplitude**2, d_space)
n = N.draw_sample()
# Creating the mock data
d = noiseless_data + n
IC1 = ift.GradientNormController(name="IC1", iteration_limit=100,
tol_abs_gradnorm=1e-4)
LS = ift.LineSearchStrongWolfe(c2=0.02)
minimizer = ift.RelaxedNewton(IC1, line_searcher=LS)
IC = ift.GradientNormController(iteration_limit=2000,
tol_abs_gradnorm=1e-3)
# initial guess
m = ift.full(h_space, 1e-7)
map_energy = ift.library.NonlinearWienerFilterEnergy(
m, d, R, nonlinearity, HT, power, N, S, IC)
# Minimization with chosen minimizer
map_energy, convergence = minimizer(map_energy)
m = map_energy.position
recsky = nonlinearity(HT(power*m))
data = R.adjoint_times(d)
lo = np.min([true_sky.min(), recsky.min(), data.min()])
hi = np.max([true_sky.max(), recsky.max(), data.max()])
plotdict = {"colormap": "Planck-like", "ymin": lo, "ymax": hi}
ift.plot(true_sky, name="true_sky.png", **plotdict)
ift.plot(recsky, name="reconstructed_sky.png", **plotdict)
ift.plot(data, name="data.png", **plotdict)
demos/paper_demos/cartesian_wiener_filter.py deleted 100644 → 0
View file @ 67e96903
import numpy as np
import nifty5 as ift
if __name__ == "__main__":
signal_to_noise = 0.5 # The signal to noise ratio
# Setting up parameters
L_1 = 2. # Total side-length of the domain
N_pixels_1 = 512 # Grid resolution (pixels per axis)
L_2 = 2. # Total side-length of the domain
N_pixels_2 = 512 # Grid resolution (pixels per axis)
correlation_length_1 = 1.
field_variance_1 = 2. # Variance of field in position space
response_sigma_1 = 0.05 # Smoothing length of response
correlation_length_2 = 1.
field_variance_2 = 2. # Variance of field in position space
response_sigma_2 = 0.01 # Smoothing length of response
def power_spectrum_1(k): # note: field_variance**2 = a*k_0/4.
a = 4 * correlation_length_1 * field_variance_1**2
return a / (1 + k * correlation_length_1) ** 4.
def power_spectrum_2(k): # note: field_variance**2 = a*k_0/4.
a = 4 * correlation_length_2 * field_variance_2**2
return a / (1 + k * correlation_length_2) ** 2.5
signal_space_1 = ift.RGSpace([N_pixels_1], distances=L_1/N_pixels_1)
harmonic_space_1 = signal_space_1.get_default_codomain()
signal_space_2 = ift.RGSpace([N_pixels_2], distances=L_2/N_pixels_2)
harmonic_space_2 = signal_space_2.get_default_codomain()
signal_domain = ift.DomainTuple.make((signal_space_1, signal_space_2))
harmonic_domain = ift.DomainTuple.make((harmonic_space_1,
harmonic_space_2))
ht_1 = ift.HarmonicTransformOperator(harmonic_domain, space=0)
ht_2 = ift.HarmonicTransformOperator(ht_1.target, space=1)
ht = ht_2*ht_1
S = (ift.create_power_operator(harmonic_domain, power_spectrum_1, 0) *
ift.create_power_operator(harmonic_domain, power_spectrum_2, 1))
np.random.seed(10)
mock_signal = S.draw_sample()
# Setting up a exemplary response
N1_10 = int(N_pixels_1/10)
mask_1 = np.ones(signal_space_1.shape)
mask_1[N1_10*7:N1_10*9] = 0.
mask_1 = ift.Field.from_global_data(signal_space_1, mask_1)
N2_10 = int(N_pixels_2/10)
mask_2 = np.ones(signal_space_2.shape)
mask_2[N2_10*7:N2_10*9] = 0.
mask_2 = ift.Field.from_global_data(signal_space_2, mask_2)
R = ift.GeometryRemover(signal_domain)
R = R*ift.DiagonalOperator(mask_1, signal_domain, spaces=0)
R = R*ift.DiagonalOperator(mask_2, signal_domain, spaces=1)
R = R*ht
R = R * ift.create_harmonic_smoothing_operator(harmonic_domain, 0,
response_sigma_1)
R = R * ift.create_harmonic_smoothing_operator(harmonic_domain, 1,
response_sigma_2)
data_domain = R.target
noiseless_data = R(mock_signal)
noise_amplitude = noiseless_data.val.std()/signal_to_noise
# Setting up the noise covariance and drawing a random noise realization
N = ift.ScalingOperator(noise_amplitude**2, data_domain)
noise = N.draw_sample()
data = noiseless_data + noise
# Wiener filter
j = R.adjoint_times(N.inverse_times(data))
ctrl = ift.GradientNormController(name="inverter", tol_abs_gradnorm=0.1)
sampling_ctrl = ift.GradientNormController(name="sampling",
tol_abs_gradnorm=1e2)
wiener_curvature = ift.library.WienerFilterCurvature(
S=S, N=N, R=R, iteration_controller=ctrl,
iteration_controller_sampling=sampling_ctrl)
m_k = wiener_curvature.inverse_times(j)
m = ht(m_k)
plotdict = {"colormap": "Planck-like"}
plot_space = ift.RGSpace((N_pixels_1, N_pixels_2))
ift.plot(ht(mock_signal).cast_domain(plot_space),
name='mock_signal.png', **plotdict)
ift.plot(data.cast_domain(plot_space), name='data.png', **plotdict)
ift.plot(m.cast_domain(plot_space), name='map.png', **plotdict)
# sampling the uncertainty map
mean, variance = ift.probe_with_posterior_samples(wiener_curvature, ht, 50)
ift.plot(ift.sqrt(variance).cast_domain(plot_space),
name="uncertainty.png", **plotdict)
ift.plot((mean+m).cast_domain(plot_space),
name="posterior_mean.png", **plotdict)
demos/paper_demos/wiener_filter.py deleted 100644 → 0
View file @ 67e96903
import nifty5 as ift
import numpy as np
if __name__ == "__main__":
# Setting up parameters
L = 2. # Total side-length of the domain
N_pixels = 512 # Grid resolution (pixels per axis)
correlation_length_scale = .2 # Typical distance over which the field is
# correlated
fluctuation_scale = 2. # Variance of field in position space
response_sigma = 0.05 # Smoothing length of response
signal_to_noise = 1.5 # The signal to noise ratio
np.random.seed(43) # Fixing the random seed
def power_spectrum(k): # Defining the power spectrum
a = 4 * correlation_length_scale * fluctuation_scale**2
return a / (1 + (k * correlation_length_scale)**2) ** 2
signal_space = ift.RGSpace([N_pixels, N_pixels], distances=L/N_pixels)
harmonic_space = signal_space.get_default_codomain()
ht = ift.HarmonicTransformOperator(harmonic_space, target=signal_space)
# Creating the mock signal
S = ift.create_power_operator(harmonic_space,
power_spectrum=power_spectrum)
mock_signal = S.draw_sample()
# Setting up an exemplary response
mask = np.ones(signal_space.shape)
N10 = int(N_pixels/10)
mask[N10*5:N10*9, N10*5:N10*9] = 0.
mask = ift.Field.from_global_data(signal_space, mask).lock()
R = ift.GeometryRemover(signal_space)
R = R*ift.DiagonalOperator(mask)
R = R*ht
R = R * ift.create_harmonic_smoothing_operator((harmonic_space,), 0,
response_sigma)
data_domain = R.target[0]
noiseless_data = R(mock_signal)
noise_amplitude = noiseless_data.val.std()/signal_to_noise
# Setting up the noise covariance and drawing a random noise realization
N = ift.ScalingOperator(noise_amplitude**2, data_domain)
noise = N.draw_sample()
data = noiseless_data + noise
# Wiener filter
j = R.adjoint_times(N.inverse_times(data))
ctrl = ift.GradientNormController(name="inverter", tol_abs_gradnorm=1e-2)
sampling_ctrl = ift.GradientNormController(name="sampling",
tol_abs_gradnorm=2e1)
wiener_curvature = ift.library.WienerFilterCurvature(
S=S, N=N, R=R, iteration_controller=ctrl,
iteration_controller_sampling=sampling_ctrl)
m_k = wiener_curvature.inverse_times(j)
m = ht(m_k)
plotdict = {"colormap": "Planck-like"}
ift.plot(ht(mock_signal), name="mock_signal.png", **plotdict)
ift.plot(data.cast_domain(signal_space), name="data.png", **plotdict)
ift.plot(m, name="map.png", **plotdict)
# sampling the uncertainty map
mean, variance = ift.probe_with_posterior_samples(wiener_curvature, ht, 50)
ift.plot(ift.sqrt(variance), name="uncertainty.png", **plotdict)
ift.plot(mean+m, name="posterior_mean.png", **plotdict)
demos/poisson_demo.py deleted 100644 → 0
View file @ 67e96903
# Program to generate figures of article "Information theory for fields"
# by Torsten Ensslin, Annalen der Physik, submitted to special edition
# "Physics of Information" in April 2018, arXiv:1804.03350
# to get exact figure of paper comment out lines marked by "COMMENT OUT"
import numpy as np
import nifty5 as ift
import matplotlib.pyplot as plt
class Exp3(object):
def __call__(self, x):
return ift.exp(3*x)
def derivative(self, x):
return 3*ift.exp(3*x)
if __name__ == "__main__":
np.random.seed(20)
# Set up physical constants
nu = 1. # excitation field level
kappa = 10. # diffusion constant
eps = 1e-8 # small number to tame zero mode
sigma_n = 0.2 # noise level
sigma_n2 = sigma_n**2
L = 1. # Total length of interval or volume the field lives on
nprobes = 1000 # Number of probes for uncertainty quantification used in paper
nprobes = 10 # COMMENT OUT TO REPRODUCE PAPER FIGURE EXACTLY
# Define resolution (pixels per dimension)
N_pixels = 1024
# Define data gaps
N1a = int(0.6*N_pixels)
N1b = int(0.64*N_pixels)
N2a = int(0.67*N_pixels)
N2b = int(0.8*N_pixels)
# Set up derived constants
amp = nu/(2*kappa) # spectral normalization
pow_spec = lambda k: amp / (eps + k**2)
lambda2 = 2*kappa*sigma_n2/nu # resulting correlation length squared
lambda1 = np.sqrt(lambda2)
pixel_width = L/N_pixels
x = np.arange(0, 1, pixel_width)
# Set up the geometry
s_domain = ift.RGSpace([N_pixels], distances=pixel_width)
h_domain = s_domain.get_default_codomain()
HT = ift.HarmonicTransformOperator(h_domain, s_domain)
aHT = HT.adjoint
# Create mock signal
Phi_h = ift.create_power_operator(h_domain, power_spectrum=pow_spec)
phi_h = Phi_h.draw_sample()
# remove zero mode
glob = phi_h.to_global_data()
glob[0] = 0.
phi_h = ift.Field.from_global_data(phi_h.domain, glob)
phi = HT(phi_h)
# Setting up an exemplary response
GeoRem = ift.GeometryRemover(s_domain)
d_domain = GeoRem.target[0]
mask = np.ones(d_domain.shape)
mask[N1a:N1b] = 0.
mask[N2a:N2b] = 0.
fmask = ift.Field.from_global_data(d_domain, mask)
Mask = ift.DiagonalOperator(fmask)
R0 = Mask*GeoRem