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Commit 7107323b authored by Martin Reinecke's avatar Martin Reinecke
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demos/critical_filtering.py
View file @ 7107323b
import numpy as np
from nifty import (VL_BFGS, DiagonalOperator, FFTOperator, Field,
LinearOperator, PowerSpace, RelaxedNewton, RGSpace,
SteepestDescent, create_power_operator, exp, log, sqrt)
from nifty.library.critical_filter import CriticalPowerEnergy
from nifty.library.wiener_filter import WienerFilterEnergy
import nifty2go as ift
import plotly.graph_objs as go
import plotly.offline as pl
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.rank
np.random.seed(42)
def plot_parameters(m, t, p, p_d):
x = log(t.domain[0].kindex)
x = ift.log(t.domain[0].kindex)
m = fft.adjoint_times(m)
m = m.val.get_full_data().real
t = t.val.get_full_data().real
p = p.val.get_full_data().real
p_d = p_d.val.get_full_data().real
m = m.val.real
t = t.val.real
p = p.val.real
p_d = p_d.val.real
pl.plot([go.Heatmap(z=m)], filename='map.html', auto_open=False)
pl.plot([go.Scatter(x=x, y=t), go.Scatter(x=x, y=p),
go.Scatter(x=x, y=p_d)], filename="t.html", auto_open=False)
class AdjointFFTResponse(LinearOperator):
class AdjointFFTResponse(ift.LinearOperator):
def __init__(self, FFT, R, default_spaces=None):
super(AdjointFFTResponse, self).__init__(default_spaces)
self._domain = FFT.target
......@@ -56,34 +47,28 @@ class AdjointFFTResponse(LinearOperator):
if __name__ == "__main__":
distribution_strategy = 'not'
# Set up position space
s_space = RGSpace([128, 128])
# s_space = HPSpace(32)
s_space = ift.RGSpace([128, 128])
# s_space = ift.HPSpace(32)
# Define harmonic transformation and associated harmonic space
fft = FFTOperator(s_space)
fft = ift.FFTOperator(s_space)
h_space = fft.target[0]
# Set up power space
p_space = PowerSpace(h_space, logarithmic=True,
distribution_strategy=distribution_strategy)
p_space = ift.PowerSpace(h_space)
# Choose the prior correlation structure and defining correlation operator
p_spec = (lambda k: (.5 / (k + 1) ** 3))
S = create_power_operator(h_space, power_spectrum=p_spec,
distribution_strategy=distribution_strategy)
S = ift.create_power_operator(h_space, power_spectrum=p_spec)
# Draw a sample sh from the prior distribution in harmonic space
sp = Field(p_space, val=p_spec,
distribution_strategy=distribution_strategy)
sp = ift.Field(p_space, val=p_spec(p_space.kindex))
sh = sp.power_synthesize(real_signal=True)
# Choose the measurement instrument
# Instrument = SmoothingOperator(s_space, sigma=0.01)
Instrument = DiagonalOperator(s_space, diagonal=1.)
Instrument = ift.DiagonalOperator(s_space, diagonal=1.)
# Instrument._diagonal.val[200:400, 200:400] = 0
# Instrument._diagonal.val[64:512-64, 64:512-64] = 0
......@@ -91,10 +76,10 @@ if __name__ == "__main__":
R = AdjointFFTResponse(fft, Instrument)
noise = 1.
N = DiagonalOperator(s_space, diagonal=noise, bare=True)
n = Field.from_random(domain=s_space,
N = ift.DiagonalOperator(s_space, diagonal=noise, bare=True)
n = ift.Field.from_random(domain=s_space,
random_type='normal',
std=sqrt(noise),
std=ift.sqrt(noise),
mean=0)
# Create mock data
......@@ -102,47 +87,43 @@ if __name__ == "__main__":
# The information source
j = R.adjoint_times(N.inverse_times(d))
realized_power = log(sh.power_analyze(binbounds=p_space.binbounds))
data_power = log(fft(d).power_analyze(binbounds=p_space.binbounds))
d_data = d.val.get_full_data().real
if rank == 0:
pl.plot([go.Heatmap(z=d_data)], filename='data.html', auto_open=False)
realized_power = ift.log(sh.power_analyze(binbounds=p_space.binbounds))
data_power = ift.log(fft(d).power_analyze(binbounds=p_space.binbounds))
d_data = d.val.real
pl.plot([go.Heatmap(z=d_data)], filename='data.html', auto_open=False)
# Minimization strategy
def convergence_measure(a_energy, iteration): # returns current energy
x = a_energy.value
print(x, iteration)
minimizer1 = RelaxedNewton(convergence_tolerance=1e-4,
convergence_level=1,
iteration_limit=5,
callback=convergence_measure)
minimizer2 = VL_BFGS(convergence_tolerance=1e-10,
convergence_level=1,
iteration_limit=30,
callback=convergence_measure,
max_history_length=20)
minimizer3 = SteepestDescent(convergence_tolerance=1e-4,
iteration_limit=100,
callback=convergence_measure)
IC1 = ift.DefaultIterationController(verbose=True,iteration_limit=5)
minimizer1 = ift.RelaxedNewton(IC1)
IC2 = ift.DefaultIterationController(verbose=True,iteration_limit=30)
minimizer2 = ift.VL_BFGS(IC2, max_history_length=20)
IC3 = ift.DefaultIterationController(verbose=True,iteration_limit=100)
minimizer3 = ift.SteepestDescent(IC3)
# Set starting position
flat_power = Field(p_space, val=1e-8)
flat_power = ift.Field(p_space, val=1e-8)
m0 = flat_power.power_synthesize(real_signal=True)
t0 = Field(p_space, val=log(1./(1+p_space.kindex)**2))
def ps0(k):
return (1./(1.+k)**2)
t0 = ift.Field(p_space, val=ift.log(1./(1+p_space.kindex)**2))
for i in range(500):
S0 = create_power_operator(h_space, power_spectrum=exp(t0),
distribution_strategy=distribution_strategy)
S0 = ift.create_power_operator(h_space, power_spectrum=ps0)
# Initialize non-linear Wiener Filter energy
map_energy = WienerFilterEnergy(position=m0, d=d, R=R, N=N, S=S0)
ICI = ift.DefaultIterationController(verbose=True,iteration_limit=60)
inverter = ift.ConjugateGradient(controller=ICI,preconditioner=S0.times)
map_energy = ift.library.WienerFilterEnergy(position=m0, d=d, R=R, N=N, S=S0, inverter=inverter)
# Solve the Wiener Filter analytically
D0 = map_energy.curvature
m0 = D0.inverse_times(j)
# Initialize power energy with updated parameters
power_energy = CriticalPowerEnergy(position=t0, m=m0, D=D0,
power_energy = ift.library.CriticalPowerEnergy(position=t0, m=m0, D=D0,
smoothness_prior=10., samples=3)
(power_energy, convergence) = minimizer2(power_energy)
......@@ -153,4 +134,4 @@ if __name__ == "__main__":
# Plot current estimate
print(i)
if i % 5 == 0:
plot_parameters(m0, t0, log(sp), data_power)
plot_parameters(m0, t0, ift.log(sp), data_power)
demos/log_normal_wiener_filter.py
View file @ 7107323b
# -*- coding: utf-8 -*-
from nifty import *
import nifty as ift
import nifty2go as ift
import numpy as np
if __name__ == "__main__":
np.random.seed(42)
# Setting up parameters |\label{code:wf_parameters}|
correlation_length = 1. # Typical distance over which the field is correlated
field_variance = 2. # Variance of field in position space
......@@ -19,74 +19,73 @@ if __name__ == "__main__":
L = 2. # Total side-length of the domain
N_pixels = 128 # Grid resolution (pixels per axis)
#signal_space = RGSpace([N_pixels, N_pixels], distances=L/N_pixels)
signal_space = HPSpace(16)
harmonic_space = FFTOperator.get_default_codomain(signal_space)
fft = FFTOperator(harmonic_space, target=signal_space)
power_space = PowerSpace(harmonic_space)
signal_space = ift.HPSpace(16)
harmonic_space = signal_space.get_default_codomain()
fft = ift.FFTOperator(harmonic_space, target=signal_space)
power_space = ift.PowerSpace(harmonic_space)
# Creating the mock signal |\label{code:wf_mock_signal}|
S = create_power_operator(harmonic_space, power_spectrum=power_spectrum)
mock_power = Field(power_space, val=power_spectrum)
S = ift.create_power_operator(harmonic_space, power_spectrum=power_spectrum)
mock_power = ift.Field(power_space, val=power_spectrum(power_space.kindex))
mock_signal = fft(mock_power.power_synthesize(real_signal=True))
# Setting up an exemplary response
mask = Field(signal_space, val=1.)
mask = ift.Field(signal_space, val=1.)
N10 = int(N_pixels/10)
#mask.val[N10*5:N10*9, N10*5:N10*9] = 0.
R = ResponseOperator(signal_space, sigma=(response_sigma,), exposure=(mask,)) #|\label{code:wf_response}|
R = ift.ResponseOperator(signal_space, sigma=(response_sigma,), exposure=(mask,)) #|\label{code:wf_response}|
data_domain = R.target[0]
R_harmonic = ComposedOperator([fft, R], default_spaces=[0, 0])
R_harmonic = ift.ComposedOperator([fft, R], default_spaces=[0, 0])
# Setting up the noise covariance and drawing a random noise realization
N = DiagonalOperator(data_domain, diagonal=mock_signal.var()/signal_to_noise, bare=True)
noise = Field.from_random(domain=data_domain, random_type='normal',
N = ift.DiagonalOperator(data_domain, diagonal=mock_signal.var()/signal_to_noise, bare=True)
noise = ift.Field.from_random(domain=data_domain, random_type='normal',
std=mock_signal.std()/np.sqrt(signal_to_noise), mean=0)
data = R(exp(mock_signal)) + noise #|\label{code:wf_mock_data}|
data = R(ift.exp(mock_signal)) + noise #|\label{code:wf_mock_data}|
# Wiener filter
m0 = Field(harmonic_space, val=0.j)
m0 = ift.Field(harmonic_space, val=0.)
ctrl = ift.DefaultIterationController(verbose=False,tol_abs_gradnorm=1)
ctrl2 = ift.DefaultIterationController(verbose=True,tol_abs_gradnorm=0.1, name="outer")
inverter = ift.ConjugateGradient(controller=ctrl, preconditioner=S.times)
energy = library.LogNormalWienerFilterEnergy(m0, data, R_harmonic, N, S, inverter=inverter)
minimizer1 = VL_BFGS(controller=ctrl2,max_history_length=20)
minimizer2 = RelaxedNewton(controller=ctrl2)
minimizer3 = SteepestDescent(controller=ctrl2)
# me1 = minimizer1(energy)
# me2 = minimizer2(energy)
energy = ift.library.LogNormalWienerFilterEnergy(m0, data, R_harmonic, N, S, inverter=inverter)
minimizer1 = ift.VL_BFGS(controller=ctrl2,max_history_length=20)
minimizer2 = ift.RelaxedNewton(controller=ctrl2)
minimizer3 = ift.SteepestDescent(controller=ctrl2)
print type(energy.value)
me1 = minimizer1(energy)
me2 = minimizer2(energy)
me3 = minimizer3(energy)
# m1 = fft(me1[0].position)
# m2 = fft(me2[0].position)
# m3 = fft(me3[0].position)
#
m1 = fft(me1[0].position)
m2 = fft(me2[0].position)
m3 = fft(me3[0].position)
# # Probing the variance
# class Proby(DiagonalProberMixin, Prober): pass
# proby = Proby(signal_space, probe_count=100)
# proby(lambda z: fft(wiener_curvature.inverse_times(fft.inverse_times(z))))
#
# sm = SmoothingOperator(signal_space, sigma=0.02)
# variance = sm(proby.diagonal.weight(-1))
# Probing the variance
class Proby(ift.DiagonalProberMixin, ift.Prober): pass
proby = Proby(signal_space, probe_count=100)
proby(lambda z: fft(wiener_curvature.inverse_times(fft.inverse_times(z))))
sm = SmoothingOperator(signal_space, sigma=0.02)
variance = sm(proby.diagonal.weight(-1))
#Plotting #|\label{code:wf_plotting}|
#plotter = plotting.RG2DPlotter(color_map=plotting.colormaps.PlankCmap())
plotter = plotting.HealpixPlotter(color_map=plotting.colormaps.PlankCmap())
plotter = ift.plotting.HealpixPlotter(color_map=ift.plotting.colormaps.PlankCmap())
plotter.figure.xaxis = plotting.Axis(label='Pixel Index')
plotter.figure.yaxis = plotting.Axis(label='Pixel Index')
plotter.figure.xaxis = ift.plotting.Axis(label='Pixel Index')
plotter.figure.yaxis = ift.plotting.Axis(label='Pixel Index')
plotter.plot.zmax = 5; plotter.plot.zmin = -5
## plotter(variance, path = 'variance.html')
plotter(variance, path = 'variance.html')
# #plotter.plot.zmin = exp(mock_signal.min());
# plotter(mock_signal.real, path='mock_signal.html')
# plotter(Field(signal_space, val=np.log(data.val.get_full_data().real).reshape(signal_space.shape)),
# path = 'log_of_data.html')
#
# plotter(m1.real, path='m_LBFGS.html')
# plotter(m2.real, path='m_Newton.html')
# plotter(m3.real, path='m_SteepestDescent.html')
plotter(m1.real, path='m_LBFGS.html')
plotter(m2.real, path='m_Newton.html')
plotter(m3.real, path='m_SteepestDescent.html')
#
nifty2go/field.py
View file @ 7107323b
......@@ -37,7 +37,7 @@ class Field(object):
In NIFTY, Fields are used to store data arrays and carry all the needed
metainformation (i.e. the domain) for operators to be able to work on them.
In addition Field has methods to work with power-spectra.
In addition, Field has methods to work with power spectra.
Parameters
----------
......@@ -52,7 +52,7 @@ class Field(object):
array's dimensions must match the domain's.
dtype : type
A numpy.type. Most common are int, float and complex.
A numpy.type. Most common are float and complex.
copy: boolean
......@@ -265,11 +265,9 @@ class Field(object):
for part in parts]
if keep_phase_information:
result_field = parts[0] + 1j*parts[1]
return parts[0] + 1j*parts[1]
else:
result_field = parts[0]
return result_field
return parts[0]
@classmethod
def _single_power_analyze(cls, work_field, space_index, binbounds):
......@@ -295,21 +293,14 @@ class Field(object):
# create the result field and put power_spectrum into it
result_domain = list(work_field.domain)
result_domain[space_index] = power_domain
result_dtype = power_spectrum.dtype
result_field = work_field.copy_empty(
domain=result_domain,
dtype=result_dtype)
result_field.set_val(new_val=power_spectrum, copy=False)
return result_field
return Field(domain=result_domain,val=power_spectrum,
dtype=power_spectrum.dtype)
@classmethod
def _calculate_power_spectrum(cls, field_val, pdomain, axes=None):
pindex = pdomain.pindex
# MR FIXME: how about iterating over slices, instead of replicating
# pindex? Would save memory and probably isn't slower.
if axes is not None:
pindex = cls._shape_up_pindex(
pindex=pindex,
......@@ -711,8 +702,6 @@ class Field(object):
The weighted field.
"""
new_field = self if inplace else self.copy_empty()
new_val = self.get_val(copy=False)
spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
......@@ -725,9 +714,10 @@ class Field(object):
power=power,
axes=self.domain_axes[ind],
inplace=inplace)
# we need at most one copy, the rest can happen in place
inplace = True
new_field.set_val(new_val=new_val, copy=False)
return new_field
return Field(self.domain, new_val, self.dtype)
def vdot(self, x=None, spaces=None, bare=False):
""" Computes the volume-factor-aware dot product of 'self' with x.
......@@ -794,7 +784,6 @@ class Field(object):
The complex conjugated field.
"""
if inplace:
self.imag*=-1
return self
......@@ -837,10 +826,7 @@ class Field(object):
for i in range(len(self.domain))
if i not in spaces)
return_field = Field(domain=return_domain,
val=data,
copy=False)
return return_field
return Field(domain=return_domain, val=data, copy=False)
def sum(self, spaces=None):
return self._contraction_helper('sum', spaces)
......
nifty2go/operators/linear_operator/linear_operator.py
View file @ 7107323b
......@@ -224,9 +224,6 @@ class LinearOperator(with_metaclass(
If the operator has an `inverse` then the inverse adjoint is identical
to the adjoint inverse. We provide both names for convenience.
See Also
--------
"""
spaces = self._check_input_compatibility(x, spaces)
......@@ -261,8 +258,7 @@ class LinearOperator(with_metaclass(
def _check_input_compatibility(self, x, spaces, inverse=False):
if not isinstance(x, Field):
raise ValueError(
"supplied object is not a `Field`.")
raise ValueError("supplied object is not a `Field`.")
if spaces is None and self.default_spaces is not None:
if not inverse:
......@@ -281,10 +277,7 @@ class LinearOperator(with_metaclass(
# 2. Case:
# The domains of self and x match completely.
if not inverse:
self_domain = self.domain
else:
self_domain = self.target
self_domain = self.target if inverse else self.domain
if spaces is None:
if self_domain != x.domain:
......
nifty2go/operators/response_operator/response_operator.py
View file @ 7107323b
......@@ -50,28 +50,22 @@ class ResponseOperator(LinearOperator):
default_spaces=None):
super(ResponseOperator, self).__init__(default_spaces)
self._domain = self._parse_domain(domain)
kernel_smoothing = len(self._domain)*[None]
kernel_exposure = len(self._domain)*[None]
if len(sigma) != len(exposure):
raise ValueError("Length of smoothing kernel and length of"
"exposure do not match")
nsigma = len(sigma)
for ii in range(len(kernel_smoothing)):
kernel_smoothing[ii] = FFTSmoothingOperator(self._domain[ii],
sigma=sigma[ii])
kernel_exposure[ii] = DiagonalOperator(self._domain[ii],
diagonal=exposure[ii])
self._domain = self._parse_domain(domain)
kernel_smoothing = [FFTSmoothingOperator(self._domain[x], sigma[x])
for x in range(nsigma)]
kernel_exposure = [DiagonalOperator(self._domain[x],
diagonal=exposure[x]) for x in range(nsigma)]
self._composed_kernel = ComposedOperator(kernel_smoothing)
self._composed_exposure = ComposedOperator(kernel_exposure)
target_list = []
for space in self.domain:
target_list += [FieldArray(space.shape)]
target_list = [FieldArray(x.shape) for x in self.domain]
self._target = self._parse_domain(target_list)
@property
......@@ -89,7 +83,6 @@ class ResponseOperator(LinearOperator):
def _times(self, x, spaces):
res = self._composed_kernel.times(x, spaces)
res = self._composed_exposure.times(res, spaces)
# res = res.weight(power=1)
# removing geometric information
return Field(self._target, val=res.val)
......@@ -98,5 +91,4 @@ class ResponseOperator(LinearOperator):
res = Field(self.domain, val=x.val)
res = self._composed_exposure.adjoint_times(res, spaces)
res = res.weight(power=-1)
res = self._composed_kernel.adjoint_times(res, spaces)
return res
return self._composed_kernel.adjoint_times(res, spaces)
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