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ift
NIFTy
Commits
412eede0
Commit
412eede0
authored
Aug 02, 2017
by
Theo Steininger
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Added demos from paper.
parent
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#15900
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demos/paper_demos/cartesian_wiener_filter.py
demos/paper_demos/cartesian_wiener_filter.py
+143
-0
demos/paper_demos/wiener_filter.py
demos/paper_demos/wiener_filter.py
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demos/paper_demos/cartesian_wiener_filter.py
0 → 100644
View file @
412eede0
# -*- coding: utf-8 -*-
import
numpy
as
np
import
nifty
as
ift
from
keepers
import
Repository
if
__name__
==
"__main__"
:
signal_to_noise
=
1.5
# The signal to noise ratioa
# Setting up parameters |\label{code:wf_parameters}|
correlation_length_1
=
1.
# Typical distance over which the field is correlated
field_variance_1
=
2.
# Variance of field in position space
response_sigma_1
=
0.05
# Smoothing length of response (in same unit as L)
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.
# Setting up the geometry |\label{code:wf_geometry}|
L_1
=
2.
# Total side-length of the domain
N_pixels_1
=
512
# Grid resolution (pixels per axis)
signal_space_1
=
ift
.
RGSpace
([
N_pixels_1
],
distances
=
L_1
/
N_pixels_1
)
harmonic_space_1
=
ift
.
FFTOperator
.
get_default_codomain
(
signal_space_1
)
fft_1
=
ift
.
FFTOperator
(
harmonic_space_1
,
target
=
signal_space_1
,
domain_dtype
=
np
.
complex
,
target_dtype
=
np
.
complex
)
power_space_1
=
ift
.
PowerSpace
(
harmonic_space_1
,
distribution_strategy
=
'fftw'
)
mock_power_1
=
ift
.
Field
(
power_space_1
,
val
=
power_spectrum_1
,
distribution_strategy
=
'not'
)
# Setting up parameters |\label{code:wf_parameters}|
correlation_length_2
=
1.
# Typical distance over which the field is correlated
field_variance_2
=
2.
# Variance of field in position space
response_sigma_2
=
0.01
# Smoothing length of response (in same unit as L)
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
# Setting up the geometry |\label{code:wf_geometry}|
L_2
=
2.
# Total side-length of the domain
N_pixels_2
=
512
# Grid resolution (pixels per axis)
signal_space_2
=
ift
.
RGSpace
([
N_pixels_2
],
distances
=
L_2
/
N_pixels_2
)
harmonic_space_2
=
ift
.
FFTOperator
.
get_default_codomain
(
signal_space_2
)
fft_2
=
ift
.
FFTOperator
(
harmonic_space_2
,
target
=
signal_space_2
,
domain_dtype
=
np
.
complex
,
target_dtype
=
np
.
complex
)
power_space_2
=
PowerSpace
(
harmonic_space_2
,
distribution_strategy
=
'not'
)
mock_power_2
=
ift
.
Field
(
power_space_2
,
val
=
power_spectrum_2
,
distribution_strategy
=
'not'
)
fft
=
ift
.
ComposedOperator
((
fft_1
,
fft_2
))
mock_power
=
ift
.
Field
(
domain
=
(
power_space_1
,
power_space_2
),
val
=
np
.
outer
(
mock_power_1
.
val
.
get_full_data
(),
mock_power_2
.
val
.
get_full_data
()),
distribution_strategy
=
'not'
)
diagonal
=
mock_power
.
power_synthesize
(
spaces
=
(
0
,
1
),
mean
=
1
,
std
=
0
,
real_signal
=
False
,
distribution_strategy
=
'fftw'
)
**
2
S
=
ift
.
DiagonalOperator
(
domain
=
(
harmonic_space_1
,
harmonic_space_2
),
diagonal
=
diagonal
)
np
.
random
.
seed
(
10
)
mock_signal
=
fft
(
mock_power
.
power_synthesize
(
real_signal
=
True
,
distribution_strategy
=
'fftw'
))
# Setting up a exemplary response
N1_10
=
int
(
N_pixels_1
/
10
)
mask_1
=
ift
.
Field
(
signal_space_1
,
val
=
1.
,
distribution_strategy
=
'fftw'
)
mask_1
.
val
[
N1_10
*
7
:
N1_10
*
9
]
=
0.
N2_10
=
int
(
N_pixels_2
/
10
)
mask_2
=
ift
.
Field
(
signal_space_2
,
val
=
1.
,
distribution_strategy
=
'not'
)
mask_2
.
val
[
N2_10
*
7
:
N2_10
*
9
]
=
0.
R
=
ift
.
ResponseOperator
((
signal_space_1
,
signal_space_2
),
sigma
=
(
response_sigma_1
,
response_sigma_2
),
exposure
=
(
mask_1
,
mask_2
))
#|\label{code:wf_response}|
data_domain
=
R
.
target
R_harmonic
=
ComposedOperator
([
fft
,
R
],
default_spaces
=
(
0
,
1
,
0
,
1
))
# Setting up the noise covariance and drawing a random noise realization
N
=
ift
.
DiagonalOperator
(
data_domain
,
diagonal
=
mock_signal
.
var
()
/
signal_to_noise
,
bare
=
True
,
distribution_strategy
=
'fftw'
)
noise
=
ift
.
Field
.
from_random
(
domain
=
data_domain
,
random_type
=
'normal'
,
std
=
mock_signal
.
std
()
/
np
.
sqrt
(
signal_to_noise
),
mean
=
0
,
distribution_strategy
=
'fftw'
)
data
=
R
(
mock_signal
)
+
noise
#|\label{code:wf_mock_data}|
# Wiener filter
j
=
R_harmonic
.
adjoint_times
(
N
.
inverse_times
(
data
))
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
)
wiener_curvature
.
_InvertibleOperatorMixin__inverter
.
convergence_tolerance
=
1e-3
m_k
=
wiener_curvature
.
inverse_times
(
j
)
#|\label{code:wf_wiener_filter}|
m
=
fft
(
m_k
)
# Probing the variance
class
Proby
(
ift
.
DiagonalProberMixin
,
ift
.
Prober
):
pass
proby
=
Proby
((
signal_space_1
,
signal_space_2
),
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))
variance
=
proby
.
diagonal
.
weight
(
-
1
)
repo
=
Repository
(
'repo_100.h5'
)
repo
.
add
(
mock_signal
,
'mock_signal'
)
repo
.
add
(
data
,
'data'
)
repo
.
add
(
m
,
'm'
)
repo
.
add
(
variance
,
'variance'
)
repo
.
commit
()
plot_space
=
ift
.
RGSpace
((
N_pixels_1
,
N_pixels_2
))
plotter
=
ift
.
plotting
.
RG2DPlotter
(
color_map
=
plotting
.
colormaps
.
PlankCmap
())
plotter
.
figure
.
xaxis
=
ift
.
plotting
.
Axis
(
label
=
'Pixel Index'
)
plotter
.
figure
.
yaxis
=
ift
.
plotting
.
Axis
(
label
=
'Pixel Index'
)
plotter
.
plot
.
zmin
=
0.
plotter
.
plot
.
zmax
=
3.
sm
=
ift
.
SmoothingOperator
(
plot_space
,
sigma
=
0.03
)
plotter
(
ift
.
log
(
sqrt
(
sm
(
ift
.
Field
(
plot_space
,
val
=
variance
.
val
.
real
)))),
path
=
'uncertainty.html'
)
plotter
.
plot
.
zmin
=
np
.
real
(
mock_signal
.
min
());
plotter
.
plot
.
zmax
=
np
.
real
(
mock_signal
.
max
());
plotter
(
ift
.
Field
(
plot_space
,
val
=
mock_signal
.
val
.
real
),
path
=
'mock_signal.html'
)
plotter
(
ift
.
Field
(
plot_space
,
val
=
data
.
val
.
get_full_data
().
real
),
path
=
'data.html'
)
plotter
(
ift
.
Field
(
plot_space
,
val
=
m
.
val
.
real
),
path
=
'map.html'
)
demos/paper_demos/wiener_filter.py
0 → 100644
View file @
412eede0
# -*- coding: utf-8 -*-
import
nifty
as
ift
import
numpy
as
np
from
keepers
import
Repository
if
__name__
==
"__main__"
:
ift
.
nifty_configuration
[
'default_distribution_strategy'
]
=
'fftw'
# Setting up parameters |\label{code:wf_parameters}|
correlation_length_scale
=
1.
# 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 (in same unit as L)
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
# Setting up the geometry |\label{code:wf_geometry}|
L
=
2.
# Total side-length of the domain
N_pixels
=
512
# Grid resolution (pixels per axis)
signal_space
=
ift
.
RGSpace
([
N_pixels
,
N_pixels
],
distances
=
L
/
N_pixels
)
harmonic_space
=
ift
.
FFTOperator
.
get_default_codomain
(
signal_space
)
fft
=
ift
.
FFTOperator
(
harmonic_space
,
target
=
signal_space
,
target_dtype
=
np
.
float
)
power_space
=
ift
.
PowerSpace
(
harmonic_space
)
# Creating the mock signal |\label{code:wf_mock_signal}|
S
=
ift
.
create_power_operator
(
harmonic_space
,
power_spectrum
=
power_spectrum
)
mock_power
=
ift
.
Field
(
power_space
,
val
=
power_spectrum
)
mock_signal
=
fft
(
mock_power
.
power_synthesize
(
real_signal
=
True
))
# Setting up an exemplary response
mask
=
ift
.
Field
(
signal_space
,
val
=
1.
)
N10
=
int
(
N_pixels
/
10
)
mask
.
val
[
N10
*
5
:
N10
*
9
,
N10
*
5
:
N10
*
9
]
=
0.
R
=
ift
.
ResponseOperator
(
signal_space
,
sigma
=
(
response_sigma
,),
exposure
=
(
mask
,))
#|\label{code:wf_response}|
data_domain
=
R
.
target
[
0
]
R_harmonic
=
ift
.
ComposedOperator
([
fft
,
R
],
default_spaces
=
[
0
,
0
])
# Setting up the noise covariance and drawing a random noise realization
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
(
mock_signal
)
+
noise
#|\label{code:wf_mock_data}|
# Wiener filter
j
=
R_harmonic
.
adjoint_times
(
N
.
inverse_times
(
data
))
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
)
m_k
=
wiener_curvature
.
inverse_times
(
j
)
#|\label{code:wf_wiener_filter}|
m
=
fft
(
m_k
)
# Probing the uncertainty |\label{code:wf_uncertainty_probing}|
class
Proby
(
ift
.
DiagonalProberMixin
,
ift
.
Prober
):
pass
proby
=
Proby
(
signal_space
,
probe_count
=
800
)
proby
(
lambda
z
:
fft
(
wiener_curvature
.
inverse_times
(
fft
.
inverse_times
(
z
))))
#|\label{code:wf_variance_fft_wrap}|
sm
=
ift
.
SmoothingOperator
(
signal_space
,
sigma
=
0.03
)
variance
=
ift
.
sqrt
(
sm
(
proby
.
diagonal
.
weight
(
-
1
)))
#|\label{code:wf_variance_weighting}|
repo
=
Repository
(
'repo_800.h5'
)
repo
.
add
(
mock_signal
,
'mock_signal'
)
repo
.
add
(
data
,
'data'
)
repo
.
add
(
m
,
'm'
)
repo
.
add
(
variance
,
'variance'
)
repo
.
commit
()
# Plotting #|\label{code:wf_plotting}|
plotter
=
ift
.
plotting
.
RG2DPlotter
(
color_map
=
plotting
.
colormaps
.
PlankCmap
())
plotter
.
figure
.
xaxis
=
ift
.
plotting
.
Axis
(
label
=
'Pixel Index'
)
plotter
.
figure
.
yaxis
=
ift
.
plotting
.
Axis
(
label
=
'Pixel Index'
)
plotter
.
plot
.
zmax
=
variance
.
max
();
plotter
.
plot
.
zmin
=
0
plotter
(
variance
,
path
=
'uncertainty.html'
)
plotter
.
plot
.
zmax
=
mock_signal
.
max
();
plotter
.
plot
.
zmin
=
mock_signal
.
min
()
plotter
(
mock_signal
,
path
=
'mock_signal.html'
)
plotter
(
ift
.
Field
(
signal_space
,
val
=
data
.
val
),
path
=
'data.html'
)
plotter
(
m
,
path
=
'map.html'
)
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