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ift
NIFTy
Commits
011fe3fa
Commit
011fe3fa
authored
Oct 17, 2017
by
Martin Reinecke
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parent
6b18bbdf
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6
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6 changed files
with
70 additions
and
46 deletions
+70
-46
demos/critical_filtering.py
demos/critical_filtering.py
+34
-21
demos/log_normal_wiener_filter.py
demos/log_normal_wiener_filter.py
+1
-1
demos/paper_demos/cartesian_wiener_filter.py
demos/paper_demos/cartesian_wiener_filter.py
+4
-3
demos/paper_demos/wiener_filter.py
demos/paper_demos/wiener_filter.py
+3
-2
demos/wiener_filter_via_curvature.py
demos/wiener_filter_via_curvature.py
+27
-18
demos/wiener_filter_via_hamiltonian.py
demos/wiener_filter_via_hamiltonian.py
+1
-1
No files found.
demos/critical_filtering.py
View file @
011fe3fa
...
...
@@ -2,17 +2,15 @@ import numpy as np
import
nifty2go
as
ift
np
.
random
.
seed
(
42
)
#np.seterr(all="raise",under="ignore")
# np.seterr(all="raise",under="ignore")
def
plot_parameters
(
m
,
t
,
p
,
p_d
):
x
=
np
.
log
(
t
.
domain
[
0
].
k_lengths
)
m
=
fft
.
adjoint_times
(
m
)
t
=
t
.
val
.
real
p
=
p
.
val
.
real
p_d
=
p_d
.
val
.
real
ift
.
plotting
.
plot
(
m
.
real
,
name
=
'map.pdf'
)
#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
(
ift
.
LinearOperator
):
...
...
@@ -52,7 +50,9 @@ if __name__ == "__main__":
h_space
=
fft
.
target
[
0
]
# Set up power space
p_space
=
ift
.
PowerSpace
(
h_space
,
binbounds
=
ift
.
PowerSpace
.
useful_binbounds
(
h_space
,
logarithmic
=
True
))
p_space
=
ift
.
PowerSpace
(
h_space
,
binbounds
=
ift
.
PowerSpace
.
useful_binbounds
(
h_space
,
logarithmic
=
True
))
# Choose the prior correlation structure and defining correlation operator
p_spec
=
(
lambda
k
:
(.
5
/
(
k
+
1
)
**
3
))
...
...
@@ -60,7 +60,7 @@ if __name__ == "__main__":
# Draw a sample sh from the prior distribution in harmonic space
sp
=
ift
.
Field
(
p_space
,
val
=
p_spec
(
p_space
.
k_lengths
))
sh
=
sp
.
power_synthesize
(
real_signal
=
True
)
sh
=
ift
.
power_synthesize
(
sp
,
real_signal
=
True
)
# Choose the measurement instrument
# Instrument = SmoothingOperator(s_space, sigma=0.01)
...
...
@@ -72,32 +72,37 @@ if __name__ == "__main__":
R
=
AdjointFFTResponse
(
fft
,
Instrument
)
noise
=
1.
N
=
ift
.
DiagonalOperator
(
ift
.
Field
.
full
(
s_space
,
noise
))
N
=
ift
.
DiagonalOperator
(
ift
.
Field
.
full
(
s_space
,
noise
))
n
=
ift
.
Field
.
from_random
(
domain
=
s_space
,
random_type
=
'normal'
,
std
=
np
.
sqrt
(
noise
),
mean
=
0
)
random_type
=
'normal'
,
std
=
np
.
sqrt
(
noise
),
mean
=
0
)
# Create mock data
d
=
R
(
sh
)
+
n
# The information source
j
=
R
.
adjoint_times
(
N
.
inverse_times
(
d
))
realized_power
=
ift
.
log
(
sh
.
power_analyze
(
binbounds
=
p_space
.
binbounds
))
data_power
=
ift
.
log
(
fft
(
d
).
power_analyze
(
binbounds
=
p_space
.
binbounds
))
realized_power
=
ift
.
log
(
ift
.
power_analyze
(
sh
,
binbounds
=
p_space
.
binbounds
))
data_power
=
ift
.
log
(
ift
.
power_analyze
(
fft
(
d
),
binbounds
=
p_space
.
binbounds
))
d_data
=
d
.
val
.
real
ift
.
plotting
.
plot
(
d
.
real
,
name
=
"data.pdf"
)
IC1
=
ift
.
GradientNormController
(
verbose
=
True
,
iteration_limit
=
100
,
tol_abs_gradnorm
=
0.1
)
IC1
=
ift
.
GradientNormController
(
verbose
=
True
,
iteration_limit
=
100
,
tol_abs_gradnorm
=
0.1
)
minimizer1
=
ift
.
RelaxedNewton
(
IC1
)
IC2
=
ift
.
GradientNormController
(
verbose
=
True
,
iteration_limit
=
100
,
tol_abs_gradnorm
=
0.1
)
IC2
=
ift
.
GradientNormController
(
verbose
=
True
,
iteration_limit
=
100
,
tol_abs_gradnorm
=
0.1
)
minimizer2
=
ift
.
VL_BFGS
(
IC2
,
max_history_length
=
20
)
IC3
=
ift
.
GradientNormController
(
verbose
=
True
,
iteration_limit
=
100
,
tol_abs_gradnorm
=
0.1
)
IC3
=
ift
.
GradientNormController
(
verbose
=
True
,
iteration_limit
=
100
,
tol_abs_gradnorm
=
0.1
)
minimizer3
=
ift
.
SteepestDescent
(
IC3
)
# Set starting position
flat_power
=
ift
.
Field
.
full
(
p_space
,
1e-8
)
m0
=
flat_power
.
power_synthesize
(
real_signal
=
True
)
m0
=
ift
.
power_synthesize
(
flat_power
,
real_signal
=
True
)
def
ps0
(
k
):
return
(
1.
/
(
1.
+
k
)
**
2
)
...
...
@@ -107,17 +112,25 @@ if __name__ == "__main__":
S0
=
ift
.
create_power_operator
(
h_space
,
power_spectrum
=
ps0
)
# Initialize non-linear Wiener Filter energy
ICI
=
ift
.
GradientNormController
(
verbose
=
False
,
iteration_limit
=
500
,
tol_abs_gradnorm
=
0.1
)
ICI
=
ift
.
GradientNormController
(
verbose
=
False
,
name
=
"ICI"
,
iteration_limit
=
500
,
tol_abs_gradnorm
=
0.1
)
map_inverter
=
ift
.
ConjugateGradient
(
controller
=
ICI
)
map_energy
=
ift
.
library
.
WienerFilterEnergy
(
position
=
m0
,
d
=
d
,
R
=
R
,
N
=
N
,
S
=
S0
,
inverter
=
map_inverter
)
map_energy
=
ift
.
library
.
WienerFilterEnergy
(
position
=
m0
,
d
=
d
,
R
=
R
,
N
=
N
,
S
=
S0
,
inverter
=
map_inverter
)
# Solve the Wiener Filter analytically
D0
=
map_energy
.
curvature
m0
=
D0
.
inverse_times
(
j
)
# Initialize power energy with updated parameters
ICI2
=
ift
.
GradientNormController
(
name
=
"powI"
,
verbose
=
True
,
iteration_limit
=
200
,
tol_abs_gradnorm
=
1e-5
)
ICI2
=
ift
.
GradientNormController
(
name
=
"powI"
,
verbose
=
False
,
iteration_limit
=
200
,
tol_abs_gradnorm
=
1e-5
)
power_inverter
=
ift
.
ConjugateGradient
(
controller
=
ICI2
)
power_energy
=
ift
.
library
.
CriticalPowerEnergy
(
position
=
t0
,
m
=
m0
,
D
=
D0
,
smoothness_prior
=
10.
,
samples
=
3
,
inverter
=
power_inverter
)
power_energy
=
ift
.
library
.
CriticalPowerEnergy
(
position
=
t0
,
m
=
m0
,
D
=
D0
,
smoothness_prior
=
10.
,
samples
=
3
,
inverter
=
power_inverter
)
(
power_energy
,
convergence
)
=
minimizer1
(
power_energy
)
...
...
demos/log_normal_wiener_filter.py
View file @
011fe3fa
...
...
@@ -25,7 +25,7 @@ if __name__ == "__main__":
# 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
(
power_space
.
k_lengths
))
mock_signal
=
fft
(
mock_power
.
power_synthesize
(
real_signal
=
True
))
mock_signal
=
fft
(
ift
.
power_synthesize
(
mock_power
,
real_signal
=
True
))
# Setting up an exemplary response
mask
=
ift
.
Field
.
ones
(
signal_space
)
...
...
demos/paper_demos/cartesian_wiener_filter.py
View file @
011fe3fa
...
...
@@ -57,14 +57,14 @@ if __name__ == "__main__":
mock_power
=
ift
.
Field
(
domain
=
(
power_space_1
,
power_space_2
),
val
=
np
.
outer
(
mock_power_1
.
val
,
mock_power_2
.
val
))
diagonal
=
mock_power
.
power_synthesize_special
(
spaces
=
(
0
,
1
))
**
2
diagonal
=
ift
.
power_synthesize_special
(
mock_power
,
spaces
=
(
0
,
1
))
**
2
diagonal
=
diagonal
.
real
S
=
ift
.
DiagonalOperator
(
diagonal
.
weight
(
-
1
))
np
.
random
.
seed
(
10
)
mock_signal
=
fft
(
mock_power
.
power_synthesize
(
real_signal
=
True
))
mock_signal
=
fft
(
ift
.
power_synthesize
(
mock_power
,
real_signal
=
True
))
# Setting up a exemplary response
N1_10
=
int
(
N_pixels_1
/
10
)
...
...
@@ -93,7 +93,8 @@ if __name__ == "__main__":
j
=
R_harmonic
.
adjoint_times
(
N
.
inverse_times
(
data
))
ctrl
=
ift
.
GradientNormController
(
verbose
=
True
,
tol_abs_gradnorm
=
0.1
)
inverter
=
ift
.
ConjugateGradient
(
controller
=
ctrl
)
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
,
inverter
=
inverter
)
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
)
wiener_curvature
=
ift
.
InversionEnabler
(
wiener_curvature
,
inverter
)
m_k
=
wiener_curvature
.
inverse_times
(
j
)
#|\label{code:wf_wiener_filter}|
m
=
fft
(
m_k
)
...
...
demos/paper_demos/wiener_filter.py
View file @
011fe3fa
...
...
@@ -24,7 +24,7 @@ if __name__ == "__main__":
# 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
(
power_space
.
k_lengths
))
mock_signal
=
fft
(
mock_power
.
power_synthesize
(
real_signal
=
True
))
mock_signal
=
fft
(
ift
.
power_synthesize
(
mock_power
,
real_signal
=
True
))
# Setting up an exemplary response
mask
=
ift
.
Field
.
ones
(
signal_space
)
...
...
@@ -45,7 +45,8 @@ if __name__ == "__main__":
j
=
R_harmonic
.
adjoint_times
(
N
.
inverse_times
(
data
))
ctrl
=
ift
.
GradientNormController
(
verbose
=
True
,
tol_abs_gradnorm
=
0.1
)
inverter
=
ift
.
ConjugateGradient
(
controller
=
ctrl
)
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
,
inverter
=
inverter
)
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
)
wiener_curvature
=
ift
.
InversionEnabler
(
wiener_curvature
,
inverter
)
m_k
=
wiener_curvature
.
inverse_times
(
j
)
#|\label{code:wf_wiener_filter}|
m
=
fft
(
m_k
)
...
...
demos/wiener_filter_via_curvature.py
View file @
011fe3fa
...
...
@@ -11,7 +11,7 @@ if __name__ == "__main__":
# Typical distance over which the field is correlated
correlation_length
=
0.05
*
nu
.
m
# sigma of field in position space sqrt(<|s_x|^2>)
field_sigma
=
2.
*
nu
.
K
field_sigma
=
2.
*
nu
.
K
# smoothing length of response
response_sigma
=
0.01
*
nu
.
m
# The signal to noise ratio
...
...
@@ -22,7 +22,8 @@ if __name__ == "__main__":
def
power_spectrum
(
k
):
cldim
=
correlation_length
**
(
2
*
dimensionality
)
a
=
4
/
(
2
*
np
.
pi
)
*
cldim
*
field_sigma
**
2
return
a
/
(
1
+
(
k
*
correlation_length
)
**
(
2
*
dimensionality
))
**
2
# to be integrated over spherical shells later on
# to be integrated over spherical shells later on
return
a
/
(
1
+
(
k
*
correlation_length
)
**
(
2
*
dimensionality
))
**
2
# Setting up the geometry
...
...
@@ -38,39 +39,47 @@ if __name__ == "__main__":
power_space
=
ift
.
PowerSpace
(
harmonic_space
)
# Creating the mock data
S
=
ift
.
create_power_operator
(
harmonic_space
,
power_spectrum
=
power_spectrum
)
S
=
ift
.
create_power_operator
(
harmonic_space
,
power_spectrum
=
power_spectrum
)
np
.
random
.
seed
(
43
)
mock_power
=
ift
.
Field
(
power_space
,
val
=
power_spectrum
(
power_space
.
k_lengths
))
mock_harmonic
=
mock_power
.
power_synthesize
(
real_signal
=
True
)
mock_power
=
ift
.
Field
(
power_space
,
val
=
power_spectrum
(
power_space
.
k_lengths
))
mock_harmonic
=
ift
.
power_synthesize
(
mock_power
,
real_signal
=
True
)
mock_harmonic
=
mock_harmonic
.
real
mock_signal
=
fft
(
mock_harmonic
)
exposure
=
1.
R
=
ift
.
ResponseOperator
(
signal_space
,
sigma
=
(
response_sigma
,),
exposure
=
(
exposure
,))
R
=
ift
.
ResponseOperator
(
signal_space
,
sigma
=
(
response_sigma
,),
exposure
=
(
exposure
,))
data_domain
=
R
.
target
[
0
]
R_harmonic
=
ift
.
ComposedOperator
([
fft
,
R
])
N
=
ift
.
DiagonalOperator
(
ift
.
Field
.
full
(
data_domain
,
mock_signal
.
var
()
/
signal_to_noise
))
noise
=
ift
.
Field
.
from_random
(
domain
=
data_domain
,
random_type
=
'normal'
,
std
=
mock_signal
.
std
()
/
np
.
sqrt
(
signal_to_noise
)
,
mean
=
0
)
N
=
ift
.
DiagonalOperator
(
ift
.
Field
.
full
(
data_domain
,
mock_signal
.
var
()
/
signal_to_noise
))
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
# Wiener filter
j
=
R_harmonic
.
adjoint_times
(
N
.
inverse_times
(
data
))
ctrl
=
ift
.
GradientNormController
(
verbose
=
True
,
tol_abs_gradnorm
=
1e-4
/
nu
.
K
)
ctrl
=
ift
.
GradientNormController
(
verbose
=
True
,
tol_abs_gradnorm
=
1e-4
/
nu
.
K
/
(
nu
.
m
**
(
0.5
*
dimensionality
)))
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
)
inverter
=
ift
.
ConjugateGradient
(
controller
=
ctrl
)
wiener_curvature
=
ift
.
library
.
WienerFilterCurvature
(
S
=
S
,
N
=
N
,
R
=
R_harmonic
,
inverter
=
inverter
)
wiener_curvature
=
ift
.
InversionEnabler
(
wiener_curvature
,
inverter
)
m
=
wiener_curvature
.
inverse_times
(
j
)
m_s
=
fft
(
m
)
sspace2
=
ift
.
RGSpace
(
shape
,
distances
=
L
/
N_pixels
/
nu
.
m
)
sspace2
=
ift
.
RGSpace
(
shape
,
distances
=
L
/
N_pixels
/
nu
.
m
)
ift
.
plotting
.
plot
(
ift
.
Field
(
sspace2
,
mock_signal
.
real
.
val
)
/
nu
.
K
,
name
=
"mock_signal.pdf"
)
ift
.
plotting
.
plot
(
ift
.
Field
(
sspace2
,
val
=
data
.
val
.
real
.
reshape
(
signal_space
.
shape
))
/
nu
.
K
,
name
=
"data.pdf"
)
ift
.
plotting
.
plot
(
ift
.
Field
(
sspace2
,
m_s
.
real
.
val
)
/
nu
.
K
,
name
=
"map.pdf"
)
ift
.
plotting
.
plot
(
ift
.
Field
(
sspace2
,
mock_signal
.
real
.
val
)
/
nu
.
K
,
name
=
"mock_signal.pdf"
)
ift
.
plotting
.
plot
(
ift
.
Field
(
sspace2
,
val
=
data
.
val
.
real
.
reshape
(
signal_space
.
shape
))
/
nu
.
K
,
name
=
"data.pdf"
)
ift
.
plotting
.
plot
(
ift
.
Field
(
sspace2
,
m_s
.
real
.
val
)
/
nu
.
K
,
name
=
"map.pdf"
)
demos/wiener_filter_via_hamiltonian.py
View file @
011fe3fa
...
...
@@ -51,7 +51,7 @@ if __name__ == "__main__":
# Drawing a sample sh from the prior distribution in harmonic space
sp
=
ift
.
Field
(
p_space
,
val
=
p_spec
(
p_space
.
k_lengths
))
sh
=
sp
.
power_synthesize
(
real_signal
=
True
)
sh
=
ift
.
power_synthesize
(
sp
,
real_signal
=
True
)
ss
=
fft
.
adjoint_times
(
sh
)
# Choosing the measurement instrument
...
...
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