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ift
IMAGINE
Commits
cc683044
Commit
cc683044
authored
Aug 27, 2017
by
Theo Steininger
Browse files
Implemented first version of OAS covariance estimator for ensemble likelihood.
parent
1d9e44ed
Changes
1
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Inline
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imagine/likelihoods/ensemble_likelihood/ensemble_likelihood.py
View file @
cc683044
...
...
@@ -2,6 +2,8 @@
import
numpy
as
np
from
nifty
import
DiagonalOperator
from
imagine.likelihoods.likelihood
import
Likelihood
from
imagine.create_ring_profile
import
create_ring_profile
...
...
@@ -24,18 +26,17 @@ class EnsembleLikelihood(Likelihood):
self
.
data_covariance_operator
,
self
.
profile
)
def
_process_simple_field
(
self
,
field
,
measured_data
,
def
_process_simple_field
(
self
,
observable
,
measured_data
,
data_covariance_operator
,
profile
):
# https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula#Generalization
# B = A^{-1} + U U^dagger
# A = data_covariance
# B^{-1} c = (A_inv -
# A_inv U (I_k + U^dagger A_inv U)^{-1} U^dagger A_inv) c
observable
=
field
k
=
observable
.
shape
[
0
]
n
=
observable
.
shape
[
1
]
A
=
data_covariance_operator
obs_val
=
observable
.
val
.
get_full_data
()
obs_mean
=
observable
.
ensemble_mean
().
get_full_data
()
...
...
@@ -45,8 +46,39 @@ class EnsembleLikelihood(Likelihood):
measured_data
=
measured_data
/
profile
u_val
=
obs_val
-
obs_mean
# compute quantities for OAS estimator
mu
=
np
.
vdot
(
u_val
,
u_val
)
/
n
alpha
=
0.
for
i
in
xrange
(
n
):
alpha
+=
np
.
sum
(
u_val
.
T
.
dot
(
u_val
[:,
i
])
**
2
)
numerator
=
alpha
+
mu
**
2
denominator
=
(
k
+
1
)
/
(
alpha
-
(
mu
**
2
)
/
n
)
if
denominator
==
0
:
rho
=
1
else
:
rho
=
np
.
min
(
1
,
numerator
/
denominator
)
# rescale U half/half
u_val
*=
np
.
sqrt
(
1
-
rho
)
U
=
observable
.
copy_empty
()
U
.
val
=
u_val
# we assume that data_covariance_operator is a DiagonalOperator
if
not
isinstance
(
data_covariance_operator
,
DiagonalOperator
):
raise
TypeError
(
"data_covariance_operator must be a NIFTY "
"DiagonalOperator."
)
A_bare_diagonal
=
data_covariance_operator
.
diagonal
(
bare
=
True
)
A_bare_diagonal
.
val
+=
rho
*
mu
A
=
DiagonalOperator
(
domain
=
data_covariance_operator
.
domain
,
diagonal
=
A_bare_diagonal
,
bare
=
True
,
copy
=
False
,
default_spaces
=
data_covariance_operator
.
default_spaces
)
a_u
=
A
.
inverse_times
(
U
,
spaces
=
1
)
# build middle-matrix (kxk)
...
...
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