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ift
NIFTy
Commits
f3abedf5
Commit
f3abedf5
authored
Apr 20, 2018
by
Reimar H Leike
Browse files
added the krylov sampling method to library
parent
3a61c518
Pipeline
#27736
passed with stage
in 1 minute and 27 seconds
Changes
2
Pipelines
1
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nifty4/library/__init__.py
View file @
f3abedf5
...
...
@@ 5,3 +5,4 @@ from .nonlinear_power_energy import NonlinearPowerEnergy
from
.nonlinear_wiener_filter_energy
import
NonlinearWienerFilterEnergy
from
.poisson_energy
import
PoissonEnergy
from
.nonlinearities
import
Exponential
,
Linear
,
Tanh
,
PositiveTanh
from
.krylov_sampling
import
generate_krylov_samples
nifty4/library/krylov_sampling.py
0 → 100644
View file @
f3abedf5
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 20132018 MaxPlanckSociety
#
# NIFTy is being developed at the MaxPlanckInstitut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
from
numpy.random
import
randn
from
numpy
import
sqrt
from
..field
import
Field
def
generate_krylov_samples
(
D_inv
,
S
,
j
=
None
,
N_samps
=
1
,
N_iter
=
10
):
"""
Generates inverse samples from a curvature D
This algorithm iteratively generates samples from
a curvature D by applying conjugate gradient steps
and resampling the curvature in search direction.
Parameters

D_inv : EndomorphicOperator
The curvature which will be the inverse of the covarianc
of the generated samples
S : EndomorphicOperator (from which one can sample)
A prior covariance operator which is used to generate prior
samples that are then iteratively updated
j : Field, optional
A Field to which the inverse of D_inv is applied. The solution
of this matrix inversion problem is a side product of generating
the samples.
If not supplied, it is sampled from the prior.
N_samps : Int, optional
How many samples to generate. Default: 1
N_iter : Int, optional
How many iterations of the conjugate gradient to run. Default: 10
Returns

(solution, samples) : A tuple of a field 'solution' and a list of fields
'samples'. The first entry of the tuple is the solution x to
D_inv(x) = j
and the second entry are a list of samples from D_inv.inverse
"""
if
j
==
None
:
j
=
S
.
draw_sample
()
space
=
D_inv
.
domain
x
=
Field
.
zeros
(
space
)
r
=
j
.
copy
()
p
=
r
.
copy
()
d
=
p
.
vdot
(
D_inv
(
p
))
y
=
[]
for
i
in
range
(
N_samps
):
y
+=
[
S
.
draw_sample
()]
for
k
in
range
(
1
,
1
+
N_iter
):
gamma
=
r
.
vdot
(
r
)
/
d
if
gamma
==
0.
:
break
x
+=
gamma
*
p
for
i
in
range
(
N_samps
):
y
[
i
]
=
p
.
vdot
(
D_inv
(
y
[
i
]))
*
p
/
d
y
[
i
]
+=
randn
()
/
sqrt
(
d
)
*
p
r_new
=
r

gamma
*
D_inv
(
p
)
beta
=
r_new
.
vdot
(
r_new
)
/
(
r
.
vdot
(
r
))
r
=
r_new
p
=
r
+
beta
*
p
d
=
p
.
vdot
(
D_inv
(
p
))
if
d
==
0.
:
break
return
x
,
y
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