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ift
NIFTy
Commits
bb413b40
Commit
bb413b40
authored
Jan 15, 2019
by
Martin Reinecke
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second round of fixes
parent
86891afb
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1
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16 additions
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17 deletions
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-17
nifty5/operators/energy_operators.py
nifty5/operators/energy_operators.py
+16
-17
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nifty5/operators/energy_operators.py
View file @
bb413b40
...
...
@@ -27,7 +27,7 @@ from .simple_linear_operators import VdotOperator
class
EnergyOperator
(
Operator
):
"""
An a
bstract class from which
"""
A
bstract class from which
other specific EnergyOperator subclasses are derived.
An EnergyOperator has a scalar domain as target domain.
...
...
@@ -50,7 +50,7 @@ class SquaredNormOperator(EnergyOperator):
E = SquaredNormOperator() represents a field energy E that is the L2 norm
of a field f:
E(f) = f^dagger f
:math:`
E(f) = f^
\
dagger f
`
"""
def
__init__
(
self
,
domain
):
self
.
_domain
=
domain
...
...
@@ -65,7 +65,7 @@ class SquaredNormOperator(EnergyOperator):
class
QuadraticFormOperator
(
EnergyOperator
):
"""
Class for quadratic field energies.
"""Class for quadratic field energies.
Parameters
----------
...
...
@@ -97,7 +97,7 @@ class QuadraticFormOperator(EnergyOperator):
class
GaussianEnergy
(
EnergyOperator
):
"""
Class for energies of fields with Gaussian probability distribution.
"""Class for energies of fields with Gaussian probability distribution.
Attributes
----------
...
...
@@ -116,6 +116,7 @@ class GaussianEnergy(EnergyOperator):
an information energy for a Gaussian distribution with mean m and covariance D.
"""
def
__init__
(
self
,
mean
=
None
,
covariance
=
None
,
domain
=
None
):
self
.
_domain
=
None
if
mean
is
not
None
:
...
...
@@ -164,7 +165,7 @@ class PoissonianEnergy(EnergyOperator):
-----
E = GaussianEnergy(d) represents (up to an f-independent term log(d!))
E(f) = -\log Poisson(d|f) = sum
(f)
- d^\dagger \log(f),
:math:`
E(f) = -\log Poisson(d|f) =
\
sum
f
- d^\dagger \log(f)
`
,
where f is a Field in data space with the expectation values for
the counts.
...
...
@@ -244,12 +245,11 @@ class Hamiltonian(EnergyOperator):
Parameters
----------
lh : EnergyOperator
a likelihood energy
a likelihood energy
ic_samp : IterationController
is passed to SamplingEnabler to draw Gaussian distributed samples
with covariance = metric of Hamiltonian
(= Hessian without terms that generate negative eigenvalues)
default = None
is passed to SamplingEnabler to draw Gaussian distributed samples
with covariance = metric of Hamiltonian
(= Hessian without terms that generate negative eigenvalues)
Notes
-----
...
...
@@ -308,9 +308,8 @@ class SampledKullbachLeiblerDivergence(EnergyOperator):
The KL divergence between those should then be optimized for m. It is
KL(Q,P) = int Df Q(f) log Q(f)/P(f)
= < log Q(f) >_Q(f) - < log P(f) >_Q(f)
= const + < H(f) >_G(f-m,D)
:math:`KL(Q,P) = \int Df Q(f) \log Q(f)/P(f)
\\
= \left< \log Q(f)
\\
right>_Q(f) - < \log P(f) >_Q(f) = const + < H(f) >_G(f-m,D)`
in essence the information Hamiltonian averaged over a Gaussian distribution
centered on the mean m.
...
...
@@ -322,15 +321,15 @@ class SampledKullbachLeiblerDivergence(EnergyOperator):
----------
h: Hamiltonian
the Hamiltonian/energy to be averaged
res_samples : iterable Field
set of residual sample points to be added to mean field
for approximate estimation of the KL
res_samples : iterable
of
Field
s
set of residual sample points to be added to mean field
for approximate estimation of the KL
Notes
-----
KL = SampledKullbachLeiblerDivergence(H, samples) represents
KL(m) = sum_i H(m+v_i) / N,
:math:`
KL(m) =
\
sum_i H(m+v_i) / N
`
,
where v_i are the residual samples, N is their number, and m is the mean field
around which the samples are drawn.
...
...
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