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Philipp Arras
whatisalikelihood
Commits
d7a4ae80
Commit
d7a4ae80
authored
Aug 26, 2018
by
Philipp Arras
Browse files
Merge branch 'mr_small_corrections' into 'master'
small tweaks See merge request
!1
parents
69a7c1cd
fdc98c53
Pipeline
#35492
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in 1 minute and 41 seconds
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main.tex
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d7a4ae80
...
@@ 15,7 +15,7 @@
...
@@ 15,7 +15,7 @@
\definecolor
{
mygray
}{
rgb
}{
0.5,0.5,0.5
}
\definecolor
{
mygray
}{
rgb
}{
0.5,0.5,0.5
}
\definecolor
{
mymauve
}{
rgb
}{
0.58,0,0.82
}
\definecolor
{
mymauve
}{
rgb
}{
0.58,0,0.82
}
\lstset
{
\lstset
{
backgroundcolor=
\color
{
white
}
,
% choose the background color; you must add \usepackage{color} or \usepackage{xcolor}; should come as last argument
backgroundcolor=
\color
{
white
}
,
% choose the background color; you must add \usepackage{color} or \usepackage{xcolor}; should come as last argument
basicstyle=
\footnotesize
,
% the size of the fonts that are used for the code
basicstyle=
\footnotesize
,
% the size of the fonts that are used for the code
breakatwhitespace=false,
% sets if automatic breaks should only happen at whitespace
breakatwhitespace=false,
% sets if automatic breaks should only happen at whitespace
...
@@ 126,7 +126,7 @@ another object is needed:
...
@@ 126,7 +126,7 @@ another object is needed:
\begin{itemize}
\begin{itemize}
\item
$
\langle
\mathcal
H'
\mathcal
H'
^
\dagger
\rangle
_{
\mathcal
P
(
ds
)
}$
.
\item
$
\langle
\mathcal
H'
\mathcal
H'
^
\dagger
\rangle
_{
\mathcal
P
(
ds
)
}$
.
\end{itemize}
\end{itemize}
Note
,
that for Gaussian, Poissonian and Bernoulli likelihoods this term doesn't
Note that for Gaussian, Poissonian and Bernoulli likelihoods this term doesn't
need to be calculated and implemented because NIFTy computes it automatically.
need to be calculated and implemented because NIFTy computes it automatically.
That's it. The rest of this paper explains what these formulae mean and how to
That's it. The rest of this paper explains what these formulae mean and how to
...
@@ 137,7 +137,7 @@ If the likelihood is Gaussian
...
@@ 137,7 +137,7 @@ If the likelihood is Gaussian
\begin{align*}
\begin{align*}
\mathcal
H(ds)
\propto
(dR(s))
^
\dagger
N
^{
1
}
(dR(s))
\mathcal
H(ds)
\propto
(dR(s))
^
\dagger
N
^{
1
}
(dR(s))
\end{align*}
\end{align*}
or Poissonian
or Poissonian
\begin{align*}
\begin{align*}
\mathcal
H(ds)
\propto

\log
(R(s))
^
\dagger
d+
\sum
_
i R(s)
_
i,
\mathcal
H(ds)
\propto

\log
(R(s))
^
\dagger
d+
\sum
_
i R(s)
_
i,
\end{align*}
\end{align*}
...
@@ 150,7 +150,7 @@ NIFTy needs:
...
@@ 150,7 +150,7 @@ NIFTy needs:
\section*
{
Even more specific
}
\section*
{
Even more specific
}
Since NIFTy is implemented in
p
ython and is based on numpy let us be as specific
Since NIFTy is implemented in
P
ython and is based on numpy let us be as specific
as possible and talk about numpy arrays. In the end,
$
s
$
and
$
d
$
will be numpy
as possible and talk about numpy arrays. In the end,
$
s
$
and
$
d
$
will be numpy
arrays.
arrays.
...
@@ 183,7 +183,7 @@ import numpy as np
...
@@ 183,7 +183,7 @@ import numpy as np
# Store the shape of s in 'shp'.
# Store the shape of s in 'shp'.
# Store the function which implements the response in 'R'.
# Store the function which implements the response in 'R'.
response
_
out = R(np.ones(shp))
response
_
out = R(np.ones(shp))
if response
_
out.shape == d.shape:
if response
_
out.shape == d.shape:
print('Yay!')
print('Yay!')
else:
else:
...
@@ 270,19 +270,20 @@ linear operator like the \texttt{FieldZeroPadder}, copy it and adopt it to your
...
@@ 270,19 +270,20 @@ linear operator like the \texttt{FieldZeroPadder}, copy it and adopt it to your
needs. The method
\texttt
{
apply()
}
takes an instance of
\texttt
{
Field
}
(which is
needs. The method
\texttt
{
apply()
}
takes an instance of
\texttt
{
Field
}
(which is
esentially a numpy array accompanied by a domain) and returns one as well.
esentially a numpy array accompanied by a domain) and returns one as well.
Some tip
p
s exclusively for you:
Some tips exclusively for you:
\begin{itemize}
\begin{itemize}
\item
Please have a look at the method
\texttt
{
weight()
}
of
\texttt
{
Field
}
. With
\item
Please have a look at the method
\texttt
{
weight()
}
of
\texttt
{
Field
}
. With
it, you can easily multiply the field values with or divide by the volume of
it, you can easily multiply the field values with or divide by the volume of
each pixel.
each pixel.
\item
The methods
\texttt
{
from
\_
global
\_
data()
}
and
\texttt
{
to
\_
global
\_
data()
}
\item
The methods
\texttt
{
from
\_
global
\_
data()
}
and
\texttt
{
to
\_
global
\_
data()
}
convert a Field to a numpy array and vice versa.
convert a Field to a numpy array and vice versa.
\item
Be aware of the fact that NIFTy fields are immu
a
table. As soon as you
\item
Be aware of the fact that NIFTy fields are immutable. As soon as you
pass a numpy array into a NIFTy field with
\texttt
{
from
\_
global
\_
data()
}
the
pass a numpy array into a NIFTy field with
\texttt
{
from
\_
global
\_
data()
}
,
the
\enquote
{
lock
}
flag will be set and the numpy array is immu
a
table
\enquote
{
lock
}
flag will be set and the numpy array is immutable
afterwards.
\texttt
{
to
\_
global
\_
data()
}
returns an object reference to this
afterwards.
\texttt
{
to
\_
global
\_
data()
}
returns an object reference to this
numpy array which is locked and cannot be modified. If you want to modify
numpy array which is locked and cannot be modified. If you want to modify
it, you may want to copy it with
\texttt
{
to
\_
global
\_
data().copy()
}
.
it, you may want to obtain an unlocked copy via
\texttt
{
to
\_
global
\_
data
\_
rw()
}
.
\end{itemize}
\end{itemize}
The point is: You need to fiddle around until the following test passes:
The point is: You need to fiddle around until the following test passes:
...
...
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