Skip to content
GitLab
Projects
Groups
Snippets
/
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
Philipp Arras
whatisalikelihood
Commits
3e40b830
Commit
3e40b830
authored
Aug 24, 2018
by
Philipp Arras
Browse files
More changes
parent
7a6efed0
Pipeline
#35440
passed with stage
in 25 seconds
Changes
1
Pipelines
1
Hide whitespace changes
Inline
Sidebyside
main.tex
View file @
3e40b830
...
...
@@ 192,18 +192,18 @@ function:
\begin{align*}
R:
\mathbb
R
^{
s.shape
}
\to
\mathbb
R
^{
d.shape
}
,
\end{align*}
its gradient at the position
\texttt
{
s=position
}
is a linear map of the
following shape:
\footnote
{
There are various ways to think about derivatives and
gradients of
multidimensional functions. A different view on gradients would
be that at a
given point
$
s
=
s
_
0
$
the gradient is a matrix with
\texttt
{
s.size
}
columns and
\texttt
{
d.size
}
rows. Obviously, it is not
feasible to store such a matrix on a
computer due to its size. There we think
of this matrix in terms of a linear
map which maps an array of shape
\texttt
{
s.shape
}
to
an array of shape
\texttt
{
d
.shape
}
. This linear map shall be implemented on the computer in terms
of a function. Think of this map as a linear approximation to
\texttt
{
R
}
based
at
\texttt
{
s
\_
0
}
.
}
its gradient at the position
\texttt
{
s=position
}
is a linear map of the
following shape:
\footnote
{
There are various ways to think about derivatives and
gradients of
multidimensional functions. A different view on gradients would
be that at a
given point
$
s
=
\text
{
position
}
$
the gradient is a matrix with
\texttt
{
s.size
}
columns and
\texttt
{
d.size
}
rows. Obviously, it is not
feasible to store such a matrix on a
computer due to its size. There we think
of this matrix in terms of a linear map which maps
an array of shape
\texttt
{
s
.shape
}
to an array of shape
\texttt
{
d.shape
}
. This linear map shall
be implemented on the computer in terms of a function. Think of this map as a
linear approximation to
\texttt
{
R
}
based at
\texttt
{
position
}
.
}
\begin{align*}
\left
.
\frac
{
dR
}{
ds
}
\right

_{
s=position
}
= R':
\mathbb
R
^{
s.shape
}
\to
\mathbb
R
^{
d.shape
}
\left
.
\frac
{
dR
}{
ds
}
\right

_{
s=
\text
{
position
}
}
= R':
\mathbb
R
^{
s.shape
}
\to
\mathbb
R
^{
d.shape
}
\end{align*}
What needs to be implemented is a function
\texttt
{
R
\_
prime(position, s0)
}
which
takes the arguments
\texttt
{
position
}
(which is an array of shape
\texttt
{
s.shape
}
...
...
@@ 315,8 +315,4 @@ Why is this already sufficient?
R
^
\dagger
$
. All in all, we need an implementation for
$
R
$
and
$
R
^
\dagger
$
.
\end{itemize}
% \section*{Bibliography test}
% RESOLVE was first presented in \cite{Resolve2016}.
% \printbibliography
\end{document}
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment