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 ... ... @@ -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 multi-dimensional 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 multi-dimensional 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}
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