--- trunk/doc/diderot.tex 2010/01/16 17:32:12 20 +++ trunk/doc/diderot.tex 2010/01/16 18:16:32 21 @@ -36,16 +36,22 @@ \begin{figure}[t] \begin{displaymath} \begin{array}{rclr} - \rho & ::= & $\ldots$ & \text{NRRD types} \\[1em] + \rho & ::= & $\ldots$ & \text{NRRD scalar types} \\[1em] \iota & ::= & \TYbool & \text{booleans} \\ & \mid & \TYint & \text{integers} \\[1em] - \theta & ::= & \TYtensor{o}{d} & \text{tensors of order $o$ and dimension $d$} \\[1em] + % \mu for memory, where images of rawtensors will live (or on disk) + \mu & ::= & \TYrawten{o}{d}{\rho} & \begin{minipage}[l]{3in}\begin{flushright} + tensors of order $o$ and dimension $d$,\\with coefficients of type $\rho$ + \end{flushright}\end{minipage}\\[1em] + \theta & ::= & \TYtensor{o}{d} & \begin{minipage}[l]{3in}\begin{flushright} + tensors of order $o$ and dimension $d$,\\with real coefficients + \end{flushright}\end{minipage}\\[1em] \tau & ::= & \iota \\ & \mid & \theta \\ & \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\ - & \mid & \TYimage{d}{\rho} & \text{image of dimension $d$ and $\rho$ elements}\\ + & \mid & \TYimage{d}{\mu} & \text{$d$-dimension image of $\mu$ values}\\ & \mid & \TYkern{k} & \text{convolution kernel with $k$ derivatives} \\ - & \mid & \TYfield{k}{d}{\theta} & \text{$d$-dimension field of $\theta$ values and $k$ derivatives} \\ + & \mid & \TYfield{k}{d}{\theta} & \text{$d$-dimension field of $\theta$ values with $k$ derivatives} \\ \end{array}% \end{displaymath}% where $o\in\Nat$ is the tensor order, $d,n,m\in\SET{2,3}$ are dimensions, @@ -111,8 +117,8 @@ \noindent{}Creation from an image: \begin{displaymath} - \BinopTy{\OPsample}{\TYkern{k}}{\TYimage{d}{\rho}}{\TYfield{k}{d}{\theta}} - \qquad\text{where $\theta$ is the real conversion of $\rho$.} + \BinopTy{\OPconvolve}{\TYkern{k}}{\TYimage{d}{\mu}}{\TYfield{k}{d}{\theta}} + \qquad\text{where $\theta$ is the real conversion of $\mu$.} \end{displaymath}% \noindent{}Scalar multiplication: @@ -128,9 +134,18 @@ \BinopTy{{/}}{\TYfield{k}{d}{\theta}}{\TYreal}{\TYfield{k}{d}{\theta}} \end{displaymath}% +\noindent{}Negation: +\begin{displaymath} + \UnopTy{-}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}} +\end{displaymath}% + \noindent{}Addition: \begin{displaymath} + \begin{array}{c} + \BinopTy{{\odot}}{\TYfield{k}{d}{\theta}}{\theta}{\TYfield{k}{d}{\theta}} \\ + \BinopTy{{\odot}}{\theta}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}} \\ \BinopTy{{\odot}}{\TYfield{k_1}{d}{\theta}}{\TYfield{k_2}{d}{\theta}}{\TYfield{\min(k_1,k_2)}{d}{\theta}} + \end{array}% \qquad\text{for $\odot\in\SET{{+},{-}}$} \end{displaymath}% @@ -145,12 +160,4 @@ \BinopTy{@}{\TYfield{k}{d}{\theta}}{\TYvec{d}}{\theta} \end{displaymath}% -\noindent{}Tensor arithmetic: -\begin{displaymath} - \begin{array}{c} - \BinopTy{{\odot}}{\TYfield{k}{d}{\tau}}{\tau}{\TYfield{k}{d}{\tau}} \\ - \BinopTy{{\odot}}{\tau}{\TYfield{k}{d}{\tau}}{\TYfield{k}{d}{\tau}} - \end{array} \qquad\text{for $\odot\in\SET{{+},{-}}$} -\end{displaymath}% - \end{document}
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The output has ended thus: tau}} - \end{array} \qquad\text{for $\odot\in\SET{{+},{-}}$} -\end{displaymath}% - \end{document}