Diff of /trunk/doc/diderot.tex

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	revision 20, Sat Jan 16 17:32:12 2010 UTC	revision 21, Sat Jan 16 18:16:32 2010 UTC
#	Line 36	Line 36
36	\begin{figure}[t]	\begin{figure}[t]
37	\begin{displaymath}	\begin{displaymath}
38	\begin{array}{rclr}	\begin{array}{rclr}
39	\rho  & ::= & $\ldots$ & \text{NRRD types} \\[1em]	\rho  & ::= & $\ldots$ & \text{NRRD scalar types} \\[1em]
40	\iota & ::= & \TYbool & \text{booleans} \\	\iota & ::= & \TYbool & \text{booleans} \\
41	& \mid & \TYint & \text{integers} \\[1em]	& \mid & \TYint & \text{integers} \\[1em]
42	\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)
43		\mu & ::= & \TYrawten{o}{d}{\rho} & \begin{minipage}[l]{3in}\begin{flushright}
44		tensors of order $o$ and dimension $d$,\\with coefficients of type $\rho$
45		\end{flushright}\end{minipage}\\[1em]
46		\theta & ::= & \TYtensor{o}{d} & \begin{minipage}[l]{3in}\begin{flushright}
47		tensors of order $o$ and dimension $d$,\\with real coefficients
48		\end{flushright}\end{minipage}\\[1em]
49	\tau & ::= & \iota \\	\tau & ::= & \iota \\
50	& \mid & \theta \\	& \mid & \theta \\
51	& \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\	& \mid & \TYmatrix{n}{m} & \text{$n\times{}m$ matrix} \\
52	& \mid & \TYimage{d}{\rho} & \text{image of dimension $d$ and $\rho$ elements}\\	& \mid & \TYimage{d}{\mu} & \text{$d$-dimension image of $\mu$ values}\\
53	& \mid & \TYkern{k} & \text{convolution kernel with $k$ derivatives} \\	& \mid & \TYkern{k} & \text{convolution kernel with $k$ derivatives} \\
54	& \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} \\
55	\end{array}%	\end{array}%
56	\end{displaymath}%	\end{displaymath}%
57	where $o\in\Nat$ is the tensor order, $d,n,m\in\SET{2,3}$ are dimensions,	where $o\in\Nat$ is the tensor order, $d,n,m\in\SET{2,3}$ are dimensions,
#	Line 111	Line 117
117
118	\noindent{}Creation from an image:	\noindent{}Creation from an image:
119	\begin{displaymath}	\begin{displaymath}
120	\BinopTy{\OPsample}{\TYkern{k}}{\TYimage{d}{\rho}}{\TYfield{k}{d}{\theta}}	\BinopTy{\OPconvolve}{\TYkern{k}}{\TYimage{d}{\mu}}{\TYfield{k}{d}{\theta}}
121	\qquad\text{where $\theta$ is the real conversion of $\rho$.}	\qquad\text{where $\theta$ is the real conversion of $\mu$.}
122	\end{displaymath}%	\end{displaymath}%
123
124	\noindent{}Scalar multiplication:	\noindent{}Scalar multiplication:
#	Line 128	Line 134
134	\BinopTy{{/}}{\TYfield{k}{d}{\theta}}{\TYreal}{\TYfield{k}{d}{\theta}}	\BinopTy{{/}}{\TYfield{k}{d}{\theta}}{\TYreal}{\TYfield{k}{d}{\theta}}
135	\end{displaymath}%	\end{displaymath}%
136
137		\noindent{}Negation:
138		\begin{displaymath}
139		\UnopTy{-}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}}
140		\end{displaymath}%
141
142	\noindent{}Addition:	\noindent{}Addition:
143	\begin{displaymath}	\begin{displaymath}
144		\begin{array}{c}
145		\BinopTy{{\odot}}{\TYfield{k}{d}{\theta}}{\theta}{\TYfield{k}{d}{\theta}} \\
146		\BinopTy{{\odot}}{\theta}{\TYfield{k}{d}{\theta}}{\TYfield{k}{d}{\theta}} \\
147	\BinopTy{{\odot}}{\TYfield{k_1}{d}{\theta}}{\TYfield{k_2}{d}{\theta}}{\TYfield{\min(k_1,k_2)}{d}{\theta}}	\BinopTy{{\odot}}{\TYfield{k_1}{d}{\theta}}{\TYfield{k_2}{d}{\theta}}{\TYfield{\min(k_1,k_2)}{d}{\theta}}
148		\end{array}%
149	\qquad\text{for $\odot\in\SET{{+},{-}}$}	\qquad\text{for $\odot\in\SET{{+},{-}}$}
150	\end{displaymath}%	\end{displaymath}%
151
#	Line 145	Line 160
160	\BinopTy{@}{\TYfield{k}{d}{\theta}}{\TYvec{d}}{\theta}	\BinopTy{@}{\TYfield{k}{d}{\theta}}{\TYvec{d}}{\theta}
161	\end{displaymath}%	\end{displaymath}%
162
	\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}%
163	\end{document}	\end{document}

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