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[diderot] Diff of /trunk/doc/diderot.tex
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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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