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Extension.m

Usage : Extension(sig)
   
Input : sig a \( n\times n\times 3 \) array corresponding to
   
  the \( (x,x) \), \( (y,y) \) and \( (x,y) \) diffusion coefficient
   
  \( \frac{d}{dx}\textrm{sig}(x,y,1)\frac{d}{dx}+\frac{d}{dy}\textrm{sig}(x,y,2)\frac{d}{dy} \)
   
  \( +\frac{d}{dx}\textrm{sig}(x,y,3)\frac{d}{dy}+\frac{d}{dy}\textrm{sig}(x,y,3)\frac{d}{dx} \)


The output is a \( (n+2)\times (n+2)\times 3 \) array, which is an extension of sig according to the following rule



\begin{displaymath}
\begin{array}{ccccccccccc}
& & & & & f & e & f & g & h & g\...
... & & & & & & & \\
& & & & & f & e & f & g & h & g
\end{array}\end{displaymath}


This corresponds to a locally periodic extension.


See also HaarSmoothing (Paragraph A.7), MWSmoothing (Paragraph A.9) and PeriodicExtension (Paragraph A.10).



Yves Capdeboscq 2002-01-15