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  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

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man/eng/elementary/eval_cshep2d.xml
 
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<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?> 
 
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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
 
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<MAN>
 
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  <LANGUAGE>eng</LANGUAGE>
 
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  <TITLE>eval_cshep2d</TITLE>
 
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  <TYPE>Scilab Function</TYPE>
 
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  <DATE>February 2004</DATE>
 
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  <SHORT_DESCRIPTION name="eval_cshep2d">bidimensional cubic shepard interpolation evaluation</SHORT_DESCRIPTION>
 
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  <CALLING_SEQUENCE>
 
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  <CALLING_SEQUENCE_ITEM>[zp [,dzpdx, dzpdy [,d2zpdxx,d2zpdxy,d2zpdyy]]] = eval_cshep2d(xp, yp, tl_coef)</CALLING_SEQUENCE_ITEM>
 
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  </CALLING_SEQUENCE>
 
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  <PARAM>
 
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    <PARAM_INDENT>
 
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     <PARAM_ITEM>
 
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        <PARAM_NAME>xp, yp</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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         <SP>: two real vectors (or matrices) of the same size</SP>
 
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        </PARAM_DESCRIPTION> 
 
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     </PARAM_ITEM>
 
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     <PARAM_ITEM>
 
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        <PARAM_NAME>tl_coef</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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         <SP>: a tlist scilab structure (of type cshep2d) defining a cubic Shepard interpolation function
 
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               (named <VERB>S</VERB> in the following)</SP>
 
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        </PARAM_DESCRIPTION> 
 
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     </PARAM_ITEM>
 
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     <PARAM_ITEM>
 
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        <PARAM_NAME>zp</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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         <SP>: vector (or matrix) of the same size than <VERB>xp</VERB> and  <VERB>yp</VERB>, 
 
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               evaluation of the interpolant <VERB>S</VERB> at these points</SP>
 
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        </PARAM_DESCRIPTION> 
 
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     </PARAM_ITEM>
 
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     <PARAM_ITEM>
 
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        <PARAM_NAME>dzpdx,dzpdy</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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         <SP>: vectors (or matrices) of the same size than <VERB>xp</VERB> and  <VERB>yp</VERB>, evaluation
 
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               of the first derivatives of <VERB>S</VERB> at these points</SP>
 
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        </PARAM_DESCRIPTION> 
 
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     </PARAM_ITEM>
 
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     <PARAM_ITEM>
 
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        <PARAM_NAME>d2zpdxx,d2zpdxy,d2zpdyy</PARAM_NAME>
 
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        <PARAM_DESCRIPTION>
 
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         <SP>: vectors (or matrices) of the same size than <VERB>xp</VERB> and  <VERB>yp</VERB>, evaluation of the
 
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               second derivatives of <VERB>S</VERB> at these points</SP>
 
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        </PARAM_DESCRIPTION> 
 
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     </PARAM_ITEM>
 
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   </PARAM_INDENT>
 
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  </PARAM>
 
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  <DESCRIPTION>
 
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    <P>
 
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    This is the evaluation routine for cubic Shepard interpolation function computed with
 
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    <LINK>cshep2d</LINK>, that is :
 
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    </P>
 
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        <VERBATIM><![CDATA[
 
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      zp(i) = S(xp(i),yp(i))   
 
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      dzpdx(i) = dS/dx(xp(i),yp(i))
 
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      dzpdy(i) = dS/dy(xp(i),yp(i))  
 
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      d2zpdxx(i) = d2S/dx2(xp(i),yp(i))
 
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      d2zpdxy(i) = d2S/dxdy(xp(i),yp(i))  
 
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      d2zpdyy(i) = d2S/dy2(xp(i),yp(i))
 
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         ]]></VERBATIM>
 
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    </DESCRIPTION>
 
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    <SECTION label="Remark">
 
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    <P>
 
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    The interpolant <EM>S</EM> is C2 (twice continuously differentiable) but is also extended by 
 
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    zero for <EM>(x,y)</EM> far enough the interpolation points. This leads to a discontinuity
 
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    in a region far outside the interpolation points, and so, is not cumbersome in practice (in a 
 
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    general manner, evaluation outside interpolation points (i.e. extrapolation) leads to very 
 
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    inacurate results).
 
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    </P>
 
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    </SECTION>
 
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  <EXAMPLE><![CDATA[
 
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// see example section of cshep2d
 
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// this example shows the behavior far from the interpolation points ...
 
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deff("z=f(x,y)","z = 1+ 50*(x.*(1-x).*y.*(1-y)).^2")
 
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x = linspace(0,1,10);
 
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[X,Y] = ndgrid(x,x);
 
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X = X(:); Y = Y(:); Z = f(X,Y);
 
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S = cshep2d([X Y Z]);
 
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// evaluation inside and outside the square [0,1]x[0,1]
 
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m = 40;
 
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xx = linspace(-1.5,0.5,m);
 
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[xp,yp] = ndgrid(xx,xx);
 
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zp = eval_cshep2d(xp,yp,S);
 
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// compute facet (to draw one color for extrapolation region
 
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// and another one for the interpolation region)
 
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[xf,yf,zf] = genfac3d(xx,xx,zp);
 
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color = 2*ones(1,size(zf,2));
 
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// indices corresponding to facet in the interpolation region
 
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ind=find( mean(xf,"r")>0 & mean(xf,"r")<1 & mean(yf,"r")>0 & mean(yf,"r")<1 );
 
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color(ind)=3;
 
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xbasc();
 
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plot3d(xf,yf,list(zf,color), flag=[2 6 4])
 
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legends(["extrapolation region","interpolation region"],[2 3],1)
 
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xselect()
 
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 ]]></EXAMPLE>
 
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  <SEE_ALSO>
 
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    <SEE_ALSO_ITEM>
 
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      <LINK>cshep2d</LINK>
 
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    </SEE_ALSO_ITEM>
 
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  </SEE_ALSO>
 
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  <AUTHORS>
 
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     <AUTHORS_ITEM> Robert J. Renka</AUTHORS_ITEM>
 
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     <AUTHORS_ITEM> B. Pincon (scilab interface)</AUTHORS_ITEM>
 
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  </AUTHORS>
 
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</MAN>