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<?xml version="1.0" encoding="UTF-8"?>
<refentry version="5.0-subset Scilab" xml:id="interp2d" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns5="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:db="http://docbook.org/ns/docbook">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>interp2d</refname>
<refpurpose>bicubic spline (2d) evaluation function</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[zp[,dzpdx,dzpdy[,d2zpdxx,d2zpdxy,d2zpdyy]]]=interp2d(xp,yp,x,y,C [,out_mode])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>xp, yp</term>
<listitem>
<para>real vectors or matrices of same size</para>
</listitem>
</varlistentry>
<varlistentry>
<term>x,y,C</term>
<listitem>
<para>real vectors defining a bicubic spline or sub-spline function
(called <literal>s</literal> in the following)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>out_mode</term>
<listitem>
<para>(optional) string defining the evaluation of
<literal>s</literal> outside [x(1),x(nx)]x[y(1),y(ny)]</para>
</listitem>
</varlistentry>
<varlistentry>
<term>zp</term>
<listitem>
<para>vector or matrix of same format than <literal>xp</literal> and
<literal>yp</literal>, elementwise evaluation of
<literal>s</literal> on these points.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>dzpdx, dzpdy</term>
<listitem>
<para>vectors (or matrices) of same format than
<literal>xp</literal> and <literal>yp</literal>, elementwise
evaluation of the first derivatives of <literal>s</literal> on these
points.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>d2zpdxx, d2zpdxy, d2zpdyy</term>
<listitem>
<para>vectors (or matrices) of same format than
<literal>xp</literal> and <literal>yp</literal>, elementwise
evaluation of the second derivatives of <literal>s</literal> on
these points.</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>Given three vectors <literal>(x,y,C)</literal> defining a bicubic
spline or sub-spline function (see <link linkend="splin2d">splin2d</link>)
this function evaluates <emphasis>s</emphasis> (and <emphasis>ds/dx,
ds/dy, d2s/dxx, d2s/dxy, d2s/dyy</emphasis> if needed) at
<emphasis>(xp(i),yp(i))</emphasis> :</para>
<informalequation>
<mediaobject>
<imageobject>
<imagedata fileref="../mml/interp2_equation_1.mml" />
</imageobject>
</mediaobject>
</informalequation>
<para>The <literal>out_mode</literal> parameter defines the evaluation
rule for extrapolation, i.e. for <emphasis>(xp(i),yp(i)) not in
[x(1),x(nx)]x[y(1),y(ny)]</emphasis>:</para>
<variablelist>
<varlistentry>
<term>"by_zero"</term>
<listitem>
<para>an extrapolation by zero is done</para>
</listitem>
</varlistentry>
<varlistentry>
<term>"by_nan"</term>
<listitem>
<para>extrapolation by Nan</para>
</listitem>
</varlistentry>
<varlistentry>
<term>"C0"</term>
<listitem>
<para>the extrapolation is defined as follows :</para>
<programlisting role = ""><![CDATA[
s(x,y) = s(proj(x,y)) where proj(x,y) is nearest point
of [x(1),x(nx)]x[y(1),y(ny)] from (x,y)
]]></programlisting>
</listitem>
</varlistentry>
<varlistentry>
<term>"natural"</term>
<listitem>
<para>the extrapolation is done by using the nearest bicubic-patch
from (x,y).</para>
</listitem>
</varlistentry>
<varlistentry>
<term>"periodic"</term>
<listitem>
<para> <literal>s</literal> is extended by periodicity.</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
// see the examples of splin2d
// this example shows some different extrapolation features
// interpolation of cos(x)cos(y)
n = 7; // a n x n interpolation grid
x = linspace(0,2*%pi,n); y = x;
z = cos(x')*cos(y);
C = splin2d(x, y, z, "periodic");
// now evaluate on a bigger domain than [0,2pi]x [0,2pi]
m = 80; // discretisation parameter of the evaluation grid
xx = linspace(-0.5*%pi,2.5*%pi,m); yy = xx;
[XX,YY] = ndgrid(xx,yy);
zz1 = interp2d(XX,YY, x, y, C, "C0");
zz2 = interp2d(XX,YY, x, y, C, "by_zero");
zz3 = interp2d(XX,YY, x, y, C, "periodic");
zz4 = interp2d(XX,YY, x, y, C, "natural");
clf()
subplot(2,2,1)
plot3d(xx, yy, zz1, flag=[2 6 4])
xtitle("extrapolation with the C0 outmode")
subplot(2,2,2)
plot3d(xx, yy, zz2, flag=[2 6 4])
xtitle("extrapolation with the by_zero outmode")
subplot(2,2,3)
plot3d(xx, yy, zz3, flag=[2 6 4])
xtitle("extrapolation with the periodic outmode")
subplot(2,2,4)
plot3d(xx, yy, zz4, flag=[2 6 4])
xtitle("extrapolation with the natural outmode")
xselect()
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member><link linkend="splin2d">splin2d</link></member>
</simplelist>
</refsection>
<refsection>
<title>Authors</title>
<para>B. Pincon</para>
</refsection>
</refentry>
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