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<HTML>
<HEAD>
<TITLE>Interpolation</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<P><font size="+3" color="green"><B>Interpolation</B></font></P>
<P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>
vout = INTERPOLATE(x,y,xout,'SPLINE')<br />
vout = INTERPOLATE(x,y,xout,'LINEAR')<BR />
vout = INTERPOLATE(x,y,xout,'LAGRANGE')<BR />
vout = INTERPOLATE(x,y,xout,'FC')<br />
mout = SPLINTERP(x,y,n)</CODE>
</TD></TR>
</table></p>
<p>
The <CODE>INTERPOLATE</CODE> function interpolates
the data contained in vector <CODE>x</CODE>, the
independent variable, and vector <CODE>y</CODE>, the
dependent variable. <CODE>x</CODE> must be
strictly monotonically increasing. The interpolant locations are given in
vector <CODE>xout</CODE>. The
<CODE>INTERPOLATE</CODE> function will return the
interpolated values as a vector with the same length as
<CODE>xout</CODE>. The algorithm that is employed
depends on the keyword that is used.</P>
<p>
The <CODE>SPLINTERP</CODE> function interpolates
the data contained in vector <CODE>x</CODE>, the
independent variable, and vector <CODE>y</CODE>, the
dependent variable. There are no restrictions on
<CODE>x</CODE>, it doesn't even need to be
increasing. The number of interpolant locations is given in scalar
<CODE>n</CODE>, which must be greater than <code>1</code>.
The output of the <CODE>SPLINTERP</CODE> function is a matrix
with <CODE>n</CODE> rows and <code>2</code> columns. The first
column will contain the output locations and the second column the interpolated values
at those locations.</p>
<P>
An interpolated curve will always pass through the original data points. If
it is not important that the curve pass through the original data, use the
<CODE><a href="smooth.htm">SMOOTH</a></CODE> function, unless your independent
variable is not monotonically increasing. In that case, use the <CODE>
<a href="smooth.htm">SPLSMOOTH</a></CODE> function.</P>
<p>
<a href="interpolateS01.htm"><font size="+1" color="olive">Linear interpolation</font></a><br />
<a href="interpolateS02.htm"><font size="+1" color="olive">Spline interpolation</font></a><br />
<a href="interpolateS03.htm"><font size="+1" color="olive">Lagrange interpolation</font></a><br />
<a href="interpolateS04.htm"><font size="+1" color="olive">Fritch-Carlson interpolation</font></a><br />
<a href="interpolateS05.htm"><font size="+1" color="olive">SPLINTERP function</font></a><br />
<a href="interpolateS06.htm"><font size="+1" color="olive">2D interpolation</font></a>
</P>
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</HTML>
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