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<title>GNU Scientific Library – Reference Manual: Interpolation Types</title>
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<a name="Interpolation-Types"></a>
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<p>
Next: <a href="Index-Look_002dup-and-Acceleration.html#Index-Look_002dup-and-Acceleration" accesskey="n" rel="next">Index Look-up and Acceleration</a>, Previous: <a href="Interpolation-Functions.html#Interpolation-Functions" accesskey="p" rel="previous">Interpolation Functions</a>, Up: <a href="Interpolation.html#Interpolation" accesskey="u" rel="up">Interpolation</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Interpolation-Types-1"></a>
<h3 class="section">27.3 Interpolation Types</h3>
<a name="index-gsl_005finterp_005ftype"></a>
<p>The interpolation library provides six interpolation types:
</p>
<dl>
<dt><a name="index-gsl_005finterp_005flinear"></a>Interpolation Type: <strong>gsl_interp_linear</strong></dt>
<dd><a name="index-linear-interpolation"></a>
<p>Linear interpolation. This interpolation method does not require any
additional memory.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005finterp_005fpolynomial"></a>Interpolation Type: <strong>gsl_interp_polynomial</strong></dt>
<dd><a name="index-polynomial-interpolation"></a>
<p>Polynomial interpolation. This method should only be used for
interpolating small numbers of points because polynomial interpolation
introduces large oscillations, even for well-behaved datasets. The
number of terms in the interpolating polynomial is equal to the number
of points.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005finterp_005fcspline"></a>Interpolation Type: <strong>gsl_interp_cspline</strong></dt>
<dd><a name="index-cubic-splines"></a>
<p>Cubic spline with natural boundary conditions. The resulting curve is
piecewise cubic on each interval, with matching first and second
derivatives at the supplied data-points. The second derivative is
chosen to be zero at the first point and last point.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005finterp_005fcspline_005fperiodic"></a>Interpolation Type: <strong>gsl_interp_cspline_periodic</strong></dt>
<dd><p>Cubic spline with periodic boundary conditions. The resulting curve
is piecewise cubic on each interval, with matching first and second
derivatives at the supplied data-points. The derivatives at the first
and last points are also matched. Note that the last point in the
data must have the same y-value as the first point, otherwise the
resulting periodic interpolation will have a discontinuity at the
boundary.
</p>
</dd></dl>
<dl>
<dt><a name="index-gsl_005finterp_005fakima"></a>Interpolation Type: <strong>gsl_interp_akima</strong></dt>
<dd><a name="index-Akima-splines"></a>
<p>Non-rounded Akima spline with natural boundary conditions. This method
uses the non-rounded corner algorithm of Wodicka.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005finterp_005fakima_005fperiodic"></a>Interpolation Type: <strong>gsl_interp_akima_periodic</strong></dt>
<dd><p>Non-rounded Akima spline with periodic boundary conditions. This method
uses the non-rounded corner algorithm of Wodicka.
</p></dd></dl>
<p>The following related functions are available:
</p>
<dl>
<dt><a name="index-gsl_005finterp_005fname"></a>Function: <em>const char *</em> <strong>gsl_interp_name</strong> <em>(const gsl_interp * <var>interp</var>)</em></dt>
<dd><p>This function returns the name of the interpolation type used by <var>interp</var>.
For example,
</p>
<div class="example">
<pre class="example">printf ("interp uses '%s' interpolation.\n",
gsl_interp_name (interp));
</pre></div>
<p>would print something like,
</p>
<div class="example">
<pre class="example">interp uses 'cspline' interpolation.
</pre></div>
</dd></dl>
<dl>
<dt><a name="index-gsl_005finterp_005fmin_005fsize"></a>Function: <em>unsigned int</em> <strong>gsl_interp_min_size</strong> <em>(const gsl_interp * <var>interp</var>)</em></dt>
<dt><a name="index-gsl_005finterp_005ftype_005fmin_005fsize"></a>Function: <em>unsigned int</em> <strong>gsl_interp_type_min_size</strong> <em>(const gsl_interp_type * <var>T</var>)</em></dt>
<dd><p>These functions return the minimum number of points required by the
interpolation object <var>interp</var> or interpolation type <var>T</var>. For
example, Akima spline interpolation requires a minimum of 5 points.
</p></dd></dl>
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