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<a name="Numerical-Differentiation-functions"></a>
<div class="header">
<p>
Next: <a href="Numerical-Differentiation-Examples.html#Numerical-Differentiation-Examples" accesskey="n" rel="next">Numerical Differentiation Examples</a>, Up: <a href="Numerical-Differentiation.html#Numerical-Differentiation" accesskey="u" rel="up">Numerical Differentiation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Functions"></a>
<h3 class="section">29.1 Functions</h3>

<dl>
<dt><a name="index-gsl_005fderiv_005fcentral"></a>Function: <em>int</em> <strong>gsl_deriv_central</strong> <em>(const gsl_function * <var>f</var>, double <var>x</var>, double <var>h</var>, double * <var>result</var>, double * <var>abserr</var>)</em></dt>
<dd><p>This function computes the numerical derivative of the function <var>f</var>
at the point <var>x</var> using an adaptive central difference algorithm with
a step-size of <var>h</var>.   The derivative is returned in <var>result</var> and an
estimate of its absolute error is returned in <var>abserr</var>.
</p>
<p>The initial value of <var>h</var> is used to estimate an optimal step-size,
based on the scaling of the truncation error and round-off error in the
derivative calculation.  The derivative is computed using a 5-point rule
for equally spaced abscissae at <em>x-h</em>, <em>x-h/2</em>, <em>x</em>,
<em>x+h/2</em>, <em>x+h</em>, with an error estimate taken from the difference
between the 5-point rule and the corresponding 3-point rule <em>x-h</em>,
<em>x</em>, <em>x+h</em>.  Note that the value of the function at <em>x</em>
does not contribute to the derivative calculation, so only 4-points are
actually used.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fderiv_005fforward"></a>Function: <em>int</em> <strong>gsl_deriv_forward</strong> <em>(const gsl_function * <var>f</var>, double <var>x</var>, double <var>h</var>, double * <var>result</var>, double * <var>abserr</var>)</em></dt>
<dd><p>This function computes the numerical derivative of the function <var>f</var>
at the point <var>x</var> using an adaptive forward difference algorithm with
a step-size of <var>h</var>. The function is evaluated only at points greater
than <var>x</var>, and never at <var>x</var> itself.  The derivative is returned in
<var>result</var> and an estimate of its absolute error is returned in
<var>abserr</var>.  This function should be used if <em>f(x)</em> has a
discontinuity at <var>x</var>, or is undefined for values less than <var>x</var>.
</p>
<p>The initial value of <var>h</var> is used to estimate an optimal step-size,
based on the scaling of the truncation error and round-off error in the
derivative calculation.  The derivative at <em>x</em> is computed using an
&ldquo;open&rdquo; 4-point rule for equally spaced abscissae at <em>x+h/4</em>,
<em>x+h/2</em>, <em>x+3h/4</em>, <em>x+h</em>, with an error estimate taken
from the difference between the 4-point rule and the corresponding
2-point rule <em>x+h/2</em>, <em>x+h</em>. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fderiv_005fbackward"></a>Function: <em>int</em> <strong>gsl_deriv_backward</strong> <em>(const gsl_function * <var>f</var>, double <var>x</var>, double <var>h</var>, double * <var>result</var>, double * <var>abserr</var>)</em></dt>
<dd><p>This function computes the numerical derivative of the function <var>f</var>
at the point <var>x</var> using an adaptive backward difference algorithm
with a step-size of <var>h</var>. The function is evaluated only at points
less than <var>x</var>, and never at <var>x</var> itself.  The derivative is
returned in <var>result</var> and an estimate of its absolute error is
returned in <var>abserr</var>.  This function should be used if <em>f(x)</em>
has a discontinuity at <var>x</var>, or is undefined for values greater than
<var>x</var>.
</p>
<p>This function is equivalent to calling <code>gsl_deriv_forward</code> with a
negative step-size.
</p></dd></dl>

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<div class="header">
<p>
Next: <a href="Numerical-Differentiation-Examples.html#Numerical-Differentiation-Examples" accesskey="n" rel="next">Numerical Differentiation Examples</a>, Up: <a href="Numerical-Differentiation.html#Numerical-Differentiation" accesskey="u" rel="up">Numerical Differentiation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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