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<title>Numerical Differentiation functions - GNU Scientific Library -- Reference Manual</title>
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<a name="Numerical-Differentiation-functions"></a>
Next: <a rel="next" accesskey="n" href="Numerical-Differentiation-Examples.html">Numerical Differentiation Examples</a>,
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<h3 class="section">28.1 Functions</h3>
<div class="defun">
— Function: int <b>gsl_deriv_central</b> (<var>const gsl_function * f, double x, double h, double * result, double * abserr</var>)<var><a name="index-gsl_005fderiv_005fcentral-2254"></a></var><br>
<blockquote><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>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 x-h, x-h/2, x,
x+h/2, x+h, with an error estimate taken from the difference
between the 5-point rule and the corresponding 3-point rule x-h,
x, x+h. Note that the value of the function at x
does not contribute to the derivative calculation, so only 4-points are
actually used.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_deriv_forward</b> (<var>const gsl_function * f, double x, double h, double * result, double * abserr</var>)<var><a name="index-gsl_005fderiv_005fforward-2255"></a></var><br>
<blockquote><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 f(x) has a
discontinuity at <var>x</var>, or is undefined for values less than <var>x</var>.
<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 x is computed using an
“open” 4-point rule for equally spaced abscissae at x+h/4,
x+h/2, x+3h/4, x+h, with an error estimate taken
from the difference between the 4-point rule and the corresponding
2-point rule x+h/2, x+h.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_deriv_backward</b> (<var>const gsl_function * f, double x, double h, double * result, double * abserr</var>)<var><a name="index-gsl_005fderiv_005fbackward-2256"></a></var><br>
<blockquote><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 f(x)
has a discontinuity at <var>x</var>, or is undefined for values greater than
<var>x</var>.
<p>This function is equivalent to calling <code>gsl_deriv_forward</code> with a
negative step-size.
</p></blockquote></div>
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