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<a name="Evaluation-of-B_002dspline-basis-function-derivatives"></a>
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Next: <a href="Working-with-the-Greville-abscissae.html#Working-with-the-Greville-abscissae" accesskey="n" rel="next">Working with the Greville abscissae</a>, Previous: <a href="Evaluation-of-B_002dspline-basis-functions.html#Evaluation-of-B_002dspline-basis-functions" accesskey="p" rel="previous">Evaluation of B-spline basis functions</a>, Up: <a href="Basis-Splines.html#Basis-Splines" accesskey="u" rel="up">Basis Splines</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Evaluation-of-B_002dspline-derivatives"></a>
<h3 class="section">40.5 Evaluation of B-spline derivatives</h3>
<a name="index-basis-splines_002c-derivatives"></a>

<dl>
<dt><a name="index-gsl_005fbspline_005fderiv_005feval"></a>Function: <em>int</em> <strong>gsl_bspline_deriv_eval</strong> <em>(const double <var>x</var>, const size_t <var>nderiv</var>, gsl_matrix * <var>dB</var>, gsl_bspline_workspace * <var>w</var>)</em></dt>
<dd><p>This function evaluates all B-spline basis function derivatives of orders
<em>0</em> through <em>nderiv</em> (inclusive) at the position <var>x</var>
and stores them in the matrix <var>dB</var>.  The <em>(i,j)</em>-th element of <var>dB</var>
is <em>d^jB_i(x)/dx^j</em>.  The matrix <var>dB</var> must be
of size <em>n = nbreak + k - 2</em> by <em>nderiv + 1</em>.
The value <em>n</em> may also be obtained
by calling <code>gsl_bspline_ncoeffs</code>.  Note that function evaluations
are included as the zeroth order derivatives in <var>dB</var>.
Computing all the basis function derivatives at once is more efficient
than computing them individually, due to the nature of the defining
recurrence relation.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fbspline_005fderiv_005feval_005fnonzero"></a>Function: <em>int</em> <strong>gsl_bspline_deriv_eval_nonzero</strong> <em>(const double <var>x</var>, const size_t <var>nderiv</var>, gsl_matrix * <var>dB</var>, size_t * <var>istart</var>, size_t * <var>iend</var>, gsl_bspline_workspace * <var>w</var>)</em></dt>
<dd><p>This function evaluates all potentially nonzero B-spline basis function
derivatives of orders <em>0</em> through <em>nderiv</em> (inclusive) at
the position <var>x</var> and stores them in the matrix <var>dB</var>.  The
<em>(i,j)</em>-th element of <var>dB</var> is <em>d^j/dx^j B_(istart+i)(x)</em>.  The last row
of <var>dB</var> contains <em>d^j/dx^j B_(iend)(x)</em>.  The matrix <var>dB</var> must be
of size <em>k</em> by at least <em>nderiv + 1</em>.  Note that function
evaluations are included as the zeroth order derivatives in <var>dB</var>.
By returning only the nonzero basis functions, this function allows
quantities involving linear combinations of the <em>B_i(x)</em> and
their derivatives to be computed without unnecessary terms.
</p></dd></dl>




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