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<title>Evaluation of B-spline basis function derivatives - GNU Scientific Library -- Reference Manual</title>
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<a name="Evaluation-of-B-spline-basis-function-derivatives"></a>
<a name="Evaluation-of-B_002dspline-basis-function-derivatives"></a>
Next: <a rel="next" accesskey="n" href="Obtaining-Greville-abscissae-for-B_002dspline-basis-functions.html">Obtaining Greville abscissae for B-spline basis functions</a>,
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<h3 class="section">39.5 Evaluation of B-spline derivatives</h3>
<p><a name="index-basis-splines_002c-derivatives-2608"></a>
<div class="defun">
— Function: int <b>gsl_bspline_deriv_eval</b> (<var>const double x, const size_t nderiv, gsl_matrix * dB, gsl_bspline_workspace * w, gsl_bspline_deriv_workspace * dw</var>)<var><a name="index-gsl_005fbspline_005fderiv_005feval-2609"></a></var><br>
<blockquote><p>This function evaluates all B-spline basis function derivatives of orders
0 through nderiv (inclusive) at the position <var>x</var>
and stores them in the matrix <var>dB</var>. The (i,j)-th element of <var>dB</var>
is d^jB_i(x)/dx^j. The matrix <var>dB</var> must be
of size n = nbreak + k - 2 by nderiv + 1.
The value n 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></blockquote></div>
<div class="defun">
— Function: int <b>gsl_bspline_deriv_eval_nonzero</b> (<var>const double x, const size_t nderiv, gsl_matrix * dB, size_t * istart, size_t * iend, gsl_bspline_workspace * w, gsl_bspline_deriv_workspace * dw</var>)<var><a name="index-gsl_005fbspline_005fderiv_005feval_005fnonzero-2610"></a></var><br>
<blockquote><p>This function evaluates all potentially nonzero B-spline basis function
derivatives of orders 0 through nderiv (inclusive) at
the position <var>x</var> and stores them in the matrix <var>dB</var>. The
(i,j)-th element of <var>dB</var> is <!-- {$d^jB_{(istart+i)}(x)/dx^j$} -->
d^j/dx^j B_(istart+i)(x). The last row
of <var>dB</var> contains <!-- {$d^jB_{iend}(x)/dx^j$} -->
d^j/dx^j B_(iend)(x). The matrix <var>dB</var> must be
of size k by at least nderiv + 1. 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 B_i(x) and
their derivatives to be computed without unnecessary terms.
</p></blockquote></div>
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