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<title>GNU Scientific Library – Reference Manual: Evaluation of B-spline basis functions</title>
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<a name="Evaluation-of-B_002dspline-basis-functions"></a>
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Next: <a href="Evaluation-of-B_002dspline-basis-function-derivatives.html#Evaluation-of-B_002dspline-basis-function-derivatives" accesskey="n" rel="next">Evaluation of B-spline basis function derivatives</a>, Previous: <a href="Constructing-the-knots-vector.html#Constructing-the-knots-vector" accesskey="p" rel="previous">Constructing the knots vector</a>, Up: <a href="Basis-Splines.html#Basis-Splines" accesskey="u" rel="up">Basis Splines</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Evaluation-of-B_002dsplines"></a>
<h3 class="section">39.4 Evaluation of B-splines</h3>
<a name="index-basis-splines_002c-evaluation"></a>
<dl>
<dt><a name="index-gsl_005fbspline_005feval"></a>Function: <em>int</em> <strong>gsl_bspline_eval</strong> <em>(const double <var>x</var>, gsl_vector * <var>B</var>, gsl_bspline_workspace * <var>w</var>)</em></dt>
<dd><p>This function evaluates all B-spline basis functions at the position
<var>x</var> and stores them in the vector <var>B</var>, so that the <em>i</em>-th element
is <em>B_i(x)</em>. The vector <var>B</var> must be of length
<em>n = nbreak + k - 2</em>. This value may also be obtained by calling
<code>gsl_bspline_ncoeffs</code>.
Computing all the basis functions 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_005feval_005fnonzero"></a>Function: <em>int</em> <strong>gsl_bspline_eval_nonzero</strong> <em>(const double <var>x</var>, gsl_vector * <var>Bk</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
functions at the position <var>x</var> and stores them in the vector <var>Bk</var>, so
that the <em>i</em>-th element is <em>B_(istart+i)(x)</em>.
The last element of <var>Bk</var> is <em>B_(iend)(x)</em>. The vector <var>Bk</var> must be
of length <em>k</em>. By returning only the nonzero basis functions,
this function
allows quantities involving linear combinations of the <em>B_i(x)</em>
to be computed without unnecessary terms
(such linear combinations occur, for example,
when evaluating an interpolated function).
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fbspline_005fncoeffs"></a>Function: <em>size_t</em> <strong>gsl_bspline_ncoeffs</strong> <em>(gsl_bspline_workspace * <var>w</var>)</em></dt>
<dd><p>This function returns the number of B-spline coefficients given by
<em>n = nbreak + k - 2</em>.
</p></dd></dl>
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