matrixForDataPoints

Evaluate terminated B-spline basis functions and optional derivatives.

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Declaration

 B = matrixForDataPoints(dataPoints, options)

Parameters

• dataPoints points at which to evaluate the splines
• options.knotPoints spline knot points
• options.S spline degree
• options.D (optional) number of spline derivatives to return, max(D)=S

Returns

• B array of size numel(dataPoints) x M x (D+1) where M = numel(knotPoints) - S - 1

Discussion

Use this to assemble a design matrix for interpolation, regression, or direct inspection of the basis functions.

For D=0, the returned matrix satisfies

\[B_{ij} = B_{j,S}(t_i;\tau), \qquad x(t_i) \approx \sum_{j=1}^{M} B_{ij}\,\xi_j.\]

When D > 0, slice B(:,:,d+1) stores the basis values for derivative order d, so B(:,:,d+1) * xi evaluates the dth derivative at dataPoints.

  B = BSpline.matrixForDataPoints(t, knotPoints=knotPoints, S=3);
  xi = B \ x;
  spline = BSpline(S=3, knotPoints=knotPoints, xi=xi);