knotPointsForDataPoints

Construct a terminated knot sequence from sample locations.

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Declaration

 knotPoints = knotPointsForDataPoints(dataPoints, options)

Parameters

• dataPoints observation times (N)
• options.S (optional) spline degree
• options.splineDOF (optional) approximate target number of splines

Returns

• knotPoints vector of knot point locations

Discussion

Use this helper to choose a knot sequence directly from sample locations before interpolation or least-squares fitting.

The implementation sorts the sample locations, optionally subsamples them to target splineDOF, constructs pseudo-sites on that reduced grid, then repeats the first and last knot values S+1 times so the spline basis is terminated at the interval endpoints.

When splineDOF is supplied, the current implementation chooses the sample stride as

\[\Delta n = \left\lceil \frac{N}{\max(\mathrm{splineDOF}, S+1)} \right\rceil,\]

where \(N = \mathrm{numel}(t)\).

To recover the old dataDOF=d behavior, convert it to splineDOF = max(S+1, ceil(numel(t)/d)):

  oldDataDOF = 3;
  S = 3;
  splineDOF = max(S+1, ceil(numel(t)/oldDataDOF));
  knotPoints = BSpline.knotPointsForDataPoints(t, S=S, splineDOF=splineDOF);

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