cumsum

Return the indefinite integral of a B-spline.

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Declaration

 intspline = cumsum(spline)

Parameters

• spline BSpline instance to integrate

Returns

• intspline BSpline representing the antiderivative

Discussion

Use this to construct an antiderivative spline that can be evaluated at arbitrary points after integration.

For coefficient vector \(\xi\), the integrated spline uses cumulative coefficients

\[\beta_0 = 0, \qquad \beta_j = \sum_{m=1}^{j} \xi_m \frac{\tau_{m+K} - \tau_m}{K}.\]

If the spline carries nontrivial xMean or xStd, the method first converts that affine output normalization into an equivalent coefficient representation before integrating.

  F = cumsum(spline);
  values = F(tQuery);