integratedSplineState

Return the canonical spline state of the zero-anchored antiderivative.

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Declaration

 [xiIntegrated,knotPointsIntegrated,SIntegrated] = integratedSplineState(xi, options)

Parameters

• xi spline coefficient vector or matrix with one spline per column
• options.knotPoints terminated knot sequence for the input spline basis
• options.S spline degree of the input coefficients
• options.xMean optional additive output offset shared by every column
• options.xStd optional multiplicative output scale shared by every column

Returns

• xiIntegrated antiderivative spline coefficient matrix with one extra row
• knotPointsIntegrated terminated knot sequence for the antiderivative spline
• SIntegrated spline degree of the antiderivative spline

Discussion

Use this expert utility when B-spline coefficients are already known and the exact antiderivative state should be computed without constructing a temporary BSpline object first.

For coefficient matrix xi, each column is integrated independently with the shared affine output normalization

\[f(t) = x_{\mathrm{Mean}} + x_{\mathrm{Std}} \sum_{j=1}^{M} \xi_j B_{j,S}(t;\tau),\]

producing the canonical antiderivative spline state

\[F(t) = \int_{\tau_1}^{t} f(s)\,ds.\]

  [xiInt, knotPointsInt, SInt] = BSpline.integratedSplineState( ...
      xi, knotPoints=knotPoints, S=3);
  intspline = BSpline(S=SInt, knotPoints=knotPointsInt, xi=xiInt);