smoothingMatrix

Return the smoothing matrix that maps observations to fitted values.

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Declaration

 S = smoothingMatrix(self)

Parameters

• self ConstrainedSpline instance

Returns

• S smoothing matrix

Discussion

Use this to inspect the linear action of the final weighted fit on the observed data.

For an unconstrained fit with diagonal weights \(W\), this matrix is the familiar linear smoother

\[S = \mathbf{B}(\mathbf{B}^{T} W \mathbf{B})^{-1}\mathbf{B}^{T}W.\]

When the fit uses a full observation covariance, the implementation uses the same linear map but applies the covariance through the stored solve object rather than explicitly forming an inverse.

  S = spline.smoothingMatrix();
  valuesFit = S * spline.dataValues;