TensorSpline

Create a tensor-product spline from canonical solved state.

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Declaration

 self = TensorSpline(options)

Parameters

• options.S spline degree scalar or vector with one entry per dimension
• options.knotAxes ordered SplineAxis array defining the tensor-product basis
• options.xi tensor-product coefficient array or vector
• options.xMean optional additive output offset
• options.xStd optional multiplicative output scale

Returns

• self TensorSpline instance

Discussion

Use this low-level constructor when you already have the spline degree, knot-axis objects, and coefficient state. For ordinary numeric knot-vector construction, use TensorSpline.fromKnotPoints(...).

The stored spline has the tensor-product form

\[f(x_1,\ldots,x_d) = x_{\mathrm{Mean}} + x_{\mathrm{Std}} \sum_{j_1,\ldots,j_d} \xi_{j_1,\ldots,j_d} \prod_{k=1}^{d} B_{j_k,S_k}(x_k;\tau_k).\]

  spline = TensorSpline(S=[3 3], knotAxes=SplineAxis.arrayFromVectors(knotPoints), xi=xi);
  [Xq,Yq] = ndgrid(linspace(0,1,40), linspace(0,1,40));
  values = spline(Xq, Yq);