valueAtPoints

Evaluate the tensor spline or a mixed partial derivative.

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Declaration

 values = valueAtPoints(self,X1,...,Xn,options)

Parameters

• self TensorSpline instance
• X1,...,Xn matching-size query locations as one array per dimension
• options.D derivative order per dimension

Returns

• values spline values reshaped to match the query input

Discussion

This is the primary explicit evaluation method. Supply one matching-size query array per tensor dimension. Paired column vectors give pointwise queries, while matching ndgrid arrays give gridded evaluation over a tensor-product lattice.

For derivative order vector D = [D_1 ... D_d], this evaluates

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

with xMean added back only when all entries of D are zero.

  values = spline.valueAtPoints(xq, yq);
  dFdx = spline.valueAtPoints(xq, yq, D=[1 0]);
  [Xq,Yq] = ndgrid(linspace(-1,1,40), linspace(0,2,50));
  F = spline.valueAtPoints(Xq, Yq);