matrixForPointMatrix

Evaluate the tensor-product basis matrix and optional derivatives.

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Declaration

 B = matrixForPointMatrix(pointMatrix, options)

Parameters

• pointMatrix query locations as a point matrix
• options.knotPoints knot vector in 1-D or cell array of knot vectors
• options.S spline degree scalar or vector with one entry per dimension
• options.D derivative order per dimension

Returns

• B basis matrix with one row per query point

Discussion

Use this to assemble a tensor-product design matrix for interpolation, regression, or basis inspection.

If pointMatrix has rows x_i, then row i of the returned matrix is the Kronecker product of the one-dimensional basis rows evaluated at x_i. In other words,

\[\mathbf{B}_{i,:} = B^{(1)}(x_{i,1}) \otimes \cdots \otimes B^{(d)}(x_{i,d}),\]

where each factor is the one-dimensional basis row in one coordinate direction, optionally replaced by its derivative row.

  [Xq, Yq] = ndgrid(xq, yq);
  B = TensorSpline.matrixForPointMatrix([Xq(:), Yq(:)], knotPoints=knotPoints, S=[3 3]);
  values = B * spline.xi(:);