object Kernel

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  6. def computeKernelMatrix[D](xs: Seq[Point[D]], k: MatrixValuedPDKernel[D]): DenseMatrix[Double]
  7. def computeKernelVectorFor[D](x: Point[D], xs: IndexedSeq[Point[D]], k: MatrixValuedPDKernel[D]): DenseMatrix[Double]

    for every domain point x in the list, we compute the kernel vector kx = (k(x, x1), ...

    for every domain point x in the list, we compute the kernel vector kx = (k(x, x1), ... k(x, xm)) since the kernel is matrix valued, kx is actually a matrix

    !! Hack - We currently return a double matrix, with the only reason that matrix multiplication (further down) is faster (breeze implementation detail). This should be replaced at some point

  8. def computeNystromApproximation[D, Value](k: MatrixValuedPDKernel[D], sampler: Sampler[D])(implicit arg0: NDSpace[D], vectorizer: Vectorizer[Value]): KLBasis[D, Value]

    Computes the leading eigenvalues / eigenfunctions of the integral operator corresponding to kernel k.

    Computes the leading eigenvalues / eigenfunctions of the integral operator corresponding to kernel k. The number of leading eigenfunctions is at most n, where n is the number of points sampled. If the eigenvalues are decaying quickly, it can be much smaller than n.

    k

    (matrix-valued) kernel

    sampler

    A point sampler, which determines the points that are used to compute the approximation.

    returns

    The leading eigenvalue / eigenfunction pairs

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