Class xlifepp::KernelExpansion#
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class KernelExpansion#
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Kernel expansion according to singularity exponents:
\(\displaystyle G(x,y) = \sum_i F_i(x,y) / |x-y|^{{\alpha_0}_i}\)
\(\displaystyle grad_x G(x,y) = \sum_i GxF_i(x,y).(x-y) / |x-y|^{{\alpha_x}_i}\)
\(\displaystyle grad_y G(x,y) = \sum_i GyF_i(x,y).(x-y) / |x-y|^{{\alpha_y}_i}\)
\(\displaystyle grad_{xy} G(x,y) = \sum_i GxyF_i(x,y).(x-y)(x-y)^T / |x-y|^{{\alpha_{xy}}_i} + \sum_i {GxyF_{diag}}_i(x,y) / |x-y|^{{{\alpha_{xy}}_{diag}}_i} *Identity\)
with the convention \(1/|x-y|^{{\alpha_x}_i} = Log(|x-y|)\) when \({\alpha_x}_i = -1\)
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