Class xlifepp::KernelExpansion#

class KernelExpansion#

Collaboration diagram for xlifepp::KernelExpansion:

Kernel expansion according to singularity exponents:

• ${\displaystyle G(x,y)=\sum _i{F}_i(x,y)/|x-y{|}^{{{\alpha }_0}_i}}$

• ${\displaystyle gra{d}_{x}G(x,y)=\sum _{i}Gx{F}_i(x,y).(x-y)/|x-y{|}^{{{\alpha }_x}_i}}$

• ${\displaystyle gra{d}_{y}G(x,y)=\sum _{i}Gy{F}_i(x,y).(x-y)/|x-y{|}^{{{\alpha }_y}_i}}$

• ${\displaystyle gra{d}_{xy}G(x,y)=\sum _{i}Gxy{F}_i(x,y).(x-y)(x-y{)}^T/|x-y{|}^{{{\alpha }_{xy}}_i}+\sum _i{Gxy{F}_{diag}}_i(x,y)/|x-y{|}^{{{{\alpha }_{xy}}_{diag}}_i}\ast Identity}$

with the convention $1/|x-y{|}^{{{\alpha }_x}_i}=Log(|x-y|)$ when ${{\alpha }_x}_i=-1$

Public Members

std::vector<int_t> alpha#

singularity exponents

Function F_i#

coefficients of F expansion

Function gradxF_i#

coefficients of gradx F expansion

Function gradxyF_i#

coefficients of gradxy F expansion

Function gradyF_i#

coefficients of grady F expansion

number_t nbterms#

number of terms in expansion