choclo.point.kernel_nne

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choclo.point.kernel_nne#

choclo.point.kernel_nne(easting_p, northing_p, upward_p, easting_q, northing_q, upward_q, distance)[source]#

Third derivative of the inverse of the distance along north-north-east.

This is equivalent to the derivatives along north-east-north and east-north-north.

Important

The coordinates of the two points must be in Cartesian coordinates and have the same units.

Parameters:
easting_p, northing_p, upward_pfloat

Easting, northing and upward coordinates of point p.

easting_q, northing_q, upward_qfloat

Easting, northing and upward coordinates of point q.

distancefloat

Euclidean distance between points p and q.

Returns:
kernelfloat

Value of the kernel function.

Notes

Given two points p=(xp,yp,zp) and q=(xq,yq,zq) defined in a Cartesian coordinate system, compute the following kernel function:

kyyx(p,q)=kyxy=kxyy=3yp2xp(1pq2)=3(xpxq)pq2515(ypyq)2(xpxq)pq27

where 2 refer to the L2 norm (the Euclidean distance between p and q).