choclo.point.kernel_pot#

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

The inverse of the distance between the two points

Important

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

Parameters:

• easting_p (float) – Easting coordinate of point $\mathbf{p}$.

• northing_p (float) – Northing coordinate of point $\mathbf{p}$.

• upward_p (float) – Upward coordinate of point $\mathbf{p}$.

• easting_q (float) – Easting coordinate of point $\mathbf{q}$.

• northing_q (float) – Northing coordinate of point $\mathbf{q}$.

• upward_q (float) – Upward coordinate of point $\mathbf{q}$.

• distance (float) – Euclidean distance between points $\mathbf{p}$ and $\mathbf{q}$.

Returns:

kernel (float) – Value of the kernel function.

Notes

Given two points $\mathbf{p}=(x_p,y_p,z_p)$ and $\mathbf{q}=(x_q,y_q,z_q)$ defined in a Cartesian coordinate system, compute the following kernel function:

$$k_V(\mathbf{p},\mathbf{q})=\frac{1}{\Vert \mathbf{p}-\mathbf{q}{\Vert }_2}$$

where $\Vert \cdot {\Vert }_2$ refer to the $L_2$ norm (the Euclidean distance between $\mathbf{p}$ and $\mathbf{q}$).