Axial Cross Moments

Axial Cross Moments

Usage

axial_cross_moments(x, nu)

Arguments

x

object of class "Vec3", "Line", "Ray", or "Plane", where the rows are the observations and the columns are the coordinates.

nu

Three Eigenvectors \(\nu\) (object of class Spherical). See ot_eigen() for details

Value

3 x 3 matrix

Details

Matrix of unit vectors x for Eigenvectors \nu is $$m_{ij} = \frac{1}{n} \sum_{k=1}^{n} \left( \mathbf{x}_k \cdot \mathbf{\nu}_i \right)^2 \left( \mathbf{x}_k \cdot \mathbf{\nu}_j \right)^2 , \qquad i, j = 1, 2, 3 $$

Examples

x <- example_planes
axial_cross_moments(x, ot_eigen(x)$vectors)
#>            [,1]       [,2]       [,3]
#> [1,] 0.48997614 0.09593684 0.04384632
#> [2,] 0.09593684 0.17415304 0.01803057
#> [3,] 0.04384632 0.01803057 0.02024336