Principal component (geodesic) analysis in the tangent space.

Principal component (geodesic) analysis in the tangent space.

Usage

# S3 method for class 'Vec3'
prcomp(x, center = geodesic_mean(x), n = 0L)

# S3 method for class 'Ray'
prcomp(x, center = geodesic_mean(x), n = 0L)

# S3 method for class 'Line'
prcomp(x, center = geodesic_mean(x), n = 0L)

# S3 method for class 'Plane'
prcomp(x, center = geodesic_mean(x), n = 0L)

# S3 method for class 'Pair'
prcomp(x, center = geodesic_mean(x), n = 0L, group = NULL)

Arguments

x

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

center

A spherical object. Typically the geodesic mean of the x.

n

real number (integer, 0 or >= 3). The number of points to return on each of the four geodesics through the center.

group

Symmetry group of x. See symmetry_group() for details If NULL, the group will be automatically picked based on the class of x.

Value

A list consisting of

rotation

3x3 rotation matrix

magnitudes

2D real vector, non-negative. Magnitudes are analogous to sample standard deviations. They are in decreasing order and quantify how dispersed the data are in those two directions.

directions

2x2 real matrix, whose columns are unit-length vectors. The corresponding directions to the magnitudes

pcsFromRay

function to convert rays to 2-dimensional vectors

rayFromPCs

function to convert 2-dimensional vectors to rays

curves

list of two lists of (2 n + 1) rays, only if n >= 1

tangents

Tangents from directions and rotation

If x is a "Pair" object the list only contains magnitudes, directions and curves (if n>=1).

Details

Appropriate only if the data set is tightly concentrated about the center.

Examples

res <- prcomp(example_lines, n = 10)

stereoplot(sub = paste("SD1:", round(res$magnitudes[1], 2), "| SD2:", round(res$magnitudes[2], 2)))
points(example_lines, pch = 16, cex = .8)
invisible(lapply(res$curves, stereo_lines, col = "red", lwd = 1.5))