proc_crr {BLSM}

Procrustean corresponding positions

Description

Given a set of starting coordinates, the function returns the Procrustean Transform of the initial points that minimizes the sum of squared positional difference from a set of reference coordinates. The (Euclidean) distances between a candidate configuration and the reference are evaluated by considering the couples of corresponding points.

The reference configuration must be centered at the origin.

Usage

proc_crr(Z, Z0)

Arguments

Z

set of initial coordinates to be transformed

Z0

set of reference coordinates centered at the origin

Value

Set of coordinates minimizing the distance between the initial configuration and the reference one

Examples

# Create configuration and center it at the origin
pos_ref = matrix(runif(20), ncol=2)
pos_ref = t(t(pos_ref)-colMeans(pos_ref))

# Create a new configuration by adding a perturbation to the previous one
pos = pos_ref + matrix(rnorm(20, mean=1, sd=0.1), ncol=2)

# Compute the Procrustean Transform and inspect the results
proc_pos = proc_crr(pos, pos_ref)
plot(pos_ref, col="blue", pch=20, xlim=c(-1,3), ylim=c(-1,3))
points(pos, col="red", pch=20)
points(proc_pos, col="purple", pch=20)