```
## Procrustes
U <- randortho(5) # random orthogonal matrix
P <- procrustes(U, eye(5))
## Kabsch
P <- matrix(c(0, 1, 0, 0, 1, 1, 0, 1,
0, 0, 1, 0, 1, 0, 1, 1,
0, 0, 0, 1, 0, 1, 1, 1), nrow = 3, ncol = 8, byrow = TRUE)
R <- c(1, 1, 1)
phi <- pi/4
U <- matrix(c(1, 0, 0,
0, cos(phi), -sin(phi),
0, sin(phi), cos(phi)), nrow = 3, ncol = 3, byrow = TRUE)
Q <- U %*% P + R
K <- kabsch(P, Q)
# K$R == R and K$U %*% P + c(K$R) == Q
```

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