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Computes the least-squares scalar \(\alpha\) that aligns estimated distances to true distances: $$\alpha^* = \frac{\sum_{i<j} \hat D_{ij}D_{ij}} {\sum_{i<j} \hat D_{ij}^2}.$$

Usage

isometry.scale(D.estimated, D.true, true.tol = sqrt(.Machine$double.eps))

Arguments

D.estimated

Estimated distance matrix or dist object.

D.true

Ground-truth distance matrix or dist object.

true.tol

Non-negative tolerance. Pairs with true distance less than or equal to this value are excluded from relative metrics.

Value

Numeric scalar calibration scale.

Examples

D <- as.matrix(dist(1:4))
isometry.scale(2 * D, D)
#> [1] 0.5