Pseudo-Mode Splitting Index

Computes the pseudo-mode splitting index of each pair of adjacent modes.

Usage

measurePMSI(modes, denominator)

Arguments

modes: Finite numeric matrix, samples by modes, with at least one column. Attributes other than dim do not reach the outputs.
denominator: "homogeneous", the sum of the squared norms of the pair, or "regularized", which adds the $10^{-8}$ of the UPEMD definition, an absolute scale absent from the homogeneous form. No default; emd 0.8.1 has only the regularized form.

Details

For each pair of adjacent columns, $$\mathrm{PMSI}(c_i, c_{i+1}) = \max\left\{\frac{\langle c_i, c_{i+1} \rangle}{\|c_i\|_2^2 + \|c_{i+1}\|_2^2}, 0\right\},$$ with $10^{-8}$ added to the denominator under "regularized".

Value

Numeric vector with one value per pair of adjacent modes, of length one less than the number of columns.

Conditions

A pair of adjacent modes with zero energy under "homogeneous" stops the function with an error of class xemdZeroEnergy.

Examples

Time <- seq_len(1000) / 1000
Tones <- cbind(cos(2 * pi * 2 * Time), 0.25 * cos(2 * pi * 24 * Time),
               0.0625 * cos(2 * pi * 288 * Time))
Mixed <- cbind(rowSums(Tones), Tones)
measurePMSI(Mixed, denominator = "homogeneous")
#> [1] 0.4839319 0.0000000 0.0000000
measurePMSI(Mixed, denominator = "regularized")
#> [1] 0.4839319 0.0000000 0.0000000