MinimumVarianceAnalysis

The main purpose of minimum or maximum variance analysis (MVA) is to find an estimator for the direction normal $\hat{𝐧}$ to one-dimensional structure, by minimisation of

$$ σ^2=\frac{1}{M} ∑_{m=1}^M | (𝐁^{(m)}-⟨𝐁⟩) · \hat{𝐧}|^2. $$

Quickstart

using Pkg; Pkg.add("MinimumVarianceAnalysis")
using MinimumVarianceAnalysis
using MinimumVarianceAnalysis: normal

Bl = cosd.(0:30:180)
Bm = sind.(0:30:180)
Bn = 0.1 .* ones(7)
B = hcat(Bl, Bm, Bn)

F = mva_eigen(B)
normal(F)          # minimum-variance direction for magnetic-field MVA
mva(B)             # rotate samples into variance frame

For electric-field maximum variance analysis, pass field = :E:

E = hcat(0.1 .* ones(7), 0.05 .* ones(7), cosd.(0:30:180))
F = mva_eigen(E; field = :E)
normal(F; field = :E)

Unitful, DynamicQuantities, FlexUnits, and DimensionalData inputs are supported:

using Unitful

F = mva_eigen(B .* u"nT")
F.values    # eigenvalues carry squared field units
F.vectors   # eigenvectors are dimensionless directions

See SPEDAS for more details. See SPEDAS validation for comparison with a Python implementation (pyspedas).

Documentation:

Reference

• Sonnerup, B. U. Ö., & Scheible, M. (1998). Minimum and maximum variance analysis. ISSI Scientific Reports Series, 1, 185–220.

Features and Roadmap

• Maximum Variance Analysis on Magnetic Field (MVAB)
  • Constraint $〈B₃〉 = 0$
• Maximum Variance Analysis on Electric Field (MVAE)
  • Transformation to/from moving frame of reference
• Minimum Variance Analysis on Mass Flux (MVAρv)
• Application to 2-D Structures

Notes

• Anisotropic fluctuations have been shown to lead to larger errors in normal determinations.

Status