Plot the eigenvalue spectrum of a diagnosed cone

Visualises the eigenvalue spectrum of the associated matrix \(M_n(C)\) as a signed bar chart. Positive eigenvalues are coloured blue; negative eigenvalues, which signal that the dispatcher must fall back to the decomposition method, are coloured red. A dashed reference line is drawn at zero.

Usage

# S3 method for class 'cone_diagnosis'
plot(x, type = "eigenvalues", ...)

Arguments

x

An object of class cone_diagnosis returned by diagnose_cone.

type

Character. Currently only "eigenvalues" is supported; future plot types will be added without breaking this argument.

...

Further arguments passed to barplot.

Value

NULL, invisibly. Called for the side effect of producing the plot.

Details

The eigenvalues of \(M_n(C)\) are the discriminant of method selection (Ribando 2006, Theorem 1.5; Fitisone & Zhou 2023, Theorem 3.3). When all eigenvalues are positive, the hypergeometric series converges and is the preferred backend; the appearance of any negative eigenvalue forces the decomposition route. The plot makes that diagnostic visible at a glance.

References

Ribando, J. M. (2006). Measuring solid angles beyond dimension three. Discrete & Computational Geometry, 36(3), 479-487. doi:10.1007/s00454-006-1253-4

Fitisone, A., & Zhou, Y. (2023). Solid angle measure of polyhedral cones. arXiv:2304.11102 (math.CO).

See also

diagnose_cone for the constructor; print.cone_diagnosis, summary.cone_diagnosis for the companion S3 methods; compute_solid_angle for the dispatcher whose method choice this plot informs.

Examples

if (FALSE) { # \dontrun{
# Positive-definite cone (orthant)
V <- diag(4)
plot(diagnose_cone(V))

# Non-positive-definite cone
V <- matrix(c(1, 0.9, 0.1,
              0, 0.5, 0.8,
              0, 0, 0.3), nrow = 3)
plot(diagnose_cone(V))
} # }