Construct a Graph Heat-Time Grid

Creates a positive heat-time grid from a "metric.graph.lowpass.basis" object.

Usage

metric.graph.heat.eta.grid(
  basis,
  rule = c("spectral_guarded", "w1_inverse_spectrum"),
  n.initial = 40L,
  include.zero = FALSE,
  truncation.tol = 1e-04,
  equilibrium.tol = 1e-04
)

Arguments

basis

A "metric.graph.lowpass.basis" object.

rule

Grid rule. "w1_inverse_spectrum" requires a complete basis and reproduces the W1 inverse-spectrum grid. "spectral_guarded" raises the lower endpoint for a truncated basis until the conservative omitted-mode attenuation bound is no larger than truncation.tol, and extends the upper endpoint until the slowest retained positive mode is attenuated to equilibrium.tol.

n.initial

Number of positive grid values.

include.zero

Logical. Include the exact no-smoothing endpoint.

truncation.tol

Positive tolerance smaller than one for the conservative omitted-mode attenuation bound.

equilibrium.tol

Positive tolerance smaller than one for the slowest positive retained mode at the upper endpoint.

Value

A numeric vector with grid-construction metadata stored as attributes.

Examples

adj <- list(2L, c(1L, 3L), c(2L, 4L), 3L)
lengths <- list(1, c(1, 1), c(1, 1), 1)
basis <- metric.graph.lowpass.basis(adj, lengths, n.eigenpairs = 4L,
                                    eigen.solver = "dense")
metric.graph.heat.eta.grid(basis, n.initial = 6L)
#> [1]  0.2928932  0.6496430  1.4409209  3.1959910  7.0887712 15.7230347
#> attr(,"rule")
#> [1] "spectral_guarded"
#> attr(,"eta.min")
#> [1] 0.2928932
#> attr(,"eta.max")
#> [1] 15.72303
#> attr(,"truncation.tol")
#> [1] 1e-04
#> attr(,"equilibrium.tol")
#> [1] 1e-04
#> attr(,"basis.complete")
#> [1] TRUE
#> attr(,"lambda.slow")
#> [1] 0.5857864
#> attr(,"lambda.cut")
#> [1] 3.414214