edge.repulsive.stage: Optimize one edge-isometric repulsive unfolding stage

Description

`edge.repulsive.stage()` performs one gradient-descent stage for the objective evaluated by `edge.repulsive.state()`. It uses Armijo backtracking, optionally recenters coordinates after each proposal, and returns the final coordinates plus a per-iteration trace.

Usage

edge.repulsive.stage(
  coords,
  edges,
  edge.lengths,
  edge.weights = NULL,
  lambda = 0,
  edge.family = c("quadratic", "upper_barrier"),
  eps.plus = 0.35,
  beta = 0,
  pair.index = NULL,
  pair.weights = NULL,
  repulsion.family = c("log", "inverse_power"),
  repulsion.delta = 0.001,
  repulsion.power = 1,
  max.iter = 80L,
  initial.step = 0.02,
  step.shrink = 0.5,
  armijo = 1e-04,
  min.step = 1e-08,
  grad.tol = 1e-07,
  recenter = TRUE,
  distance.eps = 1e-10,
  return.frames = FALSE,
  engine = c("cpp", "R")
)

Value

A list with `coords`, final `state`, a data-frame `trace`, and, when requested, a list of coordinate `frames`.

Arguments

coords: Numeric `n` by `dim` coordinate matrix.
edges: Integer or numeric matrix with two columns containing 1-based graph edge endpoints.
edge.lengths: Numeric vector of target edge lengths, parallel to `edges`.
edge.weights: Optional non-negative edge weights. Defaults to one.
lambda: Repulsion strength.
edge.family: Edge potential family, either `"quadratic"` or `"upper_barrier"`.
eps.plus: Upper-barrier slack parameter.
beta: Upper-barrier strength. When `beta <= 0`, the edge potential is quadratic.
pair.index: Optional two-column matrix of 1-based vertex pairs for the repulsion term. If `NULL` and `lambda > 0`, all unordered pairs are used.
pair.weights: Optional pair weights, parallel to `pair.index`.
repulsion.family: Repulsion potential family, either `"log"` or `"inverse_power"`.
repulsion.delta: Small positive softening parameter for pair distances.
repulsion.power: Power used by the `"inverse_power"` repulsion.
max.iter: Maximum number of gradient-descent iterations.
initial.step: Initial gradient step size.
step.shrink: Multiplicative shrink factor used by backtracking.
armijo: Armijo sufficient-decrease coefficient.
min.step: Minimum allowable step before the stage stops.
grad.tol: Gradient-norm stopping tolerance.
recenter: Logical; whether to recenter coordinates after each proposal.
distance.eps: Small positive distance floor used in derivatives.
return.frames: Logical; whether to return accepted coordinate frames. Frame 0 is the starting coordinate matrix and later frames are accepted updates.
engine: Backend engine. `"cpp"` is the default; `"R"` uses the reference implementation.