Extract a sparse coupling / map operator from UOT dual potentials (CSC)

Given translation-invariant dual potentials (fbar,gbar), compute edge weights on a sparse cost graph in CSC form and return a `dgCMatrix`.

Usage

uot_extract_coupling_sparse_csc_cpp(
  col_ptr,
  row_idx,
  cost_csc,
  n_rows,
  n_cols,
  alpha,
  beta,
  fbar,
  gbar,
  epsilon,
  weight_type = 0L,
  delta = 1e-08,
  topk_col = 0L,
  threshold = 0
)

Arguments

col_ptr

Integer vector of length m+1 with CSC column offsets (0-based or 1-based accepted; if 1-based, it must start at 0 or 1 and be nondecreasing).

row_idx

Integer vector of length nnz giving 1-based row indices.

cost_csc

Numeric vector of length nnz aligned with `row_idx`.

n_rows

Number of source nodes.

n_cols

Number of target nodes.

alpha

Source masses (length n_rows).

beta

Target masses (length n_cols).

fbar

Translation-invariant source potential (length n_rows).

gbar

Translation-invariant target potential (length n_cols).

epsilon

Entropic regularization parameter (> 0).

weight_type

See above (0,1,2).

delta

Stabilizer for weight_type=0.

topk_col

Optional top-k pruning per column (0 keeps all).

threshold

Optional threshold pruning (<= 0 keeps all).

Value

A list with `coupling` (dgCMatrix) and `log_pi2` (length n_cols).

Details

Supported weight types: - weight_type = 0: map operator weights, w_ij / (pi2_j + delta) - weight_type = 1: conditional weights, w_ij / pi2_j (column-stochastic) - weight_type = 2: raw coupling weights, w_ij

Pruning is column-wise: - keep only weights >= threshold (after weight_type transform) - optionally keep only the topk_col largest weights per column