Replicate an areal graph across the levels of a factor (replicated CAR)

Build the block-diagonal Kronecker graph I_L (x) Q and the level-offset node index for a replicated areal field: one independent copy of the graph per level of a by factor, all sharing one precision. This is the graph-side counterpart to tulpa_bar_field_specs() – that helper expands the coefficient columns and is graph-agnostic, while replication needs the graph, so it is a sibling rather than a new argument. A downstream package composes the two (column expansion x replication) from the one implementation rather than re-deriving the Kronecker remap.

Usage

tulpa_bar_field_replicate(adjacency, node, by)

Arguments

adjacency

Symmetric adjacency matrix of the base graph ([n_node x n_node], dense or sparse).

node

Integer vector of 1-based graph-node indices, one per observation (the resolved bar right-hand side).

by

A vector of the same length as node giving each observation's replication level; coerced to a factor. With L distinct levels the field is replicated L times.

Value

A list:

adjacency

the [L*n_node x L*n_node] block-diagonal Kronecker adjacency I_L (x) Q (the base graph for L == 1).

index

integer vector, one per observation: the node index offset into its level's copy (node + (level - 1) * n_node).

n_levels

the number of replication levels L.

n_nodes

the base graph node count n_node.

levels

the factor levels of by, in replicate order.

See also

tulpa_bar_field_specs() for the coefficient-column expansion, spatial() for the inline areal field constructor whose by = argument this powers.

Examples

adj <- matrix(0, 4, 4)
for (i in 1:3) adj[i, i + 1] <- adj[i + 1, i] <- 1
node <- rep(1:4, times = 2)
lev  <- rep(c("a", "b"), each = 4)
rep_info <- tulpa_bar_field_replicate(adj, node, lev)
dim(rep_info$adjacency)   # 8 x 8 (I_2 (x) Q)
rep_info$index            # level b nodes offset by 4