Functions to define mapping between a lattice and nodes — lattice2node • INLA

These functions define mapping in between two-dimensional indices on a lattice and the one-dimensional node representation used in inla.

inla.lattice2node.mapping(nrow, ncol)

inla.node2lattice.mapping(nrow, ncol)

inla.lattice2node(irow, icol, nrow, ncol)

inla.node2lattice(node, nrow, ncol)

inla.matrix2vector(a.matrix)

inla.vector2matrix(a.vector, nrow, ncol)

Arguments

nrow: Number of rows in the lattice.
ncol: Number of columns in the lattice.
irow: Lattice row index, between 1 and nrow
icol: Lattice column index, between 1 and ncol
node: The node index, between 1 and ncol*nrow
a.matrix: is a matrix to be mapped to a vector using internal representation defined by inla.lattice2node
a.vector: is a vector to be mapped into a matrix using the internal representation defined by inla.node2lattice

Value

inla.lattice2node.mapping returns the hole mapping as a matrix, and inla.node2lattice.mapping returns the hole mapping as list(irow=..., icol=...). inla.lattice2node and inla.node2lattice provide the mapping for a given set of lattice indices and nodes. inla.matrix2vector provide the mapped vector from a matrix, and inla.vector2matrix provide the inverse mapped matrix from vector.

Details

The mapping from node to lattice follows the default R behaviour (which is column based storage), and as.vector(A) and matrix(a, nrow, ncol) can be used instead of inla.matrix2vector and inla.vector2matrix.

See also

Author

Havard Rue hrue@r-inla.org

Examples


## write out the mapping using the two alternatives
nrow = 2
ncol = 3
mapping = inla.lattice2node.mapping(nrow,ncol)

for (i in 1:nrow){
    for(j in 1:ncol){
        print(paste("Alt.1: lattice index [", i,",", j,"] corresponds",
                    "to node [", mapping[i,j],"]", sep=""))
    }
}
#> [1] "Alt.1: lattice index [1,1] correspondsto node [1]"
#> [1] "Alt.1: lattice index [1,2] correspondsto node [3]"
#> [1] "Alt.1: lattice index [1,3] correspondsto node [5]"
#> [1] "Alt.1: lattice index [2,1] correspondsto node [2]"
#> [1] "Alt.1: lattice index [2,2] correspondsto node [4]"
#> [1] "Alt.1: lattice index [2,3] correspondsto node [6]"

for (i in 1:nrow){
    for(j in 1:ncol){
        print(paste("Alt.2: lattice index [", i,",", j,"] corresponds to node [",
                    inla.lattice2node(i,j,nrow,ncol), "]", sep=""))
    }
}
#> [1] "Alt.2: lattice index [1,1] corresponds to node [1]"
#> [1] "Alt.2: lattice index [1,2] corresponds to node [3]"
#> [1] "Alt.2: lattice index [1,3] corresponds to node [5]"
#> [1] "Alt.2: lattice index [2,1] corresponds to node [2]"
#> [1] "Alt.2: lattice index [2,2] corresponds to node [4]"
#> [1] "Alt.2: lattice index [2,3] corresponds to node [6]"

inv.mapping = inla.node2lattice.mapping(nrow,ncol)
for(node in 1:(nrow*ncol))
   print(paste("Alt.1: node [", node, "] corresponds to lattice index [",
               inv.mapping$irow[node], ",",
               inv.mapping$icol[node],"]", sep=""))
#> [1] "Alt.1: node [1] corresponds to lattice index [1,1]"
#> [1] "Alt.1: node [2] corresponds to lattice index [2,1]"
#> [1] "Alt.1: node [3] corresponds to lattice index [1,2]"
#> [1] "Alt.1: node [4] corresponds to lattice index [2,2]"
#> [1] "Alt.1: node [5] corresponds to lattice index [1,3]"
#> [1] "Alt.1: node [6] corresponds to lattice index [2,3]"

for(node in 1:(nrow*ncol))
   print(paste("Alt.2: node [", node, "] corresponds to lattice index [",
               inla.node2lattice(node,nrow,ncol)$irow[1], ",",
               inla.node2lattice(node,nrow,ncol)$icol[1],"]", sep=""))
#> [1] "Alt.2: node [1] corresponds to lattice index [1,1]"
#> [1] "Alt.2: node [2] corresponds to lattice index [2,1]"
#> [1] "Alt.2: node [3] corresponds to lattice index [1,2]"
#> [1] "Alt.2: node [4] corresponds to lattice index [2,2]"
#> [1] "Alt.2: node [5] corresponds to lattice index [1,3]"
#> [1] "Alt.2: node [6] corresponds to lattice index [2,3]"

## apply the mapping from matrix to vector and back
n = nrow*ncol
z = matrix(1:n,nrow,ncol)
z.vector = inla.matrix2vector(z)  # as.vector(z) could also be used
print(mapping)
#>      [,1] [,2] [,3]
#> [1,]    1    3    5
#> [2,]    2    4    6
print(z)
#>      [,1] [,2] [,3]
#> [1,]    1    3    5
#> [2,]    2    4    6
print(z.vector)
#> [1] 1 2 3 4 5 6

## the vector2matrix is the inverse, and should give us the z-matrix
## back. matrix(z.vector, nrow, ncol) could also be used here.
z.matrix = inla.vector2matrix(z.vector, nrow, ncol)
print(z.matrix)
#>      [,1] [,2] [,3]
#> [1,]    1    3    5
#> [2,]    2    4    6