Functions to define mapping between a lattice and nodes

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

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.

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.

Author

Havard Rue hrue@r-inla.org

See also

inla

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