VGAM (version 0.9-0)

iam: Index from Array to Matrix

Description

Maps the elements of an array containing symmetric positive-definite matrices to a matrix with sufficient columns to hold them (called matrix-band format.)

Usage

iam(j, k, M, both = FALSE, diag = TRUE)

Arguments

j

An integer from the set {1:M} giving the row number of an element.

k

An integer from the set {1:M} giving the column number of an element.

M

The number of linear/additive predictors. This is the dimension of each positive-definite symmetric matrix.

both

Logical. Return both the row and column indices? See below for more details.

diag

Logical. Return the indices for the diagonal elements? If FALSE then only the strictly upper triangular part of the matrix elements are used.

Value

• This function has a dual purpose depending on the value of both. If both=FALSE then the column number corresponding to the j-k element of the matrix is returned. If both = TRUE then j and k are ignored and a list with the following components are returned.
• row.index
  The row indices of the upper triangular part of the matrix (This may or may not include the diagonal elements, depending on the argument diagonal).
• col.index
  The column indices of the upper triangular part of the matrix (This may or may not include the diagonal elements, depending on the argument diagonal).

Details

Suppose we have $n$ symmetric positive-definite square matrices, each $M$ by $M$, and these are stored in an array of dimension c(n,M,M). Then these can be more compactly represented by a matrix of dimension c(n,K) where K is an integer between M and M*(M+1)/2 inclusive. The mapping between these two representations is given by this function. It firstly enumerates by the diagonal elements, followed by the band immediately above the diagonal, then the band above that one, etc. The last element is (1,M). This function performs the mapping from elements (j,k) of symmetric positive-definite square matrices to the columns of another matrix representing such. This is called the matrix-band format and is used by the VGAM package.

References

The website http://www.stat.auckland.ac.nz/~yee contains some additional information.

See Also

vglmff-class.

Examples

iam(1, 2, M = 3) # The 4th column represents element (1,2) of a 3x3 matrix
iam(NULL, NULL, M = 3, both = TRUE) # Return the row and column indices

dirichlet()@weight

M <- 4
temp1 <- iam(NA, NA, M = M, both = TRUE)
mat1 <- matrix(NA, M, M)
mat1[cbind(temp1$row, temp1$col)] = 1:length(temp1$row)
mat1 # More commonly used

temp2 <- iam(NA, NA, M = M, both = TRUE, diag = FALSE)
mat2 <- matrix(NA, M, M)
mat2[cbind(temp2$row, temp2$col)] = 1:length(temp2$row)
mat2 # Rarely used