Create a sparse symmetric block diagonal matrix object

Sparse block diagonal matrices are used in the the large parameter matrices that can arise in random-effects coxph and survReg models. This routine creates such a matrix. Methods for these matrices allow them to be manipulated much like an ordinary matrix, but the total memory use can be much smaller.

bdsmatrix(blocksize, blocks, rmat, dimnames)

Arguments

blocksize

vector of sizes for the matrices on the diagonal

blocks

contents of the diagonal blocks, strung out as a vector

rmat

the dense portion of the matrix, forming a right and lower border

dimnames

a list of dimension names for the matrix

Value

an object of type bdsmatrix

Details

Consider the following matrix, which has been divided into 4 parts.

1 2 0 0 0 | 4 5 2 1 0 0 0 | 6 7 0 0 3 1 2 | 8 8 0 0 1 4 3 | 1 1 0 0 2 3 5 | 2 2 ————–+—– 4 6 8 1 2 | 7 6 5 7 8 1 2 | 6 9

The upper left is block diagonal, and can be stored in a compressed form without the zeros. With a large number of blocks, the zeros can actually account for over 99% of a matrix; this commonly happens with the kinship matrix for a large collection of families (one block/family). The arguments to this routine would be block sizes of 2 and 3, along with a 2 by 7 "right hand" matrix. Since the matrix is symmetrical, the bottom slice is not needed.

Examples

# The matrix shown above is created by
tmat <- bdsmatrix(c(2,3), c(1,2,1, 3,1,2, 4,3, 5),
                  rmat=matrix(c(4,6,8,1,2,7,6, 5,7,8,1,2,6,9), ncol=2))

# Note that only the lower part of the blocks is needed, however, the
#  entire block set is also allowed, i.e., c(1,2,2,1, 3,1,2,1,4,3,2,3,5)