Create a sparse symmetric block diagonal matrix object

Share:

Description

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.

Usage

1
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

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.

Value

an object of type bdsmatrix

Examples

1
2
3
4
5
6
# 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)