Create a Sparse Symmetric Block Diagonal Matrix

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:

bdsmatrix(blocksize, blocks, rmat, dimnames)

REQUIRED ARGUMENTS:

blocksize
vector of sizes for the matrices on the diagonal
blocks
contents of the diagonal blocks, strung out as a vector

OPTIONAL ARGUMENTS:

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.

SEE ALSO:

, , .

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)