glmmGS (version 0.5-1)

glmmGS.SparseMatrix: Construct sparse matrix for glmmGS.CovarianceModel function

Description

Construct list of variables defining a column-sparse matrix used by the glmmGS.CovarianceModel function

Usage

glmmGS.SparseMatrix(...)

Arguments

...

can be a dense matrix or the following arguments in order: (1) a numeric (i.e., double) vector with the non-zero elements of the matrix; (2) an integer vector with the zero-based row indices of the non-zero elements of the matrix; (3) an integer

Value

• A list with variables named as the arguments, describing a column-sparse matrix.

Details

The list returned by this function defines a column-sparse matrix. The data structure is the same one used by the AMD algorithms written by Timothy A. Davis, Patrick R. Amestoy, Iain S. Duff, and the LDL algorithms written by Timothy A. Davis (see Reference). The glmmGS package implements the AMD and LDL algorithms to perform sparse LDL decompositions of sparse precision matrices.

References

http://www.cise.ufl.edu/research/sparse/amd/

http://www.cise.ufl.edu/research/sparse/ldl/

See Also

glmmGS.CovarianceModel

Examples

# Create dense matrix R
	ncols <- 100;
	R <- diag(rep(1, ncols));
	for (i in 2:ncols)
		R[i - 1, i] <- R[i, i - 1] <- 0.5;
	
# Create sparse matrix from dense matrix R

	R.sparse <- glmmGS.SparseMatrix(R);
	
# Create sparse matrix from vectors of values, indices, and counts
# maximizing performance (requires O(ncols^2) workspace memory) 

	nz <- R != 0;
	values <- c(R[nz]);
	indices <- row(R)[nz] - 1L;
	counts <- as.integer(c(0, cumsum(colSums(nz))));
	R.sparse2 <- glmmGS.SparseMatrix(values, indices, counts);

# Create sparse matrix from vectors of values, indices, and counts
# allocating O(ncols) workspace memory
	
	# 1) Set counts
	counts <- integer(ncols + 1L);
	count.total <- 0L;
	counts[1] <- 0L;
	for (j in 1:ncols)
	{
		nz <- which(R[, j] != 0);
		count.total <- count.total + length(nz);
		counts[j + 1] <- count.total;
	}
	
	# 2) Set values and indices
	values <- double(count.total);
	indices <- integer(count.total);
	index <- 0L;
	for (j in 1:ncols)
	{
		nz <- which(R[, j] != 0);
		lnz <- length(nz);
		kk <- index + 1:lnz;
		values[kk] <- R[nz, j];
		indices[kk] <- nz - 1L; # must be zero-based
		index <- index + lnz;
	}
	
	# Build sparse matrix
	R.sparse3 <- glmmGS.SparseMatrix(values, indices, counts);