glmmGS.SparseMatrix: Construct sparse matrix for 'glmmGS.CovarianceModel' function
In glmmGS: Gauss-Seidel Generalized Linear Mixed Model solver

Description Usage Arguments Details Value Author(s) References See Also Examples

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

1	glmmGS.SparseMatrix(...)

...

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 vector counts of length ncols + 1, where ncols indicates the number of columns of the matrix, such that counts[1] = 0, and counts[j] equal to the total number of non-zero elements in columns 1, ..., j - 1.

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.

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

Michele Morara, Louise Ryan, Subharup Guha, Christopher Paciorek

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

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

glmmGS.CovarianceModel

# 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);