Matrix (version 1.2-16)

bdiag: Construct a Block Diagonal Matrix

Description

Build a block diagonal matrix given several building block matrices.

Usage

bdiag(…)
.bdiag(lst)

Arguments

…

individual matrices or a list of matrices.

lst

non-empty list of matrices.

Value

A sparse matrix obtained by combining the arguments into a block diagonal matrix.

The value of bdiag() inheris from class '>CsparseMatrix, whereas .bdiag() returns a '>TsparseMatrix.

Details

For non-trivial argument list, bdiag() calls .bdiag(). The latter maybe useful to programmers.

See Also

Diagonal for constructing matrices of class '>diagonalMatrix, or kronecker which also works for "Matrix" inheriting matrices.

bandSparse constructs a banded sparse matrix from its non-zero sub-/super - diagonals.

Note that other CRAN R packages have own versions of bdiag() which return traditional matrices.

Examples

# NOT RUN {
bdiag(matrix(1:4, 2), diag(3))
## combine "Matrix" class and traditional matrices:
bdiag(Diagonal(2), matrix(1:3, 3,4), diag(3:2))

mlist <- list(1, 2:3, diag(x=5:3), 27, cbind(1,3:6), 100:101)
bdiag(mlist)
stopifnot(identical(bdiag(mlist), 
# }
# NOT RUN {
<!-- % <- used to fail in earlier versions -->
# }
# NOT RUN {
                    bdiag(lapply(mlist, as.matrix))))

ml <- c(as(matrix((1:24)%% 11 == 0, 6,4),"nMatrix"),
        rep(list(Diagonal(2, x=TRUE)), 3))
mln <- c(ml, Diagonal(x = 1:3))
stopifnot(is(bdiag(ml), "lsparseMatrix"),
# }
# NOT RUN {
<!-- % failed in Matrix <= 1.0-2 -->
# }
# NOT RUN {
          is(bdiag(mln),"dsparseMatrix") )

## random (diagonal-)block-triangular matrices:
rblockTri <- function(nb, max.ni, lambda = 3) {
   .bdiag(replicate(nb, {
         n <- sample.int(max.ni, 1)
         tril(Matrix(rpois(n*n, lambda=lambda), n,n)) }))
}

(T4 <- rblockTri(4, 10, lambda = 1))
image(T1 <- rblockTri(12, 20))


##' Fast version of Matrix :: .bdiag() -- for the case of *many*  (k x k) matrices:
##' @param lmat list(<mat1>, <mat2>, ....., <mat_N>)  where each mat_j is a  k x k 'matrix'
##' @return a sparse (N*k x N*k) matrix of class  \code{"\linkS4class{dgCMatrix}"}.
bdiag_m <- function(lmat) {
    ## Copyright (C) 2016 Martin Maechler, ETH Zurich
    if(!length(lmat)) return(new("dgCMatrix"))
    stopifnot(is.list(lmat), is.matrix(lmat[[1]]),
              (k <- (d <- dim(lmat[[1]]))[1]) == d[2], # k x k
              all(vapply(lmat, dim, integer(2)) == k)) # all of them
    N <- length(lmat)
    if(N * k > .Machine$integer.max)
        stop("resulting matrix too large; would be  M x M, with M=", N*k)
    M <- as.integer(N * k)
    ## result: an   M x M  matrix
    new("dgCMatrix", Dim = c(M,M),
        ## 'i :' maybe there's a faster way (w/o matrix indexing), but elegant?
        i = as.vector(matrix(0L:(M-1L), nrow=k)[, rep(seq_len(N), each=k)]),
        p = k * 0L:M,
        x = as.double(unlist(lmat, recursive=FALSE, use.names=FALSE)))
}

l12 <- replicate(12, matrix(rpois(16, lambda = 6.4), 4,4), simplify=FALSE)
dim(T12 <- bdiag_m(l12))# 48 x 48
T12[1:20, 1:20]
# }