Drop Non-Structural Zeros from a Sparse Matrix

Deletes “non-structural” zeros (i.e., zeros stored explicitly, in memory) from a sparse matrix and returns the result.

Usage

drop0(x, tol = 0, is.Csparse = NA, give.Csparse = TRUE)

Arguments

x: a Matrix, typically inheriting from virtual class sparseMatrix. denseMatrix and traditional vectors and matrices are coerced to CsparseMatrix, with zeros dropped automatically, hence users passing such x should consider as(x, "CsparseMatrix") instead, notably in the tol = 0 case.
tol: a non-negative number. If x is numeric, then entries less than or equal to tol in absolute value are deleted.
is.Csparse: a logical used only if give.Csparse is TRUE, indicating if x already inherits from virtual class CsparseMatrix, in which case coercion is not attempted, permitting some (typically small) speed-up.
give.Csparse: a logical indicating if the result must inherit from virtual class CsparseMatrix. If FALSE and x inherits from RsparseMatrix, TsparseMatrix, or indMatrix, then the result preserves the class of x. The default value is TRUE only for backwards compatibility.

Value

A sparseMatrix, the result of deleting non-structural zeros from x, possibly after coercion.

Note

drop0 is sometimes called in conjunction with zapsmall, e.g., when dealing with sparse matrix products; see the example.

Examples

(m <- sparseMatrix(i = 1:8, j = 2:9, x = c(0:2, 3:-1),
                   dims = c(10L, 20L)))
#> 10 x 20 sparse Matrix of class "dgCMatrix"
#>                                               
#>  [1,] . 0 . . . . . .  . . . . . . . . . . . .
#>  [2,] . . 1 . . . . .  . . . . . . . . . . . .
#>  [3,] . . . 2 . . . .  . . . . . . . . . . . .
#>  [4,] . . . . 3 . . .  . . . . . . . . . . . .
#>  [5,] . . . . . 2 . .  . . . . . . . . . . . .
#>  [6,] . . . . . . 1 .  . . . . . . . . . . . .
#>  [7,] . . . . . . . 0  . . . . . . . . . . . .
#>  [8,] . . . . . . . . -1 . . . . . . . . . . .
#>  [9,] . . . . . . . .  . . . . . . . . . . . .
#> [10,] . . . . . . . .  . . . . . . . . . . . .
drop0(m)
#> 10 x 20 sparse Matrix of class "dgCMatrix"
#>                                               
#>  [1,] . . . . . . . .  . . . . . . . . . . . .
#>  [2,] . . 1 . . . . .  . . . . . . . . . . . .
#>  [3,] . . . 2 . . . .  . . . . . . . . . . . .
#>  [4,] . . . . 3 . . .  . . . . . . . . . . . .
#>  [5,] . . . . . 2 . .  . . . . . . . . . . . .
#>  [6,] . . . . . . 1 .  . . . . . . . . . . . .
#>  [7,] . . . . . . . .  . . . . . . . . . . . .
#>  [8,] . . . . . . . . -1 . . . . . . . . . . .
#>  [9,] . . . . . . . .  . . . . . . . . . . . .
#> [10,] . . . . . . . .  . . . . . . . . . . . .

## A larger example:
t5 <- new("dtCMatrix", Dim = c(5L, 5L), uplo = "L",
          x = c(10, 1, 3, 10, 1, 10, 1, 10, 10),
          i = c(0L,2L,4L, 1L, 3L,2L,4L, 3L, 4L),
          p = c(0L, 3L, 5L, 7:9))
TT <- kronecker(t5, kronecker(kronecker(t5, t5), t5))
IT <- solve(TT)
I. <- TT %*% IT ;  nnzero(I.) # 697 ( == 625 + 72 )
#> [1] 697
I.0 <- drop0(zapsmall(I.))
## which actually can be more efficiently achieved by
I.. <- drop0(I., tol = 1e-15)
stopifnot(all(I.0 == Diagonal(625)), nnzero(I..) == 625)