Transform Triangular Matrices from Unit Triangular to General Triangular and Back

Transform a triangular matrix x, i.e., of class triangularMatrix, from (internally!) unit triangular (“unitriangular”) to “general” triangular (diagU2N(x)) or back (diagN2U(x)). Note that the latter, diagN2U(x), also sets the diagonal to one in cases where diag(x) was not all one.

.diagU2N(x) and .diagN2U(x) assume without checking that x is a triangularMatrix with suitable diag slot ("U" and "N", respectively), hence they should be used with care.

diagU2N(x, cl = getClassDef(class(x)), checkDense = FALSE)
 diagN2U(x, cl = getClassDef(class(x)), checkDense = FALSE)

.diagU2N(x, cl = getClassDef(class(x)), checkDense = FALSE)
.diagN2U(x, cl = getClassDef(class(x)), checkDense = FALSE)

Arguments

x

a triangularMatrix, often sparse.

cl

(optional, for speedup only:) class (definition) of x.

checkDense

logical indicating if dense (see denseMatrix) matrices should be considered at all; i.e., when false, as per default, the result will be sparse even when x is dense.

Details

The concept of unit triangular matrices with a diag slot of "U" stems from LAPACK.

Note

Such internal storage details should rarely be of relevance to the user. Hence, these functions really are rather internal utilities.

Value

a triangular matrix of the same class but with a different diag slot. For diagU2N (semantically) with identical entries as x, whereas in diagN2U(x), the off-diagonal entries are unchanged and the diagonal is set to all 1 even if it was not previously.

See also

"triangularMatrix", "dtCMatrix".

Examples

(T <- Diagonal(7) + triu(Matrix(rpois(49, 1/4), 7, 7), k = 1))
#> 7 x 7 sparse Matrix of class "dtCMatrix"
#>                   
#> [1,] 1 . . 1 . . .
#> [2,] . 1 . . . 1 .
#> [3,] . . 1 . . . .
#> [4,] . . . 1 . . 1
#> [5,] . . . . 1 . .
#> [6,] . . . . . 1 1
#> [7,] . . . . . . 1
(uT <- diagN2U(T)) # "unitriangular"
#> 7 x 7 sparse Matrix of class "dtCMatrix" (unitriangular)
#>                   
#> [1,] I . . 1 . . .
#> [2,] . I . . . 1 .
#> [3,] . . I . . . .
#> [4,] . . . I . . 1
#> [5,] . . . . I . .
#> [6,] . . . . . I 1
#> [7,] . . . . . . I
(t.u <- diagN2U(10*T))# changes the diagonal!
#> 7 x 7 sparse Matrix of class "dtCMatrix" (unitriangular)
#>                      
#> [1,] I . . 10 .  .  .
#> [2,] . I .  . . 10  .
#> [3,] . . I  . .  .  .
#> [4,] . . .  I .  . 10
#> [5,] . . .  . I  .  .
#> [6,] . . .  . .  I 10
#> [7,] . . .  . .  .  I
stopifnot(all(T == uT), diag(t.u) == 1,
          identical(T, diagU2N(uT)))
T[upper.tri(T)] <- 5 # still "dtC"
T <- diagN2U(as(T,"triangularMatrix"))
dT <- as(T, "denseMatrix") # (unitriangular)
dT.n <- diagU2N(dT, checkDense = TRUE)
sT.n <- diagU2N(dT)
stopifnot(is(dT.n, "denseMatrix"), is(sT.n, "sparseMatrix"),
          dT@diag == "U", dT.n@diag == "N", sT.n@diag == "N",
          all(dT == dT.n), all(dT == sT.n))