band-methods | R Documentation |

Return the matrix obtained by setting to zero elements below a diagonal
(`triu`

), above a diagonal (`tril`

), or outside of a general
band (`band`

).

```
band(x, k1, k2, ...)
triu(x, k = 0L, ...)
tril(x, k = 0L, ...)
```

`x` |
a matrix-like object |

`k,k1,k2` |
integers specifying the diagonals that are not set to
zero. These are interpreted relative to the main diagonal, which
is |

`...` |
optional arguments passed methods (currently unused by package Matrix) |

`triu(x, k)`

is equivalent to `band(x, k, dim(x)[2])`

.
Similarly,
`tril(x, k)`

is equivalent to `band(x, -dim(x)[1], k)`

.

An object of a suitable matrix class, inheriting from
`triangularMatrix`

where appropriate.
It inherits from `sparseMatrix`

if
and only if `x`

does.

- x = "CsparseMatrix"
method for compressed, sparse, column-oriented matrices.

- x = "RsparseMatrix"
method for compressed, sparse, row-oriented matrices.

- x = "TsparseMatrix"
method for sparse matrices in triplet format.

- x = "diagonalMatrix"
method for diagonal matrices.

- x = "denseMatrix"
method for dense matrices in packed or unpacked format.

- x = "matrix"
method for traditional matrices of implicit class

`matrix`

.

`bandSparse`

for the *construction* of a
banded sparse matrix directly from its non-zero diagonals.

```
## A random sparse matrix :
set.seed(7)
m <- matrix(0, 5, 5)
m[sample(length(m), size = 14)] <- rep(1:9, length=14)
(mm <- as(m, "CsparseMatrix"))
tril(mm) # lower triangle
tril(mm, -1) # strict lower triangle
triu(mm, 1) # strict upper triangle
band(mm, -1, 2) # general band
(m5 <- Matrix(rnorm(25), ncol = 5))
tril(m5) # lower triangle
tril(m5, -1) # strict lower triangle
triu(m5, 1) # strict upper triangle
band(m5, -1, 2) # general band
(m65 <- Matrix(rnorm(30), ncol = 5)) # not square
triu(m65) # result not "dtrMatrix" unless square
(sm5 <- crossprod(m65)) # symmetric
band(sm5, -1, 1)# "dsyMatrix": symmetric band preserves symmetry property
as(band(sm5, -1, 1), "sparseMatrix")# often preferable
(sm <- round(crossprod(triu(mm/2)))) # sparse symmetric ("dsC*")
band(sm, -1,1) # remains "dsC", *however*
band(sm, -2,1) # -> "dgC"
```

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