R: Up- and Down-Dating a Cholesky Decomposition

updown {Matrix} | R Documentation

## Up- and Down-Dating a Cholesky Decomposition

### Description

Compute the up- or down-dated Cholesky decomposition

### Usage

    updown(update, C, L)

### Arguments

`update` | logical (`TRUE` or `FALSE`) or `"+"` or `"-"` indicating if an up- or a down-date is to be computed.
`C` | any R object, coercable to a sparse matrix (i.e., of subclass of `sparseMatrix`).
`L` | a Cholesky factor, specifically, of class `"CHMfactor"`.

### Value

an updated Cholesky factor, of the same dimension as `L`. Typically of class `"dCHMsimpl"` (a sub class of `"CHMfactor"`).

### Methods

`signature(update = "character", C = "mMatrix", L = "CHMfactor")`

  ..

`signature(update = "logical", C = "mMatrix", L = "CHMfactor")`

  ..

### Author(s)

Contributed by Nicholas Nagle, University of Tennessee, Knoxville, USA

### References

CHOLMOD manual, currently beginning of chapter~18. ...

### See Also

`Cholesky`,

### Examples

    dn <- list(LETTERS[1:3], letters[1:5])
    ## pointer vectors can be used, and the (i,x) slots are sorted if necessary:
    m <- sparseMatrix(i = c(3,1, 3:2, 2:1), p= c(0:2, 4,4,6), x = 1:6, dimnames = dn)
    cA <- Cholesky(A <- crossprod(m) + Diagonal(5))
    166 * as(cA,"Matrix") ^ 2
    uc1 <- updown("+",   Diagonal(5), cA)
    ## Hmm: this loses positive definiteness:
    uc2 <- updown("-", 2*Diagonal(5), cA)
    image(show(as(cA, "Matrix")))
    image(show(c2 <- as(uc2,"Matrix")))# severely negative entries
    ##--> Warning

[Package Matrix version 1.1-4 Index]