# updown: Up- and Down-Dating a Cholesky Decomposition In Matrix: Sparse and Dense Matrix Classes and Methods

 updown 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. ...

`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
```

Matrix documentation built on Nov. 11, 2022, 9:06 a.m.