# ordering {spam}

Extract the permutation
Package:
spam
Version:
1.3-0

### Description

Extract the (inverse) permutation used by the Cholesky decomposition

### Usage

```ordering( x, inv=FALSE)
```

### Arguments

x
object of class `spam.chol.`method returned by the function `chol`.
inv
Return the permutation (default) or inverse thereof.

### Details

Recall that calculating a Cholesky factor from a sparse matrix consists of finding a permutation first, then calculating the factors of the permuted matrix. The ordering is important when working with the factors themselves.

The ordering from a full/regular matrix is `1:n`.
Note that there exists many different algorithms to find orderings.
See the examples, they speak more than 10 lines.

`chol.spam`, `solve.spam`.

### Examples

```# Construct a pd matrix S to work with (size n)
n <- 100    # dimension
S <- .25^abs(outer(1:n,1:n,"-"))
S <- as.spam( S, eps=1e-4)
I <- diag(n)  # Identity matrix

cholS <- chol( S)
ord <- ordering(cholS)
iord <- ordering(cholS, inv=TRUE)

R <- as.spam( cholS ) # R'R = P S P', with P=I[ord,],
# a permutation matrix (rows permuted).
RtR <- t(R) %*% R

# the following are equivalent:
as.spam( RtR -            S[ord,ord] )
as.spam( RtR[iord,iord] - S )
as.spam( t(R[,iord]) %*% R[,iord] - S )

# trivially:
as.spam( t(I[iord,]) - I[ord,])  # (P^-1)' = P
as.spam( t(I[ord,]) - I[,ord])  #
as.spam( I[iord,] - I[,ord])
as.spam( I[ord,]%*%S%*%I[,ord] - S[ord,ord] )
# pre and post multiplication with P and P' is ordering```

### Author(s)

Reinhard Furrer

Documentation reproduced from package spam, version 1.3-0. License: LGPL-2