chol {BNSP} R Documentation

## The Cholesky and modified Cholesky decompositions

### Description

Computes the Cholesky factorization and modified Cholesky factorizations of a real symmetric positive-definite square matrix.

### Usage

`chol(x, mod = TRUE, p = 1, ...)`

### Arguments

 `x` A symmetric, positive-definite matrix. `mod` Defaults to TRUE. With this choice, the function returns the modified Cholesky decomposition. When mod = FALSE, the function returns the usual Cholesky decomposition. `p` Relevant only when `mod = TRUE`. It determines the size of the blocks of the block diagonal matrix. `...` other arguments.

### Details

The function computes the modified Cholesky decomposition of a real symmetric positive-definite square matrix Σ. This is given by

L Σ L^{\top} = D,

where L is a lower tringular matrix with ones on its main diagonal and D is a block diagonal matrix with block size determined by argument `p`.

### Value

The function returns matrices L and D.

### Author(s)

Georgios Papageorgiou gpapageo@gmail.com

The default function from base, `chol`

### Examples

```Sigma <- matrix(c(1.21,0.18,0.13,0.41,0.06,0.23,
0.18,0.64,0.10,-0.16,0.23,0.07,
0.13,0.10,0.36,-0.10,0.03,0.18,
0.41,-0.16,-0.10,1.05,-0.29,-0.08,
0.06,0.23,0.03,-0.29,1.71,-0.10,
0.23,0.07,0.18,-0.08,-0.10,0.36),6,6)
LD <- chol(Sigma)
L <- LD\$L
D <- LD\$D
round(L,5)
round(D,5)
solve(L) %*% D %*% solve(t(L))
LD <- chol(Sigma, p = 2)
L <- LD\$L
D <- LD\$D
round(L, 5)
round(D, 5)
solve(L) %*% D %*% solve(t(L))
```

[Package BNSP version 2.1.6 Index]