mat.sar2 {dae} | R Documentation |

## Forms an sar2 correlation matrix

### Description

Form the correlation `matrix`

of order `order`

whose
correlations follow the sar2 pattern, a pattern used in crop competition
models. The resulting `matrix`

is banded and is a constrained AR3 matrix.

### Usage

`mat.sar2(gamma, order, print = NULL)`

### Arguments

`gamma` |
A |

`order` |
The order of the |

`print` |
A |

### Details

The values of the AR3 parameters, phi, are calculated from the gammas as follows:

`phi[1] = gamma[1] + 2 * gamma[2]`

; `phi[2] = -gamma[2] * (2*gamma[2] + gamma[1])`

;

`phi[3] = gamma[1] * gamma[2] * gamma[2]`

.

Then the correlations in the correlation matrix, `corr`

say, are calculated
from the correlation parameters, phi.
Let `omega = 1 - phi[2] - phi[3] * (phi[1] + phi[3])`

.
Then the values in

the diagonal of

`corr`

(`k = 1`

) are one;the first subdiagonal band (

`k = 2`

) of`corr`

are equal to`(phi[1] + phi[2]*phi[3]) / omega`

;the second subdiagonal band (

`k = 3`

) of`corr`

are equal to

`(phi[1] * (phi[1] + phi[3]) + phi[2] * (1 - phi[2])) / omega`

;the subsequent subdiagonal bands, (

`k = 4:order`

), of`corr`

are equal to

`phi[1]*corr[k-1] + phi[2]*corr[k-2] + phi[3]*corr[k-3]`

.

### Value

A banded correlation `matrix`

whose elements follow an sar2 pattern.

### Author(s)

Chris Brien

### See Also

`mat.I`

, `mat.J`

, `mat.cor`

, `mat.corg`

,
`mat.banded`

, `mat.exp`

,
`mat.gau`

, `mat.ar1`

, `mat.ar2`

, `mat.ar3`

, `mat.sar`

,
`mat.ma1`

, `mat.ma2`

, `mat.arma`

### Examples

```
corr <- mat.sar2(gamma = c(-0.4, 0.2), order = 4)
corr <- mat.sar2(gamma = c(-0.4, 0.2), order = 4, print = "ar3")
```

*dae*version 3.2.28 Index]