mat.sar2 {dae} | R Documentation |
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.
mat.sar2(gamma, order, print = NULL)
gamma |
A |
order |
The order of the |
print |
A |
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]
.
A banded correlation matrix
whose elements follow an sar2 pattern.
Chris Brien
mat.I
, mat.J
, mat.banded
, mat.exp
,
mat.gau
, mat.ar1
, mat.ar2
, mat.ar3
, mat.sar
,
mat.ma1
, mat.ma2
, mat.arma
corr <- mat.sar2(gamma = c(-0.4, 0.2), order = 4)
corr <- mat.sar2(gamma = c(-0.4, 0.2), order = 4, print = "ar3")