spec_root1: Give the spectral parameters for eigenvalues of mc-matrices...

In mcompanion: Objects and Methods for Multi-Companion Matrices

Give the spectral parameters for eigenvalues of mc-matrices equal to one

Description

Give the spectral parameters for eigenvalues of mc-matrices equal to one.

Usage

spec_root1(mo, root1 = numeric(0), iorder = 0, siorder = 0)

Arguments

mo	mc order.
root1	Jordan block lengths for the unit roots, a vector of positive integer numbers.
iorder	order of integration, a non-negative integer.
siorder	order of seasonal integration, a non-negative integer.

Details

The specifications given by root1, iorder and siorder are combined and the spectral parameters prepared.

In principle, argument root1 is sufficient, the other two are for convenient specification of integration and seasonal integration.

TODO: rename argument root1!

Value

a list with the following components:

mo	multi-companion order
ev.type	type of the eigenvalues
co.type	not used currently (:todo:)
n.root	number of non-zero roots
ev.abs	absolute values of roots
ev.arg	arguments of eigenvalues (0 for positive ev)
block.length	lengths of Jordan blocks
co.abs	absolute values of seed parameters
co.arg	arguments of seed parameters (Hz: 0 for positive; 1/2 for negative)
co1	temporary hack; TODO: check the calling code and remove it!

Author(s)

Georgi N. Boshnakov

See Also

mcSpec, spec_root0

Examples

spec_root1(4, root1 = 1)
spec_root1(4, root1 = c(1,0,0,0))  # same
spec_root1(4, iorder = 1)          # same

spec_root1(4, root1 = 2)
spec_root1(4, root1 = c(2,0,0,0))  # same
spec_root1(4, iorder = 2)          # same

spec_root1(4, root1 = c(1,1,1,1))
spec_root1(4, siorder = 1)          # same

spec_root1(4, root1 = c(2,2,2,2))
spec_root1(4, siorder = 2)          # same


spec_root1(4, root1 = c(2,1,1,1))
spec_root1(4, iorder = 1, siorder = 1) # same


spec_root1(4, root1 = c(2,1))
spec_root1(4, root1 = c(2,1,1))

mcompanion documentation built on Sept. 22, 2023, 5:12 p.m.