Give the spectral parameters for eigenvalues of mc-matrices equal to one
spec_root1.RdGive 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!
Examples
spec_root1(4, root1 = 1)
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r"
#>
#> $co.type
#> [1] "r"
#>
#> $n.root
#> [1] 1
#>
#> $ev.abs
#> [1] 1
#>
#> $ev.arg
#> [1] 0
#>
#> $block.length
#> [1] 1
#>
#> $co.abs
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
#> $co.arg
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
#> $co1
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
spec_root1(4, root1 = c(1,0,0,0)) # same
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r"
#>
#> $co.type
#> [1] "r"
#>
#> $n.root
#> [1] 1
#>
#> $ev.abs
#> [1] 1
#>
#> $ev.arg
#> [1] 0
#>
#> $block.length
#> [1] 1
#>
#> $co.abs
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
#> $co.arg
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
#> $co1
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
spec_root1(4, iorder = 1) # same
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r"
#>
#> $co.type
#> [1] "r"
#>
#> $n.root
#> [1] 1
#>
#> $ev.abs
#> [1] 1
#>
#> $ev.arg
#> [1] 0
#>
#> $block.length
#> [1] 1
#>
#> $co.abs
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
#> $co.arg
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
#> $co1
#> [,1]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#>
spec_root1(4, root1 = 2)
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r"
#>
#> $co.type
#> [1] "r"
#>
#> $n.root
#> [1] 2
#>
#> $ev.abs
#> [1] 1
#>
#> $ev.arg
#> [1] 0
#>
#> $block.length
#> [1] 2
#>
#> $co.abs
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
#> $co.arg
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
#> $co1
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
spec_root1(4, root1 = c(2,0,0,0)) # same
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r"
#>
#> $co.type
#> [1] "r"
#>
#> $n.root
#> [1] 2
#>
#> $ev.abs
#> [1] 1
#>
#> $ev.arg
#> [1] 0
#>
#> $block.length
#> [1] 2
#>
#> $co.abs
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
#> $co.arg
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
#> $co1
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
spec_root1(4, iorder = 2) # same
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r"
#>
#> $co.type
#> [1] "r"
#>
#> $n.root
#> [1] 2
#>
#> $ev.abs
#> [1] 1
#>
#> $ev.arg
#> [1] 0
#>
#> $block.length
#> [1] 2
#>
#> $co.abs
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
#> $co.arg
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
#> $co1
#> [,1] [,2]
#> [1,] NA 0
#> [2,] NA 0
#> [3,] NA 0
#> [4,] NA 0
#>
spec_root1(4, root1 = c(1,1,1,1))
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r" "r" "r"
#>
#> $co.type
#> [1] "r" "r" "r" "r"
#>
#> $n.root
#> [1] 4
#>
#> $ev.abs
#> [1] 1 1 1 1
#>
#> $ev.arg
#> [1] 0 0 0 0
#>
#> $block.length
#> [1] 1 1 1 1
#>
#> $co.abs
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 0
#> [2,] 0 1 0 0
#> [3,] 0 0 1 0
#> [4,] 0 0 0 1
#>
#> $co.arg
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 0 0 0 0
#> [3,] 0 0 0 0
#> [4,] 0 0 0 0
#>
#> $co1
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 0
#> [2,] 0 1 0 0
#> [3,] 0 0 1 0
#> [4,] 0 0 0 1
#>
spec_root1(4, siorder = 1) # same
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r" "r" "r"
#>
#> $co.type
#> [1] "r" "r" "r" "r"
#>
#> $n.root
#> [1] 4
#>
#> $ev.abs
#> [1] 1 1 1 1
#>
#> $ev.arg
#> [1] 0 0 0 0
#>
#> $block.length
#> [1] 1 1 1 1
#>
#> $co.abs
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 0
#> [2,] 0 1 0 0
#> [3,] 0 0 1 0
#> [4,] 0 0 0 1
#>
#> $co.arg
#> [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 0 0 0 0
#> [3,] 0 0 0 0
#> [4,] 0 0 0 0
#>
#> $co1
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 0
#> [2,] 0 1 0 0
#> [3,] 0 0 1 0
#> [4,] 0 0 0 1
#>
spec_root1(4, root1 = c(2,2,2,2))
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r" "r" "r"
#>
#> $co.type
#> [1] "r" "r" "r" "r"
#>
#> $n.root
#> [1] 8
#>
#> $ev.abs
#> [1] 1 1 1 1
#>
#> $ev.arg
#> [1] 0 0 0 0
#>
#> $block.length
#> [1] 2 2 2 2
#>
#> $co.abs
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1 0 0 0 0 0 0 0
#> [2,] 0 0 1 0 0 0 0 0
#> [3,] 0 0 0 0 1 0 0 0
#> [4,] 0 0 0 0 0 0 1 0
#>
#> $co.arg
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0 0
#>
#> $co1
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1 0 0 0 0 0 0 0
#> [2,] 0 0 1 0 0 0 0 0
#> [3,] 0 0 0 0 1 0 0 0
#> [4,] 0 0 0 0 0 0 1 0
#>
spec_root1(4, siorder = 2) # same
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r" "r" "r"
#>
#> $co.type
#> [1] "r" "r" "r" "r"
#>
#> $n.root
#> [1] 8
#>
#> $ev.abs
#> [1] 1 1 1 1
#>
#> $ev.arg
#> [1] 0 0 0 0
#>
#> $block.length
#> [1] 2 2 2 2
#>
#> $co.abs
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1 0 0 0 0 0 0 0
#> [2,] 0 0 1 0 0 0 0 0
#> [3,] 0 0 0 0 1 0 0 0
#> [4,] 0 0 0 0 0 0 1 0
#>
#> $co.arg
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0 0
#>
#> $co1
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 1 0 0 0 0 0 0 0
#> [2,] 0 0 1 0 0 0 0 0
#> [3,] 0 0 0 0 1 0 0 0
#> [4,] 0 0 0 0 0 0 1 0
#>
spec_root1(4, root1 = c(2,1,1,1))
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r" "r" "r"
#>
#> $co.type
#> [1] "r" "r" "r" "r"
#>
#> $n.root
#> [1] 5
#>
#> $ev.abs
#> [1] 1 1 1 1
#>
#> $ev.arg
#> [1] 0 0 0 0
#>
#> $block.length
#> [1] 2 1 1 1
#>
#> $co.abs
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] Inf 0 Inf Inf Inf
#> [2,] Inf 0 Inf Inf Inf
#> [3,] Inf 0 Inf Inf Inf
#> [4,] Inf 0 Inf Inf Inf
#>
#> $co.arg
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.5 0 0 0 0
#> [2,] 0.5 0 0 0 0
#> [3,] 0.5 0 0 0 0
#> [4,] 0.5 0 0 0 0
#>
#> $co1
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -Inf 0 Inf Inf Inf
#> [2,] -Inf 0 Inf Inf Inf
#> [3,] -Inf 0 Inf Inf Inf
#> [4,] -Inf 0 Inf Inf Inf
#>
spec_root1(4, iorder = 1, siorder = 1) # same
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r" "r" "r"
#>
#> $co.type
#> [1] "r" "r" "r" "r"
#>
#> $n.root
#> [1] 5
#>
#> $ev.abs
#> [1] 1 1 1 1
#>
#> $ev.arg
#> [1] 0 0 0 0
#>
#> $block.length
#> [1] 2 1 1 1
#>
#> $co.abs
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] Inf 0 Inf Inf Inf
#> [2,] Inf 0 Inf Inf Inf
#> [3,] Inf 0 Inf Inf Inf
#> [4,] Inf 0 Inf Inf Inf
#>
#> $co.arg
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.5 0 0 0 0
#> [2,] 0.5 0 0 0 0
#> [3,] 0.5 0 0 0 0
#> [4,] 0.5 0 0 0 0
#>
#> $co1
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -Inf 0 Inf Inf Inf
#> [2,] -Inf 0 Inf Inf Inf
#> [3,] -Inf 0 Inf Inf Inf
#> [4,] -Inf 0 Inf Inf Inf
#>
spec_root1(4, root1 = c(2,1))
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r"
#>
#> $co.type
#> [1] "r" "r"
#>
#> $n.root
#> [1] 3
#>
#> $ev.abs
#> [1] 1 1
#>
#> $ev.arg
#> [1] 0 0
#>
#> $block.length
#> [1] 2 1
#>
#> $co.abs
#> [,1] [,2] [,3]
#> [1,] NA NA NA
#> [2,] NA NA NA
#> [3,] NA NA NA
#> [4,] NA NA NA
#>
#> $co.arg
#> [,1] [,2] [,3]
#> [1,] NA NA NA
#> [2,] NA NA NA
#> [3,] NA NA NA
#> [4,] NA NA NA
#>
#> $co1
#> [,1] [,2] [,3]
#> [1,] NA NA NA
#> [2,] NA NA NA
#> [3,] NA NA NA
#> [4,] NA NA NA
#>
spec_root1(4, root1 = c(2,1,1))
#> $mo
#> [1] 4
#>
#> $ev.type
#> [1] "r" "r" "r"
#>
#> $co.type
#> [1] "r" "r" "r"
#>
#> $n.root
#> [1] 4
#>
#> $ev.abs
#> [1] 1 1 1
#>
#> $ev.arg
#> [1] 0 0 0
#>
#> $block.length
#> [1] 2 1 1
#>
#> $co.abs
#> [,1] [,2] [,3] [,4]
#> [1,] NA NA NA NA
#> [2,] NA NA NA NA
#> [3,] NA NA NA NA
#> [4,] NA NA NA NA
#>
#> $co.arg
#> [,1] [,2] [,3] [,4]
#> [1,] NA NA NA NA
#> [2,] NA NA NA NA
#> [3,] NA NA NA NA
#> [4,] NA NA NA NA
#>
#> $co1
#> [,1] [,2] [,3] [,4]
#> [1,] NA NA NA NA
#> [2,] NA NA NA NA
#> [3,] NA NA NA NA
#> [4,] NA NA NA NA
#>