Combine Rational Matrices by Rows or Columns
bind.RdThe function `rbind()` and `cbind()` take a sequence of rational matrix objects
(i.e. polm, lmfd, stsp, pseries
or zvalues objects) and combines these matrices by
rows or columns.
Details
The input matrices are first coerced to objects of the same class,
as described for the group operator methods in Ops.ratm.
Examples
a1 = test_polm(dim = c(2,3), degree = 2)
a2 = test_polm(dim = c(1,3), degree = 1)
rbind(a1, a2) # => polm object
#> ( 3 x 3 ) matrix polynomial with degree <= 2
#> z^0 [,1] [,2] [,3] z^1 [,1] [,2] [,3] z^2 [,1] [,2] [,3]
#> [1,] 110 120 130 111 121 131 112 122 132
#> [2,] 210 220 230 211 221 231 212 222 232
#> [3,] 110 120 130 111 121 131 0 0 0
rbind(lmfd(diag(2), a1), a2) # => stsp object
#> statespace realization [3,3] with s = 5 states
#> s[1] s[2] s[3] s[4] s[5] u[1] u[2] u[3]
#> s[1] 0 0 0 0 0 112 122 132
#> s[2] 0 0 0 0 0 212 222 232
#> s[3] 1 0 0 0 0 111 121 131
#> s[4] 0 1 0 0 0 211 221 231
#> s[5] 0 0 0 0 0 111 121 131
#> x[1] 0 0 1 0 0 110 120 130
#> x[2] 0 0 0 1 0 210 220 230
#> x[3] 0 0 0 0 1 110 120 130
rbind(a1, as.stsp(a2)) # => stsp object
#> statespace realization [3,3] with s = 5 states
#> s[1] s[2] s[3] s[4] s[5] u[1] u[2] u[3]
#> s[1] 0 0 1 0 0 111 121 131
#> s[2] 0 0 0 1 0 211 221 231
#> s[3] 0 0 0 0 0 112 122 132
#> s[4] 0 0 0 0 0 212 222 232
#> s[5] 0 0 0 0 0 111 121 131
#> x[1] 1 0 0 0 0 110 120 130
#> x[2] 0 1 0 0 0 210 220 230
#> x[3] 0 0 0 0 1 110 120 130
rbind(a1, pseries(a2)) # pseries object
#> ( 3 x 3 ) impulse response with maximum lag = 5
#> lag=0 [,1] [,2] [,3] lag=1 [,1] [,2] [,3] lag=2 [,1] [,2] [,3]
#> [1,] 110 120 130 111 121 131 112 122 132
#> [2,] 210 220 230 211 221 231 212 222 232
#> [3,] 110 120 130 111 121 131 0 0 0
#> lag=3 [,1] [,2] [,3] lag=4 [,1] [,2] [,3] lag=5 [,1] [,2] [,3]
#> [1,] 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0 0
rbind(zvalues(a1), a2) # zvalues object
#> ( 3 x 3 ) frequency response
#> z[1] [,1] [,2] [,3] z[2] [,1] [,2]
#> [1,] 333+0i 363+0i 393+0i 53.6910-171.3992i 58.6910-186.7876i
#> [2,] 633+0i 663+0i 693+0i 103.6910-325.2834i 108.6910-340.6718i
#> [3,] 221+0i 241+0i 261+0i 144.3009-105.5673i 157.3911-115.0778i
#> [,3] z[3] [,1] [,2]
#> [1,] 63.6910-202.1761i 54.80902+41.27417i 59.80902+44.90688i
#> [2,] 113.6910-356.0602i 104.80902+77.60129i 109.80902+81.23401i
#> [3,] 170.4812-124.5884i 20.19911-65.24416i 22.10894-71.12202i
#> [,3] z[4] [,1] [,2]
#> [1,] 64.80902+48.53959i 54.80902-41.27417i 59.80902-44.90688i
#> [2,] 114.80902+84.86672i 104.80902-77.60129i 109.80902-81.23401i
#> [3,] 24.01877-76.99987i 20.19911+65.24416i 22.10894+71.12202i
#> [,3] z[5] [,1] [,2]
#> [1,] 64.80902-48.53959i 53.6910+171.3992i 58.6910+186.7876i
#> [2,] 114.80902-84.86672i 103.6910+325.2834i 108.6910+340.6718i
#> [3,] 24.01877+76.99987i 144.3009+105.5673i 157.3911+115.0778i
#> [,3]
#> [1,] 63.6910+202.1761i
#> [2,] 113.6910+356.0602i
#> [3,] 170.4812+124.5884i
a2 = test_polm(dim = c(2,1), degree = 3)
cbind(a1, a2)
#> ( 2 x 4 ) matrix polynomial with degree <= 3
#> z^0 [,1] [,2] [,3] [,4] z^1 [,1] [,2] [,3] [,4] z^2 [,1] [,2] [,3]
#> [1,] 110 120 130 110 111 121 131 111 112 122 132
#> [2,] 210 220 230 210 211 221 231 211 212 222 232
#> [,4] z^3 [,1] [,2] [,3] [,4]
#> [1,] 112 0 0 0 113
#> [2,] 212 0 0 0 213
cbind(lmfd(diag(2), a1), a2)
#> statespace realization [2,4] with s = 7 states
#> s[1] s[2] s[3] s[4] s[5] s[6] s[7] u[1] u[2] u[3] u[4]
#> s[1] 0 0 0 0 0 0 0 112 122 132 0
#> s[2] 0 0 0 0 0 0 0 212 222 232 0
#> s[3] 1 0 0 0 0 0 0 111 121 131 0
#> s[4] 0 1 0 0 0 0 0 211 221 231 0
#> s[5] 0 0 0 0 0 0 0 0 0 0 1
#> s[6] 0 0 0 0 1 0 0 0 0 0 0
#> s[7] 0 0 0 0 0 1 0 0 0 0 0
#> x[1] 0 0 1 0 111 112 113 110 120 130 110
#> x[2] 0 0 0 1 211 212 213 210 220 230 210
cbind(a1, as.stsp(a2))
#> statespace realization [2,4] with s = 7 states
#> s[1] s[2] s[3] s[4] s[5] s[6] s[7] u[1] u[2] u[3] u[4]
#> s[1] 0 0 1 0 0 0 0 111 121 131 0
#> s[2] 0 0 0 1 0 0 0 211 221 231 0
#> s[3] 0 0 0 0 0 0 0 112 122 132 0
#> s[4] 0 0 0 0 0 0 0 212 222 232 0
#> s[5] 0 0 0 0 0 0 0 0 0 0 1
#> s[6] 0 0 0 0 1 0 0 0 0 0 0
#> s[7] 0 0 0 0 0 1 0 0 0 0 0
#> x[1] 1 0 0 0 111 112 113 110 120 130 110
#> x[2] 0 1 0 0 211 212 213 210 220 230 210
cbind(a1, pseries(a2))
#> ( 2 x 4 ) impulse response with maximum lag = 5
#> lag=0 [,1] [,2] [,3] [,4] lag=1 [,1] [,2] [,3] [,4] lag=2 [,1] [,2]
#> [1,] 110 120 130 110 111 121 131 111 112 122
#> [2,] 210 220 230 210 211 221 231 211 212 222
#> [,3] [,4] lag=3 [,1] [,2] [,3] [,4] lag=4 [,1] [,2] [,3] [,4]
#> [1,] 132 112 0 0 0 113 0 0 0 0
#> [2,] 232 212 0 0 0 213 0 0 0 0
#> lag=5 [,1] [,2] [,3] [,4]
#> [1,] 0 0 0 0
#> [2,] 0 0 0 0
cbind(zvalues(a1), a2)
#> ( 2 x 4 ) frequency response
#> z[1] [,1] [,2] [,3] [,4] z[2] [,1] [,2]
#> [1,] 333+0i 363+0i 393+0i 446+0i 53.691-171.3992i 58.691-186.7876i
#> [2,] 633+0i 663+0i 693+0i 846+0i 103.691-325.2834i 108.691-340.6718i
#> [,3] [,4] z[3] [,1]
#> [1,] 63.691-202.1761i -37.7279-104.9795i 54.80902+41.27417i
#> [2,] 113.691-356.0602i -68.6296-200.0851i 104.80902+77.60129i
#> [,2] [,3] [,4]
#> [1,] 59.80902+44.90688i 64.80902+48.53959i 89.72794- 66.19522i
#> [2,] 109.80902+81.23401i 114.80902+84.86672i 170.62964-124.97374i
#> z[4] [,1] [,2] [,3]
#> [1,] 54.80902-41.27417i 59.80902-44.90688i 64.80902-48.53959i
#> [2,] 104.80902-77.60129i 109.80902-81.23401i 114.80902-84.86672i
#> [,4] z[5] [,1] [,2] [,3]
#> [1,] 89.72794+ 66.19522i 53.691+171.3992i 58.691+186.7876i 63.691+202.1761i
#> [2,] 170.62964+124.97374i 103.691+325.2834i 108.691+340.6718i 113.691+356.0602i
#> [,4]
#> [1,] -37.7279+104.9795i
#> [2,] -68.6296+200.0851i
# the following exmpales throw an error
if (FALSE) {
rbind(a1, a2) # the number of columns does not coincide
cbind(pseries(a1), zvalues(a2)) # there is no automatic coercion
# from pseries to zvalues
}