Derivative of a rational Matrix

Computes the derivative of a rational matrix \(k(z)\) (with repect to the complex variable \(z\)). Note that computing the derivative for an impulse response object decreases the number of lags by one!

Usage

derivative(obj, ...)

# S3 method for lpolm
derivative(obj, ...)

# S3 method for polm
derivative(obj, ...)

# S3 method for lmfd
derivative(obj, ...)

# S3 method for rmfd
derivative(obj, ...)

# S3 method for stsp
derivative(obj, ...)

# S3 method for pseries
derivative(obj, ...)

# S3 method for zvalues
derivative(obj, ...)

Arguments

obj

an object of class polm, stsp or pseries.

...

not used

Value

an object of the same class as the argument obj

Examples

# create random (3 by 2) polynomial matrix with degree 2
K = test_polm(dim = c(3,2), degree = 2)
derivative(K)
#> ( 3 x 2 ) matrix polynomial with degree <= 1 
#>      z^0 [,1]  [,2] z^1 [,1]  [,2]
#> [1,]      111   121      224   244
#> [2,]      211   221      424   444
#> [3,]      311   321      624   644
derivative(derivative(K))
#> ( 3 x 2 ) matrix polynomial with degree <= 0 
#>      z^0 [,1]  [,2]
#> [1,]      224   244
#> [2,]      424   444
#> [3,]      624   644
derivative(derivative(derivative(K)))
#> ( 3 x 2 ) matrix polynomial with degree <= -1 

# note: computing the derivative of the impulse response 
# decreases "lag.max" by one!
all.equal(pseries(derivative(K)), derivative(pseries(K, lag.max = 6)))
#> [1] TRUE

# create statespace realization of a random (3 by 2) rational matrix
# with statespace dimension s = 4
K = test_stsp(dim = c(2,2), s = 4, bpoles = 1)
all.equal(pseries(derivative(K)), derivative(pseries(K, lag.max = 6)))
#> [1] TRUE

if (FALSE) {
# 'lmfd' objects and 'zvalues' objects are not supported
derivative(test_lmfd(dim = c(3,3), degrees = c(1,1)))
derivative(zvalues(K))
}