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 class 'lpolm'
derivative(obj, ...)

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

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

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

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

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

# S3 method for class '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) { # \dontrun{
# 'lmfd' objects and 'zvalues' objects are not supported
derivative(test_lmfd(dim = c(3,3), degrees = c(1,1)))
derivative(zvalues(K))
} # }