from .statesp import StateSpace

from .statefbk import gram

__all__ = ['hsvd', 'balred', 'modred', 'era', 'markov', 'minreal']

__all__ = ['hankel_singular_values', 'balanced_reduction', 'model_reduction',

'minimal_realization', 'eigensys_realization', 'markov', 'hsvd',

'balred', 'modred', 'minreal', 'era']

# Hankel Singular Value Decomposition

#

# The following returns the Hankel singular values, which are singular values

# of the matrix formed by multiplying the controllability and observability

# Gramians

def hsvd(sys):

def hankel_singular_values(sys):

"""Calculate the Hankel singular values.

Parameters

return hsv[::-1]

def modred(sys, ELIM, method='matchdc'):

def model_reduction(sys, ELIM, method='matchdc'):

"""

Model reduction of `sys` by eliminating the states in `ELIM` using a given

method.

return rsys

def balred(sys, orders, method='truncate', alpha=None):

def balanced_reduction(sys, orders, method='truncate', alpha=None):

"""Balanced reduced order model of sys of a given order.

States are eliminated based on Hankel singular value.

If sys has unstable modes, they are removed, the

return rsys

def minreal(sys, tol=None, verbose=True):

def minimal_realization(sys, tol=None, verbose=True):

'''

Eliminates uncontrollable or unobservable states in state-space

models or cancelling pole-zero pairs in transfer functions. The

return sysr

def era(YY, m, n, nin, nout, r):

def eigensys_realization(YY, m, n, nin, nout, r):

"""Calculate an ERA model of order `r` based on the impulse-response data

`YY`.

# Return the first m Markov parameters

return H if transpose else np.transpose(H)

# Function aliases

hsvd = hankel_singular_values

balred = balanced_reduction

modred = model_reduction

minreal = minimal_realization

era = eigensys_realization