def num_min_controls(G):
"""
Return the smallest number of controls that are required to control the graph ``G``
assuming structural controllability conditions.
"""
type_check(G, DiGraph)
matched_edges = None
matched_edges = maximum_matching_(G)
return max([len(G) - len(matched_edges), 1])
def num_min_controls(G): """ Return the smallest number of controls that are required to control the graph ``G`` assuming structural controllability conditions. """ type_check(G,DiGraph) matched_edges = None matched_edges = maximum_matching_(G) return max([len(G) - len(matched_edges),1])
def profile(G, **kwargs):
"""
Compute the control profile for the directed network ``G``.
**KwArgs**:
* ``normalized [=True]`` (``boolean``). Indicates whether each element in the control
profile should be normalized by the number of controls.
**Returns**:
``(s,e,i)``. The control profile consisting of the source controls, external-dilation controls,
and internal-dilation controls. Un-normalized, these values with the the number of each. Normalized
these values will be the fraction of all controls needed by the network belonging to each type.
"""
# this only works on directed graphs
type_check(G, DiGraph, 'Only directed graphs are supported')
# load keyword arguments
normalized = kwargs.pop('normalized', True)
type_check(normalized, bool)
Nc = float(num_min_controls(G))
# source dilations
Ns = float(G.num_sources)
# external dilations
Nsink = float(G.num_sinks)
Ne = max([0.0, Nsink - Ns])
# internal dilations
if Nc == 1 and Ns == 0 and Nsink == 0:
# this condition handles the case where the network consists of one or more cycles
# thereby requiring only one control to drive all of them.
Ni = 0
else:
Ni = Nc - Ns - Ne
if normalized:
return (Ns / Nc, Ne / Nc, Ni / Nc)
else:
return (Ns, Ne, Ni)
def profile(G,**kwargs):
"""
Compute the control profile for the directed network ``G``.
**KwArgs**:
* ``normalized [=True]`` (``boolean``). Indicates whether each element in the control
profile should be normalized by the number of controls.
**Returns**:
``(s,e,i)``. The control profile consisting of the source controls, external-dilation controls,
and internal-dilation controls. Un-normalized, these values with the the number of each. Normalized
these values will be the fraction of all controls needed by the network belonging to each type.
"""
# this only works on directed graphs
type_check(G,DiGraph,'Only directed graphs are supported')
# load keyword arguments
normalized = kwargs.pop('normalized',True)
type_check(normalized,bool)
Nc = float(num_min_controls(G))
# source dilations
Ns = float(G.num_sources)
# external dilations
Nsink = float(G.num_sinks)
Ne = max([0.0,Nsink - Ns])
# internal dilations
if Nc == 1 and Ns == 0 and Nsink == 0:
# this condition handles the case where the network consists of one or more cycles
# thereby requiring only one control to drive all of them.
Ni = 0
else:
Ni = Nc - Ns - Ne
if normalized:
return (Ns/Nc, Ne/Nc, Ni/Nc)
else:
return (Ns,Ne,Ni)
