splane_contour = 1j * omega_sys

# Bend the contour around any poles on/near the imaginary axis

# TODO: smarter indent radius that depends on dcgain of system

# and timebase of discrete system.

if isinstance(sys, (StateSpace, TransferFunction)) \

and indent_direction != 'none':

if sys.isctime():

splane_poles = sys.pole()

else:

# map z-plane poles to s-plane

splane_poles = np.log(sys.pole())/sys.dt

# map z-plane poles to s-plane, ignoring any at the origin

# because we don't need to indent for them

zplane_poles = sys.pole()

zplane_poles = zplane_poles[~np.isclose(abs(zplane_poles), 0.)]

splane_poles = np.log(zplane_poles)/sys.dt

if splane_contour[1].imag > indent_radius \

and 0. in splane_poles and not omega_range_given:

and np.any(np.isclose(abs(splane_poles), 0)) \

and not omega_range_given:

# add some points for quarter circle around poles at origin

splane_contour = np.concatenate(

(1j * np.linspace(0., indent_radius, 50),

p = splane_poles[(np.abs(splane_poles - s)).argmin()]

# See if we need to indent around it

if abs(s - p) < indent_radius:

if p.real < 0 or \

(p.real == 0 and indent_direction == 'right'):

if p.real < 0 or (np.isclose(p.real, 0) \

and indent_direction == 'right'):

# Indent to the right

splane_contour[i] += \

np.sqrt(indent_radius ** 2 - (s-p).imag ** 2)

elif p.real > 0 or \

(p.real == 0 and indent_direction == 'left'):

elif p.real > 0 or (np.isclose(p.real, 0) \

and indent_direction == 'left'):

# Indent to the left

splane_contour[i] -= \

np.sqrt(indent_radius ** 2 - (s-p).imag ** 2)