def compute_dt_matrices(A, B, h, TV=False):
# variable declaration
t0 = 0.0 # start time
T = 1 # end time
n, m = B.shape
# Matrix declaration
x0 = np.random.random(n)
Csurface = np.random.random((m, n))
# Declaration of the Dynamical System
if TV:
process_ds = SK.FirstOrderLinearDS(x0, A)
else:
process_ds = SK.FirstOrderLinearTIDS(x0, A)
# Model
process = SK.Model(t0, T)
process.nonSmoothDynamicalSystem().insertDynamicalSystem(process_ds)
# time discretisation
process_time_discretisation = SK.TimeDiscretisation(t0, h)
# Creation of the Simulation
process_simu = SK.TimeStepping(process_time_discretisation, 0)
process_simu.setName("plant simulation")
# Declaration of the integrator
process_integrator = SK.ZeroOrderHoldOSI()
process_integrator.insertDynamicalSystem(process_ds)
process_simu.insertIntegrator(process_integrator)
rel = SK.FirstOrderLinearTIR(Csurface, B)
nslaw = SK.RelayNSL(m)
inter = SK.Interaction(m, nslaw, rel)
#process.nonSmoothDynamicalSystem().insertInteraction(inter, True)
process.nonSmoothDynamicalSystem().link(inter, process_ds)
process.nonSmoothDynamicalSystem().setControlProperty(inter, True)
# Initialization
process.initialize(process_simu)
# Main loop
process_simu.computeOneStep()
Ad = SK.getMatrix(process_integrator.Ad(process_ds)).copy()
Bd = SK.getMatrix(process_integrator.Bd(process_ds)).copy()
return (Ad, Bd)
Vinit = 1.0
theta = 0.5
N = int((T - t0) / h)
# Dynamical systems
A = np.zeros((2, 2))
x0 = np.array([Vinit, -Vinit])
B = 2.0 * np.eye(2)
C = np.eye(2)
D = np.zeros((2, 2))
process = sk.FirstOrderLinearDS(x0, A)
process.setComputebFunction('plugins', 'computeB')
# Interactions
myNslaw = sk.RelayNSL(2)
myProcessRelation = sk.FirstOrderLinearR(C, B)
myProcessRelation.setComputeEFunction('plugins', 'computeE')
# myProcessRelation.setDPtr(D)
myProcessInteraction = sk.Interaction(myNslaw, myProcessRelation)
# NSDS
simplerelay = sk.NonSmoothDynamicalSystem(t0, T)
simplerelay.insertDynamicalSystem(process)
simplerelay.link(myProcessInteraction, process)
# myProcessRelation.computeJachx(0, x0, x0 , x0, C)
# Simulation
s = sk.TimeStepping(simplerelay, sk.TimeDiscretisation(t0, h),
# r = B.lambda ninter = 2 B = np.zeros((ndof, ninter), dtype=np.float64) B[0, 0] = -alpha * 0.5 B[0, 1] = 1 + alpha * 0.5 B[1, 0] = -B[0, 1] B[1, 1] = B[0, 0] B[2, 0] = gamma * 0.5 B[2, 1] = gamma * 0.5 C = np.zeros((ninter, ndof), dtype=np.float64) C[0, 0] = C[1, 1] = -1. particle_relation = sk.FirstOrderLinearR(C, B) nslaw = sk.RelayNSL(ninter) particle_interaction = sk.Interaction(nslaw, particle_relation) # -- The Model -- filippov = sk.Model(t0, T) nsds = filippov.nonSmoothDynamicalSystem() nsds.insertDynamicalSystem(particle) nsds.link(particle_interaction, particle) # -- Simulation -- td = sk.TimeDiscretisation(t0, h) simu = sk.TimeStepping(td) # osi theta = 0.5 myIntegrator = sk.EulerMoreauOSI(theta)