print("Timestep : ", h) # Number of time steps N = (T - t0) / h print("Number of steps : ", N) # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import zeros dataPlot = zeros([N, 10]) x = LSDiodeBridge.x() print("Initial state : ", x) y = InterDiodeBridge.y(0) print("First y : ", y) lambda_ = InterDiodeBridge.lambda_(0) # For the initial time step: # time # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode R1 current dataPlot[k, 3] = y[0] # diode R1 voltage dataPlot[k, 4] = -lambda_[0]
# the number of time steps N = (T - t0) / h # Get the values to be plotted # ->saved in a matrix dataPlot dataPlot = empty((N+1, 5)) # # numpy pointers on dense Siconos vectors # q = ball.q() v = ball.velocity() p = ball.p(1) lambda_ = inter.lambda_(1) # # initial data # dataPlot[0, 0] = t0 dataPlot[0, 1] = q[0] dataPlot[0, 2] = v[0] dataPlot[0, 3] = p[0] dataPlot[0, 4] = lambda_[0] k = 1 # time loop while s.hasNextEvent():
def test_serialization4(): from siconos.kernel import LagrangianLinearTIDS, NewtonImpactNSL, \ LagrangianLinearTIR, Interaction, Model, MoreauJeanOSI, TimeDiscretisation, LCP, TimeStepping from numpy import array, eye, empty t0 = 0 # start time T = 10 # end time h = 0.005 # time step r = 0.1 # ball radius g = 9.81 # gravity m = 1 # ball mass e = 0.9 # restitution coeficient theta = 0.5 # theta scheme # # dynamical system # x = array([1, 0, 0]) # initial position v = array([0, 0, 0]) # initial velocity mass = eye(3) # mass matrix mass[2, 2] = 3./5 * r * r # the dynamical system ball = LagrangianLinearTIDS(x, v, mass) # set external forces weight = array([-m * g, 0, 0]) ball.setFExtPtr(weight) # # Interactions # # ball-floor H = array([[1, 0, 0]]) nslaw = NewtonImpactNSL(e) relation = LagrangianLinearTIR(H) inter = Interaction(1, nslaw, relation) # # Model # first_bouncingBall = Model(t0, T) # add the dynamical system to the non smooth dynamical system first_bouncingBall.nonSmoothDynamicalSystem().insertDynamicalSystem(ball) # link the interaction and the dynamical system first_bouncingBall.nonSmoothDynamicalSystem().link(inter, ball) # # Simulation # # (1) OneStepIntegrators OSI = MoreauJeanOSI(theta) # (2) Time discretisation -- t = TimeDiscretisation(t0, h) # (3) one step non smooth problem osnspb = LCP() # (4) Simulation setup with (1) (2) (3) s = TimeStepping(t) s.insertIntegrator(OSI) s.insertNonSmoothProblem(osnspb) # end of model definition # # computation # # simulation initialization first_bouncingBall.setSimulation(s) first_bouncingBall.initialize() # # save and load data from xml and .dat # from siconos.io.io_base import save, load save(first_bouncingBall, "bouncingBall.xml") bouncingBall = load("bouncingBall.xml") # the number of time steps N = (T-t0)/h+1 # Get the values to be plotted # ->saved in a matrix dataPlot dataPlot = empty((N, 5)) # # numpy pointers on dense Siconos vectors # q = ball.q() v = ball.velocity() p = ball.p(1) lambda_ = inter.lambda_(1) # # initial data # dataPlot[0, 0] = t0 dataPlot[0, 1] = q[0] dataPlot[0, 2] = v[0] dataPlot[0, 3] = p[0] dataPlot[0, 4] = lambda_[0] k = 1 # time loop while(s.hasNextEvent()): s.computeOneStep() dataPlot[k, 0] = s.nextTime() dataPlot[k, 1] = q[0] dataPlot[k, 2] = v[0] dataPlot[k, 3] = p[0] dataPlot[k, 4] = lambda_[0] k += 1 print(s.nextTime()) s.nextStep() # # comparison with the reference file # from siconos.kernel import SimpleMatrix, getMatrix from numpy.linalg import norm ref = getMatrix(SimpleMatrix(os.path.join(working_dir, "data/result.ref"))) assert (norm(dataPlot - ref) < 1e-12)
print("Timestep : ", h) # Number of time steps N = (int)((T - t0) / h) print("Number of steps : ", N) # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import empty dataPlot = empty([N + 1, 8]) x = LSRelayOscillator.x() print("Initial state : ", x) y = InterRelayOscillator.y(0) print("First y : ", y) lambda_ = InterRelayOscillator.lambda_(0) while (k < N): aTS.computeOneStep() #aLCP.display() dataPlot[k, 0] = aTS.nextTime() # inductor voltage dataPlot[k, 1] = x[0] dataPlot[k, 2] = x[1] dataPlot[k, 3] = x[2] dataPlot[k, 4] = y[0] dataPlot[k, 5] = lambda_[0] k += 1 if k % 1000 == 0: print("step =", k, " < ", N)
#TODO python <- SICONOS_RELAY_LEMKE # access dparam osnspb = Relay() s.insertNonSmoothProblem(osnspb) s.setComputeResiduY(True) s.setComputeResiduR(True) filippov.initialize(s); # matrix to save data dataPlot = empty((N+1,5)) control = empty((N+1,)) dataPlot[0, 0] = t0 dataPlot[0, 1:3] = process.x() dataPlot[0, 3] = myProcessInteraction.lambda_(0)[0] dataPlot[0, 4] = myProcessInteraction.lambda_(0)[1] # time loop k = 1 while(s.hasNextEvent()): s.newtonSolve(1e-14, 30) dataPlot[k, 0] = s.nextTime() dataPlot[k, 1] = process.x()[0] dataPlot[k, 2] = process.x()[1] dataPlot[k, 3] = myProcessInteraction.lambda_(0)[0] dataPlot[k, 4] = myProcessInteraction.lambda_(0)[1] control[k] = process.r()[1] k += 1 s.nextStep() #print s.nextTime()
def test_bouncing_ball1(): from siconos.kernel import LagrangianLinearTIDS, NewtonImpactNSL, \ LagrangianLinearTIR, Interaction, Model, MoreauJeanOSI, TimeDiscretisation, LCP, TimeStepping from numpy import array, eye, empty t0 = 0 # start time T = 10 # end time h = 0.005 # time step r = 0.1 # ball radius g = 9.81 # gravity m = 1 # ball mass e = 0.9 # restitution coeficient theta = 0.5 # theta scheme # # dynamical system # x = array([1, 0, 0]) # initial position v = array([0, 0, 0]) # initial velocity mass = eye(3) # mass matrix mass[2, 2] = 3./5 * r * r # the dynamical system ball = LagrangianLinearTIDS(x, v, mass) # set external forces weight = array([-m * g, 0, 0]) ball.setFExtPtr(weight) # # Interactions # # ball-floor H = array([[1, 0, 0]]) nslaw = NewtonImpactNSL(e) relation = LagrangianLinearTIR(H) inter = Interaction(1, nslaw, relation) # # Model # bouncingBall = Model(t0, T) # add the dynamical system to the non smooth dynamical system bouncingBall.nonSmoothDynamicalSystem().insertDynamicalSystem(ball) # link the interaction and the dynamical system bouncingBall.nonSmoothDynamicalSystem().link(inter, ball) # # Simulation # # (1) OneStepIntegrators OSI = MoreauJeanOSI(theta) OSI.insertDynamicalSystem(ball) # (2) Time discretisation -- t = TimeDiscretisation(t0, h) # (3) one step non smooth problem osnspb = LCP() # (4) Simulation setup with (1) (2) (3) s = TimeStepping(t) s.insertIntegrator(OSI) s.insertNonSmoothProblem(osnspb) # end of model definition # # computation # # simulation initialization bouncingBall.initialize(s) # # save and load data from xml and .dat # try: from siconos.io import save save(bouncingBall, "bouncingBall.xml") save(bouncingBall, "bouncingBall.bin") except: print("Warning : could not import save from siconos.io") # the number of time steps N = (T-t0)/h+1 # Get the values to be plotted # ->saved in a matrix dataPlot dataPlot = empty((N, 5)) # # numpy pointers on dense Siconos vectors # q = ball.q() v = ball.velocity() p = ball.p(1) lambda_ = inter.lambda_(1) # # initial data # dataPlot[0, 0] = t0 dataPlot[0, 1] = q[0] dataPlot[0, 2] = v[0] dataPlot[0, 3] = p[0] dataPlot[0, 4] = lambda_[0] k = 1 # time loop while(s.hasNextEvent()): s.computeOneStep() dataPlot[k, 0] = s.nextTime() dataPlot[k, 1] = q[0] dataPlot[k, 2] = v[0] dataPlot[k, 3] = p[0] dataPlot[k, 4] = lambda_[0] k += 1 #print(s.nextTime()) s.nextStep() # # comparison with the reference file # from siconos.kernel import SimpleMatrix, getMatrix from numpy.linalg import norm ref = getMatrix(SimpleMatrix(os.path.join(working_dir, "data/result.ref"))) assert (norm(dataPlot - ref) < 1e-12)
print("Timestep : ", h) # Number of time steps N = (T - t0) / h print("Number of steps : ", N) # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import zeros dataPlot = zeros([N, 10]) x = LSDiodeBridge.x() print("Initial state : ", x) y = InterDiodeBridge.y(0) print("First y : ", y) lambda_ = InterDiodeBridge.lambda_(0) # For the initial time step: # time # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode R1 current dataPlot[k, 3] = y[0] # diode R1 voltage dataPlot[k, 4] = - lambda_[0]
print("Timestep : ", h) # Number of time steps N = (T - t0) / h print("Number of steps : ", N) # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import zeros dataPlot = zeros([N + 1, 6]) x = LSCircuitRLCD.x() print("Initial state : ", x) y = InterCircuitRLCD.y(0) print("First y : ", y) lambda_ = InterCircuitRLCD.lambda_(0) # For the initial time step: # time # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode voltage dataPlot[k, 3] = -y[0] # diode current dataPlot[k, 4] = lambda_[0]
print "Timestep : ", h # Number of time steps N = (T - t0) / h print "Number of steps : ", N # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import zeros dataPlot = zeros([N-1, 10]) x = LS1DiodeBridgeCapFilter.x() print "Initial state : ", x y = InterDiodeBridgeCapFilter.y(0) print "First y : ", y lambda_ = InterDiodeBridgeCapFilter.lambda_(0) # For the initial time step: # time # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode R1 current dataPlot[k, 3] = lambda_[0] # diode R1 voltage dataPlot[k, 4] = - y[0]
print "Timestep : ", h # Number of time steps N = (T - t0) / h print "Number of steps : ", N # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import zeros dataPlot = zeros([N+1, 6]) x = LSCircuitRLCD.x() print "Initial state : ", x y = InterCircuitRLCD.y(0) print "First y : ", y lambda_ = InterCircuitRLCD.lambda_(0) # For the initial time step: # time # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode voltage dataPlot[k, 3] = -y[0] # diode current dataPlot[k, 4] = lambda_[0]
print("Timestep : ", h) # Number of time steps N = int((T - t0) / h) print("Number of steps : ", N) # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import zeros dataPlot = zeros([N - 1, 10]) x = LS1DiodeBridgeCapFilter.x() print("Initial state : ", x) y = InterDiodeBridgeCapFilter.y(0) print("First y : ", y) lambda_ = InterDiodeBridgeCapFilter.lambda_(0) # For the initial time step: # time # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode R1 current dataPlot[k, 3] = lambda_[0] # diode R1 voltage dataPlot[k, 4] = -y[0]
def test_diode_bridge(): """Build diode bridge model""" # dynamical system bridge_ds = FirstOrderLinearDS(init_state, A) # interaction diode_bridge_relation = FirstOrderLinearTIR(C, B) diode_bridge_relation.setDPtr(D) nslaw = ComplementarityConditionNSL(4) bridge_interaction = Interaction(4, nslaw, diode_bridge_relation, 1) # Model diode_bridge = Model(t0, total_time, model_title) # add the dynamical system in the non smooth dynamical system diode_bridge.nonSmoothDynamicalSystem().insertDynamicalSystem(bridge_ds) # link the interaction and the dynamical system diode_bridge.nonSmoothDynamicalSystem().link(bridge_interaction, bridge_ds) # Simulation # (1) OneStepIntegrators theta = 0.5 integrator = EulerMoreauOSI(theta) # (2) Time discretisation time_discretisation = TimeDiscretisation(t0, time_step) # (3) Non smooth problem non_smooth_problem = LCP() # (4) Simulation setup with (1) (2) (3) bridge_simulation = TimeStepping(time_discretisation, integrator, non_smooth_problem) # simulation initialization diode_bridge.setSimulation(bridge_simulation) diode_bridge.initialize() k = 0 h = bridge_simulation.timeStep() # Number of time steps N = (total_time - t0) / h # Get the values to be plotted # ->saved in a matrix dataPlot data_plot = empty([N, 8]) x = bridge_ds.x() print("Initial state : ", x) y = bridge_interaction.y(0) print("First y : ", y) lambda_ = bridge_interaction.lambda_(0) # For the initial time step: # time data_plot[k, 0] = t0 # inductor voltage data_plot[k, 1] = x[0] # inductor current data_plot[k, 2] = x[1] # diode R1 current data_plot[k, 3] = y[0] # diode R1 voltage data_plot[k, 4] = - lambda_[0] # diode F2 voltage data_plot[k, 5] = - lambda_[1] # diode F1 current data_plot[k, 6] = lambda_[2] # resistor current data_plot[k, 7] = y[0] + lambda_[2] k += 1 while k < N: bridge_simulation.computeOneStep() #non_smooth_problem.display() data_plot[k, 0] = bridge_simulation.nextTime() # inductor voltage data_plot[k, 1] = x[0] # inductor current data_plot[k, 2] = x[1] # diode R1 current data_plot[k, 3] = y[0] # diode R1 voltage data_plot[k, 4] = - lambda_[0] # diode F2 voltage data_plot[k, 5] = - lambda_[1] # diode F1 current data_plot[k, 6] = lambda_[2] # resistor current data_plot[k, 7] = y[0] + lambda_[2] k += 1 bridge_simulation.nextStep() # # comparison with the reference file # ref = getMatrix(SimpleMatrix(os.path.join(working_dir, "data/diode_bridge.ref"))) assert norm(data_plot - ref) < 1e-12 return ref, data_plot
def test_diode_bridge(): """Build diode bridge model""" # dynamical system bridge_ds = FirstOrderLinearDS(init_state, A) # interaction diode_bridge_relation = FirstOrderLinearTIR(C, B) diode_bridge_relation.setDPtr(D) nslaw = ComplementarityConditionNSL(4) bridge_interaction = Interaction(4, nslaw, diode_bridge_relation, 1) # Model diode_bridge = Model(t0, total_time, model_title) # add the dynamical system in the non smooth dynamical system diode_bridge.nonSmoothDynamicalSystem().insertDynamicalSystem(bridge_ds) # link the interaction and the dynamical system diode_bridge.nonSmoothDynamicalSystem().link(bridge_interaction, bridge_ds) # Simulation # (1) OneStepIntegrators theta = 0.5 integrator = EulerMoreauOSI(theta) integrator.insertDynamicalSystem(bridge_ds) # (2) Time discretisation time_discretisation = TimeDiscretisation(t0, time_step) # (3) Non smooth problem non_smooth_problem = LCP() # (4) Simulation setup with (1) (2) (3) bridge_simulation = TimeStepping(time_discretisation, integrator, non_smooth_problem) # simulation initialization diode_bridge.initialize(bridge_simulation) k = 0 h = bridge_simulation.timeStep() # Number of time steps N = (total_time - t0) / h # Get the values to be plotted # ->saved in a matrix dataPlot data_plot = empty([N, 8]) x = bridge_ds.x() print("Initial state : ", x) y = bridge_interaction.y(0) print("First y : ", y) lambda_ = bridge_interaction.lambda_(0) # For the initial time step: # time data_plot[k, 0] = t0 # inductor voltage data_plot[k, 1] = x[0] # inductor current data_plot[k, 2] = x[1] # diode R1 current data_plot[k, 3] = y[0] # diode R1 voltage data_plot[k, 4] = -lambda_[0] # diode F2 voltage data_plot[k, 5] = -lambda_[1] # diode F1 current data_plot[k, 6] = lambda_[2] # resistor current data_plot[k, 7] = y[0] + lambda_[2] k += 1 while k < N: bridge_simulation.computeOneStep() #non_smooth_problem.display() data_plot[k, 0] = bridge_simulation.nextTime() # inductor voltage data_plot[k, 1] = x[0] # inductor current data_plot[k, 2] = x[1] # diode R1 current data_plot[k, 3] = y[0] # diode R1 voltage data_plot[k, 4] = -lambda_[0] # diode F2 voltage data_plot[k, 5] = -lambda_[1] # diode F1 current data_plot[k, 6] = lambda_[2] # resistor current data_plot[k, 7] = y[0] + lambda_[2] k += 1 bridge_simulation.nextStep() # # comparison with the reference file # ref = getMatrix( SimpleMatrix(os.path.join(working_dir, "data/diode_bridge.ref"))) assert norm(data_plot - ref) < 1e-12 return ref, data_plot
#TODO python <- SICONOS_RELAY_LEMKE # access dparam osnspb = Relay() s.insertNonSmoothProblem(osnspb) s.setComputeResiduY(True) s.setComputeResiduR(True) s.setNewtonMaxIteration(30) s.setNewtonTolerance(1e-14) # matrix to save data dataPlot = empty((N + 1, 5)) control = empty((N + 1, )) dataPlot[0, 0] = t0 dataPlot[0, 1:3] = process.x() dataPlot[0, 3] = myProcessInteraction.lambda_(0)[0] dataPlot[0, 4] = myProcessInteraction.lambda_(0)[1] # time loop k = 1 while (s.hasNextEvent()): s.advanceToEvent() dataPlot[k, 0] = s.nextTime() dataPlot[k, 1] = process.x()[0] dataPlot[k, 2] = process.x()[1] dataPlot[k, 3] = myProcessInteraction.lambda_(0)[0] dataPlot[k, 4] = myProcessInteraction.lambda_(0)[1] control[k] = process.r()[1] k += 1 s.nextStep() #print s.nextTime()
print("Timestep : ",h) # Number of time steps N = (T-t0)/h print("Number of steps : ",N) # Get the values to be plotted # ->saved in a matrix dataPlot from numpy import empty dataPlot = empty([N+1,8]) x = LSRelayOscillator.x() print("Initial state : ",x) y = InterRelayOscillator.y(0) print("First y : ",y) lambda_ = InterRelayOscillator.lambda_(0) while (k < N): aTS.computeOneStep() #aLCP.display() dataPlot[k, 0] = aTS.nextTime() # inductor voltage dataPlot[k, 1] = x[0] dataPlot[k, 2] = x[1] dataPlot[k, 3] = x[2] dataPlot[k, 4] = y[0] dataPlot[k, 5] = lambda_[0] k += 1 if k%1000==0:
t = TimeDiscretisation(t0,h) # -- (3) one step non smooth problem osnspb = LCP() s = TimeStepping(impactingBar, t,OSI,osnspb) k =0 N = int((T-t0)/h) dataPlot = np.zeros((N+1, 5)) q = bar.q() v = bar.velocity() p = bar.p(1) lambda_ = inter.lambda_(1) # time loop while s.hasNextEvent(): s.computeOneStep() dataPlot[k, 0] = s.nextTime() print('time=', dataPlot[k, 0]) dataPlot[k, 1] = q[0] dataPlot[k, 2] = v[0] dataPlot[k, 3] = p[0]/h dataPlot[k, 4] = lambda_[0] k += 1 s.nextStep() dataPlot.resize(k,5)
def test_diodebridge1(): from siconos.kernel import FirstOrderLinearDS, FirstOrderLinearTIR, \ ComplementarityConditionNSL, Interaction,\ Model, EulerMoreauOSI, TimeDiscretisation, LCP, \ TimeStepping from numpy import empty from siconos.kernel import SimpleMatrix, getMatrix from numpy.linalg import norm t0 = 0.0 T = 5.0e-3 # Total simulation time h_step = 1.0e-6 # Time step Lvalue = 1e-2 # inductance Cvalue = 1e-6 # capacitance Rvalue = 1e3 # resistance Vinit = 10.0 # initial voltage Modeltitle = "DiodeBridge" # # dynamical system # init_state = [Vinit, 0] A = [[0, -1.0/Cvalue], [1.0/Lvalue, 0 ]] LSDiodeBridge=FirstOrderLinearDS(init_state, A) # # Interactions # C = [[0., 0.], [0, 0.], [-1., 0.], [1., 0.]] D = [[1./Rvalue, 1./Rvalue, -1., 0.], [1./Rvalue, 1./Rvalue, 0., -1.], [1., 0., 0., 0.], [0., 1., 0., 0.]] B = [[0., 0., -1./Cvalue, 1./Cvalue], [0., 0., 0., 0. ]] LTIRDiodeBridge=FirstOrderLinearTIR(C, B) LTIRDiodeBridge.setDPtr(D) LTIRDiodeBridge.display() nslaw=ComplementarityConditionNSL(4) InterDiodeBridge=Interaction(4, nslaw, LTIRDiodeBridge, 1) # # Model # DiodeBridge=Model(t0, T, Modeltitle) # add the dynamical system in the non smooth dynamical system DiodeBridge.nonSmoothDynamicalSystem().insertDynamicalSystem(LSDiodeBridge) # link the interaction and the dynamical system DiodeBridge.nonSmoothDynamicalSystem().link(InterDiodeBridge, LSDiodeBridge) # # Simulation # # (1) OneStepIntegrators theta = 0.5 aOSI = EulerMoreauOSI(LSDiodeBridge, theta) # (2) Time discretisation aTiDisc = TimeDiscretisation(t0, h_step) # (3) Non smooth problem aLCP = LCP() # (4) Simulation setup with (1) (2) (3) aTS = TimeStepping(aTiDisc, aOSI, aLCP) # end of model definition # # computation # # simulation initialization DiodeBridge.initialize(aTS) k = 0 h = aTS.timeStep() print("Timestep : ", h) # Number of time steps N = (T-t0)/h print("Number of steps : ", N) # Get the values to be plotted # ->saved in a matrix dataPlot dataPlot = empty([N, 8]) x = LSDiodeBridge.x() print("Initial state : ", x) y = InterDiodeBridge.y(0) print("First y : ", y) lambda_ = InterDiodeBridge.lambda_(0) # For the initial time step: # time dataPlot[k, 0] = t0 # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode R1 current dataPlot[k, 3] = y[0] # diode R1 voltage dataPlot[k, 4] = - lambda_[0] # diode F2 voltage dataPlot[k, 5] = - lambda_[1] # diode F1 current dataPlot[k, 6] = lambda_[2] # resistor current dataPlot[k, 7] = y[0] + lambda_[2] k += 1 while (k < N): aTS.computeOneStep() #aLCP.display() dataPlot[k, 0] = aTS.nextTime() # inductor voltage dataPlot[k, 1] = x[0] # inductor current dataPlot[k, 2] = x[1] # diode R1 current dataPlot[k, 3] = y[0] # diode R1 voltage dataPlot[k, 4] = - lambda_[0] # diode F2 voltage dataPlot[k, 5] = - lambda_[1] # diode F1 current dataPlot[k, 6] = lambda_[2] # resistor current dataPlot[k, 7] = y[0] + lambda_[2] k += 1 aTS.nextStep() # # comparison with the reference file # ref = getMatrix(SimpleMatrix(os.path.join(working_dir,"data/diode_bridge.ref"))) print(norm(dataPlot - ref)) assert (norm(dataPlot - ref) < 1e-12) return ref, dataPlot