def test_FundamentalSolution(self):
"""Transient fundamental solution."""
filename = 'UNITTEST_FundamentalSolution'
num_nodes = 101
mesh = mesh_1D.mesh1D(begin=0, end=35, numnodes=num_nodes)
init = np.array([math.exp(-(x - 15)**2) for x in getattr(mesh, 'X')])
alpha = None
D = np.ones(num_nodes)
sim = solver.Transient_1D_Diffusion(mesh,
D,
init,
0,
0,
Nt=2000,
alpha=alpha)
sim.calculatePrimal()
eta = np.sqrt(1. + 4 * D * sim.dt * sim.Nt)
analytical_solution = np.exp(-(
(np.array(sim.mesh.X) - 15.)**2) / eta**2) / eta
self.assertTrue(
np.allclose(sim.full_solution[1999],
analytical_solution,
rtol=1e-3,
atol=1e-2))
if 0:
plt.close("all")
plt.plot([sim.mesh.X for i in range(2)],
[sim.full_solution[1999], analytical_solution
]) # pretty solution again
plt.plot(sim.mesh.X, analytical_solution)
plt.plot(sim.mesh.X, sim.full_solution[1999])
plt.show()
def test_sampleSens(self):
"""All zero Test. BC, INIT is zero, solution is all zero at all times."""
filename = 'UNITTEST_ZeroBCandINIT'
num_nodes = 11
mesh = mesh_1D.mesh1D(begin=0, end=35, numnodes=num_nodes)
init = np.array([math.exp(-(x - 15)**2) for x in getattr(mesh, 'X')])
alpha = np.array([math.exp(-(x - 20)**2) for x in getattr(mesh, 'X')
]) # for objective function
D = np.ones(num_nodes) * 2
sim = solver.Transient_1D_Diffusion(mesh,
D,
init,
0,
0,
Nt=4000,
alpha=alpha)
sim.calculatePrimal()
sim.calculateAdjoint()
sim.calculateSensitivities()
sampled_solution = np.array([
6.33679663013598e-12, 4.9957544564639285e-09,
2.116753281502067e-06, -7.509729851704717e-06,
-0.00012598770243236774, -0.0015673884803163137
])
self.assertTrue(np.allclose(sim.Dderivative[:6], sampled_solution))
if 0:
plt.plot(sim.mesh.X[:6], sampled_solution, label='sampled')
plt.plot(sim.mesh.X[:6], sim.Dderivative[:6], label='sol')
plt.legend()
plt.show()
def primal(D): # Preprocessing filename = "Trans_1D_Diffusion" mesh = mesh_1D.mesh1D(begin=0, end=35, numnodes=num_nodes) init = np.array([math.exp(-(x-15)**2) for x in getattr(mesh,'X')]) alpha = np.array([math.exp(-(x-20)**2) for x in getattr(mesh,'X')]) # for objective function #sim = TransHeatEq1D(filename, mesh, init, alpha, D, T0=0, T1=0, Nt=4000) sim = transient_1D.Transient_1D_Diffusion(mesh, D, init, 0, 0 , Nt=4000, alpha=alpha) # Solver sim.calculatePrimal() J = sim.calculateObjectiveFunction() return J
def test_ZeroBCandINIT(self):
"""All zero Test. BC, INIT is zero, solution is all zero at all times."""
filename = 'UNITTEST_ZeroBCandINIT'
num_nodes = 11
mesh = mesh_1D.mesh1D(begin=0, end=1, numnodes=num_nodes)
init = np.zeros(num_nodes)
alpha = None
D = np.ones(num_nodes)
sim = solver.Transient_1D_Diffusion(mesh,
D,
init,
0,
0,
Nt=2,
alpha=alpha)
sim.calculatePrimal()
self.assertTrue(np.allclose(sim.full_solution[0], np.zeros(num_nodes)))
self.assertTrue(np.allclose(sim.full_solution[1], np.zeros(num_nodes)))
def test_LinearSolution2(self):
"""Linear Solution. INIT is zero. BC are u(0)=1 and u(0)=0."""
filename = 'UNITTEST_LinearSolution2'
num_nodes = 10
mesh = mesh_1D.mesh1D(begin=0, end=1, numnodes=num_nodes)
init = np.zeros(num_nodes)
alpha = None
D = np.ones(num_nodes)
sim = solver.Transient_1D_Diffusion(mesh,
D,
init,
0,
1,
Nt=2000,
alpha=alpha)
sim.calculatePrimal()
self.assertTrue(
np.allclose(sim.full_solution[1999],
np.linspace(1, 0, num_nodes),
rtol=1e-3,
atol=1e-3))
def test_FundamentalSolution(self):
"""All zero Test. BC, INIT is zero, solution is all zero at all times."""
filename = 'UNITTEST_ZeroBCandINIT'
num_nodes = 101
mesh = mesh_1D.mesh1D(begin=0, end=35, numnodes=num_nodes)
init = np.array([math.exp(-(x - 15)**2) for x in getattr(mesh, 'X')])
alpha = np.array([math.exp(-(x - 20)**2) for x in getattr(mesh, 'X')
]) # for objective function
D = np.ones(num_nodes)
sim = solver.Transient_1D_Diffusion(mesh,
D,
init,
0,
0,
Nt=4000,
alpha=alpha)
sim.calculatePrimal()
sim.calculateAdjoint()
eta = np.sqrt((1. + 4 * D * sim.dt * sim.Nt) / 1.)
analytical_solution = -np.exp(-(
(np.array(sim.mesh.X) - 20.)**2) / eta**2) / eta
self.assertTrue(
np.allclose(sim.adjoint_solution[0],
analytical_solution,
rtol=1e-3,
atol=1e-2))
if 0:
plt.close("all")
plt.plot(sim.mesh.X, analytical_solution, label="ana")
plt.plot(sim.mesh.X,
sim.adjoint_solution[0],
marker=".",
label="num")
plt.legend()
plt.axis([0, 35, 1, -1])
plt.savefig('adjoint_sol_unittest', bbox_inches='tight')
plt.show()
import pandas as pd
import mesh_1D
import transient_1D
import visualization
#---------------------------------------------------------------------------------------#
num_nodes = 11
mesh = mesh_1D.mesh1D(begin=0, end=35, numnodes=num_nodes)
D = np.ones(num_nodes) * 2.
init = np.array([math.exp(-(x - 15)**2) for x in getattr(mesh, 'X')])
alpha = np.array([math.exp(-(x - 20)**2)
for x in getattr(mesh, 'X')]) # for objective function
sim = transient_1D.Transient_1D_Diffusion(mesh,
D,
init,
0,
0,
Nt=4000,
alpha=alpha)
#---------------------------------------------------------------------------------------#
t0 = time.time()
sim.calculatePrimal()
t1 = time.time()
print(sim.calculateObjectiveFunction())
sim.calculateAdjoint()
t2 = time.time()
sim.calculateSensitivities()
AdjointDerivative = copy.copy(sim.Dderivative)
t3 = time.time()
print(t1 - t0, t2 - t1, t3 - t2)