def test_not_monotonous():
# ts not strictly monotonous
ts = np.random.rand(1000)
ws = ts
gs = ws
ti = ts[0]
tf = ts[-1]
x0 = 1.0
dx0 = 0.0
with pytest.raises(TypeError):
pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0)
return None
def test_outside_range_tf():
# ti outside ts
ts = np.linspace(1, 50, 1000)
ws = np.linspace(1, 50, 1000)
gs = np.zeros_like(ws)
ti = 1.0
tf = -5.0
x0 = 1.0
dx0 = 0.0
with pytest.raises(TypeError):
pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0)
return None
def test_too_small():
# Same size arrays but too small
ts = np.linspace(1, 50, 1)
ws = np.linspace(1, 50, 1)
gs = np.zeros_like(ws)
ti = 1.0
tf = 50.0
x0 = 1.0
dx0 = 0.0
with pytest.raises(TypeError):
pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0)
return None
def test_different_size():
# Different size arrays
ts = np.linspace(1, 50, 2000)
ws = np.linspace(1, 50, 2001)
gs = np.zeros_like(ws)
ti = 1.0
tf = 50.0
x0 = 1.0
dx0 = 0.0
with pytest.raises(TypeError):
pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0)
return None
def test_dense_output_range():
# Dense output outside integration range
ts = np.linspace(1, 50, 2000)
ws = np.linspace(1, 50, 2000)
gs = np.zeros_like(ws)
t_eval = np.linspace(0, 60, 1000)
ti = 1.0
tf = 50.0
x0 = 1.0
dx0 = 0.0
with pytest.raises(TypeError):
pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0, t_eval=t_eval)
return None
def test_dense_output_sorted():
# Dense output not sorted
ts = np.linspace(1, 50, 2000)
ws = np.linspace(1, 50, 2000)
t_eval = np.linspace(1, 50, 100)
t_eval = np.flip(t_eval)
gs = np.zeros_like(ws)
ti = 1.0
tf = 50.0
x0 = 1.0
dx0 = 0.0
with pytest.raises(TypeError):
pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0, t_eval=t_eval)
return None
def test_airy_backward_even():
# Integration backwards on even grid
ts = np.linspace(1, 100, 5000)
ws = np.sqrt(ts)
gs = np.zeros_like(ws)
ti = 1.0
tf = 100.0
t_eval = np.linspace(ti, tf, 5000)
x0 = airy(-tf)[0] + 1j * airy(-tf)[2]
dx0 = -airy(-tf)[1] - 1j * airy(-tf)[3]
sol = pyoscode.solve(ts,
ws,
gs,
tf,
ti,
x0,
dx0,
t_eval=t_eval,
even_grid=True)
t = np.asarray(sol['t'])
x = np.asarray(sol['sol'])
dense = np.asarray(sol['x_eval'])
dense_d = np.asarray(sol['dx_eval'])
types = np.asarray(sol['types'])
ana_t = np.linspace(ti, tf, 5000)
ana_x = np.asarray([airy(-T)[0] + 1j * airy(-T)[2] for T in t])
dense_ana_x = np.asarray([airy(-T)[0] + 1j * airy(-T)[2] for T in ana_t])
dense_ana_dx = np.asarray([-airy(-T)[1] - 1j * airy(-T)[3] for T in ana_t])
dense_error = np.abs((dense - dense_ana_x) / dense_ana_x) / 0.01 > 1.0
dense_error_d = np.abs(
(dense_d - dense_ana_dx) / dense_ana_dx) / 0.01 > 1.0
error = np.abs((x - ana_x) / ana_x) / 0.01 > 1.0
assert (np.any(dense_error) == False and np.any(dense_error_d) == False
and np.any(error) == False)
def test_no_integration():
# Tests the case when ti=tf
ts = np.linspace(1, 100, 5000)
ws = np.sqrt(ts)
gs = np.zeros_like(ws)
ti = 1.0
tf = ti
x0 = airy(-ti)[0] + 1j * airy(-ti)[2]
dx0 = -airy(-ti)[1] - 1j * airy(-ti)[3]
sol = pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0, even_grid=True)
t = np.asarray(sol['t'])
x = np.asarray(sol['sol'])
dx = np.asarray(sol['dsol'])
assert (x.shape[0] == 1 and dx.shape[0] == 1 and x[0] == x0
and dx[0] == dx0)
gs = np.zeros_like(ws)
# Define the range of integration and the initial conditions
ti = 1.0
tf = 100.0
x0 = airy(-ti)[0] + 1j * airy(-ti)[2]
dx0 = -airy(-ti)[1] - 1j * airy(-ti)[3]
t_eval = np.linspace(ti, ti + 1.0, 10)
# Solve the system
# Test forward integration
#sol = pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0,t_eval=t_eval) # Uneven grid assumed, even grid given
#sol = pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0,t_eval=t_eval,even_grid=True) # Even grid expected, even grid given
# Test backward integration
#x0 = airy(-tf)[0] + 1j*airy(-tf)[2]
#dx0 = -airy(-tf)[1] - 1j*airy(-tf)[3]
#sol = pyoscode.solve(ts, ws, gs, tf, ti, x0, dx0,t_eval=t_eval,even_grid=True) # X
sol = pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0, t_eval=t_eval) # X
t = np.asarray(sol['t'])
x = np.asarray(sol['sol'])
dense = np.asarray(sol['x_eval'])
print("dense output: ", dense[0])
types = np.asarray(sol['types'])
# Plot the solution
ana_t = np.linspace(ti, tf, 5000)
plt.plot(ana_t, [1j * airy(-T)[0] - airy(-T)[2] for T in ana_t],
color='black',
lw=0.5,
label='true solution')
plt.plot(t[types == 0], 1j * x[types == 0], '.', color='C0', label='RK steps')
plt.plot(t[types == 1], 1j * x[types == 1], '.', color='C1', label='WKB steps')
plt.plot(t_eval, 1j * dense, color='C1', label='dense output')
plt.legend()
import pyoscode
import numpy
from scipy.special import airy
from matplotlib import pyplot as plt
# Define the frequency and friction term over the range of integration
ts = numpy.linspace(1, 1000, 5000)
ws = numpy.sqrt(ts)
gs = numpy.zeros_like(ws)
# Define the range of integration and the initial conditions
ti = 1.0
tf = 1000.0
x0 = airy(-ti)[0] + 1j * airy(-ti)[2]
dx0 = -airy(-ti)[1] - 1j * airy(-ti)[3]
# Solve the system
sol = pyoscode.solve(ts, ws, gs, ti, tf, x0, dx0)
t = numpy.asarray(sol['t'])
x = numpy.asarray(sol['sol'])
types = numpy.asarray(sol['types'])
# Plot the solution
ana_t = numpy.linspace(1, 35.0, 1000)
plt.plot(ana_t, [airy(-T)[0] for T in ana_t], label='true solution')
plt.plot(t[types == 0], x[types == 0], '.', color='red', label='RK steps')
plt.plot(t[types == 1], x[types == 1], '.', color='green', label='WKB steps')
plt.legend()
plt.xlim((1.0, 35.0))
plt.ylim((-1.0, 1.0))
plt.xlabel('t')
plt.ylabel('Ai(-t)')
plt.savefig('airy-example.png')
