def draw_streamlines(self, res=200, show=True):
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
plt.xlim(-0.5, 1.5)
plt.ylim(-0.5, 0.5)
xrng = np.diff(np.array(ax.get_xlim()))
yrng = np.diff(np.array(ax.get_ylim()))
x = np.linspace(*ax.get_xlim(), int(np.round(res * xrng / yrng)))
y = np.linspace(*ax.get_ylim(), res)
X, Y = np.meshgrid(x, y)
shape = X.shape
X = X.flatten()
Y = Y.flatten()
U, V = self.calculate_velocity(X, Y)
X = X.reshape(shape)
Y = Y.reshape(shape)
U = U.reshape(shape)
V = V.reshape(shape)
# NaN out any points inside the airfoil
for airfoil in self.airfoils:
contains = airfoil.contains_points(X, Y)
U[contains] = np.NaN
V[contains] = np.NaN
speed = (U**2 + V**2)**0.5
Cp = 1 - speed**2
### Draw the airfoils
for airfoil in self.airfoils:
plt.fill(airfoil.x(), airfoil.y(), "k", linewidth=0, zorder=4)
plt.streamplot(
x,
y,
U,
V,
color=speed,
density=2.5,
arrowsize=0,
cmap=plt.get_cmap('coolwarm_r'),
)
CB = plt.colorbar(
orientation="horizontal",
shrink=0.8,
aspect=40,
)
CB.set_label(r"Relative Airspeed ($U/U_\infty$)")
plt.clim(0.6, 1.4)
plt.gca().set_aspect('equal', adjustable='box')
plt.xlabel(r"$x/c$")
plt.ylabel(r"$y/c$")
plt.title(rf"Inviscid Airfoil: Flow Field")
plt.tight_layout()
if show:
plt.show()
def draw(
self,
scalar_to_plot:
str = "potential", # "potential", "streamfunction", "xvel", "yvel", "velmag", "Cp"
x_points: np.ndarray = np.linspace(-10, 10, 400),
y_points: np.ndarray = np.linspace(-10, 10, 300),
percentiles_to_include=99.7,
show=True,
):
X, Y = np.meshgrid(x_points, y_points)
X_r = np.reshape(X, -1)
Y_r = np.reshape(Y, -1)
points = np.vstack((X_r, Y_r)).T
if scalar_to_plot == "potential":
scalar_to_plot_value = sum(
[object.get_potential_at(points) for object in self.objects])
elif scalar_to_plot == "streamfunction":
scalar_to_plot_value = sum([
object.get_streamfunction_at(points) for object in self.objects
])
elif scalar_to_plot == "xvel":
scalar_to_plot_value = sum(
[object.get_x_velocity_at(points) for object in self.objects])
elif scalar_to_plot == "yvel":
scalar_to_plot_value = sum(
[object.get_y_velocity_at(points) for object in self.objects])
elif scalar_to_plot == "velmag":
x_vels = sum(
[object.get_x_velocity_at(points) for object in self.objects])
y_vels = sum(
[object.get_y_velocity_at(points) for object in self.objects])
scalar_to_plot_value = np.sqrt(x_vels**2 + y_vels**2)
elif scalar_to_plot == "Cp":
x_vels = sum(
[object.get_x_velocity_at(points) for object in self.objects])
y_vels = sum(
[object.get_y_velocity_at(points) for object in self.objects])
V = np.sqrt(x_vels**2 + y_vels**2)
scalar_to_plot_value = 1 - V**2
else:
raise ValueError("Bad value of `scalar_to_plot`!")
min = np.nanpercentile(scalar_to_plot_value,
50 - percentiles_to_include / 2)
max = np.nanpercentile(scalar_to_plot_value,
50 + percentiles_to_include / 2)
contour(x_points,
y_points,
scalar_to_plot_value.reshape(X.shape),
levels=np.linspace(min, max, 80),
linelabels=False,
cmap=plt.get_cmap("rainbow"),
contour_kwargs={
"linestyles": 'solid',
"alpha": 0.4
})
plt.gca().set_aspect("equal", adjustable='box')
show_plot(f"Potential Flow: {scalar_to_plot}", "$x$", "$y$", show=show)
def test_interpn_fill_value():
def value_func_3d(x, y, z):
return 2 * x + 3 * y - z
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 20)
z = np.linspace(0, 5, 30)
points = (x, y, z)
values = value_func_3d(*np.meshgrid(*points, indexing="ij"))
point = np.array([5.21, 3.12, 1.15])
value = np.interpn(
points, values, point,
method="bspline",
bounds_error=False,
fill_value=-17
)
assert value == pytest.approx(-17)
value = np.interpn(
points, values, point,
method="bspline",
bounds_error=False,
)
assert np.isnan(value)
value = np.interpn(
points, values, point,
method="bspline",
bounds_error=None,
fill_value=None
)
assert value == pytest.approx(value_func_3d(5, 3.12, 1.15))
def test_interpn_bounds_error_multiple_samples():
def value_func_3d(x, y, z):
return 2 * x + 3 * y - z
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 20)
z = np.linspace(0, 5, 30)
points = (x, y, z)
values = value_func_3d(*np.meshgrid(*points, indexing="ij"))
point = np.array([
[2.21, 3.12, 1.15],
[3.42, 5.81, 2.43]
])
with pytest.raises(ValueError):
value = np.interpn(
points, values, point
)
### CasADi test
point = cas.DM(point)
with pytest.raises(ValueError):
value = np.interpn(
points, values, point
)
def plot(self, resolution=250):
def axis_range(x_data_axis: np.ndarray) -> Tuple[float, float]:
"""
Given the entries of one axis of the dependent variable, determine a min/max range over which to plot the fit.
Args:
x_data_axis: The entries of one axis of the dependent variable, i.e. x_data["x1"].
Returns: A tuple representing the (min, max) value over which to plot that axis.
"""
minval = np.min(x_data_axis)
maxval = np.max(x_data_axis)
return (minval, maxval)
if self.input_dimensionality() == 1:
### Parse the x_data
if self.input_names() is not None:
x_name = self.x_data.keys()[0]
x_data = self.x_data.values()[0]
minval, maxval = axis_range(x_data)
x_fit = {x_name: np.linspace(minval, maxval, resolution)}
y_fit = self(x_fit)
else:
x_name = "x"
x_data = self.x_data
minval, maxval = axis_range(x_data)
x_fit = np.linspace(minval, maxval, resolution)
y_fit = self(x_fit)
### Plot the 2D figure
fig = plt.figure(dpi=200)
plt.plot(
x_data,
self.y_data,
".k",
label="Data",
)
plt.plot(
x_fit,
y_fit,
"-",
color="#cb3bff",
label="Fit",
zorder=4,
)
plt.xlabel(x_name)
plt.ylabel(rf"$f({x_name})$")
plt.title(r"Fit of FittedModel")
plt.tight_layout()
plt.legend()
plt.show()
else:
raise NotImplementedError()
def plot_tropopause_altitude():
fig, ax = plt.subplots()
day_of_years = np.linspace(0, 365, 250)
latitudes = np.linspace(-80, 80, 200)
Day_of_years, Latitudes = np.meshgrid(day_of_years, latitudes)
trop_alt = tropopause_altitude(
Latitudes.flatten(),
Day_of_years.flatten()
).reshape(Latitudes.shape)
args = [
day_of_years,
latitudes,
trop_alt / 1e3
]
levels = np.arange(10, 20.1, 1)
CS = plt.contour(*args, levels=levels, linewidths=0.5, colors="k", alpha=0.7)
CF = plt.contourf(*args, levels=levels, cmap='viridis_r', alpha=0.7, extend="both")
cbar = plt.colorbar(label="Tropopause Altitude [km]", extendrect=True)
ax.clabel(CS, inline=1, fontsize=9, fmt="%.0f km")
plt.xticks(
np.linspace(0, 365, 13)[:-1],
(
"Jan. 1",
"Feb. 1",
"Mar. 1",
"Apr. 1",
"May 1",
"June 1",
"July 1",
"Aug. 1",
"Sep. 1",
"Oct. 1",
"Nov. 1",
"Dec. 1"
),
rotation=40
)
lat_label_vals = np.arange(-80, 80.1, 20)
lat_labels = []
for lat in lat_label_vals:
if lat >= 0:
lat_labels.append(f"{lat:.0f}N")
else:
lat_labels.append(f"{-lat:.0f}S")
plt.yticks(
lat_label_vals,
lat_labels
)
show_plot(
f"Tropopause Altitude by Season and Latitude",
xlabel="Day of Year",
ylabel="Latitude",
)
def test_opti_hanging_chain_with_callback(plot=False):
N = 40
m = 40 / N
D = 70 * N
g = 9.81
L = 1
opti = asb.Opti()
x = opti.variable(init_guess=np.linspace(-2, 2, N))
y = opti.variable(
init_guess=1,
n_vars=N,
)
distance = np.sqrt( # Distance from one node to the next
np.diff(x)**2 + np.diff(y)**2)
potential_energy_spring = 0.5 * D * np.sum((distance - L / N)**2)
potential_energy_gravity = g * m * np.sum(y)
potential_energy = potential_energy_spring + potential_energy_gravity
opti.minimize(potential_energy)
# Add end point constraints
opti.subject_to([x[0] == -2, y[0] == 1, x[-1] == 2, y[-1] == 1])
# Add a ground constraint
opti.subject_to(y >= np.cos(0.1 * x) - 0.5)
# Add a callback
if plot:
def my_callback(iter: int):
plt.plot(opti.debug.value(x),
opti.debug.value(y),
".-",
label=f"Iter {iter}",
zorder=3 + iter)
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
x_ground = np.linspace(-2, 2, N)
y_ground = np.cos(0.1 * x_ground) - 0.5
plt.plot(x_ground, y_ground, "--k", zorder=2)
else:
def my_callback(iter: int):
print(f"Iter {iter}")
print(f"\tx = {opti.debug.value(x)}")
print(f"\ty = {opti.debug.value(y)}")
sol = opti.solve(callback=my_callback)
assert sol.value(potential_energy) == pytest.approx(626.462, abs=1e-3)
if plot:
plt.show()
def test_quadcopter_navigation():
opti = asb.Opti()
N = 300
time_final = 1
time = np.linspace(0, time_final, N)
left_thrust = opti.variable(init_guess=0.5, scale=1, n_vars=N, lower_bound=0, upper_bound=1)
right_thrust = opti.variable(init_guess=0.5, scale=1, n_vars=N, lower_bound=0, upper_bound=1)
mass = 0.1
dyn = asb.FreeBodyDynamics(
opti_to_add_constraints_to=opti,
time=time,
xe=opti.variable(init_guess=np.linspace(0, 1, N)),
ze=opti.variable(init_guess=np.linspace(0, -1, N)),
u=opti.variable(init_guess=0, n_vars=N),
w=opti.variable(init_guess=0, n_vars=N),
theta=opti.variable(init_guess=np.linspace(np.pi / 2, np.pi / 2, N)),
q=opti.variable(init_guess=0, n_vars=N),
X=left_thrust + right_thrust,
M=(right_thrust - left_thrust) * 0.1 / 2,
mass=mass,
Iyy=0.5 * mass * 0.1 ** 2,
g=9.81,
)
opti.subject_to([ # Starting state
dyn.xe[0] == 0,
dyn.ze[0] == 0,
dyn.u[0] == 0,
dyn.w[0] == 0,
dyn.theta[0] == np.radians(90),
dyn.q[0] == 0,
])
opti.subject_to([ # Final state
dyn.xe[-1] == 1,
dyn.ze[-1] == -1,
dyn.u[-1] == 0,
dyn.w[-1] == 0,
dyn.theta[-1] == np.radians(90),
dyn.q[-1] == 0,
])
effort = np.sum( # The average "effort per second", where effort is integrated as follows:
np.trapz(left_thrust ** 2 + right_thrust ** 2) * np.diff(time)
) / time_final
opti.minimize(effort)
sol = opti.solve()
dyn.substitute_solution(sol)
assert sol.value(effort) == pytest.approx(0.714563, rel=0.01)
print(sol.value(effort))
def test_block_move_fixed_time():
opti = asb.Opti()
n_timesteps = 300
time = np.linspace(0, 1, n_timesteps)
dyn = asb.DynamicsPointMass1DHorizontal(
mass_props=asb.MassProperties(mass=1),
x_e=opti.variable(init_guess=np.linspace(0, 1, n_timesteps)),
u_e=opti.variable(init_guess=1, n_vars=n_timesteps),
)
u = opti.variable(init_guess=np.linspace(1, -1, n_timesteps))
dyn.add_force(
Fx=u
)
dyn.constrain_derivatives(
opti=opti,
time=time
)
opti.subject_to([
dyn.x_e[0] == 0,
dyn.x_e[-1] == 1,
dyn.u_e[0] == 0,
dyn.u_e[-1] == 0,
])
# effort = np.sum(
# np.trapz(dyn.X ** 2) * np.diff(time)
# )
effort = np.sum( # More sophisticated integral-of-squares integration (closed form correct)
np.diff(time) / 3 *
(u[:-1] ** 2 + u[:-1] * u[1:] + u[1:] ** 2)
)
opti.minimize(effort)
sol = opti.solve()
dyn.substitute_solution(sol)
assert dyn.x_e[0] == pytest.approx(0)
assert dyn.x_e[-1] == pytest.approx(1)
assert dyn.u_e[0] == pytest.approx(0)
assert dyn.u_e[-1] == pytest.approx(0)
assert np.max(dyn.u_e) == pytest.approx(1.5, abs=0.01)
assert sol.value(u)[0] == pytest.approx(6, abs=0.05)
assert sol.value(u)[-1] == pytest.approx(-6, abs=0.05)
def test_quadcopter_flip():
opti = asb.Opti()
N = 300
time_final = opti.variable(init_guess=1, lower_bound=0)
time = np.linspace(0, time_final, N)
left_thrust = opti.variable(init_guess=0.7, scale=1, n_vars=N, lower_bound=0, upper_bound=1)
right_thrust = opti.variable(init_guess=0.6, scale=1, n_vars=N, lower_bound=0, upper_bound=1)
mass = 0.1
dyn = asb.FreeBodyDynamics(
opti_to_add_constraints_to=opti,
time=time,
xe=opti.variable(init_guess=np.linspace(0, 1, N)),
ze=opti.variable(init_guess=0, n_vars=N),
u=opti.variable(init_guess=0, n_vars=N),
w=opti.variable(init_guess=0, n_vars=N),
theta=opti.variable(init_guess=np.linspace(np.pi / 2, np.pi / 2 - 2 * np.pi, N)),
q=opti.variable(init_guess=0, n_vars=N),
X=left_thrust + right_thrust,
M=(right_thrust - left_thrust) * 0.1 / 2,
mass=mass,
Iyy=0.5 * mass * 0.1 ** 2,
g=9.81,
)
opti.subject_to([ # Starting state
dyn.xe[0] == 0,
dyn.ze[0] == 0,
dyn.u[0] == 0,
dyn.w[0] == 0,
dyn.theta[0] == np.radians(90),
dyn.q[0] == 0,
])
opti.subject_to([ # Final state
dyn.xe[-1] == 1,
dyn.ze[-1] == 0,
dyn.u[-1] == 0,
dyn.w[-1] == 0,
dyn.theta[-1] == np.radians(90 - 360),
dyn.q[-1] == 0,
])
opti.minimize(time_final)
sol = opti.solve(verbose=False)
dyn.substitute_solution(sol)
assert sol.value(time_final) == pytest.approx(0.824, abs=0.01)
def test_block_move_minimum_time():
opti = asb.Opti()
n_timesteps = 300
time = np.linspace(
0,
opti.variable(init_guess=1, lower_bound=0),
n_timesteps,
)
dyn = asb.DynamicsPointMass1DHorizontal(
mass_props=asb.MassProperties(mass=1),
x_e=opti.variable(init_guess=np.linspace(0, 1, n_timesteps)),
u_e=opti.variable(init_guess=1, n_vars=n_timesteps),
)
u = opti.variable(init_guess=np.linspace(1, -1, n_timesteps), lower_bound=-1, upper_bound=1)
dyn.add_force(
Fx=u
)
dyn.constrain_derivatives(
opti=opti,
time=time
)
opti.subject_to([
dyn.x_e[0] == 0,
dyn.x_e[-1] == 1,
dyn.u_e[0] == 0,
dyn.u_e[-1] == 0,
])
opti.minimize(
time[-1]
)
sol = opti.solve()
dyn.substitute_solution(sol)
assert dyn.x_e[0] == pytest.approx(0)
assert dyn.x_e[-1] == pytest.approx(1)
assert dyn.u_e[0] == pytest.approx(0)
assert dyn.u_e[-1] == pytest.approx(0)
assert np.max(dyn.u_e) == pytest.approx(1, abs=0.01)
assert sol.value(u)[0] == pytest.approx(1, abs=0.05)
assert sol.value(u)[-1] == pytest.approx(-1, abs=0.05)
assert np.mean(np.abs(sol.value(u))) == pytest.approx(1, abs=0.01)
def plot_winds_at_tropopause_altitude():
fig, ax = plt.subplots()
day_of_years = np.linspace(0, 365, 150)
latitudes = np.linspace(-80, 80, 120)
Day_of_years, Latitudes = np.meshgrid(day_of_years, latitudes)
winds = wind_speed_world_95(
altitude=tropopause_altitude(Latitudes.flatten(),
Day_of_years.flatten()),
latitude=Latitudes.flatten(),
day_of_year=Day_of_years.flatten(),
).reshape(Latitudes.shape)
args = [day_of_years, latitudes, winds]
levels = np.arange(0, 80.1, 5)
CS = plt.contour(*args,
levels=levels,
linewidths=0.5,
colors="k",
alpha=0.7)
CF = plt.contourf(*args,
levels=levels,
cmap='viridis_r',
alpha=0.7,
extend="max")
cbar = plt.colorbar(label="Wind Speed [m/s]", extendrect=True)
ax.clabel(CS, inline=1, fontsize=9, fmt="%.0f m/s")
plt.xticks(
np.linspace(0, 365, 13)[:-1],
("Jan. 1", "Feb. 1", "Mar. 1", "Apr. 1", "May 1", "June 1",
"July 1", "Aug. 1", "Sep. 1", "Oct. 1", "Nov. 1", "Dec. 1"),
rotation=40)
lat_label_vals = np.arange(-80, 80.1, 20)
lat_labels = []
for lat in lat_label_vals:
if lat >= 0:
lat_labels.append(f"{lat:.0f}N")
else:
lat_labels.append(f"{-lat:.0f}S")
plt.yticks(lat_label_vals, lat_labels)
show_plot(
f"95th-Percentile Wind Speeds at Tropopause Altitude",
xlabel="Day of Year",
ylabel="Latitude",
)
def test_fit_model_weighting():
x = np.linspace(0, 10)
y = np.sin(x)
fm = FittedModel(
model=lambda x, p: p["m"] * x + p["b"],
x_data=x,
y_data=y,
parameter_guesses={
"m": 0,
"b": 0,
},
weights=None
) # Fit a model with no weighting
assert fm(10) != pytest.approx(5, abs=1) # Doesn't give a high value at x = 10
fm = FittedModel(
model=lambda x, p: p["m"] * x + p["b"],
x_data=x,
y_data=y,
parameter_guesses={
"m": 0,
"b": 0,
},
weights=(x > 0) & (x < 2)
) # Fit a model with weighting
assert fm(10) == pytest.approx(5, abs=1) # Gives a high value at x = 10
fm.plot()
def interpolated_model():
np.random.seed(0) # Set a seed for repeatability.
### Make some data
x1 = np.linspace(0, 10, 11)
x2 = np.linspace(0, 10, 21)
X1, X2 = np.meshgrid(x1, x2, indexing="ij")
return InterpolatedModel(
x_data_coordinates={
"x1": x1,
"x2": x2,
},
y_data_structured=underlying_function_2D(X1, X2),
)
def test_rosenbrock_constrained(plot=False):
opti = asb.Opti()
x = opti.variable(init_guess=0)
y = opti.variable(init_guess=0)
r = opti.parameter()
f = (1 - x)**2 + (y - x**2)**2
opti.minimize(f)
con = x**2 + y**2 <= r
dual = opti.subject_to(con)
r_values = np.linspace(1, 3)
sols = [opti.solve({r: r_value}) for r_value in r_values]
fs = [sol.value(f) for sol in sols]
duals = [
sol.value(dual) # Ensure the dual can be evaluated
for sol in sols
]
if plot:
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
plt.plot(r_values, fs, label="$f$")
plt.plot(r_values, duals, label=r"Dual var. ($\frac{df}{dr}$)")
plt.legend()
plt.xlabel("$r$")
plt.show()
assert dual is not None # The dual should be a real value
assert r_values[0] == pytest.approx(1)
assert duals[0] == pytest.approx(0.10898760051521068, abs=1e-6)
def test_Linf_without_x_in_dict():
np.random.seed(0) # Set a seed for repeatability
### Making data
hour = np.linspace(1, 10, 100)
noise = 0.1 * np.random.randn(len(hour))
temperature_c = np.log(hour) + noise
### Fit
def model(x, p):
return p["m"] * x + p["b"]
x_data = hour
y_data = temperature_c
fitted_model = FittedModel(
model=model,
x_data=x_data,
y_data=y_data,
parameter_guesses={
"m": 0,
"b": 0,
},
residual_norm_type="Linf",
)
# Check that the fit is right
assert fitted_model.parameters["m"] == pytest.approx(0.247116, abs=1e-5)
assert fitted_model.parameters["b"] == pytest.approx(0.227797, abs=1e-5)
def test_softmax(plot=False):
# Test softmax
x = np.linspace(-10, 10, 100)
y1 = x
y2 = -2 * x - 3
hardness = 0.5
y_soft = np.softmax(y1, y2, hardness=hardness)
assert np.softmax(0, 0, hardness=1) == np.log(2)
if plot:
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(font_scale=1)
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
plt.plot(x, y1, label="y1")
plt.plot(x, y2, label="y2")
plt.plot(x, y_soft, label="softmax")
plt.xlabel(r"x")
plt.ylabel(r"y")
plt.title(r"Softmax")
plt.tight_layout()
plt.legend()
plt.show()
def test_calculate_induced_velocity_panel_coordinates():
X, Y = np.meshgrid(
np.linspace(-1, 2, 50),
np.linspace(-1, 1, 50),
indexing='ij',
)
X = X.flatten()
Y = Y.flatten()
U, V = calculate_induced_velocity_line_singularities(
x_field=X,
y_field=Y,
x_panels=np.array([-0.5, 1.5]),
y_panels=np.array([0, 0]),
gamma=np.array([1, 1]),
sigma=np.array([1, 1]),
)
def test_rocket_control_problem(plot=False):
### Constants
T = 100
d = 50
delta = 1e-3
f = 1000
c = np.ones(T)
### Optimization
opti = asb.Opti() # set up an optimization environment
x = opti.variable(init_guess=np.linspace(0, d, T)) # position
v = opti.variable(init_guess=d / T, n_vars=T) # velocity
a = opti.variable(init_guess=0, n_vars=T) # acceleration
gamma = opti.variable(init_guess=0,
n_vars=T) # instantaneous fuel consumption
a_max = opti.variable(init_guess=0) # maximum acceleration
opti.subject_to([
cas.diff(x) == v[:-1], # physics
cas.diff(v) == a[:-1], # physics
x[0] == 0, # boundary condition
v[0] == 0, # boundary condition
x[-1] == d, # boundary condition
v[-1] == 0, # boundary condition
gamma >= c * a, # lower bound on instantaneous fuel consumption
gamma >= -c * a, # lower bound on instantaneous fuel consumption
cas.sum1(gamma) <= f, # fuel consumption limit
cas.diff(a) <= delta, # jerk limits
cas.diff(a) >= -delta, # jerk limits
a_max >= a, # lower bound on maximum acceleration
a_max >= -a, # lower bound on maximum acceleration
])
opti.minimize(a_max) # minimize the peak acceleration
sol = opti.solve() # solve
assert sol.value(a_max) == pytest.approx(
0.02181991952, rel=1e-3) # solved externally with Julia JuMP
if plot:
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(palette=sns.color_palette("husl"))
fig, ax = plt.subplots(1, 1, figsize=(8, 6), dpi=200)
for i, val, lab in zip(np.arange(3), [x, v, a], ["$x$", "$v$", "$a$"]):
plt.subplot(3, 1, i + 1)
plt.plot(sol.value(val), label=lab)
plt.xlabel(r"Time [s]")
plt.ylabel(lab)
plt.legend()
plt.suptitle(r"Rocket Trajectory")
plt.tight_layout()
plt.show()
def interpolated_model():
np.random.seed(0) # Set a seed for repeatability.
### Make some data
x = np.linspace(0, 10, 11)
return InterpolatedModel(
x_data_coordinates=x,
y_data_structured=underlying_function_1D(x),
)
def test_interpn_linear_multiple_samples():
### NumPy test
def value_func_3d(x, y, z):
return 2 * x + 3 * y - z
x = np.linspace(0, 5, 10)
y = np.linspace(0, 5, 20)
z = np.linspace(0, 5, 30)
points = (x, y, z)
values = value_func_3d(*np.meshgrid(*points, indexing="ij"))
point = np.array([
[2.21, 3.12, 1.15],
[3.42, 0.81, 2.43]
])
value = np.interpn(
points, values, point
)
assert np.all(
value == pytest.approx(
value_func_3d(
*[
point[:, i] for i in range(point.shape[1])
]
)
)
)
assert len(value) == 2
### CasADi test
point = cas.DM(point)
value = np.interpn(
points, values, point
)
value_actual = value_func_3d(
*[
np.array(point[:, i]) for i in range(point.shape[1])
]
)
for i in range(len(value)):
assert value[i] == pytest.approx(float(value_actual[i]))
assert value.shape == (2,)
def plot_winds_at_day(day_of_year=0):
fig, ax = plt.subplots()
altitudes = np.linspace(0, 30000, 150)
latitudes = np.linspace(-80, 80, 120)
Altitudes, Latitudes = np.meshgrid(altitudes, latitudes)
winds = wind_speed_world_95(
altitude=Altitudes.flatten(),
latitude=Latitudes.flatten(),
day_of_year=day_of_year * np.ones_like(Altitudes.flatten()),
).reshape(Altitudes.shape)
args = [altitudes / 1e3, latitudes, winds]
levels = np.arange(0, 80.1, 5)
CS = plt.contour(*args,
levels=levels,
linewidths=0.5,
colors="k",
alpha=0.7)
CF = plt.contourf(*args,
levels=levels,
cmap='viridis_r',
alpha=0.7,
extend="max")
cbar = plt.colorbar(label="Wind Speed [m/s]", extendrect=True)
ax.clabel(CS, inline=1, fontsize=9, fmt="%.0f m/s")
lat_label_vals = np.arange(-80, 80.1, 20)
lat_labels = []
for lat in lat_label_vals:
if lat >= 0:
lat_labels.append(f"{lat:.0f}N")
else:
lat_labels.append(f"{-lat:.0f}S")
plt.yticks(lat_label_vals, lat_labels)
show_plot(
f"95th-Percentile Wind Speeds at Day {day_of_year:.0f}",
xlabel="Altitude [km]",
ylabel="Latitude",
)
def plot_underlying_function():
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(palette=sns.color_palette("husl"))
x = np.linspace(-10, 10, 500)
f = underlying_function(x)
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
plt.plot(x, f)
plt.title("Underlying Function")
plt.show()
def contour(
func: Callable,
x_range: Tuple[Union[float,int],Union[float,int]],
y_range: Tuple[Union[float,int],Union[float,int]],
resolution:int =50,
show:bool=True, # type: bool
):
"""
Makes a contour plot of a function of 2 variables. Can also plot a list of functions.
:param func: function of form f(x,y) to plot.
:param x_range: Range of x values to plot, expressed as a tuple (x_min, x_max)
:param y_range: Range of y values to plot, expressed as a tuple (y_min, y_max)
:param resolution: Resolution in x and y to plot. [int]
:param show: Should we show the plot?
:return:
"""
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
x = np.linspace(x_range[0], x_range[1], resolution)
y = np.linspace(y_range[0], y_range[1], resolution)
# TODO finish function
def main():
time = np.linspace(0, 10, 100) # Time in seconds
wing_velocity = 2 # Wing horizontal velocity in m/s
chord = 2
reduced_time = calculate_reduced_time(
time, wing_velocity, chord) # Number of semi chords travelled
# Visualize the gust profiles as well as the pitch maneuvers
fig, ax1 = plt.subplots(dpi=300)
ln1 = ax1.plot(reduced_time,
np.array([top_hat_gust(s) for s in reduced_time]),
label="Top-Hat Gust",
lw=3)
ln2 = ax1.plot(reduced_time,
np.array([sine_squared_gust(s) for s in reduced_time]),
label="Sine-Squared Gust",
lw=3)
ax1.set_xlabel("Reduced time")
ax1.set_ylabel("Velocity (m/s)")
ax2 = ax1.twinx()
ln3 = ax2.plot(reduced_time,
np.array([gaussian_pitch(s) for s in reduced_time]),
label="Guassian Pitch",
c="red",
ls="--",
lw=3)
ax2.set_ylabel("Angle of Attack, degrees")
lns = ln1 + ln2 + ln3
labs = [l.get_label() for l in lns]
ax2.legend(lns, labs, loc="lower right")
plt.title("Gust and pitch example profiles")
total_lift = pitching_through_transverse_gust(reduced_time, top_hat_gust,
wing_velocity,
gaussian_pitch)
gust_lift = calculate_lift_due_to_transverse_gust(reduced_time,
top_hat_gust,
wing_velocity,
gaussian_pitch)
pitch_lift = calculate_lift_due_to_pitching_profile(
reduced_time, gaussian_pitch)
added_mass_lift = added_mass_due_to_pitching(reduced_time, gaussian_pitch)
# Visualize the different sources of lift
plt.figure(dpi=300)
plt.plot(reduced_time, total_lift, label="Total Lift", lw=2)
plt.plot(reduced_time, gust_lift, label="Gust Lift", lw=2)
plt.plot(reduced_time, pitch_lift, label="Pitching Lift", lw=2)
plt.plot(reduced_time, added_mass_lift, label="Added Mass Lift", lw=2)
plt.legend()
plt.xlabel("Reduced time")
plt.ylabel("$C_\ell$")
plt.title("Guassian Pitch Maneuver Through Top-Hat Gust")
def max_thickness(
self, x_over_c_sample: np.ndarray = np.linspace(0, 1, 101)) -> float:
"""
Returns the maximum thickness of the airfoil.
Args:
x_over_c_sample: Where should the airfoil be sampled to determine the max thickness?
Returns: The maximum thickness, as a fraction of chord.
"""
return np.max(self.local_thickness(x_over_c=x_over_c_sample))
def draw(self, draw_mcl=True, backend="matplotlib", show=True):
"""
Draw the airfoil object.
:param draw_mcl: Should we draw the mean camber line (MCL)? [boolean]
:param backend: Which backend should we use? "plotly" or "matplotlib"
:return: None
"""
x = np.array(self.x()).reshape(-1)
y = np.array(self.y()).reshape(-1)
if draw_mcl:
x_mcl = np.linspace(np.min(x), np.max(x), len(x))
y_mcl = self.local_camber(x_mcl)
if backend == "matplotlib":
color = '#280887'
plt.plot(x, y, ".-", zorder=11, color=color)
plt.fill(x, y, zorder=10, color=color, alpha=0.2)
if draw_mcl:
plt.plot(x_mcl, y_mcl, "-", zorder=4, color=color, alpha=0.4)
plt.axis("equal")
plt.xlabel(r"$x/c$")
plt.ylabel(r"$y/c$")
plt.title(f"{self.name} Airfoil")
plt.tight_layout()
if show:
plt.show()
elif backend == "plotly":
from aerosandbox.visualization.plotly import go
fig = go.Figure()
fig.add_trace(
go.Scatter(x=x,
y=y,
mode="lines+markers",
name="Airfoil",
fill="toself",
line=dict(color="blue")), )
if draw_mcl:
fig.add_trace(
go.Scatter(x=x_mcl,
y=y_mcl,
mode="lines+markers",
name="Mean Camber Line (MCL)",
line=dict(color="navy")))
fig.update_layout(xaxis_title="x/c",
yaxis_title="y/c",
yaxis=dict(scaleanchor="x", scaleratio=1),
title=f"{self.name} Airfoil")
if show:
fig.show()
else:
return fig
def test_interpn_bspline_casadi():
"""
The bspline method should interpolate seperable cubic multidimensional polynomials exactly.
"""
def func(x, y, z): # Sphere function
return x ** 3 + y ** 3 + z ** 3
x = np.linspace(-5, 5, 10)
y = np.linspace(-5, 5, 20)
z = np.linspace(-5, 5, 30)
points = (x, y, z)
values = func(
*np.meshgrid(*points, indexing="ij")
)
point = np.array([0.4, 0.5, 0.6])
value = np.interpn(
points, values, point, method="bspline"
)
assert value == pytest.approx(func(*point))
def test_diff_atmosphere():
altitudes = np.linspace(-50e2, 150e3, 1000)
atmo_isa = Atmosphere(altitude=altitudes, method='isa')
atmo_diff = Atmosphere(altitude=altitudes)
temp_isa = atmo_isa.temperature()
pressure_isa = atmo_isa.pressure()
temp_diff = atmo_diff.temperature()
pressure_diff = atmo_diff.pressure()
assert max(abs(
(temp_isa - temp_diff) /
temp_isa)) < 0.025, "temperature failed for differentiable model"
assert max(abs(
(pressure_isa - pressure_diff) /
pressure_isa)) < 0.01, "pressure failed for differentiable model"
def draw(self, draw_mcl=True, backend="plotly", show=True):
"""
Draw the airfoil object.
:param draw_mcl: Should we draw the mean camber line (MCL)? [boolean]
:param backend: Which backend should we use? "plotly" or "matplotlib"
:return: None
"""
x = np.array(self.x()).reshape(-1)
y = np.array(self.y()).reshape(-1)
if draw_mcl:
x_mcl = np.linspace(np.min(x), np.max(x), len(x))
y_mcl = self.local_camber(x_mcl)
if backend == "plotly":
fig = go.Figure()
fig.add_trace(
go.Scatter(x=x,
y=y,
mode="lines+markers",
name="Airfoil",
fill="toself",
line=dict(color="blue")), )
if draw_mcl:
fig.add_trace(
go.Scatter(x=x_mcl,
y=y_mcl,
mode="lines+markers",
name="Mean Camber Line (MCL)",
line=dict(color="navy")))
fig.update_layout(xaxis_title="x/c",
yaxis_title="y/c",
yaxis=dict(scaleanchor="x", scaleratio=1),
title="%s Airfoil" % self.name)
if show:
fig.show()
else:
return fig
elif backend == "matplotlib":
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
plt.plot(x, y, ".-", zorder=11, color='#280887')
if draw_mcl:
plt.plot(x_mcl, y_mcl, "-", zorder=4, color='#28088744')
plt.axis("equal")
plt.xlabel(r"$x/c$")
plt.ylabel(r"$y/c$")
plt.title("%s Airfoil" % self.name)
plt.tight_layout()
if show:
plt.show()
else:
return fig, ax