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 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 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 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",
)
import aerosandbox.numpy as np
np.random.seed(0) # Fix a seed for reproducibility
### Create some data (some fictional system where temperature is a function of time, and we're measuring it)
n = 20
time = 100 * np.random.rand(n)
actual_temperature = 2 * time + 20 # True physics of the system
noise = 10 * np.random.randn(n)
measured_temperature = actual_temperature + noise # Measured temperature of the system
### Add in a dropout measurement (say, the sensor wire randomly came loose and gave us a 0 reading)
time = np.hstack((time, 90))
measured_temperature = np.hstack((measured_temperature, 0))
if __name__ == '__main__':
from aerosandbox.tools.pretty_plots import plt, sns, mpl, show_plot
fig, ax = plt.subplots()
plt.plot(time, measured_temperature, ".")
show_plot(xlabel="Time", ylabel="Measured Temperature")
af = asb.Airfoil("dae11")
af.generate_polars()
alpha = np.linspace(-40, 40, 300)
re = np.geomspace(1e4, 1e12, 100)
Alpha, Re = np.meshgrid(alpha, re)
af.CL_function(alpha=0, Re=1e6)
CL = af.CL_function(Alpha.flatten(), Re.flatten()).reshape(Alpha.shape)
CD = af.CD_function(Alpha.flatten(), Re.flatten()).reshape(Alpha.shape)
CM = af.CM_function(Alpha.flatten(), Re.flatten()).reshape(Alpha.shape)
##### Plot alpha-Re contours
from aerosandbox.tools.pretty_plots import plt, show_plot, contour
fig, ax = plt.subplots()
contour(Alpha, Re, CL, levels=30, colorbar_label=r"$C_L$")
plt.scatter(af.xfoil_data["alpha"],
af.xfoil_data["Re"],
color="k",
alpha=0.2)
plt.yscale('log')
show_plot(
f"Auto-generated Polar for {af.name} Airfoil",
"Angle of Attack [deg]",
"Reynolds Number [-]",
)
fig, ax = plt.subplots()
contour(Alpha,
Re,
##### Tangential force calculation
CT = (pt1_star + pt2_star * cosa + pt3_star * cosa**3) * sina**2
##### Conversion to wind axes
CL = CN * cosa + CT * sina
CD = CN * sina - CT * cosa
CM = np.zeros_like(CL) # TODO
return CL, CD, CM
if __name__ == '__main__':
af = Airfoil("naca0012")
alpha = np.linspace(0, 360, 721)
CL, CD, CM = airfoil_coefficients_post_stall(af, alpha)
from aerosandbox.tools.pretty_plots import plt, show_plot, set_ticks
fig, ax = plt.subplots(1, 2, figsize=(8, 5))
plt.sca(ax[0])
plt.plot(alpha, CL)
plt.xlabel("AoA")
plt.ylabel("CL")
set_ticks(45, 15, 0.5, 0.1)
plt.sca(ax[1])
plt.plot(alpha, CD)
plt.xlabel("AoA")
plt.ylabel("CD")
set_ticks(45, 15, 0.5, 0.1)
show_plot()
from aerosandbox.tools.pretty_plots import plt, show_plot, equal
vars_to_plot = {
**dyn.state,
"alpha" : dyn.alpha,
"beta" : dyn.beta,
"speed" : dyn.speed,
"altitude": dyn.altitude,
"CL" : aero["CL"],
"CY" : aero["CY"],
"CD" : aero["CD"],
"Cl" : aero["Cl"],
"Cm" : aero["Cm"],
"Cn" : aero["Cn"],
}
fig, axes = plt.subplots(6, 4, figsize=(15, 10), sharex=True)
for var_to_plot, ax in zip(vars_to_plot.items(), axes.flatten(order="F")):
plt.sca(ax)
k, v = var_to_plot
plt.plot(dyn.time, v)
plt.ylabel(k)
show_plot()
fig, ax = plt.subplots()
plt.plot(dyn.xe, dyn.altitude, "k")
sc = plt.scatter(dyn.xe, dyn.altitude, c=dyn.speed, cmap=plt.get_cmap("rainbow"), zorder=4)
plt.axis('equal')
plt.colorbar(label="Airspeed [m/s]")
show_plot("Trajectory using `asb.AeroBuildup` Flight Dynamics", "$x_e$", "$-z_e$")
"m_b": M_b[1],
"n_b": M_b[2]
}
if __name__ == '__main__':
from aerosandbox.aerodynamics.aero_3D.test_aero_3D.geometries.conventional import airplane
aero = AeroBuildup(
airplane=airplane,
op_point=OperatingPoint(alpha=0, beta=1),
).run()
from aerosandbox.tools.pretty_plots import plt, show_plot, contour, equal, set_ticks
fig, ax = plt.subplots(2, 2)
alpha = np.linspace(-10, 10, 1000)
aero = AeroBuildup(
airplane=airplane,
op_point=OperatingPoint(velocity=100, alpha=alpha, beta=0),
).run()
plt.sca(ax[0, 0])
plt.plot(alpha, aero["CL"])
plt.xlabel(r"$\alpha$ [deg]")
plt.ylabel(r"$C_L$")
set_ticks(5, 1, 0.5, 0.1)
plt.sca(ax[0, 1])
plt.plot(alpha, aero["CD"])
plt.xlabel(r"$\alpha$ [deg]")
