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)
np.linspace(Y.min(), Y.max(), 500),
)
F_plot = interp({
"x": X_plot.flatten(),
"y": Y_plot.flatten()
}).reshape(X_plot.shape)
ax.plot_surface(
X_plot, Y_plot, F_plot,
color="red",
edgecolors=(1, 1, 1, 0.5),
linewidth=0.5,
alpha=0.2,
rcount=40,
ccount=40,
shade=True,
)
plt.xlabel("x")
plt.ylabel("y")
plt.show()
import aerosandbox as asb
import aerosandbox.numpy as np
opti = asb.Opti()
x = opti.variable(init_guess=0)
y = opti.variable(init_guess=0)
opti.minimize(interp({"x": x, "y": y}))
sol = opti.solve()
print(sol.value(x))
print(sol.value(y))
##### Plot Polars
fig, ax = plt.subplots(2, 2, figsize=(8, 8))
Re = 1e6
alpha_lowres = np.linspace(-15, 15, 31)
ma = alpha
mCL = af.CL_function(alpha, Re)
mCD = af.CD_function(alpha, Re)
xf_run = asb.XFoil(af, Re=Re, max_iter=20).alpha(alpha_lowres)
xa = xf_run["alpha"]
xCL = xf_run["CL"]
xCD = xf_run["CD"]
plt.sca(ax[0, 0])
plt.plot(ma, mCL)
plt.plot(xa, xCL, ".")
plt.xlabel("Angle of Attack [deg]")
plt.ylabel("Lift Coefficient $C_L$ [-]")
plt.sca(ax[0, 1])
plt.plot(ma, mCD)
plt.plot(xa, xCD, ".")
plt.ylim(0, 0.05)
plt.xlabel("Angle of Attack [deg]")
plt.ylabel("Drag Coefficient $C_D$ [-]")
plt.sca(ax[1, 0])
plt.plot(mCD, mCL)
plt.plot(xCD, xCL, ".")
plt.xlim(0, 0.05)
plt.xlabel("Drag Coefficient $C_D$ [-]")
plt.ylabel("Lift Coefficient $C_L$ [-]")
##### 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()
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]")
plt.ylabel(r"$C_D$")
set_ticks(5, 1, 0.05, 0.01)
plt.ylim(bottom=0)
plt.sca(ax[1, 0])
plt.plot(alpha, aero["Cm"])
plt.xlabel(r"$\alpha$ [deg]")
plt.ylabel(r"$C_m$")
set_ticks(5, 1, 0.5, 0.1)