def test_sigeq(self):
x = Variable("x")
y = VectorVariable(1, "y")
c = Variable("c")
# test left vector input to sigeq
with SignomialsEnabled():
m = Model(c, [
c >= (x + 0.25)**2 + (y - 0.5)**2,
SignomialEquality(x**2 + x, y)
])
sol = m.localsolve(solver=self.solver, verbosity=0, mutategp=False)
self.assertAlmostEqual(sol("x"), 0.1639472, self.ndig)
self.assertAlmostEqual(sol("y")[0], 0.1908254, self.ndig)
self.assertAlmostEqual(sol("c"), 0.2669448, self.ndig)
# test right vector input to sigeq
with SignomialsEnabled():
m = Model(c, [
c >= (x + 0.25)**2 + (y - 0.5)**2,
SignomialEquality(y, x**2 + x)
])
sol = m.localsolve(solver=self.solver, verbosity=0)
self.assertAlmostEqual(sol("x"), 0.1639472, self.ndig)
self.assertAlmostEqual(sol("y")[0], 0.1908254, self.ndig)
self.assertAlmostEqual(sol("c"), 0.2669448, self.ndig)
# test scalar input to sigeq
y = Variable("y")
with SignomialsEnabled():
m = Model(c, [
c >= (x + 0.25)**2 + (y - 0.5)**2,
SignomialEquality(x**2 + x, y)
])
sol = m.localsolve(solver=self.solver, verbosity=0)
self.assertAlmostEqual(sol("x"), 0.1639472, self.ndig)
self.assertAlmostEqual(sol("y"), 0.1908254, self.ndig)
self.assertAlmostEqual(sol("c"), 0.2669448, self.ndig)
def test_sp_substitutions(self):
x = Variable("x")
y = Variable("y", 1)
z = Variable("z", 4)
from io import StringIO
old_stdout = sys.stdout
sys.stdout = stringout = StringIO()
with SignomialsEnabled():
m1 = Model(x, [x + z >= y])
with self.assertRaises(UnnecessarySGP):
m1.localsolve(verbosity=0, solver=self.solver)
with self.assertRaises(UnboundedGP):
m1.solve(verbosity=0, solver=self.solver)
with SignomialsEnabled():
m2 = Model(x, [x + y >= z])
m2.substitutions[y] = 1
m2.substitutions[z] = 4
sol = m2.solve(self.solver, verbosity=0)
self.assertAlmostEqual(sol["cost"], 3, self.ndig)
sys.stdout = old_stdout
self.assertEqual(
stringout.getvalue(),
("Warning: SignomialConstraint %s became the tautological"
" constraint 0 <= 3 + x after substitution.\n"
"Warning: SignomialConstraint %s became the tautological"
" constraint 0 <= 3 + x after substitution.\n" %
(str(m1[0]), str(m1[0]))))
def test_sp_relaxation(self):
w = Variable("w")
x = Variable("x")
y = Variable("y")
z = Variable("z")
with SignomialsEnabled():
m = Model(x, [x + y >= w, x + y <= z / 2, y <= x, y >= 1], {
z: 3,
w: 3
})
r1 = ConstantsRelaxed(m)
self.assertEqual(len(r1.varkeys), 8)
with self.assertRaises(ValueError):
_ = Model(x * r1.relaxvars, r1) # no "prod"
sp = Model(x * r1.relaxvars.prod()**10, r1).sp(use_pccp=False)
cost = sp.localsolve(verbosity=0, solver=self.solver)["cost"]
self.assertAlmostEqual(cost / 1024, 1, self.ndig)
m.debug(verbosity=0, solver=self.solver)
with SignomialsEnabled():
m = Model(x, [x + y >= z, x + y <= z / 2, y <= x, y >= 1], {z: 3})
m.debug(verbosity=0, solver=self.solver)
r2 = ConstraintsRelaxed(m)
self.assertEqual(len(r2.varkeys), 7)
sp = Model(x * r2.relaxvars.prod()**10, r2).sp(use_pccp=False)
cost = sp.localsolve(verbosity=0, solver=self.solver)["cost"]
self.assertAlmostEqual(cost / 1024, 1, self.ndig)
with SignomialsEnabled():
m = Model(x, [x + y >= z, x + y <= z / 2, y <= x, y >= 1], {z: 3})
m.debug(verbosity=0, solver=self.solver)
r3 = ConstraintsRelaxedEqually(m)
self.assertEqual(len(r3.varkeys), 4)
sp = Model(x * r3.relaxvar**10, r3).sp(use_pccp=False)
cost = sp.localsolve(verbosity=0, solver=self.solver)["cost"]
self.assertAlmostEqual(cost / (32 * 0.8786796585), 1, self.ndig)
def test_sp_bounded(self):
x = Variable("x")
y = Variable("y")
with SignomialsEnabled():
m = Model(x, [x + y >= 1, y <= 0.1]) # solves
cost = m.localsolve(verbosity=0, solver=self.solver)["cost"]
self.assertAlmostEqual(cost, 0.9, self.ndig)
with SignomialsEnabled():
m = Model(x, [x + y >= 1]) # dual infeasible
with self.assertRaises(UnboundedGP):
m.localsolve(verbosity=0, solver=self.solver)
gp = m.sp(checkbounds=False).gp()
self.assertRaises(DualInfeasible,
gp.solve,
solver=self.solver,
verbosity=0)
with SignomialsEnabled():
m = Model(x, Bounded([x + y >= 1], verbosity=0))
sol = m.localsolve(verbosity=0, solver=self.solver)
boundedness = sol["boundedness"]
# depends on solver, platform, whims of the numerical deities
if "value near lower bound" in boundedness: # pragma: no cover
self.assertIn(x.key, boundedness["value near lower bound"])
else: # pragma: no cover
self.assertIn(y.key, boundedness["value near upper bound"])
def test_trivial_sp2(self):
x = Variable("x")
y = Variable("y")
# converging from above
with SignomialsEnabled():
constraints = [y + x >= 2, y >= x]
objective = y
x0 = 1
y0 = 2
m = Model(objective, constraints)
sol1 = m.localsolve(x0={x: x0, y: y0}, verbosity=0, solver=self.solver)
# converging from right
with SignomialsEnabled():
constraints = [y + x >= 2, y <= x]
objective = x
x0 = 2
y0 = 1
m = Model(objective, constraints)
sol2 = m.localsolve(x0={x: x0, y: y0}, verbosity=0, solver=self.solver)
self.assertAlmostEqual(sol1["variables"]["x"], sol2["variables"]["x"],
self.ndig)
self.assertAlmostEqual(sol1["variables"]["y"], sol2["variables"]["x"],
self.ndig)
def test_sp_bounded(self):
x = Variable("x")
y = Variable("y")
with SignomialsEnabled():
m = Model(x, [x + y >= 1, y <= 0.1]) # solves
cost = m.localsolve(verbosity=0, solver=self.solver)["cost"]
self.assertAlmostEqual(cost, 0.9, self.ndig)
with SignomialsEnabled():
m = Model(x, [x + y >= 1]) # dual infeasible
with self.assertRaises(UnboundedGP):
m.localsolve(verbosity=0, solver=self.solver)
gp = m.sp(allow_missingbounds=True).gp(allow_missingbounds=True)
self.assertRaises(DualInfeasible,
gp.solve,
solver=self.solver,
verbosity=0)
with SignomialsEnabled():
m = Model(x, Bounded([x + y >= 1], verbosity=0))
sol = m.localsolve(verbosity=0, solver=self.solver)
boundedness = sol["boundedness"]
if "value near lower bound" in boundedness:
self.assertIn(x.key, boundedness["value near lower bound"])
if "value near upper bound" in boundedness:
self.assertIn(y.key, boundedness["value near upper bound"])
def test_sp_substitutions(self):
x = Variable('x')
y = Variable('y', 1)
z = Variable('z', 4)
from io import StringIO
old_stdout = sys.stdout
sys.stdout = stringout = StringIO()
with SignomialsEnabled():
m = Model(x, [x + z >= y])
with self.assertRaises(ValueError):
m.localsolve(verbosity=0, solver=self.solver)
with SignomialsEnabled():
m = Model(x, [x + y >= z])
m.substitutions[y] = 1
m.substitutions[z] = 4
sol = m.solve(self.solver, verbosity=0)
self.assertAlmostEqual(sol["cost"], 3, self.ndig)
sys.stdout = old_stdout
self.assertEqual(
stringout.getvalue(),
("Warning: SignomialConstraint x + z >= y became the tautological"
" constraint 0 <= 3 + x after substitution.\n"
"Warning: SignomialConstraint x + z >= y became the tautological"
" constraint 0 <= 3 + x after substitution.\n"))
def test_sp_relaxation(self):
w = Variable('w')
x = Variable('x')
y = Variable('y')
z = Variable('z')
with SignomialsEnabled():
m = Model(x, [x+y >= w, x+y <= z/2, y <= x, y >= 1], {z: 3, w: 3})
r1 = ConstantsRelaxed(m)
self.assertEqual(len(r1.varkeys), 8)
with self.assertRaises(ValueError):
mr1 = Model(x*r1.relaxvars, r1) # no 'prod'
mr1 = Model(x*r1.relaxvars.prod()**10, r1)
cost1 = mr1.localsolve(verbosity=0)["cost"]
self.assertAlmostEqual(cost1/1024, 1, self.ndig)
m.debug(verbosity=0)
with SignomialsEnabled():
m = Model(x, [x+y >= z, x+y <= z/2, y <= x, y >= 1], {z: 3})
if self.solver != "cvxopt":
m.debug(verbosity=0)
r2 = ConstraintsRelaxed(m)
self.assertEqual(len(r2.varkeys), 7)
mr2 = Model(x*r2.relaxvars.prod()**10, r2)
cost2 = mr2.localsolve(verbosity=0)["cost"]
self.assertAlmostEqual(cost2/1024, 1, self.ndig)
with SignomialsEnabled():
m = Model(x, [x+y >= z, x+y <= z/2, y <= x, y >= 1], {z: 3})
if self.solver != "cvxopt":
m.debug(verbosity=0)
r3 = ConstraintsRelaxedEqually(m)
self.assertEqual(len(r3.varkeys), 4)
mr3 = Model(x*r3.relaxvar**10, r3)
cost3 = mr3.localsolve(verbosity=0)["cost"]
self.assertAlmostEqual(cost3/(32*0.8786796585), 1, self.ndig)
def test_chop(self):
"Test Signomial deconstruction"
x = Variable('x')
y = Variable('y')
with SignomialsEnabled():
c = x + 5. * y**2 - 0.2 * x * y**0.78
monomials = c.chop()
with self.assertRaises(InvalidPosynomial):
c.chop()
with SignomialsEnabled():
self.assertIn(-0.2 * x * y**0.78, monomials)
def test_trivial_sp(self):
x = Variable('x')
y = Variable('y')
with SignomialsEnabled():
m = Model(x, [x >= 1 - y, y <= 0.1])
sol = m.localsolve(verbosity=0, solver=self.solver)
self.assertAlmostEqual(sol["variables"]["x"], 0.9, self.ndig)
with SignomialsEnabled():
m = Model(x, [x + y >= 1, y <= 0.1])
sol = m.localsolve(verbosity=0, solver=self.solver)
self.assertAlmostEqual(sol["variables"]["x"], 0.9, self.ndig)
def test_trivial_sp(self):
x = Variable('x')
y = Variable('y')
with SignomialsEnabled():
m = Model(x, [x >= 1 - y, y <= 0.1])
with self.assertRaises(InvalidGPConstraint):
m.solve(verbosity=0)
sol = m.localsolve(self.solver, verbosity=0)
self.assertAlmostEqual(sol["variables"]["x"], 0.9, self.ndig)
with SignomialsEnabled():
m = Model(x, [x + y >= 1, y <= 0.1])
sol = m.localsolve(self.solver, verbosity=0)
self.assertAlmostEqual(sol["variables"]["x"], 0.9, self.ndig)
def test_sp_substitutions(self):
x = Variable('x')
y = Variable('y', 1)
z = Variable('z', 4)
with self.assertRaises(ValueError):
with SignomialsEnabled():
m = Model(x, [x + z >= y])
m.localsolve()
with SignomialsEnabled():
m = Model(x, [x + y >= z])
self.assertAlmostEqual(m.solve(self.solver, verbosity=0)["cost"], 3)
def test_trivial_sp(self):
x = Variable('x')
y = Variable('y')
with SignomialsEnabled():
m = Model(x, [x >= 1 - y, y <= 0.1])
with self.assertRaises(ValueError):
# solve should catch the TypeError raised by an SP constraints
# and raise its own ValueError instead
m.solve(verbosity=0)
sol = m.localsolve(self.solver, verbosity=0)
self.assertAlmostEqual(sol["variables"]["x"], 0.9, self.ndig)
with SignomialsEnabled():
m = Model(x, [x + y >= 1, y <= 0.1])
sol = m.localsolve(self.solver, verbosity=0)
self.assertAlmostEqual(sol["variables"]["x"], 0.9, self.ndig)
def setup(self, N):
edgeCost = VectorVariable([N, N], 'edgeCost')
edgeMaxFlow = VectorVariable([N, N], 'edgeMaxFlow')
connect = VectorVariable([N, N], 'connectivity')
flow = VectorVariable([N, N], 'flow')
source = VectorVariable(N, 'source')
sink = VectorVariable(N, 'sink')
totalCost = Variable('totalCost')
constraints = []
with SignomialsEnabled():
for i in range(0, N):
constraints.extend([
sink[i] + sum(flow[i, :]) <= source[i] + sum(flow[:, i]),
])
for j in range(0, N):
constraints.extend(
[flow[i, j] <= connect[i, j] * edgeMaxFlow[i, j]])
for i in range(0, N):
for j in range(i + 1, N):
constraints.extend([flow[i, j] * flow[j, i] <= 1e-5])
constraints.extend([totalCost >= sum(edgeCost * flow)])
return constraints
def test_tautological(self):
x = Variable('x')
y = Variable('y')
z = Variable('z')
from io import StringIO
old_stdout = sys.stdout
sys.stdout = stringout = StringIO()
with SignomialsEnabled():
m1 = Model(x, [x + y >= z, x >= y])
m2 = Model(x, [x + 1 >= 0, x >= y])
m1.substitutions.update({'z': 0, 'y': 1})
m2.substitutions.update({'y': 1})
self.assertAlmostEqual(
m1.solve(self.solver, verbosity=0)["cost"],
m2.solve(self.solver, verbosity=0)["cost"])
sys.stdout = old_stdout
self.assertEqual(
stringout.getvalue(),
("Warning: SignomialConstraint x + y >= z became the tautological"
" constraint 0 <= 1 + x after substitution.\n"
"Warning: SignomialConstraint x + 1 >= 0 became the tautological"
" constraint 0 <= 1 + x after substitution.\n"))
def setup(self):
self.engine = Engine()
self.wing = Wing()
self.fuse = Fuselage()
self.components = [self.engine, self.wing, self.fuse]
# Environmental constants
g = Variable("g", 9.81, "m/s^2", "gravitational acceleration")
rho_f = Variable("\\rho_f", 817, "kg/m^3", "density of fuel")
# Free Variables
W = Variable("W", "N", "maximum takeoff weight")
W_f = Variable("W_f", "N", "maximum fuel weight")
V_f = Variable("V_f", "m^3", "maximum fuel volume")
V_f_avail = Variable("V_{f_{avail}}", "m^3", "fuel volume available")
constraints = []
# Thrust and drag model
constraints += [
self.fuse['C_{D_{fuse}}'] == self.fuse['(CDA0)'] / self.wing['S']
]
# Fuel volume model
with SignomialsEnabled():
constraints += [
V_f == W_f / g / rho_f,
V_f_avail <=
self.wing['V_{f_{wing}}'] + self.fuse['V_{f_{fuse}}'], #[SP]
V_f_avail >= V_f
]
return constraints, self.components
def setup(self, static, state, N=5):
exec parse_variables(BladeElementProp.__doc__)
with Vectorize(N):
blade = BladeElementPerf(static, state)
constraints = [
blade.dr == static.R / (N), blade.omega == omega,
blade.r[0] == static.R / (2. * N)
]
for n in range(1, N):
constraints += [
TCS([blade.r[n] >= blade.r[n - 1] + static.R / N]),
blade.eta_i[n] == blade.eta_i[n - 1],
]
constraints += [
TCS([Q >= sum(blade.dQ)]), eta == state.V * T / (omega * Q),
blade.M[-1] <= Mtip, static.T_m >= T, omega <= omega_max
]
with SignomialsEnabled():
constraints += [TCS([T <= sum(blade.dT)])]
return constraints, blade
def setup(self, engine, state):
self.engine = engine
# Dimensional constants
# Free variables
BSFC = Variable("BSFC", "lbf/(hp*hr)",
"brake specific fuel consumption")
P_shaft = Variable("P_{shaft}", "kW", "shaft power")
P_shaft_alt = Variable("P_{shaft,alt}", "kW",
'maximum shaft power at altitude')
Thrust = Variable("T", "N", "propeller thrust")
L = Variable("L", "-", "power lapse percentage")
constraints = []
with SignomialsEnabled():
constraints += [
P_shaft <= P_shaft_alt,
L == (0.937 *
(state['h'] / self.engine['h_{ref}'])**0.0922)**10,
SignomialEquality(
1, L + P_shaft_alt / self.engine['P_{shaft,max}']),
(BSFC / self.engine['BSFC_{ref}'])**(0.1) >= 0.984 *
(P_shaft / P_shaft_alt)**-0.0346,
BSFC / self.engine['BSFC_{ref}'] >= 1.,
]
return constraints
def setup(self):
self.HTns = HorizontalTailNoStruct()
self.wb = WingBox(self.HTns, "horizontal_tail")
#HT system weight variable
Wht = Variable('W_{ht}', 'N', 'HT System Weight')
fht = Variable('f_{ht}' ,'-', 'Rudder etc. fractional weight')
#margin and sensitivity
Cht = Variable('C_{ht}', 1, '-', 'HT Weight Margin and Sensitivity Factor')
#variables only used for the TASOPT tail drag formulation
cdfh = Variable('c_{d_{fh}}', '-', 'VT friction drag coefficient')
cdph = Variable('c_{d_{ph}}', '-', 'VT pressure drag coefficient')
coslamcube = Variable('\\cos(\\Lambda_{ht})^3', '-', 'Cosine of tail sweep cubed')
constraints = []
with SignomialsEnabled():
constraints.append([
self.wb['L_{ht_{rect}}'] >= self.HTns['L_{ht_{max}}']/2.*self.HTns['c_{tip_{ht}}']*self.HTns['b_{ht}']/self.HTns['S_{ht}'],
self.wb['L_{ht_{tri}}'] >= self.HTns['L_{ht_{max}}']/4.*(1-self.wb['taper'])*self.HTns['c_{root_{ht}}']*self.HTns['b_{ht}']/self.HTns['S_{ht}'], #[SP]
Wht >= Cht*(self.wb['W_{struct}'] + self.wb['W_{struct}'] * fht),
])
return self.HTns, self.wb, constraints
def test_tiny_sp_1(self):
"""
A signomial inequality constraint.
"""
from gpkit import Variable, Model, SignomialsEnabled
#
# Build GPKit model
#
x = Variable('x')
y = Variable('y')
with SignomialsEnabled():
constraints = [x >= 1 - y, y <= 0.5]
gpkm = Model(x, constraints)
#
# Recover data for a sageopt model
#
som = gpkit_model_to_sageopt_model(gpkm)
f = som['f']
gp_ineqs = som['gp_gts']
X = infer_domain(f, gp_ineqs, [])
sp_ineqs = som['sp_gts']
prob = sig_constrained_relaxation(f, sp_ineqs, [], X)
#
# Solve the sageopt model and check optimality
#
prob.solve(solver='ECOS', verbose=False)
self.assertAlmostEqual(prob.value, 0.5, places=3)
soln = sig_solrec(prob)[0]
soln = local_refine(f, sp_ineqs + gp_ineqs, [], x0=soln)
self.assertAlmostEqual(f(soln), 0.5, places=3)
pass
def setup(self, **kwargs):
self.wns = WingNoStruct()
self.wb = WingBox(self.wns, "wing")
Wwing = Variable('W_{wing}', 'N', 'Wing System Weight')
Cwing = Variable('C_{wing}', 1, '-', 'Wing Weight Margin and Sensitivity Factor')
# w.r.t. the quarter chord of the root of the wing.
dxACwing = Variable('\\Delta x_{AC_{wing}}','m','Wing Aerodynamic Center Shift')
#wing induced drag reduction due to wing tip devices
TipReduct = Variable('TipReduct', '-', 'Induced Drag Reduction Factor from Wing Tip Devices')
constraints = []
with SignomialsEnabled():
constraints.extend([
self.wns['\\lambda'] == self.wb['taper'],
TCS([Wwing >= Cwing * self.wb['W_{struct}'] + self.wb['W_{struct}']*(self.wns['f_{flap}'] + \
self.wns['f_{slat}'] + self.wns['f_{aileron}'] + self.wns['f_{lete}'] + self.wns['f_{ribs}'] + \
self.wns['f_{spoiler}'] + self.wns['f_{watt}'])]),
TCS([dxACwing <= 1./24.*(self.wns['c_{root}'] + 5.*self.wns['c_{tip}'])/self.wns['S'] \
*self.wns['b']**2*self.wns['\\tan(\\Lambda)']]),
])
return self.wns, self.wb, constraints
def test_sp_initial_guess_sub(self):
x = Variable("x")
y = Variable("y")
x0 = 1
y0 = 2
with SignomialsEnabled():
constraints = [y + x >= 2, y <= x]
objective = x
m = Model(objective, constraints)
try:
sol = m.localsolve(x0={x: x0, y: y0}, verbosity=0,
solver=self.solver)
except TypeError:
self.fail("Call to local solve with only variables failed")
self.assertAlmostEqual(sol(x), 1, self.ndig)
self.assertAlmostEqual(sol["cost"], 1, self.ndig)
try:
sol = m.localsolve(x0={"x": x0, "y": y0}, verbosity=0,
solver=self.solver)
except TypeError:
self.fail("Call to local solve with only variable strings failed")
self.assertAlmostEqual(sol("x"), 1, self.ndig)
self.assertAlmostEqual(sol["cost"], 1, self.ndig)
try:
sol = m.localsolve(x0={"x": x0, y: y0}, verbosity=0,
solver=self.solver)
except TypeError:
self.fail("Call to local solve with a mix of variable strings "
"and variables failed")
self.assertAlmostEqual(sol["cost"], 1, self.ndig)
def setup(self, htail, hbending, wing):
exec parse_variables(TailBoomFlexibility.__doc__)
mh = htail.mh
mw = wing.mw
Vh = htail.Vh
th = hbending.th
CLhmin = htail.CLhmin
CLwmax = wing.planform.CLmax
Sw = wing.planform.S
bw = wing.planform.b
lh = htail.lh
CM = wing.planform.CM
constraints = [
Fne >= 1 + mh * th,
sph1 * (mw * Fne / mh / Vh) + deda <= 1,
sph2 <= Vh * CLhmin / CLwmax,
# (sph1 + sph2).mono_lower_bound({"sph1": .48, "sph2": .52}) >= (
# SMcorr + wing["C_M"]/wing["C_{L_{max}}"]),
deda >= mw * Sw / bw / 4 / pi / lh
]
with SignomialsEnabled():
constraints.extend([sph1 + sph2 >= SMcorr + CM / CLwmax])
return constraints
def setup(self, N):
edgeCost = VectorVariable([N, N], 'edgeCost')
edgeMaxFlow = VectorVariable([N, N], 'edgeMaxFlow')
slackCost = Variable('slackCost', 1000)
connect = VectorVariable([N, N], 'connectivity')
flow = VectorVariable([N, N], 'flow')
source = VectorVariable(N, 'source')
sink = VectorVariable(N, 'sink')
slack = VectorVariable(N, 'slack')
constraints = []
with SignomialsEnabled():
for i in range(0, N):
constraints.extend([
Tight([
sink[i] + sum(flow[i, :]) <= slack[i] *
(source[i] + sum(flow[:, i]))
]),
Tight([slack[i] >= 1])
])
for j in range(0, N):
constraints += [
flow[i, j] <= connect[i, j] * edgeMaxFlow[i, j],
connect[i, j] <= 1., flow[i, j] >= 1e-20
]
for i in range(0, N):
for j in range(i + 1, N):
constraints.extend(
[connect[i, j] * connect[j, i] <= 1e-20])
return constraints
def setup(self, ht, state, fitDrag):
self.HT = ht
#variables
D = Variable('D_{ht}', 'N', 'Horizontal tail drag')
Lh = Variable('L_{ht}', 'N', 'Horizontal tail downforce')
Rec = Variable('Re_{c_h}', '-',
'Cruise Reynolds number (Horizontal tail)')
CLah = Variable('C_{L_{\\alpha,ht}}', '-', 'Lift curve slope (htail)')
CLah0 = Variable('C_{L_{\\alpha,ht_0}}', '-',
'Isolated lift curve slope (htail)')
CLh = Variable('C_{L_{ht}}', '-', 'Lift coefficient (htail)')
CDh = Variable('C_{D_{ht}}', '-', 'Horizontal tail drag coefficient')
CD0h = Variable('C_{D_{0,ht}}', '-',
'Horizontal tail parasitic drag coefficient')
alphah = Variable('\\alpha_{ht}', '-', 'Horizontal tail angle of attack')
constraints = []
with SignomialsEnabled():
constraints.extend([
Lh == 0.5*state['\\rho']*state['V']**2*self.HT['S_{ht}']*CLh,
# Angle of attack and lift slope constraints
CLh == CLah*alphah,
alphah <= self.HT['\\alpha_{ht,max}'],
# Currently using TAT to approximate
CLah0 == 2*3.14,
# Drag
D == 0.5*state['\\rho']*state['V']**2*self.HT['S_{ht}']*CDh,
CDh >= CD0h + CLh**2/(pi*self.HT['e_{ht}']*self.HT['AR_{ht}']),
#cruise Reynolds number
Rec == state['\\rho']*state['V']*self.HT['\\bar{c}_{ht}']/state['\\mu'],
])
if fitDrag:
constraints.extend([
#Martin's TASOPT tail drag fit
CD0h**6.48983 >= (5.28751e-20 * (Rec)**0.900672 * (self.HT['\\tau_{ht}'])**0.912222 * (state['M'])**8.64547
+ 1.67605e-28 * (Rec)**0.350958 * (self.HT['\\tau_{ht}'])**6.29187 * (state['M'])**10.2559
+ 7.09757e-25 * (Rec)**1.39489 * (self.HT['\\tau_{ht}'])**1.96239 * (state['M'])**0.567066
+ 3.73076e-14 * (Rec)**-2.57406 * (self.HT['\\tau_{ht}'])**3.12793 * (state['M'])**0.448159
+ 1.44343e-12 * (Rec)**-3.91046 * (self.HT['\\tau_{ht}'])**4.66279 * (state['M'])**7.68852)
#Philippe thesis drag fit
## CD0h**0.125 >= 0.19*(self.HT['\\tau_{ht}'])**0.0075 *(Rec)**0.0017
## + 1.83e+04*(self.HT['\\tau_{ht}'])**3.54*(Rec)**-0.494
## + 0.118*(self.HT['\\tau_{ht}'])**0.0082 *(Rec)**0.00165
## + 0.198*(self.HT['\\tau_{ht}'])**0.00774*(Rec)**0.00168,
])
else:
#HT drag constraints in AircraftP
None
return constraints
def test_sigs_not_allowed_in_cost(self):
with SignomialsEnabled():
x = Variable('x')
y = Variable('y')
J = 0.01 * ((x - 1)**2 + (y - 1)**2) + (x * y - 1)**2
m = Model(J)
with self.assertRaises(TypeError):
m.localsolve(verbosity=0)
def test_init(self):
"Test initialization and types"
D = Variable('D', units="N")
x1, x2, x3 = (Variable("x_%s" % i, units="N") for i in range(3))
with SignomialsEnabled():
sc = (D >= x1 + x2 - x3)
self.assertTrue(isinstance(sc, SignomialInequality))
self.assertFalse(isinstance(sc, Posynomial))
def setup(self):
x = Variable("x")
y = Variable("y", 2.)
z = Variable("z")
with SignomialsEnabled():
constraints = [z <= x**2 + y, x * z == 2]
self.cost = 1 / z
return constraints
def test_posyslt1(self):
x = Variable("x")
y = Variable("y")
with SignomialsEnabled():
sc = (x + y >= x * y)
# make sure that the error type doesn't change on our users
with self.assertRaises(InvalidGPConstraint):
_ = sc.as_posyslt1()
def test_zeroing(self):
L = Variable("L")
k = Variable("k", 0)
with SignomialsEnabled():
constr = [L - 5 * k <= 10]
sol = Model(1 / L, constr).solve(self.solver, verbosity=0)
self.assertAlmostEqual(sol(L), 10, self.ndig)
self.assertAlmostEqual(sol["cost"], 0.1, self.ndig)