def meti10(numSolutions="all"):
start = time.time()
epsilon = 1e-14
lenV = 1
x = Variable('x')
allSolutions = []
while True:
if numSolutions != "all" and len(allSolutions) == numSolutions:
break
allConstraints = []
allConstraints.append((2 * x) / (2 + x) >= log(1 + x))
allConstraints.append(x >= 0.0)
allConstraints.append(x <= 1000)
excludingConstraints = []
for solution in allSolutions:
singleExcludingConstraints = []
singleExcludingConstraints.append(x <= solution[0][0])
singleExcludingConstraints.append(x >= solution[0][1])
excludingConstraints.append(singleExcludingConstraints)
#print ("allConstraints")
#print (allConstraints)
#print ("numConstraints", len(allConstraints))
f_sat = logical_and(*allConstraints)
if len(excludingConstraints) > 0:
for constraints in excludingConstraints:
f_sat = logical_and(f_sat, logical_or(*constraints))
#print ("f_sat")
#print (f_sat)
result = CheckSatisfiability(f_sat, epsilon)
#print (result)
if result is None:
break
hyper = np.zeros((1, 2))
hyper[0, :] = [
result[x].lb() - 1000 * epsilon, result[x].ub() + 1000 * epsilon
]
print("hyper", hyper)
allSolutions.append(hyper)
print("num solutions found", len(allSolutions))
'''constraints = []
x = Variable('x')
#constraints.append(x >= 0.0)
#constraints.append(x <= 64.0)
constraints.append(2*math.pi - 2*x*asin(cos(0.797)*sin(math.pi/x)) == 2.097 - 0.0331*x)
f_sat = logical_and(*constraints)
result = CheckSatisfiability(f_sat, epsilon)
print (result)'''
end = time.time()
print("time taken", end - start)
def test_functions_with_variable(self):
self.assertEqual(str(log(x)), "log(x)")
self.assertEqual(str(abs(x)), "abs(x)")
self.assertEqual(str(exp(x)), "exp(x)")
self.assertEqual(str(sqrt(x)), "sqrt(x)")
self.assertEqual(str(pow(x, y)), "pow(x, y)")
self.assertEqual(str(sin(x)), "sin(x)")
self.assertEqual(str(cos(x)), "cos(x)")
self.assertEqual(str(tan(x)), "tan(x)")
self.assertEqual(str(asin(x)), "asin(x)")
self.assertEqual(str(acos(x)), "acos(x)")
self.assertEqual(str(atan(x)), "atan(x)")
self.assertEqual(str(atan2(x, y)), "atan2(x, y)")
self.assertEqual(str(sinh(x)), "sinh(x)")
self.assertEqual(str(cosh(x)), "cosh(x)")
self.assertEqual(str(tanh(x)), "tanh(x)")
self.assertEqual(str(min(x, y)), "min(x, y)")
self.assertEqual(str(max(x, y)), "max(x, y)")
self.assertEqual(str(if_then_else(x > y, x, y)),
"(if (x > y) then x else y)")
def mvs_id(fetType, Vs, Vg, Vd, I, shape):
params = model_params(fetType)
version = params['version']
mType = params['mType']
W = params['W']
Lgdr = params['Lgdr']
dLg = params['dLg']
Cg = params['Cg']
etov = params['etov']
delta = params['delta']
n0 = params['n0']
Rs0 = params['Rs0']
Rd0 = params['Rd0']
Cif = params['Cif']
Cof = params['Cof']
vxo = params['vxo'] * 1e7
mu = params['mu']
beta = params['beta']
Tjun = params['Tjun']
phib = params['phib']
gamma = params['gamma']
Vt0 = params['Vt0']
alpha = params['alpha']
mc = params['mc']
CTM_select = params['CTM_select']
CC = params['CC']
nd = params['nd']
zeta = params['zeta']
# SMALL_VALUE
SMALL_VALUE = 1e-10
# LARGE_VALUE
LARGE_VALUE = 40
if mType == 1.0:
Vb = 0.0
Vdsi = Variable("Vdsin")
Vgsi = Variable("Vgsin")
Vbsi = Variable("Vbsin")
n = Variable("nn")
nphit = Variable("nphitn")
phibVbs = Variable("phibVbsn")
Vtpcorr = Variable("Vtpcorrn")
eVgpre = Variable("eVgpren")
FFpre = Variable("FFpren")
ab = Variable("abn")
Vcorr = Variable("Vcorrn")
Vgscorr = Variable("Vgscorrn")
Vbscorr = Variable("Vbscorrn")
phibVbscorr = Variable("phibVbscorrn")
Vt0bs = Variable("Vt0bsn")
phibVbsi = Variable("phibVbsin")
Vt0bs0 = Variable("Vt0bs0n")
Vtp = Variable("Vtpn")
Vtp0 = Variable("Vtp0n")
eVg = Variable("eVgn")
FF = Variable("FFn")
eVg0 = Variable("eVg0n")
FF0 = Variable("FF0n")
Qref = Variable("Qrefn")
eta = Variable("etan")
Qinv_corr = Variable("Qinv_corrn")
Vdsat = Variable("Vdsatn")
VdsiVdsat = Variable("VdsiVdsatn")
powVal = Variable("powValn")
Fsat = Variable("Fsatn")
else:
Vb = 1.8
Vdsi = Variable("Vdsip")
Vgsi = Variable("Vgsip")
Vbsi = Variable("Vbsip")
n = Variable("np")
nphit = Variable("nphitp")
phibVbs = Variable("phibVbsp")
Vtpcorr = Variable("Vtpcorrp")
eVgpre = Variable("eVgprep")
FFpre = Variable("FFprep")
ab = Variable("abp")
Vcorr = Variable("Vcorrp")
Vgscorr = Variable("Vgscorrp")
Vbscorr = Variable("Vbscorrp")
phibVbscorr = Variable("phibVbscorrp")
Vt0bs = Variable("Vt0bsp")
phibVbsi = Variable("phibVbsip")
Vt0bs0 = Variable("Vt0bs0p")
Vtp = Variable("Vtpp")
Vtp0 = Variable("Vtp0p")
eVg = Variable("eVgp")
FF = Variable("FFp")
eVg0 = Variable("eVg0p")
FF0 = Variable("FF0p")
Qref = Variable("Qrefp")
eta = Variable("etap")
Qinv_corr = Variable("Qinv_corrp")
Vdsat = Variable("Vdsatp")
VdsiVdsat = Variable("VdsiVdsatp")
powVal = Variable("powValp")
Fsat = Variable("Fsatp")
constraints = []
if mType == 1:
constraints.append(
logical_or(logical_and(Vs <= Vd, Vdsi == mType * (Vd - Vs)),
logical_and(Vs > Vd, Vdsi == mType * (Vs - Vd))))
constraints.append(
logical_or(logical_and(Vs <= Vd, Vgsi == mType * (Vg - Vs)),
logical_and(Vs > Vd, Vgsi == mType * (Vg - Vd))))
constraints.append(
logical_or(logical_and(Vs <= Vd, Vbsi == mType * (Vb - Vs)),
logical_and(Vs > Vd, Vbsi == mType * (Vb - Vd))))
else:
constraints.append(
logical_or(logical_and(Vd <= Vs, Vdsi == mType * (Vd - Vs)),
logical_and(Vd > Vs, Vdsi == mType * (Vs - Vd))))
constraints.append(
logical_or(logical_and(Vd <= Vs, Vgsi == mType * (Vg - Vs)),
logical_and(Vd > Vs, Vgsi == mType * (Vg - Vd))))
constraints.append(
logical_or(logical_and(Vd <= Vs, Vbsi == mType * (Vb - Vs)),
logical_and(Vd > Vs, Vbsi == mType * (Vb - Vd))))
Cofs = 0 * (0.345e-12 / etov) * dLg / 2.0 + Cof
# s-terminal outer fringing cap [F/cm]
Cofd = 0 * (0.345e-12 / etov) * dLg / 2.0 + Cof
# d-terminal outer fringing cap [F/cm]
Leff = Lgdr - dLg
# Effective channel length [cm]. After subtracting overlap lengths on s and d side
kB = 8.617e-5
# Boltzmann constant [eV/K]
phit = kB * Tjun
# Thermal voltage, kT/q [V]
me = (9.1e-31) * mc
# Carrier mass [Kg]
constraints.append(n == n0 + nd * Vdsi)
constraints.append(nphit == n * phit)
aphit = alpha * phit
constraints.append(phibVbs == dabs(phib - Vbsi))
constraints.append(Vtpcorr == Vt0 + gamma * (sqrt(phibVbs) - sqrt(phib)) -
Vdsi * delta)
constraints.append(eVgpre == exp((Vgsi - Vtpcorr) / (aphit * 1.5)))
constraints.append(FFpre == 1.0 / (1.0 + eVgpre))
constraints.append(ab == 2 * (1 - 0.99 * FFpre) * phit)
constraints.append(Vcorr == (1.0 + 2.0 * delta) * (ab / 2.0) *
(exp(-Vdsi / ab)))
constraints.append(Vgscorr == Vgsi + Vcorr)
constraints.append(Vbscorr == Vbsi + Vcorr)
constraints.append(phibVbscorr == dabs(phib - Vbscorr))
constraints.append(Vt0bs == Vt0 + gamma * (sqrt(phibVbscorr) - sqrt(phib)))
constraints.append(phibVbsi == dabs(phib - Vbsi))
constraints.append(Vt0bs0 == Vt0 + gamma * (sqrt(phibVbsi) - sqrt(phib)))
constraints.append(Vtp == Vt0bs - Vdsi * delta - 0.5 * aphit)
constraints.append(Vtp0 == Vt0bs0 - Vdsi * delta - 0.5 * aphit)
constraints.append(eVg == exp((Vgscorr - Vtp) / (aphit)))
constraints.append(FF == 1.0 / (1.0 + eVg))
constraints.append(eVg0 == exp((Vgsi - Vtp0) / (aphit)))
constraints.append(Qref == Cg * nphit)
constraints.append(eta == (Vgscorr - (Vt0bs - Vdsi * delta - FF * aphit)) /
(nphit))
constraints.append(Qinv_corr == Qref * log(1.0 + exp(eta)))
vx0 = vxo
Vdsats = vx0 * Leff / mu
constraints.append(Vdsat == Vdsats * (1.0 - FF) + phit * FF)
constraints.append(VdsiVdsat == Vdsi / Vdsat)
constraints.append(powVal == pow(VdsiVdsat, beta))
constraints.append(Fsat == VdsiVdsat / (pow((1 + powVal), (1.0 / beta))))
if mType == 1:
constraints.append(
logical_or(
logical_and(Vs <= Vd,
I == Qinv_corr * vx0 * Fsat * W * mType * shape),
logical_and(
Vs > Vd,
I == Qinv_corr * vx0 * Fsat * W * mType * -1.0 * shape)))
else:
constraints.append(
logical_or(
logical_and(Vd <= Vs,
I == Qinv_corr * vx0 * Fsat * W * mType * shape),
logical_and(
Vd > Vs,
I == Qinv_corr * vx0 * Fsat * W * mType * -1.0 * shape)))
return constraints
def objective(x1, x2):
t1 = -1 * exp(-2 * log(2) * ((x1 - 0.1) / 0.8)**2) * (
sin(5 * math.pi * x1)**6 + 0.1 * cos(500 * math.pi * x1)**2)
t2 = -1 * exp(-2 * log(2) * ((x2 - 0.1) / 0.8)**2) * (
sin(5 * math.pi * x2)**6 + 0.1 * cos(500 * math.pi * x2)**2)
return t1 + t2