def test_pow4(self):
y_bounds = [(0.5, 2.8), (0, 2.8), (1, 2.8), (0.5, 1), (0, 0.5)]
exp_vals = [-3, -2.5, -2, -1.5, -1, -0.5, 0.5, 1, 1.5, 2, 2.5, 3]
for yl, yu in y_bounds:
for _exp_val in exp_vals:
m = pyo.Block(concrete=True)
m.x = pyo.Var()
m.y = pyo.Var(bounds=(yl, yu))
m.c = pyo.Constraint(expr=m.x**_exp_val == m.y)
fbbt(m)
y = np.linspace(pyo.value(m.y.lb) + 1e-6,
pyo.value(m.y.ub),
100,
endpoint=True)
if m.x.lb is None:
xl = -np.inf
else:
xl = m.x.lb
if m.x.ub is None:
xu = np.inf
else:
xu = m.x.ub
_x = np.exp(np.log(y) / _exp_val)
self.assertTrue(np.all(xl <= _x))
self.assertTrue(np.all(xu >= _x))
def test_pow2(self):
if not numpy_available:
raise unittest.SkipTest('Numpy is not available')
x_bounds = [(-2.5, 2.8), (-2.5, -0.5), (0.5, 2.8), (-2.5, 0), (0, 2.8),
(-2.5, -1), (1, 2.8), (-1, -0.5), (0.5, 1)]
c_bounds = [(-2.5, 2.8), (0.5, 2.8), (0, 2.8), (1, 2.8), (0.5, 1)]
for xl, xu in x_bounds:
for cl, cu in c_bounds:
m = pyo.Block(concrete=True)
m.x = pyo.Var(bounds=(xl, xu))
m.y = pyo.Var()
m.c = pyo.Constraint(
expr=pyo.inequality(body=m.y**m.x, lower=cl, upper=cu))
self.tightener(m)
x = np.linspace(pyo.value(m.x.lb) + 1e-6,
pyo.value(m.x.ub),
100,
endpoint=False)
z = np.linspace(pyo.value(m.c.lower) + 1e-6,
pyo.value(m.c.upper),
100,
endpoint=False)
if m.y.lb is None:
yl = -np.inf
else:
yl = m.y.lb
if m.y.ub is None:
yu = np.inf
else:
yu = m.y.ub
y = np.exp(np.split(np.log(np.abs(z)), len(z)) / x)
self.assertTrue(np.all(yl <= y))
self.assertTrue(np.all(yu >= y))
def test_pow2(self):
x_bounds = [(-2.5, 2.8), (-2.5, -0.5), (0.5, 2.8), (-2.5, 0), (0, 2.8),
(-2.5, -1), (1, 2.8), (-1, -0.5), (0.5, 1)]
c_bounds = [(-2.5, 2.8), (0.5, 2.8), (0, 2.8), (1, 2.8), (0.5, 1)]
for xl, xu in x_bounds:
for cl, cu in c_bounds:
m = pyo.Block(concrete=True)
m.x = pyo.Var(bounds=(xl, xu))
m.y = pyo.Var()
m.c = pyo.Constraint(
expr=pyo.inequality(body=m.y**m.x, lower=cl, upper=cu))
fbbt(m)
x = np.linspace(pyo.value(m.x.lb) + 1e-6,
pyo.value(m.x.ub),
100,
endpoint=False)
z = np.linspace(pyo.value(m.c.lower) + 1e-6,
pyo.value(m.c.upper),
100,
endpoint=False)
if m.y.lb is None:
yl = -np.inf
else:
yl = m.y.lb
if m.y.ub is None:
yu = np.inf
else:
yu = m.y.ub
for _x in x:
_y = np.exp(np.log(abs(z)) / _x)
self.assertTrue(np.all(yl <= _y))
self.assertTrue(np.all(yu >= _y))
def test_exp(self):
xl = -2.5
xu = 2.8
zl, zu = interval.exp(xl, xu)
x = np.linspace(xl, xu, 100)
_z = np.exp(x)
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
def test_exp(self):
if not numpy_available:
raise unittest.SkipTest('Numpy is not available.')
xl = -2.5
xu = 2.8
zl, zu = self.exp(xl, xu)
x = np.linspace(xl, xu, 100)
_z = np.exp(x)
self.assertTrue(np.all(zl <= _z))
self.assertTrue(np.all(zu >= _z))
def model(theta, t):
'''
Model to be fitted y = model(theta, t)
Arguments:
theta: vector of fitted parameters
t: independent variable [hours]
Returns:
y: model predictions [need to check paper for units]
'''
asymptote = theta[0]
rate_constant = theta[1]
return asymptote * (1 - np.exp(-rate_constant * t))
def test_log(self):
c_bounds = [(-2.5, 2.8), (-2.5, -0.5), (0.5, 2.8), (-2.5, 0), (0, 2.8),
(-2.5, -1), (1, 2.8), (-1, -0.5), (0.5, 1)]
for cl, cu in c_bounds:
m = pyo.Block(concrete=True)
m.x = pyo.Var()
m.c = pyo.Constraint(
expr=pyo.inequality(body=pyo.log(m.x), lower=cl, upper=cu))
fbbt(m)
z = np.linspace(pyo.value(m.c.lower), pyo.value(m.c.upper), 100)
if m.x.lb is None:
xl = -np.inf
else:
xl = pyo.value(m.x.lb)
if m.x.ub is None:
xu = np.inf
else:
xu = pyo.value(m.x.ub)
x = np.exp(z)
self.assertTrue(np.all(xl <= x))
self.assertTrue(np.all(xu >= x))
def test_log(self):
if not numpy_available:
raise unittest.SkipTest('Numpy is not available')
c_bounds = [(-2.5, 2.8), (-2.5, -0.5), (0.5, 2.8), (-2.5, 0), (0, 2.8), (-2.5, -1), (1, 2.8), (-1, -0.5), (0.5, 1)]
for cl, cu in c_bounds:
m = pyo.Block(concrete=True)
m.x = pyo.Var()
m.c = pyo.Constraint(expr=pyo.inequality(body=pyo.log(m.x), lower=cl, upper=cu))
self.tightener(m)
z = np.linspace(pyo.value(m.c.lower), pyo.value(m.c.upper), 100)
if m.x.lb is None:
xl = -np.inf
else:
xl = pyo.value(m.x.lb)
if m.x.ub is None:
xu = np.inf
else:
xu = pyo.value(m.x.ub)
x = np.exp(z)
self.assertTrue(np.all(xl <= x))
self.assertTrue(np.all(xu >= x))
def model(t, asymptote, rate_constant):
return asymptote * (1 - np.exp(-rate_constant * t))
