def link_consumption(T, f, g, M):
L = f(T)
R = g(T)
max_t_idx = np.iinfo(np.dtype('uint32')).max
opt_H = np.full_like(L, float('inf'))
opt_delta_idx = np.full_like(L, max_t_idx, dtype='uint32')
for d_idx in range(len(L)):
R_d = np.roll(R, d_idx)
R_d[:d_idx] = float('inf')
if L[d_idx] >= float('inf'):
continue
H_d = np.maximum(0, L[d_idx] + R_d)
H_d[R_d >= float('inf')] = float('inf')
index = opt_H > H_d
opt_H[index] = H_d[index]
opt_delta_idx[index] = d_idx
opt_H[opt_H > M] = float('inf')
opt_delta_idx[opt_H > M] = max_t_idx
opt_delta = np.full_like(T, float('inf'), dtype='float')
opt_delta[opt_delta_idx < max_t_idx] = T[opt_delta_idx[
opt_delta_idx < max_t_idx]]
d = PiecewiseFunction(
T,
np.concatenate((make_piecewise_linear(T, opt_delta),
[LinearFunction(0, opt_delta[-1])])))
h = PiecewiseFunction(
T,
np.concatenate(
(make_piecewise_linear(T, opt_H), [LinearFunction(0, opt_H[-1])])))
return d, h
def test_lin_lin_same_linking(self):
T = np.arange(0, 20, eps)
M = 10
f = PiecewiseFunction([0], [LinearFunction(0, 5)])
g = PiecewiseFunction([0], [LinearFunction(0, 5)])
numeric_opt_d, numeric_h = numeric.link_consumption(T, f, g, M)
analytic_opt_d, analytic_h = analytic.link_consumption(f, g)
self.assertTrue(equal("opt_d", T, numeric_opt_d, analytic_opt_d))
self.assertTrue(equal("h", T, numeric_h, analytic_h))
self.assertEqual(analytic_h(0), 10)
self.assertEqual(analytic_h(20), 10)
def test_linking_analytic(self):
link_consumption = lambda f, g, M: analytic.link_consumption(f, g)
link_charging = lambda f, cf, M: analytic.link_charging(f, cf, M)
f = PiecewiseFunction([0], [LinearFunction(0, 5)])
cf = PiecewiseFunction(
[0, 10],
[LinearFunction(1, 0), LinearFunction(0, 10)])
graph = Graph([(0, 1, (False, f)), (1, 2, (True, cf))])
ds, h = link_path(graph, [0, 1, 2], 10, link_consumption,
link_charging)
self.assertEqual(h(0), 5)
self.assertEqual(h(5), 0)
def test_linking_lin_cf(self):
T = np.arange(0, 20, eps)
M = 10
f = PiecewiseFunction([0], [LinearFunction(0, 5)])
cf = PiecewiseFunction(
[0, 10],
[LinearFunction(1, 0), LinearFunction(0, 10)])
numeric_opt_d, numeric_h = numeric.link_charging(T, f, cf, M)
analytic_opt_d, analytic_h = analytic.link_charging(f, cf, M)
self.assertTrue(equal("opt_d", T, numeric_opt_d, analytic_opt_d))
self.assertTrue(equal("h", T, numeric_h, analytic_h))
self.assertEqual(analytic_h(0), 5)
self.assertEqual(analytic_h(10), 0)
def test_linking_numeric(self):
T = np.arange(0, 20, 0.1)
link_consumption = lambda f, g, M: numeric.link_consumption(T, f, g, M)
link_charging = lambda f, cf, M: numeric.link_charging(T, f, cf, M)
f = PiecewiseFunction([0], [LinearFunction(0, 5)])
cf = PiecewiseFunction(
[0, 10],
[LinearFunction(1, 0), LinearFunction(0, 10)])
graph = Graph([(0, 1, (False, f)), (1, 2, (True, cf))])
ds, h = link_path(graph, [0, 1, 2], 10, link_consumption,
link_charging)
self.assertEqual(h(0), 5)
self.assertEqual(h(5), 0)
def link_charging(T, f, cf, M):
L = f(T)
CF = cf(T)
max_t_idx = np.iinfo(np.dtype('uint32')).max
opt_H = np.full_like(L, float('inf'))
opt_delta_idx = np.full_like(L, max_t_idx, dtype='uint32')
ts = []
for d_idx in range(len(L)):
if L[d_idx] >= float('inf'):
continue
y = M - L[d_idx]
if y < 0:
continue
assert (y <= M)
t_idx = np.argmax(CF > y)
CF_y = np.roll(CF, -t_idx)
CF_y[-t_idx:] = CF[-1]
assert (len(CF_y) == len(L))
CF_d = np.roll(CF_y, d_idx)
CF_d[:d_idx] = -float('inf')
H_d = np.maximum(0, M - CF_d)
index = opt_H > H_d
opt_H[index] = H_d[index]
opt_delta_idx[index] = d_idx
opt_H[opt_H > M] = float('inf')
opt_delta_idx[opt_H > M] = max_t_idx
print(list(ts))
opt_delta = np.full_like(T, float('inf'), dtype='float')
opt_delta[opt_delta_idx < max_t_idx] = T[opt_delta_idx[
opt_delta_idx < max_t_idx]]
d = PiecewiseFunction(
T,
np.concatenate((make_piecewise_linear(T, opt_delta),
[LinearFunction(0, opt_delta[-1])])))
h = PiecewiseFunction(
T,
np.concatenate(
(make_piecewise_linear(T, opt_H), [LinearFunction(0, opt_H[-1])])))
return d, h
def test_linking_hyp_cf(self):
T = np.arange(0, 20, eps)
M = 10
f = PiecewiseFunction([0, 2, 6], [
LinearFunction(0, float('inf')),
HypLinFunction(5, 1, 1, 0),
LinearFunction(0, 6 / 5.)
])
cf = PiecewiseFunction(
[0, 10],
[LinearFunction(1, 0), LinearFunction(0, 10)])
numeric_opt_d, numeric_h = numeric.link_charging(T, f, cf, M)
analytic_opt_d, analytic_h = analytic.link_charging(f, cf, M)
# Wrong due to numeric instabilities between 3.16 and 40
#self.assertTrue(equal("opt_d", T, numeric_opt_d, analytic_opt_d))
self.assertTrue(
equal("opt_d", T[T < 3.16], numeric_opt_d, analytic_opt_d))
self.assertTrue(equal("h", T, numeric_h, analytic_h))
self.assertEqual(analytic_h(0), float('inf'))
self.assertEqual(analytic_h(2), 6)
self.assertEqual(analytic_h(8), 0)
def test_hyp_lin_linking(self):
T = np.arange(0, 20, eps)
M = 10
f = PiecewiseFunction([0, 2, 6], [
LinearFunction(0, float('inf')),
HypLinFunction(5, 1, 1, 0),
LinearFunction(0, 6 / 5.)
])
self.assertEqual(f(2), 6)
self.assertEqual(f(6), 1.2)
self.assertEqual(f(10), 1.2)
g = PiecewiseFunction([0, 4, 9], [
LinearFunction(0, float('inf')),
LinearFunction(-1, 9),
LinearFunction(0, 0)
])
numeric_opt_d, numeric_h = numeric.link_consumption(T, f, g, M)
analytic_opt_d, analytic_h = analytic.link_consumption(f, g)
self.assertTrue(equal("opt_d", T, numeric_opt_d, analytic_opt_d))
self.assertTrue(equal("h", T, numeric_h, analytic_h))
self.assertEqual(analytic_h(6), 11)
self.assertEqual(analytic_h(16), 6 / 5.)
def link_path(graph,
path,
M,
link_consumption,
link_charging,
initial_soc=None):
"""Takes graph with data of form (is_charging, weight_function) and link_consumption(f, g, M), link_charging(f, cf, M).
Returns a tuple (optimal_deltas, consumption)
"""
if initial_soc is None:
initial_soc = M
consumption = PiecewiseFunction([0], [LinearFunction(M - initial_soc, 0)])
ds = []
for u, v in zip(path[:-1], path[1:]):
is_charging, w = graph.data(graph.edge(u, v))
if is_charging:
opt_d, consumption = link_charging(consumption, w, M)
else:
opt_d, consumption = link_consumption(consumption, w, M)
ds.append(opt_d)
return ds, consumption