def compute_f_fprime_t_(W,
perturbation,
max_dist=1): # max dist added 10/14/20
Wmx, Wmy, Wsx, Wsy, s02, k, kappa, T, XX, XXp, Eta, Xi, h1, h2, Eta1, Eta2 = parse_W(
W)
fval = compute_f_(Eta, Xi, s02)
fprimeval = compute_fprime_(Eta, Xi, s02)
resEta = Eta - u_fn(XX, fval, Wmx, Wmy, k, kappa, T)
resXi = Xi - u_fn(XX, fval, Wsx, Wsy, k, kappa)
YY = fval + perturbation
YYp = fprimeval
def dYYdt(YY, Eta1, Xi1):
return -YY + compute_f_(Eta1, Xi1, s02)
def dYYpdt(YYp, Eta1, Xi1):
return -YYp + compute_fprime_(Eta1, Xi1, s02)
for t in range(niter):
if np.mean(np.abs(YY - fval)) < max_dist:
Eta1 = resEta + u_fn(XX, YY, Wmx, Wmy, k, kappa, T)
Xi1 = resXi + u_fn(XX, YY, Wmx, Wmy, k, kappa, T)
YY = YY + dt * dYYdt(YY, Eta1, Xi1)
YYp = YYp + dt * dYYpdt(YYp, Eta1, Xi1)
elif np.remainder(t, 500) == 0:
print('unstable fixed point?')
#YYp = compute_fprime_(Eta1,Xi1,s02)
return YY, YYp
def compute_f_fprime_t_(W1,W2,perturbation,max_dist=1): # max dist added 10/14/20
#Wmx,Wmy,Wsx,Wsy,s02,Kin,Kout,kappa,Tin,Tout,XX,XXp,Eta,Xi,h1,h2 = parse_W(W)
W0x,W0y,W1x,W1y,W2x,W2y,W3x,W3y,s02,Kin0,Kin1,Kxout0,Kyout0,Kxout1,Kyout1,kappa,Tin0,Tin1,Txout0,Tyout0,Txout1,Tyout1,h1,h2,bl,amp = parse_W1(W1)
XX,XXp,Eta,Xi = parse_W2(W2)
fval = compute_f_(Eta,Xi,s02)
fprimeval = compute_fprime_(Eta,Xi,s02)
u0,u1,u2,u3 = compute_us(W1,W2,fval,fprimeval)
resEta = Eta - u0 - u2
resXi = Xi - u1 - u3
YY = fval + perturbation
YYp = fprimeval
def dYYdt(YY,Eta1,Xi1):
return -YY + compute_f_(Eta1,Xi1,s02)
def dYYpdt(YYp,Eta1,Xi1):
return -YYp +compute_fprime_(Eta1,Xi1,s02)
for t in range(niter):
if np.mean(np.abs(YY-fval)) < max_dist:
u0,u1,u2,u3 = compute_us(W1,W2,YY,YYp)
Eta1 = resEta + u0 + u2
Xi1 = resXi + u1 + u3
YY = YY + dt*dYYdt(YY,Eta1,Xi1)
YYp = YYp + dt*dYYpdt(YYp,Eta1,Xi1)
elif np.remainder(t,500)==0:
print('unstable fixed point?')
#YY = YY + np.tile(bl,nS*nT)[np.newaxis,:]
#YYp = compute_fprime_(Eta1,Xi1,s02)
return YY,YYp
def compute_f_fprime_t_avg_(W, perturbation, burn_in=0.5, max_dist=1):
W0x, W0y, W1x, W1y, W2x, W2y, W3x, W3y, s02, k0, k1, k2, k3, kappa, T0, T1, T2, T3, XX, XXp, Eta, Xi, h = parse_W(
W)
fval = compute_f_(Eta, Xi, s02)
fprimeval = compute_fprime_(Eta, Xi, s02)
u0, u1, u2, u3 = compute_us(W, fval, fprimeval)
resEta = Eta - u0 - u2
resXi = Xi - u1 - u3
YY = fval + perturbation
YYp = fprimeval + 0
YYmean = np.zeros_like(Eta)
YYprimemean = np.zeros_like(Eta)
def dYYdt(YY, Eta1, Xi1):
return -YY + compute_f_(Eta1, Xi1, s02)
def dYYpdt(YYp, Eta1, Xi1):
return -YYp + compute_fprime_(Eta1, Xi1, s02)
for t in range(niter):
if np.mean(np.abs(YY - fval)) < max_dist:
u0, u1, u2, u3 = compute_us(W, YY, YYp)
Eta1 = resEta + u0 + u2
Xi1 = resXi + u1 + u3
YY = YY + dt * dYYdt(YY, Eta1, Xi1)
YYp = YYp + dt * dYYpdt(YYp, Eta1, Xi1)
elif np.remainder(t, 500) == 0:
print('unstable fixed point?')
if t > niter * burn_in:
YYmean = YYmean + 1 / niter / burn_in * YY
YYprimemean = YYprimemean + 1 / niter / burn_in * YYp
return YYmean, YYprimemean
def compute_f_fprime_t_(W,
perturbation,
max_dist=1): # max dist added 10/14/20
W0x, W0y, W1x, W1y, W2x, W2y, W3x, W3y, s02, k0, k1, k2, k3, kappa, T0, T1, T2, T3, XX, XXp, Eta, Xi, h = parse_W(
W)
fval = compute_f_(Eta, Xi, s02)
fprimeval = compute_fprime_(Eta, Xi, s02)
u0, u1, u2, u3 = compute_us(W, fval, fprimeval)
resEta = Eta - u0 - u2
resXi = Xi - u1 - u3
YY = fval + perturbation
YYp = fprimeval + 0
def dYYdt(YY, Eta1, Xi1):
return -YY + compute_f_(Eta1, Xi1, s02)
def dYYpdt(YYp, Eta1, Xi1):
return -YYp + compute_fprime_(Eta1, Xi1, s02)
for t in range(niter):
if np.mean(np.abs(YY - fval)) < max_dist:
u0, u1, u2, u3 = compute_us(W, YY, YYp)
Eta1 = resEta + u0 + u2
Xi1 = resXi + u1 + u3
YY = YY + dt * dYYdt(YY, Eta1, Xi1)
YYp = YYp + dt * dYYpdt(YYp, Eta1, Xi1)
elif np.remainder(t, 500) == 0:
print('unstable fixed point?')
#YYprime = compute_fprime_(Eta1,Xi1,s02)
return YY, YYp
def __init__(self, configurations, parameters, controls):
self.configurations = configurations
self.parameters = parameters
self.controls = controls
flat_args, self.unflatten = flatten(self.controls)
self.gx = grad(self.cost)
self.J = jacobian(self.forward)
self.hx = hessian_vector_product(self.cost)
self.hvp = hvp(self.hx)
y0, t_total, N_total, number_group, population_proportion, \
t_control, number_days_per_control_change, number_control_change_times, number_time_dependent_controls = configurations
self.N_total = N_total
self.number_group = number_group
self.t_control = t_control
self.dimension = len(self.t_control)
self.number_time_dependent_controls = number_time_dependent_controls
self.y0 = y0
self.t_total = t_total
self.interpolation = piecewiseLinear
self.load_data(fips)
self.initialization()
if number_group > 1:
# contact matrix
school_closure = True
# calendar from February 15th
weekday = [2, 3, 4, 5, 6]
# calendar from April 1st
# weekday = [0, 1, 2, 5, 6]
# calendar from May 1st
# weekday = [0, 3, 4, 5, 6]
calendar = np.zeros(1000 + 1, dtype=int)
# set work days as 1 and school days as 2
for i in range(1001):
if np.remainder(i, 7) in weekday:
calendar[i] = 1
if not school_closure: # and i < 45
calendar[i] = 2
self.calendar = calendar
contact = np.load("utils/contact_matrix.npz")
self.c_home = contact["home"]
self.c_school = contact["school"]
self.c_work = contact["work"]
self.c_other = contact["other"]
self.contact_full = self.c_home + 5. / 7 * (
(1 - school_closure) * self.c_school +
self.c_work) + self.c_other
def compute_f_fprime_t_avg_12_(W1,
W2,
perturbation,
max_dist=1,
burn_in=0.5): # max dist added 10/14/20
#Wmx,Wmy,Wsx,Wsy,s02,Kin,Kout,kappa,Tin,Tout,XX,XXp,Eta,Xi,h1,h2 = parse_W(W)
W0x, W0y, W1x, W1y, W2x, W2y, W3x, W3y, W0xrun, W0yrun, s02, Kin0, Kin1, Kxout0, Kyout0, Kxout1, Kyout1, kappa, Tin0, Tin1, Txout0, Tyout0, Txout1, Tyout1, h1, h2, bl, amp = parse_W1(
W1)
XX, XXp, Eta, Xi = parse_W2(W2)
fval = compute_f_(Eta, Xi, s02)
fprimeval = compute_fprime_(Eta, Xi, s02)
u0, u1, u2, u3 = compute_us(W1, W2, fval, fprimeval)
if share_residuals:
resEta = Eta - u0 - u2
resXi = Xi - u1 - u3
resEta12 = np.concatenate((resEta, resEta), axis=0)
resXi12 = np.concatenate((resXi, resXi), axis=0)
else:
resEta12 = 0
resXi12 = 0
dHH = np.zeros((nN, nQ * nS * nT))
dHH[:, np.arange(2, nQ * nS * nT, nQ)] = 1
dHH = np.concatenate((dHH * h1, dHH * h2), axis=0)
YY = fval + perturbation
YYp = fprimeval
XX12 = np.concatenate((XX, XX), axis=0)
YY12 = np.concatenate((YY, YY), axis=0)
YYp12 = np.concatenate((YYp, YYp), axis=0)
YYmean = np.zeros_like(YY12)
YYprimemean = np.zeros_like(YY12)
def dYYdt(YY, Eta1, Xi1):
return -YY + compute_f_(Eta1, Xi1, s02)
def dYYpdt(YYp, Eta1, Xi1):
return -YYp + compute_fprime_(Eta1, Xi1, s02)
for t in range(niter):
if np.mean(np.abs(YY - fval)) < max_dist:
u0, u1, u2, u3 = compute_us(W1, W2, YY12, YYp12)
Eta121 = resEta12 + u0 + u2 + dHH
Xi121 = resXi12 + u1 + u3
YY12 = YY12 + dt * dYYdt(YY12, Eta121, Xi121)
YYp12 = YYp12 + dt * dYYpdt(YYp12, Eta121, Xi121)
elif np.remainder(t, 500) == 0:
print('unstable fixed point?')
if t > niter * burn_in:
YYmean = YYmean + 1 / niter / burn_in * YY12
YYprimemean = YYprimemean + 1 / niter / burn_in * YYp12
#YYmean = YYmean + np.tile(bl,nS*nT)[np.newaxis,:]
return YYmean, YYprimemean
def compute_f_fprime_t_avg_12_(W1,
W2,
perturbation,
max_dist=1,
burn_in=0.5): # max dist added 10/14/20
#Wmx,Wmy,Wsx,Wsy,s02,K,kappa,T,XX,XXp,Eta,Xi,h1,h2 = parse_W(W)
Wmx, Wmy, Wsx, Wsy, s02, K, kappa, T, h1, h2 = parse_W1(W1)
XX, XXp, Eta, Xi = parse_W2(W2)
fval = compute_f_(Eta, Xi, s02)
fprimeval = compute_fprime_(Eta, Xi, s02)
if share_residuals:
resEta = Eta - u_fn(XX, fval, Wmx, Wmy, K, kappa, T)
resXi = Xi - u_fn(XX, fval, Wsx, Wsy, K, kappa, T)
resEta12 = np.concatenate((resEta, resEta), axis=0)
resXi12 = np.concatenate((resXi, resXi), axis=0)
else:
resEta12 = 0
resXi12 = 0
dHH = np.zeros((nN, nQ * nS * nT))
dHH[:, np.arange(2, nQ * nS * nT, nQ)] = 1
dHH = np.concatenate((dHH * h1, dHH * h2), axis=0)
YY = fval + perturbation
YYp = fprimeval
XX12 = np.concatenate((XX, XX), axis=0)
YY12 = np.concatenate((YY, YY), axis=0)
YYp12 = np.concatenate((YYp, YYp), axis=0)
YYmean = np.zeros_like(YY12)
YYprimemean = np.zeros_like(YY12)
def dYYdt(YY, Eta1, Xi1):
return -YY + compute_f_(Eta1, Xi1, s02)
def dYYpdt(YYp, Eta1, Xi1):
return -YYp + compute_fprime_(Eta1, Xi1, s02)
for t in range(niter):
if np.mean(np.abs(YY - fval)) < max_dist:
Eta121 = resEta12 + u_fn(XX12, YY12, Wmx, Wmy, K, kappa,
T) + dHH
Xi121 = resXi12 + u_fn(XX12, YY12, Wmx, Wmy, K, kappa, T)
YY12 = YY12 + dt * dYYdt(YY12, Eta121, Xi121)
YYp12 = YYp12 + dt * dYYpdt(YYp12, Eta121, Xi121)
elif np.remainder(t, 500) == 0:
print('unstable fixed point?')
if t > niter * burn_in:
YYmean = YYmean + 1 / niter / burn_in * YY12
YYprimemean = YYprimemean + 1 / niter / burn_in * YYp12
return YYmean, YYprimemean
def evaluate(variable_values, parameters):
ax = variable_values[parameters["ax"]]
bx = variable_values[parameters["bx"]]
dx = bx - ax
ay = variable_values[parameters["ay"]]
by = variable_values[parameters["by"]]
dy = by - ay
angle = numpy.arctan2(dy, dx)
error1 = angle - parameters["angle"]
# Normalize the angular differnce using
# (a + 180°) % 360° - 180°
# https://stackoverflow.com/questions/1878907/the-smallest-difference-between-2-angles
return numpy.remainder(error1 + math.pi, 2 * math.pi) - math.pi
def __init__(self, configurations, parameters, controls):
y0, t_total, N_total, number_group, population_proportion, \
t_control, number_days_per_control_change, number_control_change_times, number_time_dependent_controls = configurations
self.N_total = N_total
self.number_group = number_group
self.t_control = t_control
self.number_time_dependent_controls = number_time_dependent_controls
self.configurations = configurations
self.parameters = parameters
self.controls = controls
self.interpolation = piecewiseLinear
if number_group > 1:
# contact matrix
school_closure = True
# calendar from February 15th
weekday = [2, 3, 4, 5, 6]
# calendar from April 1st
# weekday = [0, 1, 2, 5, 6]
# calendar from May 1st
# weekday = [0, 3, 4, 5, 6]
calendar = np.zeros(1000 + 1, dtype=int)
# set work days as 1 and school days as 2
for i in range(1001):
if np.remainder(i, 7) in weekday:
calendar[i] = 1
if not school_closure: # and i < 45
calendar[i] = 2
self.calendar = calendar
contact = np.load("../../utils/parameters/contact/contact_matrix.npz")
self.c_home = contact["home"]
self.c_school = contact["school"]
self.c_work = contact["work"]
self.c_other = contact["other"]
self.contact_full = self.c_home + 5. / 7 * ((1 - school_closure) * self.c_school + self.c_work) + self.c_other
