xMean[j] = Xprev[i, j, row - 1, col]
elif ind == 3:
xMean[j] = Xprev[i, j, row, col + 1]
elif ind == 4:
xMean[j] = Xprev[i, j, row + 1, col]
Xcur[i, :, row, col] = xMean + np.random.normal(size=M)
# Weight
logW = logPhi(Xcur[i, :, row, col], y[t, row, col])
maxLogW = np.max(logW)
w = np.exp(logW - maxLogW)
logZ[i] += maxLogW + np.log(np.sum(w)) - np.log(M)
w /= np.sum(w)
# Resample
ancestors = res.resampling(w, scheme='systematic')
Xprev[i, :, :, :] = Xprev[i, ancestors, :, :]
Xcur[i, :, :row, col] = Xcur[i, ancestors, :row, col]
Xcur[i, :, :, :col] = Xcur[i, ancestors, :, :col]
Xcur[i, :, row, col] = Xcur[i, ancestors, row, col]
# Outer resampling
maxLogZ = np.max(logZ)
outerW = np.exp(logZ - maxLogZ)
outerW /= np.sum(outerW)
outerAncestors = res.resampling(outerW, scheme='systematic')
Xprev = Xcur[outerAncestors, :, :, :]
ESS[t] = 1 / np.sum(outerW**2)
f = open(filename, 'a')
tmpVec = np.r_[
def __init__(self, t, N, xCond=None):
def phi(x, y, sig2, mu_ab, mu_norm):
return np.exp(-0.5 * (y - mu_ab * x.astype('float') - mu_norm *
(1. - x.astype('float')))**2 / sig2)
def rho(xp, x):
return np.exp(
C2 * (xp.astype('bool') == x.astype('bool')).astype('float'))
def psi(xp, x):
return np.exp(C1 * (xp == x).astype('float'))
C1 = 0.5
C2 = 3.
# Model init
xDomain = np.arange(2)
psiMat = np.array([
np.exp(C1 * (xDomain.astype('bool') == False).astype('float')),
np.exp(C1 * (xDomain.astype('bool') == True).astype('float'))
])
# Load parameters
#region = 'dustBowl'
region = 'sahel'
filename = 'parameters/' + region + 'Sigma2_N35-55_W90-120_downsampled.csv'
sigma2 = np.loadtxt(filename, delimiter=',')
filename = 'parameters/' + region + 'MuAb_N35-55_W90-120_downsampled.csv'
muAb = np.loadtxt(filename, delimiter=',')
filename = 'parameters/' + region + 'MuNorm_N35-55_W90-120_downsampled.csv'
muNorm = np.loadtxt(filename, delimiter=',')
filename = 'processedData/' + region + 'Yt' + str(
t) + '_N35-55_W90-120_downsampled.csv'
Y = np.loadtxt(filename, delimiter=',')
I = Y.shape[0]
J = Y.shape[1]
# SMC init
X = np.zeros((N, I, J), dtype=bool)
ancestors = np.zeros(N)
logZ = 0.
logW = np.zeros(N)
w = np.zeros(N)
ESS = np.zeros(J)
msg = np.zeros((N, I, 2))
c = np.zeros((N, I))
# ---------------
# SMC
# ---------------
# SMC first iteration, j = 0
# Forward filtering
unaryFactor = np.ones((N, I, 2))
for n in range(N):
unaryFactor[n, 0, :] *= phi(xDomain, Y[0, 0], sigma2[0, 0],
muAb[0, 0], muNorm[0, 0])
unaryFactor[n, 0, :] *= rho(xDomain, xCond[0, 0])
msg[n, 0, :] = np.dot(psiMat, unaryFactor[n, 0, :])
c[n, 0] = np.sum(msg[n, 0, :])
msg[n, 0, :] /= c[n, 0]
for i in np.arange(1, I - 1):
unaryFactor[n, i, :] *= phi(xDomain, Y[i, 0], sigma2[i, 0],
muAb[i, 0], muNorm[i, 0])
unaryFactor[n, i, :] *= rho(xDomain, xCond[i, 0])
msg[n, i, :] = np.dot(psiMat,
unaryFactor[n, i, :] * msg[n, i - 1, :])
c[n, i] = np.sum(msg[n, i, :])
msg[n, i, :] /= c[n, i]
unaryFactor[n, I - 1, :] *= phi(xDomain, Y[I - 1, 0], sigma2[I - 1,
0],
muAb[I - 1, 0], muNorm[I - 1, 0])
unaryFactor[n, I - 1, :] *= rho(xDomain, xCond[I - 1, 0])
# Backward sampling
for n in range(N):
tempDist = unaryFactor[n, I - 1, :] * msg[n, I - 2, :]
tempDist /= np.sum(tempDist)
X[n, I - 1, 0] = hlp.discreteSampling(tempDist, xDomain, 1)
for i in np.arange(2, I - 1)[::-1]:
tempDist = unaryFactor[n, i, :] * msg[n, i - 1, :]
tempDist /= np.sum(tempDist)
X[n, i, 0] = hlp.discreteSampling(
tempDist * psiMat[:, X[n, i + 1, 0]], xDomain, 1)
logW = np.sum(np.log(c[:, :I - 1]), axis=1) + np.log(
np.sum(unaryFactor[:, I - 1, :] * msg[:, I - 2, :], axis=1))
maxLogW = np.max(logW)
w = np.exp(logW - maxLogW)
logZ += maxLogW + np.log(np.sum(w)) - np.log(N)
# SMC iteration j = 1 to J
for j in np.arange(1, J):
# Forward filtering
unaryFactor = np.ones((N, I, 2))
for n in range(N):
unaryFactor[n, 0, :] *= phi(xDomain, Y[0, j], sigma2[0, j],
muAb[0, j], muNorm[0, j])
unaryFactor[n, 0, :] *= rho(xDomain, xCond[0, j])
unaryFactor[n, 0, :] *= psi(xDomain, X[n, 0, j - 1])
msg[n, 0, :] = np.dot(psiMat, unaryFactor[n, 0, :])
c[n, 0] = np.sum(msg[n, 0, :])
msg[n, 0, :] /= c[n, 0]
for i in np.arange(1, I - 1):
unaryFactor[n, i, :] *= phi(xDomain, Y[i, j], sigma2[i, j],
muAb[i, j], muNorm[i, j])
unaryFactor[n, i, :] *= rho(xDomain, xCond[i, j])
unaryFactor[n, i, :] *= psi(xDomain, X[n, i, j - 1])
msg[n,
i, :] = np.dot(psiMat,
unaryFactor[n, i, :] * msg[n, i - 1, :])
c[n, i] = np.sum(msg[n, i, :])
msg[n, i, :] /= c[n, i]
unaryFactor[n,
I - 1, :] *= phi(xDomain, Y[I - 1,
j], sigma2[I - 1, j],
muAb[I - 1, j], muNorm[I - 1, j])
unaryFactor[n, I - 1, :] *= rho(xDomain, xCond[I - 1, j])
unaryFactor[n, I - 1, :] *= psi(xDomain, X[n, I - 1, j - 1])
logW = np.sum(np.log(c[:, :I - 1]), axis=1) + np.log(
np.sum(unaryFactor[:, I - 1, :] * msg[:, I - 2, :], axis=1))
maxLogW = np.max(logW)
w = np.exp(logW - maxLogW)
logZ += maxLogW + np.log(np.sum(w)) - np.log(N)
ancestors = res.resampling(w, 'stratified')
# Backward sampling
for n in range(N):
tempDist = unaryFactor[ancestors[n],
I - 1, :] * msg[ancestors[n], I - 2, :]
tempDist /= np.sum(tempDist)
X[n, I - 1, j] = hlp.discreteSampling(tempDist, xDomain, 1)
for i in np.arange(2, I - 1)[::-1]:
tempDist = unaryFactor[ancestors[n],
i, :] * msg[ancestors[n], i - 1, :]
tempDist /= np.sum(tempDist)
X[n, i, j] = hlp.discreteSampling(
tempDist * psiMat[:, X[n, i + 1, j]], xDomain, 1)
## Save init to class object
self.N = N
self.J = J
self.I = I
self.X = X
self.logZ = logZ
self.w = w
self.xCond = xCond
self.ESS = ESS
def __init__(self, t, N, xCond=None):
def phi(x, y, sig2, mu_ab, mu_norm):
return np.exp(-0.5 * (y - mu_ab * x.astype("float") - mu_norm * (1.0 - x.astype("float"))) ** 2 / sig2)
def rho(xp, x):
return np.exp(C2 * (xp.astype("bool") == x.astype("bool")).astype("float"))
def psi(xp, x):
return np.exp(C1 * (xp == x).astype("float"))
C1 = 0.5
C2 = 3.0
# Model init
xDomain = np.arange(2)
psiMat = np.array(
[
np.exp(C1 * (xDomain.astype("bool") == False).astype("float")),
np.exp(C1 * (xDomain.astype("bool") == True).astype("float")),
]
)
# Load parameters
# region = 'dustBowl'
region = "sahel"
filename = "parameters/" + region + "Sigma2_N35-55_W90-120_downsampled.csv"
sigma2 = np.loadtxt(filename, delimiter=",")
filename = "parameters/" + region + "MuAb_N35-55_W90-120_downsampled.csv"
muAb = np.loadtxt(filename, delimiter=",")
filename = "parameters/" + region + "MuNorm_N35-55_W90-120_downsampled.csv"
muNorm = np.loadtxt(filename, delimiter=",")
filename = "processedData/" + region + "Yt" + str(t) + "_N35-55_W90-120_downsampled.csv"
Y = np.loadtxt(filename, delimiter=",")
I = Y.shape[0]
J = Y.shape[1]
# SMC init
X = np.zeros((N, I, J), dtype=bool)
ancestors = np.zeros(N)
logZ = 0.0
logW = np.zeros(N)
w = np.zeros(N)
ESS = np.zeros(J)
msg = np.zeros((N, I, 2))
c = np.zeros((N, I))
# ---------------
# SMC
# ---------------
# SMC first iteration, j = 0
# Forward filtering
unaryFactor = np.ones((N, I, 2))
for n in range(N):
unaryFactor[n, 0, :] *= phi(xDomain, Y[0, 0], sigma2[0, 0], muAb[0, 0], muNorm[0, 0])
unaryFactor[n, 0, :] *= rho(xDomain, xCond[0, 0])
msg[n, 0, :] = np.dot(psiMat, unaryFactor[n, 0, :])
c[n, 0] = np.sum(msg[n, 0, :])
msg[n, 0, :] /= c[n, 0]
for i in np.arange(1, I - 1):
unaryFactor[n, i, :] *= phi(xDomain, Y[i, 0], sigma2[i, 0], muAb[i, 0], muNorm[i, 0])
unaryFactor[n, i, :] *= rho(xDomain, xCond[i, 0])
msg[n, i, :] = np.dot(psiMat, unaryFactor[n, i, :] * msg[n, i - 1, :])
c[n, i] = np.sum(msg[n, i, :])
msg[n, i, :] /= c[n, i]
unaryFactor[n, I - 1, :] *= phi(xDomain, Y[I - 1, 0], sigma2[I - 1, 0], muAb[I - 1, 0], muNorm[I - 1, 0])
unaryFactor[n, I - 1, :] *= rho(xDomain, xCond[I - 1, 0])
# Backward sampling
for n in range(N):
tempDist = unaryFactor[n, I - 1, :] * msg[n, I - 2, :]
tempDist /= np.sum(tempDist)
X[n, I - 1, 0] = hlp.discreteSampling(tempDist, xDomain, 1)
for i in np.arange(2, I - 1)[::-1]:
tempDist = unaryFactor[n, i, :] * msg[n, i - 1, :]
tempDist /= np.sum(tempDist)
X[n, i, 0] = hlp.discreteSampling(tempDist * psiMat[:, X[n, i + 1, 0]], xDomain, 1)
logW = np.sum(np.log(c[:, : I - 1]), axis=1) + np.log(
np.sum(unaryFactor[:, I - 1, :] * msg[:, I - 2, :], axis=1)
)
maxLogW = np.max(logW)
w = np.exp(logW - maxLogW)
logZ += maxLogW + np.log(np.sum(w)) - np.log(N)
# SMC iteration j = 1 to J
for j in np.arange(1, J):
# Forward filtering
unaryFactor = np.ones((N, I, 2))
for n in range(N):
unaryFactor[n, 0, :] *= phi(xDomain, Y[0, j], sigma2[0, j], muAb[0, j], muNorm[0, j])
unaryFactor[n, 0, :] *= rho(xDomain, xCond[0, j])
unaryFactor[n, 0, :] *= psi(xDomain, X[n, 0, j - 1])
msg[n, 0, :] = np.dot(psiMat, unaryFactor[n, 0, :])
c[n, 0] = np.sum(msg[n, 0, :])
msg[n, 0, :] /= c[n, 0]
for i in np.arange(1, I - 1):
unaryFactor[n, i, :] *= phi(xDomain, Y[i, j], sigma2[i, j], muAb[i, j], muNorm[i, j])
unaryFactor[n, i, :] *= rho(xDomain, xCond[i, j])
unaryFactor[n, i, :] *= psi(xDomain, X[n, i, j - 1])
msg[n, i, :] = np.dot(psiMat, unaryFactor[n, i, :] * msg[n, i - 1, :])
c[n, i] = np.sum(msg[n, i, :])
msg[n, i, :] /= c[n, i]
unaryFactor[n, I - 1, :] *= phi(
xDomain, Y[I - 1, j], sigma2[I - 1, j], muAb[I - 1, j], muNorm[I - 1, j]
)
unaryFactor[n, I - 1, :] *= rho(xDomain, xCond[I - 1, j])
unaryFactor[n, I - 1, :] *= psi(xDomain, X[n, I - 1, j - 1])
logW = np.sum(np.log(c[:, : I - 1]), axis=1) + np.log(
np.sum(unaryFactor[:, I - 1, :] * msg[:, I - 2, :], axis=1)
)
maxLogW = np.max(logW)
w = np.exp(logW - maxLogW)
logZ += maxLogW + np.log(np.sum(w)) - np.log(N)
ancestors = res.resampling(w, "stratified")
# Backward sampling
for n in range(N):
tempDist = unaryFactor[ancestors[n], I - 1, :] * msg[ancestors[n], I - 2, :]
tempDist /= np.sum(tempDist)
X[n, I - 1, j] = hlp.discreteSampling(tempDist, xDomain, 1)
for i in np.arange(2, I - 1)[::-1]:
tempDist = unaryFactor[ancestors[n], i, :] * msg[ancestors[n], i - 1, :]
tempDist /= np.sum(tempDist)
X[n, i, j] = hlp.discreteSampling(tempDist * psiMat[:, X[n, i + 1, j]], xDomain, 1)
## Save init to class object
self.N = N
self.J = J
self.I = I
self.X = X
self.logZ = logZ
self.w = w
self.xCond = xCond
self.ESS = ESS
xMean[j] = Xprev[i,j,row-1,col]
elif ind == 3:
xMean[j] = Xprev[i,j,row,col+1]
elif ind == 4:
xMean[j] = Xprev[i,j,row+1,col]
Xcur[i,:,row,col] = xMean + np.random.normal(size=M)
# Weight
logW = logPhi(Xcur[i,:,row,col],y[t,row,col])
maxLogW = np.max(logW)
w = np.exp(logW - maxLogW)
logZ[i] += maxLogW + np.log(np.sum(w)) - np.log(M)
w /= np.sum(w)
# Resample
ancestors = res.resampling(w, scheme='systematic')
Xprev[i,:,:,:] = Xprev[i,ancestors,:,:]
Xcur[i,:,:row,col] = Xcur[i,ancestors,:row,col]
Xcur[i,:,:,:col] = Xcur[i,ancestors,:,:col]
Xcur[i,:,row,col] = Xcur[i,ancestors,row,col]
# Outer resampling
maxLogZ = np.max(logZ)
outerW = np.exp(logZ - maxLogZ)
outerW /= np.sum(outerW)
outerAncestors = res.resampling(outerW, scheme='systematic')
Xprev = Xcur[outerAncestors,:,:,:]
ESS[t] = 1/np.sum(outerW**2)
f = open(filename, 'a')
tmpVec = np.r_[t+1, ESS[t], np.mean(np.mean(Xprev,axis=0),axis=0).reshape(d**2), np.mean(np.mean(Xprev**2,axis=0),axis=0).reshape(d**2)]