def plot_fit(series, filename):
y = series.tolist()
x = np.array(range(len(y)))
gauss = Gauss(x, y)
y_pred = gauss.fit()
fit_series = pd.Series(y_pred, series.index, name="Fitted Curve")
_, m, s = gauss.par
current = int(sum(y))
estimate = gauss.estimate_total()
fig1 = series.iplot(kind="bar", asFigure=True)
fig2 = fit_series.iplot(asFigure=True,
colors=['blue'],
width=2,
dash="dashdot")
fig = cf.tools.merge_figures([fig1, fig2])
fig = go.Figure(fig)
fig.update_layout(
title_text="Total Infection Estimate<br>-------------------------------"\
"<br>Current: {} people,"\
" Estimate: {} people".format(current,estimate),
yaxis_title="Capita [-]")
cf.iplot(figure=fig, asUrl=True, filename=filename)
return
def test_gauss(): mu0 = [0,0] cov0 = (0.8**2)*np.identity(2) g0 = 50*Gauss(numN=(mu0,cov0)) mu1 = [1,0] cov1 = (0.1**2)*np.array([[2,1],[1,1]]) g1 = Gauss(numN=(mu1,cov1)) mu2 = [0,1.5] cov2 = (0.3**2)*np.identity(2) g2 = 8*Gauss(numN=(mu2,cov2)) g3 = g2 + g1 + g0 import code; code.interact(local=locals())
def test_gradient_implementation(): cov = np.array([[2,1],[1,1]]) mu = np.array([0.1,0.2]) g = 2 * Gauss(numN=[(mu,cov)]) x = np.array([0.2,0.4]) print(g.grad(x)) g.single_gaussian = False print(g.grad(x)) print(g.grad())
def soft_assign(self,x,mixmean=None,mixcoef=None, mixcov=None):
"""
Calculate the probability of x for each of the k classes.
Typically the sample is assigned to class n with n = arg max(resp).
Parameters
----------
x : (d,n) ndarray
The observations that need to be classified.
mixmeans : (d,k), ndarray, or None
The means of the k mixture components.
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components
If `None` use the values of the class.
Return
------
prob : (k,) ndarray
The probabilities for each of the k classes.
"""
if len(x.shape)==1: x = x[:,None]
d,n = x.shape
# Get the necessary parameters from the class
mixmean = self.mixmean
mixcoef = self.mixcoef
mixcov = self.mixcov
k = len(mixcoef)
prob = np.zeros((k,n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:,i],mixcov[i])
prob[i,j] = g.f(x[:,j])*mixcoef[i]
return prob/np.sum(prob,axis=0)[None,:]
def Run(e):
global powerFlow
if admittance == None:
return
# Else
frm.SetStatusText('Running Gauss-Seidel Power Flow')
# Takes admittance matrix and known values at each bus
with wx.FileDialog(frm, 'PQVd Information') as fileDialog:
if fileDialog.ShowModal() == wx.ID_CANCEL:
return
fname = fileDialog.GetPath()
pqvd = pd.read_csv(fname, header=None)
powerFlow = Gauss(admittance.admittance, pqvd[0].values, pqvd[1].values,
pqvd[2].values, pqvd[3].values)
powerFlow.solve()
wx.StaticText(
frm, 2, 'V = ' + np.array2string(np.array(powerFlow.V)) + '\n S = ' +
np.array2string(np.array(powerFlow.S)) + '\n')
frm.SetStatusText('')
def _respon(self,mixmean,mixcoef,mixcov):
"""
Calculate the responsibilities of each data point for each class k.
Parameters
----------
mixmean : (d,k) ndarray
The means of the k mixture components
mixcoef : (d,) array
The mixture coefficient for each component
mixcov : (k,d,d) ndarray
The covariance matrices of the k mixture components
Return
------
gam : (k,n) ndarray
The responsibilities of data point x_n to the mixture components k
"""
data = self.data
d,n = data.shape
k = self.k
# TODO TEST THIS
gam = np.zeros((k,n))
# print "inside _respons"
# print np.shape(self.logf(data.T[0], mixmean, (mixcoef), mixcov))
# print np.sum(mixcoef,axis = 0)
gaussian = np.zeros((k,n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:,i],mixcov[i])
gaussian[i,j] = np.log(g.f(data[:,j])) + np.log(mixcoef[i])
# for i in range(k):
# gaussian_nominator = self.logf(data[j], mixmean, mixcoef, mixcov) + np.log(mixcoef)
# print "---------"
# print gaussian_nominator.shape
# print gaussian_denominator_total.shape
# print gam.shape
gaussian = gaussian - np.log(np.sum(np.exp(gaussian),axis=0)[None,:])
# gam[:,j] = np.exp(gaussian_nominator - gaussian_denominator_total)
gam = np.exp(gaussian)
return gam
def soft_assign(self, x, mixmean=None, mixcoef=None, mixcov=None):
"""
Calculate the probability of x for each of the k classes.
Typically the sample is assigned to class n with n = arg max(resp).
Parameters
----------
x : (d,n) ndarray
The observations that need to be classified.
mixmeans : (d,k), ndarray, or None
The means of the k mixture components.
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components
If `None` use the values of the class.
Return
------
prob : (k,) ndarray
The probabilities for each of the k classes.
"""
if len(x.shape) == 1: x = x[:, None]
d, n = x.shape
# Get the necessary parameters from the class
mixmean = self.mixmean
mixcoef = self.mixcoef
mixcov = self.mixcov
k = len(mixcoef)
prob = np.zeros((k, n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:, i], mixcov[i])
prob[i, j] = g.f(x[:, j]) * mixcoef[i]
return prob / np.sum(prob, axis=0)[None, :]
def _respon(self, mixmean, mixcoef, mixcov):
"""
Calculate the responsibilities of each data point for each class k.
Parameters
----------
mixmean : (d,k) ndarray
The means of the k mixture components
mixcoef : (d,) array
The mixture coefficient for each component
mixcov : (k,d,d) ndarray
The covariance matrices of the k mixture components
Return
------
gam : (k,n) ndarray
The responsibilities of data point x_n to the mixture components k
"""
data = self.data
d, n = data.shape
k = self.k
# TODO TEST THIS
gam = np.zeros((k, n))
# print "inside _respons"
# print np.shape(self.logf(data.T[0], mixmean, (mixcoef), mixcov))
# print np.sum(mixcoef,axis = 0)
gaussian = np.zeros((k, n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:, i], mixcov[i])
gaussian[i, j] = np.log(g.f(data[:, j])) + np.log(mixcoef[i])
# for i in range(k):
# gaussian_nominator = self.logf(data[j], mixmean, mixcoef, mixcov) + np.log(mixcoef)
# print "---------"
# print gaussian_nominator.shape
# print gaussian_denominator_total.shape
# print gam.shape
gaussian = gaussian - np.log(np.sum(np.exp(gaussian), axis=0)[None, :])
# gam[:,j] = np.exp(gaussian_nominator - gaussian_denominator_total)
gam = np.exp(gaussian)
return gam
def test_gradient():
cov = np.array([[2,1],[1,1]])
mu = np.array([0.1,0.2])
g = 2 * Gauss(numN=[(mu,cov)])
x = np.array([0.2,0.4])
dx = 0.000001
dgdx = np.array([ (g[x+np.array([dx,0])] - g[x]) / dx, (g[x+np.array([0,dx])] - g[x]) / dx ])
dgdx2 = -g[x] * np.linalg.inv(g.numN[0].cov) @ (x.reshape((-1,)) - g.numN[0].mean)
print(np.linalg.inv(g.numN[0].cov))
print("%s - %s" % (x.reshape((-1,)), g.numN[0].mean))
print("computed dgdx: %s" % dgdx)
print("calculated dgdx: %s" % dgdx2)
import code; code.interact(local=locals())
def f(self,x,mixmean=None, mixcoef=None, mixcov=None):
"""
Evaluate the gmm at x.
Parameters
----------
x : (d,) ndarray
A single d-dimensional observation
mixmean : (d,k), ndarray, or None
The means of the k mixture components
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components.
If `None` use the values of the class.
Return
------
val : float
The value of the gmm at given x.
"""
if mixmean == None: mixmean = self.mixmean
if mixcoef == None: mixcoef = self.mixcoef
if mixcov == None: mixcov = self.mixcov
# print mixcoef
# print np.shape(mixcoef)
k = len(mixcoef)
comp = np.zeros((k,))
for j in range(k):
g = Gauss(mixmean[:,j],mixcov[j])
comp[j] = g.f(x)
return mixcoef.dot(comp)
def f(self, x, mixmean=None, mixcoef=None, mixcov=None):
"""
Evaluate the gmm at x.
Parameters
----------
x : (d,) ndarray
A single d-dimensional observation
mixmean : (d,k), ndarray, or None
The means of the k mixture components
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components.
If `None` use the values of the class.
Return
------
val : float
The value of the gmm at given x.
"""
if mixmean == None: mixmean = self.mixmean
if mixcoef == None: mixcoef = self.mixcoef
if mixcov == None: mixcov = self.mixcov
# print mixcoef
# print np.shape(mixcoef)
k = len(mixcoef)
comp = np.zeros((k, ))
for j in range(k):
g = Gauss(mixmean[:, j], mixcov[j])
comp[j] = g.f(x)
return mixcoef.dot(comp)
def Nt(T, P):
X = [-1, 3, -1, -10, -20, -35]
while True:
gamma = dichotomy(0, 3, EPS,
lambda cur_gamma: gamma_func(cur_gamma, T, X))
d_e = find_d_e(T, gamma)
K = find_K(T, d_e)
alpha = 0.285 * pow(10, -11) * pow(gamma * T, 3)
system = [[1, -1, 1, 0, 0, 0,
log(K[0]) + X[1] - X[2] - X[0]],
[1, 0, -1, 1, 0, 0,
log(K[1]) + X[2] - X[3] - X[0]],
[1, 0, 0, -1, 1, 0,
log(K[2]) + X[3] - X[4] - X[0]],
[1, 0, 0, 0, -1, 1,
log(K[3]) + X[4] - X[5] - X[0]],
[
-exp(X[0]), -exp(X[1]), -exp(X[2]), -exp(X[3]),
-exp(X[4]), -exp(X[5]),
exp(X[0]) + exp(X[1]) + exp(X[2]) + exp(X[3]) +
exp(X[4]) + exp(X[5]) - alpha - P * 7243 / T
],
[
exp(X[0]), 0, -Z_c[1] * exp(X[2]), -Z_c[2] * exp(X[3]),
-Z_c[3] * exp(X[4]), -Z_c[4] * exp(X[5]),
Z_c[1] * exp(X[2]) + Z_c[2] * exp(X[3]) +
Z_c[3] * exp(X[4]) + Z_c[4] * exp(X[5]) - exp(X[0])
]]
d_X = Gauss(system)
if max([d_X[i] / X[i] for i in range(len(X))]) < 1e-4:
break
for i in range(len(X)):
X[i] += d_X[i]
return sum([exp(i) for i in X])
class TestGauss(unittest.TestCase):
def setUp(self):
self.gauss = Gauss([[10, 2, 1], [1, 5, 1], [2, 3, 10]])
def test_convergencia_d1_igual_a_0_3(self):
self.gauss.convergencia_d1() | should | equal_to(0.3)
def test_convergencia_d2_igual_a_0_26(self):
self.gauss.convergencia_d2() | should | equal_to(0.26)
def test_convergencia_d3_igual_a_0_138(self):
self.gauss.convergencia_d3() | should | equal_to(0.138)
def test_validar_convergencia(self):
self.gauss.convergencia_d1() | should | be_less_than(1)
self.gauss.convergencia_d2() | should | be_less_than(1)
self.gauss.convergencia_d3() | should | be_less_than(1)
def test_primeira_iteracao_x(self):
self.gauss.iteraX(0, 0) | should | equal_to(0.7)
def setUp(self):
self.gauss = Gauss([[10, 2, 1], [1, 5, 1], [2, 3, 10]])
import inference
from gauss import Gauss
# Handles for readability.
inf = np.inf
# HMM parameters
# prior
pi = np.array([0.6, 0.4])
# state transition matrix
A = np.array([[0.7, 0.3],
[0.2, 0.8]])
# state emission probabilities
B = np.array([Gauss(mean=np.array([1.0, 2.0]),
cov=np.eye(2)),
Gauss(mean=np.array([0.0, -1.0]),
cov=np.eye(2))
])
# DBN
intra = np.array([[0,1],[0,0]]) # Intra-slice dependencies
inter = np.array([[1,0],[0,0]]) # Inter-slice dependencies
node_sizes = np.array([2,inf])
discrete_nodes = [0]
continuous_nodes = [1]
node_cpds = [cpds.TabularCPD(pi),
cpds.GaussianCPD(B),
cpds.TabularCPD(A)]
def buildCylinder(a, b):
cylinder = Gauss(cylinderG[0], cylinderG[1], a, b)
return [[cylinder.func(x, y) for x in range(xmin, xmax + 1)] for y in range(ymin, ymax + 1)]
def test_ghmm():
"""
Testing: GHMM
"""
# Handles for readability.
inf = np.inf
# HMM parameters
# prior
pi = np.array([0.6, 0.4])
# state transition matrix
A = np.array([[0.7, 0.3], [0.2, 0.8]])
# state emission probabilities
B = np.array([
Gauss(mean=np.array([1.0, 2.0]), cov=np.eye(2)),
Gauss(mean=np.array([0.0, -1.0]), cov=np.eye(2))
])
# DBN
intra = np.array([[0, 1], [0, 0]]) # Intra-slice dependencies
inter = np.array([[1, 0], [0, 0]]) # Inter-slice dependencies
node_sizes = np.array([2, inf])
discrete_nodes = [0]
continuous_nodes = [1]
node_cpds = [cpds.TabularCPD(pi), cpds.GaussianCPD(B), cpds.TabularCPD(A)]
dbn = models.DBN(intra, inter, node_sizes, discrete_nodes,
continuous_nodes, node_cpds)
inference_engine = inference.JTreeUnrolledDBNInferenceEngine()
inference_engine.model = dbn
inference_engine.initialize(T=5)
dbn.inference_engine = inference_engine
# INERENCE
evidence = [[None, [1.0, 2.0]], [None, [3.0, 4.0]], [None, [5.0, 6.0]],
[None, [7.0, 8.0]], [None, [9.0, 10.0]]]
dbn.enter_evidence(evidence)
print "Likelihood of single sample: %f" % dbn.sum_product()
# LEARNING
samples = [[[None, [-0.9094, -3.3056]], [None, [2.7887, 2.3908]],
[None, [1.0203, 1.5940]], [None, [-0.5349, 2.2214]],
[None, [-0.3745, 1.1607]]],
[[None, [0.7914, 2.7559]], [None, [0.3757, -2.3454]],
[None, [2.4819, 2.0327]], [None, [2.8705, 0.7910]],
[None, [0.2174, 1.2327]]]]
print "\nEM parameter learning:"
dbn.learn_params_EM(samples, max_iter=10)
print "\nPrior (pi):"
print dbn.node_cpds[0]
print "\nTransition matrx (A):"
print dbn.node_cpds[2]
print "\nEmission probabilities (B):"
print dbn.node_cpds[1]
