def condition_distribution(year, bridge_db, pmatrix):
cs_dist = []
cs = np.arange(8,0,-1)
pmatrix = pmatrix.item()
if int(year) % 2 !=0:
print 'illegal year of interest, must be even number'
else:
indx = int(year)/2
for (name, lat, long, length, width, deck_cs0, super_cs0, sub_cs0, detour, onlink) in bridge_db:
# create reliability index distribution of deck
deck_cs0_array = (cs==deck_cs0).astype('float')
deck_pk = np.dot(np.linalg.matrix_power(pmatrix['deck'].T,indx),deck_cs0_array)
deck_cs_dist = stats.rv_discrete(name='deck_cs_dist', values=(cs,deck_pk))
# create super
super_cs0_array = (cs==super_cs0).astype('float')
super_pk = np.dot(np.linalg.matrix_power(pmatrix['super'].T,indx),super_cs0_array)
super_cs_dist = stats.rv_discrete(name='super_cs_dist', values=(cs,super_pk))
# create sub
sub_cs0_array = (cs==sub_cs0).astype('float')
sub_pk = np.dot(np.linalg.matrix_power(pmatrix['sub'].T,indx),sub_cs0_array)
sub_cs_dist = stats.rv_discrete(name='sub_cs_dist', values=(cs,sub_pk))
cs_dist.append( (name, deck_cs_dist, super_cs_dist, sub_cs_dist) )
return cs_dist
def processDomain(self, X, Y):
for i in range(len(X)):
self.processLine(X[i],Y[i]==1)
self.sentWordPercentageInPos = self.sentWordPercentageInPos / self.totalPosInstances
self.sentWordPercentageInNeg = self.sentWordPercentageInNeg / self.totalNegInstances
#build word distribution for positive words
for word in self.totalPosFreq :
self.totalPosFreq[word] = self.totalPosFreq[word] / self.totalPosWordsInDomain
self.posTokenizer = dict(zip(list(range(len(self.totalPosFreq.keys()))), list(self.totalPosFreq.keys())))
self.posDist = stats.rv_discrete(name='positiveDist', values=(list(range(len(self.totalPosFreq.keys()))), list(self.totalPosFreq.values())))
#build word distribution for negative words
for word in self.totalNegFreq :
self.totalNegFreq[word] = self.totalNegFreq[word] / self.totalNegWordsInDomain
self.negTokenizer = dict(zip(list(range(len(self.totalNegFreq.keys()))), list(self.totalNegFreq.keys())))
self.negDist = stats.rv_discrete(name='negativeDist', values=(list(range(len(self.totalNegFreq.keys()))), list(self.totalNegFreq.values())))
#build word distribution for objective words
for word in self.totalObjFreq :
self.totalObjFreq[word] = self.totalObjFreq[word] / self.totalObjWordsInDomain
self.objTokenizer = dict(zip(list(range(len(self.totalObjFreq.keys()))), list(self.totalObjFreq.keys())))
self.objDist = stats.rv_discrete(name='objectiveDist', values=(list(range(len(self.totalObjFreq.keys()))), list(self.totalObjFreq.values())))
#build positive line length distribution
for length in self.posLineLengthDict:
self.posLineLengthDict[length] = self.posLineLengthDict[length] / self.totalPosInstances
self.posLineLengthDist = stats.rv_discrete(name='posLineLengthDist', values=(list(self.posLineLengthDict.keys()), list(self.posLineLengthDict.values())))
#build negative line length distribution
for length in self.negLineLengthDict:
self.negLineLengthDict[length] = self.negLineLengthDict[length] / self.totalNegInstances
self.negLineLengthDist = stats.rv_discrete(name='negLineLengthDist', values=(list(self.negLineLengthDict.keys()), list(self.negLineLengthDict.values())))
def MakeData(number_of_students, actref_dist,senint_dist,visver_dist,seqglo_dist): # Range of possible values. # -1 = active/sensing/visual/global # +1 = reflective/intuitive/verbal/sequential xk = (-1,1) # Create random number generators that spit out numbers # according to their pre-set distributions. actref_custm = stats.rv_discrete(name = 'actref_custm', values=(xk,actref_dist)) senint_custm = stats.rv_discrete(name = 'senint_custm', values=(xk,senint_dist)) visver_custm = stats.rv_discrete(name = 'visver_custm', values=(xk,visver_dist)) seqglo_custm = stats.rv_discrete(name = 'seqglo_custm', values=(xk,seqglo_dist)) for i in range(number_of_students): #generate a fake name name = ''.join(random.choice(string.letters) for h in range(14)) #generate a learning styles profile act_ref = actref_custm.rvs() sen_int = senint_custm.rvs() vis_ver = visver_custm.rvs() seq_glo = seqglo_custm.rvs() # Uncomment for debug code print name, act_ref, sen_int, vis_ver, seq_glo # Write to file w.writerow([name, act_ref, sen_int, vis_ver, seq_glo])
def __init__(self, state, record):
self.consequences = [['Test: CT scan'],
['Plan: Chemo', 'Plan: Surgery']]
self.t_distributions = [[st.norm(loc=7, scale=2)],
[st.rv_discrete(values=([0], [1])),
st.rv_discrete(values=([0], [1]))]]
self.c_distribution = [st.rv_discrete(values=([0], [1])),
st.rv_discrete(values=([0, 1], [0.5, 0.5]))]
def RandomizedFictitiousPlay(A, Epsilon):
n = len(A[0])
m = len(A)
X = numpy.matrix(numpy.zeros((m, 1), dtype=int))
Y = numpy.matrix(numpy.zeros((n, 1), dtype=int))
X[0] = 1
Y[0] = 1
numpy.random.shuffle(X)
numpy.random.shuffle(Y)
t = int(round(6*math.log(2*n*m)/pow(Epsilon, 2)))
for i in range(t):
Ax = numpy.array(numpy.transpose(A) * X).tolist()
#print Ax
Ay = numpy.array(A * Y).tolist()
#print Ay
values = Ay
probabilities = []
for item in Ay:
probabilities.append(pow(math.e, Epsilon*item[0]/2))
while True:
try:
theprobabilities = []
temp = sum(probabilities)
theprobabilities[:] = [x / temp for x in probabilities]
distrib = stats.rv_discrete(values=(values, theprobabilities))
xchoice = Ay.index(distrib.rvs(size=1)[0])
break
except:
pass
values = Ax
probabilities = []
for item in Ax:
probabilities.append(pow(math.e, -Epsilon*item[0]/2))
while True:
try:
theprobabilities = []
temp = sum(probabilities)
theprobabilities[:] = [x / temp for x in probabilities]
distrib = stats.rv_discrete(values=(values, theprobabilities))
ychoice = Ax.index(distrib.rvs(size=1)[0])
break
except:
pass
#print xchoice
X[xchoice] += 1
#print X
#print ychoice
Y[ychoice] += 1
#print Y
return X/float(t+1), Y/float(t+1)
def prop(q):
"""
Returns a dictionary with keys tau_1 and tau_2 and values discrete RV
with probabilities determined by $q$ as in the matrix above.
"""
proposal = {}
proposal[tau.xk[0]] = rv_discrete(values = [(tau.xk[0], tau.xk[1]),
(q, 1-q)])
proposal[tau.xk[1]] = rv_discrete(values = [(tau.xk[0], tau.xk[1]),
(1-q, q)])
return proposal
def test_entropy(self):
# Basic tests of entropy.
pvals = np.array([0.25, 0.45, 0.3])
p = stats.rv_discrete(values=([0, 1, 2], pvals))
expected_h = -sum(xlogy(pvals, pvals))
h = p.entropy()
assert_allclose(h, expected_h)
p = stats.rv_discrete(values=([0, 1, 2], [1.0, 0, 0]))
h = p.entropy()
assert_equal(h, 0.0)
def perform(self, action):
# get distribution about outcomes
probabilities = self.belief[action] / np.sum(self.belief[action])
distrib = rv_discrete(values=(range(len(probabilities)),
probabilities))
# draw sample
sample = distrib.rvs()
# update belief accordingly
belief = copy(self.belief)
belief[action][sample] += 1
# manual found
if (self.pos == self.world.manual).all():
print("m", end="")
belief = {ToyWorldAction(np.array([0, 1])): [50, 1, 1, 1],
ToyWorldAction(np.array([0, -1])): [1, 50, 1, 1],
ToyWorldAction(np.array([1, 0])): [1, 1, 50, 1],
ToyWorldAction(np.array([-1, 0])): [1, 1, 1, 50]}
# build next state
pos = self._correct_position(self.pos + self.actions[sample].action)
return ToyWorldState(pos, self.world, belief)
def discrete_sample(values, probabilities, ns=1):
distrib = rv_discrete(values=(range(len(values)), probabilities))
indices = distrib.rvs(size=ns)
if ns == 1:
return map(values.__getitem__, indices)[0]
else:
return map(values.__getitem__, indices)
def SequenceDynSelf(protocell,mu,L,N):
q = (1-mu)**L
total=np.sum(protocell)
global test
while (total != 2*N):
"Pick the sequence type"
sec_freq=protocell/total
values=np.arange(len(protocell))
custm = sps.rv_discrete(name='custm', values=(values, sec_freq))
R = custm.rvs(size=1)
R=R.tolist()
R=int(R[0])
sample=R
test = nprandom.binomial(1,q)
if sample == 0:
protocell[0]=protocell[0]+1
elif test == 1:
protocell[sample]=protocell[sample]+1
else:
protocell[0]=protocell[0]+1
total=np.sum(protocell)
return protocell
def __init__(self, len_dist, dataset, max_width=None, max_height=None,
rotate=False, resize=False, crazy=False, max_dist=None):
""" len_dist: a dict containing the distribution of length.
max_dist: maximum distance between digits, to make them closer to each other
"""
lens = len_dist.keys()
self.max_len = max(lens)
probs = [len_dist[k] for k in lens]
self.do_rotate = rotate
self.do_resize = resize
self.crazy = crazy
self.max_dist = max_dist
self.len_rvg = stats.rv_discrete(values=(lens, probs))
# merge train/valid/test
self.dataset = dataset
shape = self.dataset[0][0][0].shape
self.orig_image_shape = int(np.sqrt(shape[0]))
assert self.orig_image_shape ** 2 == int(shape[0])
if max_width is None:
max_width = self.orig_image_shape * self.max_len
if max_height is None:
max_height = self.orig_image_shape
self.img_size = (max_height, max_width)
print "Original dataset size: {0}, {1}, {2}".format(len(dataset[0][0]),
len(dataset[1][0]),
len(dataset[2][0]))
print "Image size: {0}".format(self.img_size)
def plot_boxplot(karr,xdistr,ydistr,name,color,ax=None,dx=.1):
if ax==None: ax = plt.gca()
minarr = []; maxarr = []; meanarr = []
leftarr = []; q1arr = []; medarr = []; q3arr = []; rightarr = []
for k in karr:
ik = k-1
distr = stats.rv_discrete(name=name,values=(xdistr,ydistr[ik,:]))
minarr.append(distr.ppf(0))
leftarr.append(distr.ppf(.05))
q1arr.append(distr.ppf(.25))
meanarr.append(distr.mean())
medarr.append(distr.median())
q3arr.append(distr.ppf(.75))
rightarr.append(distr.ppf(.95))
maxarr.append(distr.ppf(1))
minarr = np.array(minarr)
leftarr = np.array(leftarr)
q1arr = np.array(q1arr)
meanarr = np.array(meanarr)
medarr = np.array(medarr)
q3arr = np.array(q3arr)
rightarr= np.array(rightarr)
maxarr = np.array(maxarr)
ax.plot(karr,leftarr,linestyle='--',color=color)
ax.plot(karr+dx,meanarr,marker='s',linestyle='None',color=color)
ax.errorbar(karr,medarr,yerr=[medarr-q1arr,q3arr-medarr],
marker='o',ls='-',lw=1.8,label=name,color=color)
ax.plot(karr,rightarr,linestyle='--',color=color)
return ax
def profileRandomlyGeneratedKmer(k, sequence, profile):
bases = {'A': 0, 'C': 1, 'G': 2, 'T': 3}
kmerProbabilities = []
# loop through all kmers in sequence
for index in range(len(sequence) - k):
kmerP = 1
# compute probability of kmer starting at sequence[index]
for kmerIndex in range(k):
baseIndex = bases[sequence[index + kmerIndex]]
kmerP *= profile[baseIndex][kmerIndex]
kmerProbabilities.append(kmerP)
sumP = sum(kmerProbabilities)
# normalize to total probability of 1
for i in range(len(kmerProbabilities)):
kmerProbabilities[i] /= sumP
# generate probability distribution based on kmer
xk = np.arange(len(kmerProbabilities))
custm = stats.rv_discrete(name='custm', values=(xk, kmerProbabilities))
randKmerIndex = custm.rvs()
return sequence[randKmerIndex:randKmerIndex + k]
def add_vertex(self):
# Step 1. Choose cluster
clusters = sorted(self.clusters.keys())
new_cluster = len(clusters) + 1
if self.cluster_attachment == "preferential":
# probability of new cluster is 1 / (n_vertices + 1)
norm = float(sum(self.clusters.values()) + 1)
p_new = 1.0 / norm
probas = [self.clusters[cl] / norm for cl in clusters]
elif self.cluster_attachment == "uniform":
# probability of new cluster is 1 / (n_clusters + 1)
norm = float(len(self.clusters.keys()) + 1)
p_new = 1.0 / norm
probas = [1.0 / norm for cl in clusters]
# determine if new cluster appears
if np.random.random() < p_new:
self.clusters[new_cluster] = 1
# generate new vertex
# coord = self._gen_1d_vertex(self.bbox[0], self.bbox[1])
coord = np.random.choice(self.bbox) # select one boundary
new_vertex = ((coord,), new_cluster)
else:
distr = rv_discrete(values=(clusters, probas))
cl = distr.rvs(size=1)[0]
self.clusters[cl] += 1
# generate vertex from existing cluster
cluster_vertices = np.array([v[0][0] for v in self.graph.nodes() if v[1] == cl])
pivot = np.random.choice(cluster_vertices)
coord = self._gen_1d_vertex(pivot - 0.5, pivot + 0.5)
new_vertex = ((coord,), cl)
old_vertices = self.graph.nodes()
self.graph.add_node(new_vertex)
for v in old_vertices:
if abs(v[0][0] - new_vertex[0][0]) < 0.5:
self.graph.add_edge(v, new_vertex)
def run_episode(policy, num_episodes, max_time,
transitions, rewards, time_based=False, repeating=True):
"""Runs NUM_EPISODES episodes using the policy given and returns the results."""
random.seed()
deviation_prob = 0.05
lives = np.zeros([num_episodes, max_time, 4])
# lives = np.zeros(max_time, 4 * num_episodes)
num_actions = rewards.shape[0]
num_states = rewards.shape[1]
for n in range(num_episodes):
# or start at random: random.randrange(num_states)
state = 0
life = np.zeros([max_time, 4])
for t in range(max_time):
action = policy[t, state]
deviated = random.random() < deviation_prob
if deviated:
# perform any other action
action = random.choice([x for x in range(num_actions) if x != action])
life[t, 0] = rewards[action, state]
life[t, 1] = state
life[t, 2] = int(deviated)
life[t, 3] = action
# rv for next state with distribution from transition probabilites
if time_based:
rv_vals = (range(num_states), transitions[t, action, state, :])
else:
rv_vals = (range(num_states), transitions[action, state, :])
next_rv = stats.rv_discrete(name="next_state", values=rv_vals)
state = next_rv.rvs()
lives[n] = life
# lives[:, (n*4):((n+1)*4)] = life
return lives
def softmax_rv(masses, values=None, z=0.05):
""" Returns a discrete random variable based on the softmax function. """
nums = np.exp(np.array(masses) / z)
dist = nums / np.sum(nums)
if values is None:
values = np.arange(len(masses))
return stats.rv_discrete(name='softmax', values=(values, dist))
def create_concordance_probability(d):
word_list = list(d.keys())
freq_list = list(d.values())
word_order_list = [x for x in range(len(word_list))]
probs = stats.rv_discrete(a=0, values=(word_order_list, freq_list))
return CacheResult(word_list, probs)
def __init__(self, state, record):
stage = np.random.choice([1, 2, 3, 4],
p=[1/100, 6/100, 14/100, 79/100])
self.consequences = [['Test: Endoscopy']]
self.t_distributions = [[st.norm(loc=14, scale=3)]]
self.c_distribution = [st.rv_discrete(values=([0], [1]))]
state.add(('C16', stage))
def sample_child(self, model):
values = [i for i in xrange(len(self.children))]
probabilities = [model.get_probability(self, self.children[i]) for i in xrange(len(self.children))]
distrib = rv_discrete(values=(range(len(values)), probabilities))
d = distrib.rvs(size=1)[0]
return self.children[d]
def get_empirical_pmf(values, probabilities, name="Empirical PMF"):
"""Return custom Scipy.stats discrete PMF.
*Arguments*
``values`` [Integer]
The random variable represented by the emperical pmf can
assume the values in this Python list of integers.
``probabilities`` [float]
This Python list of positive floats should be the same
length as ``values.`` The floats should be between zero and
one. Each float is the probability that the corresponding
(i.e., has same index) item in the ``values`` list will
occur.
``name`` String, optional
Assign ``name`` to the emperical_pmf. Default value is
'Empirical PMF`.
"""
return stats.rv_discrete(values=(values, probabilities), name=name)
def getCDF(self, points=None):
# Approssimation of PDF integral (not into the original version of custom class)
# given a set of points: what is the cdf, staring from the PDF of data?
#------------------------------------
# version 1:
#---------------------------------------------------------------------
#x = sorted(points) # points can be different from self.data
#
#y = self.getPDF(x) # pdf function associated with self.data and points
#
#c = [] # list for future CDF array
#c.append( 0.) # initialization
#
#for i in range(1,len(points)):
# c.append((y[i-1]+y[i] )*.5*(x[i]-x[i-1])+c[i-1] )
#for i in range(1,len(points)):
# c[i] = c[i]/c[len(points)-1]
#return c
#--------------------------------------------------------------------
# version 2
points = np.matrix(points)
y = self.getPDF(self.data)
summ = np.sum(y)
p = np.array(y/summ)
custom = stats.rv_discrete(name='custom', values=(self.data, p))
return custom.cdf(points)
def getiCDF(self, xx):
"""
A custom inverse cumulative distribution function.
:param Custom self:
An instance of Custom class.
:param array xx:
An array of points in which the inverse cumulative density function needs to be evaluated.
:return:
Inverse cumulative density function values of the Custom distribution.
"""
#x = self.data
#y = self.getPDF(x)
#c = []
#yy = []
#c.append(0.0)
#for i in range(1, len(x)):
# c.append(c[i-1]+(x[i]-x[i-1])*(y[i]+y[i-1])*.5)
#for i in range(1, len(x)):
# c[i]=c[i]/c[len(x)-1]
#for k in range(0, len(x)):
# for i in range(0, len(x)):
# if ((xx[k]>=c[i]) and (xx[k]<=c[i+1])):
# value = float((xx[k]-c[i])/(c[i+1]-c[i])*(x[i+1]-x[i])+x[i])
# yy.append(value)
# break
#return yy
xx = np.matrix(xx)
y = self.getPDF(self.data)
summ = np.sum(y)
p = np.array(y/summ)
custom = stats.rv_discrete(name='custom', values=(self.data, p))
return custom.ppf(xx)
def get_next_chord_conditional(self, chord, note):
"""
Given a chord, draws a random next chord according to its probability distribution conditioned
on the proceeding note.
note here is a note
"""
chords = self.key.c_chord_given_c_note(note[:-1])
idxs = []
for j in range(len(chords)):
for i in range(len(self.key.chords)):
if chords[j] == self.key.chords[i]:
idxs.append(i)
idxs = list(set(idxs))
chord = self.specified_chord_to_chord(chord)
cond_dist_dict = self.chord_chord_map[chord] # Gets list of candidate chords
next_chords = sorted(cond_dist_dict.keys())
next_probs = [cond_dist_dict[next_chord] for next_chord in next_chords]
true_next_chords = [next_chords[int(i)] for i in idxs]
true_next_probs = [next_probs[int(i)] for i in idxs]
allsum = sum(true_next_probs)
for i in range(len(true_next_probs)):
true_next_probs[i] = true_next_probs[i] / allsum
cond_dist = stats.rv_discrete(name='cond_dist', values=(true_next_chords, true_next_probs))
return self.key.chords[cond_dist.rvs(size=1)-1]
def simplify3(nk): result=[] nk=np.array(nk) xk = nk/float(np.sum(nk)) #print nk #X_plot = np.linspace(0, len(nk), 1000)[:, np.newaxis] sdiv=1000 X_plot = np.linspace(0, len(xk), sdiv)[:, np.newaxis] custm = stats.rv_discrete(name='custm',a=0,b=7, values=(range(len(xk)), xk)) yk= custm.rvs(size=100000) #yk.flatten() #fig, ax = plt.subplots(1, 1) #ax.hist(yk, normed=True, histtype='stepfilled', alpha=0.2) # gaussian KDE X=yk.reshape(-1, 1) kde = KernelDensity(kernel='gaussian', bandwidth=0.6).fit(X) log_dens = kde.score_samples(X_plot) mi, ma = argrelextrema(log_dens, np.less)[0], argrelextrema(log_dens, np.greater)[0] mi=np.rint(mi*float(len(xk))/float(sdiv)) ma=np.rint(ma*float(len(xk))/float(sdiv)) start=0 #print mi for i in mi: i=int(i) if start!=i: val=np.average(nk[start:i]) for j in xrange(start,i): result.append(val) start=i val=np.average(nk[start:]) for j in xrange(start,len(nk)): result.append(val) return np.array(result)
def main():
fig = plt.figure(figsize=(3.2, 1.8))
ax = fig.add_axes([0, 0, 1, 1])
signal = create_gammapy_skymap().data
background = np.ones(signal.shape)
background /= background.sum()
data = (1 * signal + background) / 2.
# setup counts generator
pdf = data.copy().flatten()
x = np.arange(pdf.size)
counts_generator = rv_discrete(name='counts', values=(x, pdf))
counts = np.zeros_like(data)
image = ax.imshow(counts, cmap='afmhot', origin='lower', vmin=0, vmax=9,
interpolation='None')
bins = np.arange(counts.size + 1) - 0.5
anim = FuncAnimation(fig, animate, fargs=[image, counts, bins, counts_generator],
frames=200, interval=50)
filename = 'gammapy_logo.gif'
anim.save(filename, writer='imagemagick')
def getRandomGenerator(freqs):
s = sum(freqs)
l = len(freqs)
probs = [float(freqs[i])/float(s) for i in range(l)]
quals = np.arange(l)
dist = stats.rv_discrete(name='custm', values=(quals, probs))
return dist
def simulate(self, N, start=None, stop=None, dt=1):
"""
generates a realization of the Hidden Markov Model
:param N: int trajectory length in steps of the lag time
:param start: int (default=None) - starting hidden state. If not given, will sample from the stationary
distribution of the hidden transition matrix
:param stop: int or int-array-like (default=None) - stopping hidden set. If given, the trajectory will be stopped before
N steps once a hidden state of the stop set is reached
:param dt: int - trajectory will be saved every dt time steps. Internally, the dt'th power of P is taken to ensure a more efficient simulation
:return: ndarray, ndarray - tuple of (hidden state trajectory with length N/dt, observable state discrete trajectory with length N/dt)
"""
from scipy import stats
import msmtools.generation as msmgen
# generate output distributions
output_distributions = [stats.rv_discrete(values=(np.arange(self.pobs.shape[1]), pobs_i)) for pobs_i in self.pobs]
# sample hidden trajectory
htraj = msmgen.generate_traj(self.transition_matrix, N, start=start, stop=stop, dt=dt)
otraj = np.zeros(htraj.size, dtype=int)
# for each time step, sample microstate
for t, h in enumerate(htraj):
otraj[t] = output_distributions[h].rvs() # current cluster
return htraj, otraj
def non_uniform_approx(A, B, S, R):
"""Creates non-uniformly approximate matrices of A and B, C and R."""
# Pick rows from A and corresponding column from B uniformly random
n = A.shape[1]
s = S.shape[1]
rows = np.arange(0, n) # The list of rows
probs = np.zeros(n) # The probability of each column
# Calculate the probability of selecting each column based on the amount of
# information using the method proposed by Drineas and Kannan. The probability
# is based on the product of the row and column euclidean norms divided by
# the cumulative sum of the product of euclidean norms for all rows and columns
D = 0.0
for i in range(0, n):
prod = np.sqrt((A[i, :]*A[i, :]).sum()) * np.sqrt((B[:, i]*B[:, i]).sum())
D += prod
probs[i] = prod / D
# Use the probabilities to pick the rows and columns non-uniformly
distrib = rv_discrete(values=(rows, probs))
for t, i_t in enumerate(distrib.rvs(size=s)):
S[:, t] = A[i_t, :]
R[t, :] = B[:, i_t]
# Apply scaling
scaling = np.sqrt(s * probs[i_t])
S[:, t] /= scaling
R[t, :] /= scaling
def __call__(self, *args, **kwargs):
frozen = self.underlying(*args, **kwargs)
return stats.rv_discrete(
a = 0, b = self.max_value,
values = (np.arange(self.max_value + 1), truncated_pmf(frozen, self.max_value + 1))
)
def getadm(psrcatdm, iseed, nbins, n):
"""Function to randomly select a dm value from the known pulsar dms in the catalogue.
Creates a distribution of the dm values given their probabilities, and randomly select
a dm value to use for scattering.
Args:
-----
psrcatdmfile : a file containing psrcat dm values in 1 column (nan values replaced with zeros)
iseed : seed for the random number generator [int].
nbins : number of bins.
n : size of the samples to draw
Returns:
--------
rand_dm : randomly selected dm value (pc cm^-3).
"""
dm_file_name = str(psrcatdm)
dm_file = np.loadtxt(dm_file_name) # Load the txt file containing the DM
dm_dat = dm_file[np.where(dm_file > 0)] # Exclude the zero dms used to replace null values from psrcat
hist, bin_edges = np.histogram(dm_dat, bins=nbins) # creates a histogram distribution
probs = hist/float(len(dm_dat)) # Compute probabilities
dm_range = np.linspace(np.min(dm_dat), np.max(dm_dat), endpoint=True, num=len(probs))
normdiscrete = stats.rv_discrete(values=(dm_range, probs), seed=iseed) # Find an arbitrary distribution
rand_dm = normdiscrete.rvs(size=n) # draw a sample of size n
return rand_dm
def measure_cheat(self):
#Measure but ignore 0 state, for debugging shors
data = self.array.toarray()[0]
pos = np.arange(len(data))
probs = np.abs(np.square(data))
probs[0] = 0
#If probs is not normalised (usually due to rounding errors), re-normalise
probs = probs / np.sum(probs)
#print(probs)
dist = stats.rv_discrete(values=(pos, probs))
self.array = np.zeros(data.shape)
self.array[dist.rvs()] = 1
self.array = sp.bsr_matrix(self.array)
def generator(self):
# construct a generator using the PDF
if self.my_generator is None:
N = len(self.dz)
xk = np.arange(N)
pk = self.dz
pk = pk / pk.sum()
self.my_generator = stats.rv_discrete(name='zdist', values=(xk, pk))
return self.my_generator
def _make_gp_list(self, mean, samples):
"""
Generating a list of numbers of pixels discharged based on the total mean
discharges using the generalized poisson function.
"""
width = np.sqrt(mean)
k_min = max([min([0, mean - 3 * width]), 0])
k_max = mean + 3 * width + 10
k_arr = np.arange(k_min, k_max)
gp_prob = _general_poisson(k_arr, mean, self.lamb)
gp_prob = gp_prob / np.sum(gp_prob) ## Additional normalization
dist = stats.rv_discrete('GeneralizedPoisson', values=(k_arr, gp_prob))
return dist.rvs(size=samples)
def get_chord_single_distr(start_prob, end_prob, time, composition_length):
cs_probs = []
unnormed_prob = 0.
tc = time / composition_length
chord_prob = filt(start_prob + (end_prob - start_prob) * tc)
single_prob = 1. - chord_prob
distrib = stats.rv_discrete(name='csd',
values=([0, 1], [chord_prob, single_prob]))
return distrib
def generate_padding(plain_samples, blocksize):
padding_length = blocksize * blocksize - len(plain_samples)
bincount = (-1 * (np.amin(plain_samples)))
bincount += (np.amax(plain_samples) + 1) # add the zero bin
hist, bins = np.histogram(plain_samples, bincount, density=True)
pk = hist / np.sum(hist)
xk = np.arange(np.amin(plain_samples), np.amax(plain_samples) + 1)
sampdist = stats.rv_discrete(name='Sample distribution', values=(xk, pk))
randsamples = sampdist.rvs(size=padding_length)
return randsamples
def total_correlation(Xs):
pmf = []
Xs = np.asarray(Xs)
for stock in range(len(Xs)):
s = pd.Series(Xs[stock])
b = (s.groupby(s).transform('count') / len(s)).values
pmf.append(b)
pmf = np.asarray(pmf)
pmf /= pmf.sum()
custm = stats.rv_discrete(name='custm', values=(Xs, pmf))
d = Distribution.from_ndarray(pmf)
t = T(d)
return t
def getWarmingLevelMixDistributions(warmingLev, startYear=2000, endYear=2150):
pdfR8 = getWarmingLevelMixDistributionByScen('rcp85',
warmingLev,
startYear=startYear,
endYear=endYear)
pdfR4 = getWarmingLevelMixDistributionByScen('rcp45',
warmingLev,
startYear=startYear,
endYear=endYear)
yrs = pdfR8.xk
mixDist = (pdfR8.pk + pdfR4.pk) / 2.
pdf = st.rv_discrete(values=(yrs, mixDist))
return pdf, pdfR8, pdfR4
def __init__(self, name, min_included, max_included, null_default_value, **kwargs):
scipy_dist_obj = rv_discrete(
name=name,
a=min_included,
b=max_included,
**kwargs
)
scipy_dist_obj._pmf = self._pmf
ScipyDiscreteDistributionWrapper.__init__(
self,
scipy_distribution=scipy_dist_obj,
null_default_value=null_default_value
)
def erdos_renyi_ternary(num_genes: int, prob_conn: float) -> np.ndarray:
"""Generate ternary valued ER graph.
Args:
num_genes: Number of genes/nodes.
prob_conn: Probability of connection.
Returns:
Adjacency matrix.
"""
signed_edge_dist = rv_discrete(
values=([-1, 0, 1], [prob_conn / 2, 1 - prob_conn, prob_conn / 2]))
return signed_edge_dist.rvs(size=(num_genes, num_genes))
def var(self, only_missense=False):
if only_missense:
return self.missense_scores.var()
else:
mean_of_type_vars = self.f_missense * self.missense_scores.var()
type_means_dist = rv_discrete(
values=([1, self.missense_scores.mean(), 0],
self.get_type_freqs()))
var_of_type_means = type_means_dist.var()
# According the the law of total variance.
return mean_of_type_vars + var_of_type_means
def measure(self):
"""Measure qubit register. Collapses to 1 definite state. Simulates real measurement, as
intermediate values of qubit registers during computation remain unknown.
"""
self.normalise()
pos = np.arange(len(self.array))
probs = self.array * np.conjugate(self.array)
#If probs is not normalised (usually due to rounding errors), re-normalise
#probs = probs/np.sum(probs)
dist = stats.rv_discrete(values=(pos, probs))
self.array = np.zeros(self.array.shape)
self.array[dist.rvs()] = 1
return self.array
def get_for(self, var: str, constr: str):
"""
Returns the randomness associated with the given variable and
constraint pair. Returns a ``scipy.stats`` distribution (possibly
discrete).
"""
logger.debug(f"Retrieving randomness for ({var}, {constr}).")
if self.is_finite():
return rv_discrete(values=zip(*self._discrete[var, constr]),
name="discrete")
else:
return self._randomness[var, constr]
def statistics_back(self):
counter = [0] * (len(self.class_back)+1)
for i in self.back:
counter[i[0]] += 1
counter[i[1]] += 1
total = 0.0
for i in counter:
total += i
counter = [i/total for i in counter]
candinate = list(range((len(self.class_back)+1)))
custm = stats.rv_discrete(name='custm', values=(candinate, counter))
num = custm.rvs(size=2)
return num
def generateSamples(w, mu, cov, s):
dim = len(mu[0])
d = rv_discrete(values=(range(len(w)), w))
components = d.rvs(size=s)
# generate samples of size of each component, then shuffle
if dim > 1:
return components, np.array([
np.random.multivariate_normal(mu[i], cov[i], 1)[0]
for i in components
])
else:
return components, np.asmatrix(
[np.random.normal(mu[i], cov[i], 1)[0] for i in components]).T
def test_rvs(self):
states = [-1, 0, 1, 2, 3, 4]
probability = [0.0, 0.3, 0.4, 0.0, 0.3, 0.0]
samples = 1000
r = stats.rv_discrete(name='sample', values=(states, probability))
x = r.rvs(size=samples)
assert_(isinstance(x, numpy.ndarray))
for s, p in zip(states, probability):
assert_(abs(sum(x == s) / float(samples) - p) < 0.05)
x = r.rvs()
assert_(isinstance(x, int))
def fit_variational_inference(self,
data,
est_cluster,
a,
b,
alpha,
max_iter=50):
self.lam_history = np.zeros((max_iter, est_cluster))
self.pi_history = np.zeros((max_iter, est_cluster))
a_hat = a.copy()
b_hat = b.copy()
alpha_hat = alpha.copy()
print("start fitting...")
for iteration in tqdm(range(max_iter)):
_loglam = scipy.special.digamma(a_hat) - np.log(b_hat)
_lam = a_hat / b_hat
_logpie = scipy.special.digamma(alpha_hat) - scipy.special.digamma(
np.sum(alpha_hat))
# data shape = (data_len, 1)
# param shape = (1, category_len)
# nu shape = (data_len, category_len)
nu = np.exp(data * _loglam - _lam + _logpie)
nu = nu / np.sum(nu, axis=1, keepdims=True)
a_hat = np.sum(data * nu, axis=0) + a
b_hat = np.sum(nu, axis=0) + b
alpha_hat = np.sum(nu, axis=0) + alpha
self.pi_history[iteration, :] = np.random.dirichlet(
alpha_hat[0], 1)
self.lam_history[iteration, :] = stats.gamma.rvs(a_hat[0],
scale=1 /
b_hat[0],
size=est_cluster,
random_state=0)
for cls in range(est_cluster):
print("estimation of cluster {}: lambda = {:.2f}, real={}".format(
cls, self.lam_history[iteration, cls], self.real_lam[cls]))
_s = np.zeros((data.shape[0], est_cluster))
for _n in range(data.shape[0]):
cat = stats.rv_discrete(name='custm',
values=(range(est_cluster), nu[_n, :]))
_class = cat.rvs(size=1)
_s[_n, _class] = 1
self.estimate_cluster = _s
self.cluster_proba = nu
def bootstrap_counts(dtrajs, lagtime, corrlength=None):
"""
Generates a randomly resampled count matrix given the input coordinates.
See API function for full documentation.
"""
from scipy.stats import rv_discrete
# if we have just one trajectory, put it into a one-element list:
if not isinstance(dtrajs, list):
dtrajs = [dtrajs]
ntraj = len(dtrajs)
# can we do the estimate?
lengths = determine_lengths(dtrajs)
Lmax = np.max(lengths)
Ltot = np.sum(lengths)
if lagtime >= Lmax:
raise ValueError('Cannot estimate count matrix: lag time '
+ str(lagtime) + ' is longer than the longest trajectory length ' + str(Lmax))
# how many counts can we sample?
if corrlength is None:
corrlength = lagtime
nsample = int(Ltot / corrlength)
# determine number of states n
from deeptime.markov import number_of_states
n = number_of_states(dtrajs)
# assigning trajectory sampling weights
w_trajs = np.maximum(0.0, lengths - lagtime)
w_trajs /= np.sum(w_trajs) # normalize to sum 1.0
distrib_trajs = rv_discrete(values=(list(range(ntraj)), w_trajs))
# sample number of counts from each trajectory
n_from_traj = np.bincount(distrib_trajs.rvs(size=nsample), minlength=ntraj)
# for each trajectory, sample counts and stack them
rows = np.zeros((nsample,))
cols = np.zeros((nsample,))
ones = np.ones((nsample,))
ncur = 0
for i in range(len(n_from_traj)):
if n_from_traj[i] > 0:
(r, c) = bootstrap_counts_singletraj(dtrajs[i], lagtime, n_from_traj[i])
rows[ncur:ncur + n_from_traj[i]] = r
cols[ncur:ncur + n_from_traj[i]] = c
ncur += n_from_traj[i]
# sum over counts
Csparse = scipy.sparse.coo_matrix((ones, (rows, cols)), shape=(n, n))
return Csparse.tocsr()
def batch_size_dist(min_num: int, max_num: int):
"""Function for sampling powers of 2.
:param min_num: minimum number (a power of 2)
:param max_num: maximum number (a power of 2)
"""
assert math.log(min_num, 2).is_integer() and math.log(max_num, 2).is_integer(),\
'Supplied minimum and maximum have to be powers of 2'
min_pow = int(math.log(min_num, 2))
max_pow = int(math.log(max_num, 2))
no = max_pow - min_pow + 1
return stats.rv_discrete(
values=([2**p for p in np.arange(min_pow, max_pow + 1)],
[1 / no for _ in np.arange(min_pow, max_pow + 1)]))
def generiere_termine(self):
arten = []
wahrscheinlichkeiten = []
for k, v in self.terminarten.iteritems():
arten.append(k)
wahrscheinlichkeiten.append(v[0])
verteilung = stats.rv_discrete(name='verteilung',
values=(arten, wahrscheinlichkeiten))
self.grundtermine = verteilung.rvs(size=self.anzahlTermine)
for t in self.grundtermine:
reale_dauer = random.gauss(t, self.terminarten[t][1])
self.termine.append(
model.Termin(random.choice(self.kunden), t, reale_dauer))
def generate_age_group_distribution(name, age_groups, probabilities):
'''
Generates discrete distribution from age demography data.
'''
probabilities = np.array(probabilities) / np.sum(probabilities)
xk = np.arange(age_groups[-1][-1] + 1) # max age
pk = []
for group, prob in zip(age_groups_demography, probabilities):
a, b = group
n = b - a + 1
pk += n * [prob / n]
return stats.rv_discrete(name=name, values=(xk, pk))
def get_area_distribution(tracks, fit=False):
area = np.sum(tracks > 0, axis=(1, 2))
if not fit:
count = np.bincount(area)
probability = count / float(np.sum(count))
return stats.rv_discrete(a=0,
b=np.max(probability.shape[0]),
name='signal distribution',
values=(np.arange(count.shape[0]),
probability))
else:
exp_params = stats.expon.fit(area)
return stats.expon(*exp_params)
def _hist_fill(data, bins, entries=0, freeze=None):
if type(bins) == int:
if bins == 0:
bins = np.arange(data.size + 1, dtype=float)
else:
bins = np.linspace(data.min(), data.max(), bins)
binc = (bins[1:] + bins[:-1]) / 2
if freeze:
return lambda: data
else:
rv = rv_discrete(values=(binc, data / data.sum()))
return lambda: np.histogram(
rv.rvs(size=data.sum()
if entries == 0 else entries), bins)[0].astype(float)
def mm():
# 两袋各取一颗，黄，绿， 求黄色来自1994的概率
# m&m problem
color_1994 = ('brown', 'yellow', 'red', 'green', 'orange', 'yellow_brown')
color_1996 = ('blue', 'green', 'orange', 'yellow', 'red', 'brown')
p_1994 = (.3, .2, .2, .1, .1, .1)
p_1996 = (.24, .2, .16, .14, .13, .13)
# 把所有颜色转为对应的数字保存在字典中
color = set(color_1996).union(set(color_1994))
color_dict = {i: c for c, i in enumerate(color)}
color_1996 = [color_dict[c] for c in color_1996]
color_1994 = [color_dict[c] for c in color_1994]
mm_1994 = st.rv_discrete(values=(color_1994, p_1994))
mm_1996 = st.rv_discrete(values=(color_1996, p_1996))
# s为取到一黄一绿的可能性
# p(黄=1994|s) = p(s|黄=1994) * p(黄=1994)/p(s)= p(s，黄=1994)/p(s), 这里
p1 = mm_1994.pmf(color_dict['yellow']) * mm_1996.pmf(color_dict['green'])
p2 = mm_1996.pmf(color_dict['yellow']) * mm_1994.pmf(color_dict['green'])
p = p1 / (p1 + p2)
print(p)
def generate_data(self, model_params, my_N):
"""
Generate data according to the model. Internally uses generate_data_from_hidden.
This method does _not_ obey gamma: The generated data may have more
than gamma active causes for a given datapoint.
"""
D = self.D
H = self.H
s = stats.rv_discrete(values = (np.arange(H),model_params['pies']), name = 'compProbDistr').rvs(size=my_N)
return self.generate_from_hidden(model_params, {'s': s})
def choice_faces(verts, faces):
num = 4000
u1, u2, u3 = np.split(verts[faces[:, 0]] - verts[faces[:, 1]], 3, axis=1)
v1, v2, v3 = np.split(verts[faces[:, 1]] - verts[faces[:, 2]], 3, axis=1)
a = (u2 * v3 - u3 * v2)**2
b = (u3 * v1 - u1 * v3)**2
c = (u1 * v2 - u2 * v1)**2
Areas = np.sqrt(a + b + c) / 2
Areas = Areas / np.sum(Areas)
choices = np.expand_dims(np.arange(Areas.shape[0]), 1)
dist = stats.rv_discrete(name='custm', values=(choices, Areas))
choices = dist.rvs(size=num)
select_faces = faces[choices]
return select_faces
def get_rolling_boundary(closing_values, bound, window, direction):
coll = [np.nan] * window
for i in range(window, closing_values.shape[0]):
values = closing_values[i - window:i]
# Create distribution
perc = np.ones(values.shape[0]) / values.shape[0]
dist = rv_discrete(values=(values, perc))
# Get bounding of distribution
if direction == 'upper' or direction == 'long':
coll.append(dist.ppf(1 - bound))
else:
coll.append(dist.ppf(bound))
return np.array(coll)
def _assign_sub_sector(self, person):
"""
Assign sub-sector job as defined in config
"""
MC_random = np.random.uniform()
ratio = self.sub_sector_ratio[person.sector][person.sex]
distr = self.sub_sector_distr[person.sector][person.sex]
if MC_random < ratio:
sub_sector_idx = stats.rv_discrete(
values=(np.arange(len(distr)), distr)
).rvs()
person.sub_sector = self.sub_sector_distr[person.sector]["label"][
sub_sector_idx
]
def get_power_law(a, m):
"""
Defining a discrete power law probability density function of length
a : a parameter of the distribution that controls
m : number of discrete values in the range of the r.v
following the power law
"""
values = np.arange(1, m + 1, dtype='float')
pmf = 1 / values**a
pmf /= pmf.sum()
return stats.rv_discrete(values=(range(1, m + 1), pmf)), pmf
def get_initial_probs(filename):
positions = []
initial_probs = []
reader = csv.DictReader(open(filename))
for row in reader:
positions.append(row["Position"])
initial_probs.append(float(row["p"]))
return (positions,
stats.rv_discrete(name="initial_probs",
values=(range(0,
len(positions)), initial_probs)))
def __init__(self,
data_sketch_root,
net,
plotter,
n=1000,
transform=None,
visdom=True,
model_train="",
image_size=224,
triplet=True):
self.corr_files = []
self.visdom = visdom
self.data_sketch_root = data_sketch_root
self.transform = transform
self.n = n
self.n_all = []
self.df = []
self.views = []
self.image_size = image_size
self.triplet = (triplet * 4) + 1
for i in range(3):
for j in range(3):
self.views.append([dic_indices.get(i), dic_indices.get(j)])
self.corr_files.append("{}/dataset_{}_train_{}_{}.csv".format(
data_sketch_root, model_train, i, j))
self.df.append(pd.read_csv(self.corr_files[-1], index_col=0))
self.n_all.append(self.df[-1].shape[0])
self.prob = stats.rv_discrete(name='custm',
values=([0, 1], [0.95, 0.05]))
self.plotter = plotter
self.n_part_len = np.array(self.n_all) // self.n
self.part = np.zeros(9)
self.prob_rotations = stats.rv_discrete(
name='custm', values=([0, 1, 2, 3], [0.25, 0.25, 0.25, 0.25]))
self.rotations = [
lambda x: x, np.rot90, lambda x: np.rot90(np.rot90(x)),
lambda x: np.rot90(np.rot90(np.rot90(x)))
]
self.net = net
self.prob_show_image = stats.rv_discrete(name='custm',
values=([0, 1], [0.95, 0.05]))
self.prob_pixear_image = stats.rv_discrete(name='custm',
values=([0, 1, 2],
[0.60, 0.20, 0.20]))
self.prob_view = stats.rv_discrete(name='custm',
values=(np.arange(9),
np.ones(9) * 1 / 9))
self.prob_view_negative = stats.rv_discrete(
name='custm', values=(np.arange(9), np.ones(9) * 1 / 9))
self.pixear = [
lambda x: x,
lambda x: cv2.resize(x, (64, 64), interpolation=cv2.INTER_CUBIC),
lambda x: cv2.resize(x, (128, 128), interpolation=cv2.INTER_CUBIC)
]
self.init_csv()