def g():
d = len(Mu)
assert Mu.shape == (d,), "Mu must be a vector"
assert A.shape == (d, d), "A must be a square matrix"
assert (A.T == A).all(), "and symmetric"
assert V.shape == (d, d), "V must be a square matrix"
assert (V.T == V).all(), "and symmetric"
a = chol(A)
v = chol(V)
B = dot(V, inv(V + A))
_a2 = V - dot(B, V)
_a2 = chol(_a2)
Y, U = array([0.0] * d), array([0.0] * d)
for i in range(n + burnin):
for _ in range(thin): # skipe
# sample Y | U ~ N(U, V)
Y = U + dot(v, random.normal(size=d))
# sample U | Y ~ N(A(A+V)^-1)(Y-Mu) + Mu,
# A - A(A+V)^-1A)
U = dot(B, (Mu - Y)) + Y + +dot(_a2, random.normal(size=d))
if i >= burnin:
yield [U, Y]
def whitenoise(data, wpow=10**(-11), fs=2.5 * 10**6):
l = len(data[0])
sig_noise = sqrt((wpow) * fs / 2)
out1 = data[0] + sig_noise * random.normal(0, 1, l)
out2 = data[1] + sig_noise * random.normal(0, 1, l)
out3 = data[2] + sig_noise * random.normal(0, 1, l)
out4 = data[3] + sig_noise * random.normal(0, 1, l)
#datagenerator.writefile(out1,out2,out3,out4)
return out1, out2, out3, out4
def testRewardFunction(self, x, typ, noise=0.000001):
if typ == "growSin":
return (sin((x - self.rangeMin) / 3.0) + 1.5 + x / self.distRange) / 4.0 + random.normal(0, noise)
if typ == "rastrigin":
n = x / self.distRange * 10.0
if abs(n) > 5.0: n = 0.0
# FIXME: imprecise reimplementation of the Rastrigin function that exists already
# in rl/environments/functions...
return (20.0 + n ** 2 - 10.0 * cos(2.0 * 3.1416 * n)) / 55.0 + random.normal(0, noise)
if typ == "singleGaus":
return self.getStND(x) + random.normal(0, noise)
return 0.0
def testRewardFunction(self, x, typ, noise=0.000001):
if typ=="growSin":
return (sin((x-self.rangeMin)/3.0)+1.5+x/self.distRange)/4.0+random.normal(0,noise)
if typ=="rastrigin":
n=x/self.distRange*10.0
if abs(n) > 5.0: n=0.0
# FIXME: imprecise reimplementation of the Rastrigin function that exists already
# in rl/environments/functions...
return (20.0 + n**2 -10.0*cos(2.0*3.1416*n))/55.0+random.normal(0,noise)
if typ=="singleGaus":
return self.getStND(x)+random.normal(0,noise)
return 0.0
def quadthermo_agent_gen(): targetT=spr.normal(18,2) tolerance=2 absmax=max(spr.normal(21,1),targetT+tolerance) #no support absmin=min(spr.gamma(4,1),targetT-tolerance) #no support vec=[0.0,0.21,0.135,0.205,0.115,0.115,0.095,0.065,0.03,0.03] r=sp.random.uniform() nres=1 i=0 while i<7 and r>vec[i]: r-=vec[i] i+=1 nres=i+1 occ=active.get_occ_p(nres) cons=[] for p in occ: p.extend([targetT,tolerance]) cons.append(p) q=sp.exp(sp.random.normal(-9.3,2.0)) fa=28.39+sp.random.gamma(shape=2.099,scale=28.696) #floor area from cabe dwelling survey flat=sp.random.uniform(0,1)<0.365 # flat or house if flat: U = 3.3*sp.sqrt(fa) #insulation in W/K floor area else: U= 3.6*sp.sqrt(fa)+0.14*fa k=U #insulation in W/K cm=1000*sp.exp(sp.random.normal(5.5,0.35)) #thermal capacity in J P=sp.random.uniform(6000,15000)# power in W Prequ=k*20 if Prequ>P: print "!!!!!!!!!!!" s=str(["quadthermo_agent",absmax,absmin,cons,q,P,cm,k]) return s
def thompson_sampling(y, std):
"""
Thompson sampling was first described by Thompson in 1933 as a solution to
the multi-arm bandit problem.
Thompson, W. 1933. “On the likelihood that one unknown probability
exceeds another in view of the evidence of two samples”. Biometrika.
25(3/4): 285–294.
Parameters
----------
y : 1D vector Numpy Array
The mean of the surrogate model at all test points used in the optimization.
std : 1D vector Numpy Array
The standard deviation from the surrogate model at all test points
used in the optimization.
Returns
-------
nu_star : float
The maximum value from the Thompson Sampling.
x_star : integer
The index of the test point with the maximum value.
tsVal : TYPE
Sampled values for all test points.
"""
tsVal = random.normal(loc=y, scale=std)
nu_star = np.max(tsVal)
x_star = int(np.where(tsVal == nu_star)[0])
return nu_star, x_star, tsVal
def main():
ITERATIONS = 100
mc = zeros(ITERATIONS)
og = zeros(ITERATIONS)
#farby =
QS = 10
colors = [
[0, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 0, 0],
[0, 1, 1],
[1, 0, 1],
[0, 1, 1],
]
for qpre in range(QS):
q = qpre + 2
for it in range(ITERATIONS):
W = random.normal(0, 0.1, [q, q])
WI = random.uniform(-.1, .1, [q, 1])
mc[it] = sum(memory_capacity(W, WI, memory_max=200, runs=1, iterations_coef_measure=5000)[0][:q+2])
og[it] = matrix_orthogonality(W)
print(qpre, QS, it, ITERATIONS)
plt.scatter(og, mc, marker='+', label=q, c=(colors[qpre % len(colors)]))
plt.xlabel("orthogonality")
plt.ylabel("memory capacity")
plt.grid(True)
plt.legend()
plt.show()
def find_conservative_MPPS(self, n_MPP=2, n_MPP_tries=100, err_g_max=0.2):
"""
Search for MPPs
Input:
n_MPP - try to find this number of MPP's
n_MPP_tries - max number of tries in search for new MPP
err_g_max - convergence criterion in MPP search
"""
k = 0
U_MPP = []
for i in range(n_MPP_tries):
u0 = random.normal(size=(self.X_dist.dim))
self.e = self.E_conservative[random.randint(
len(self.E_conservative))]
conv, u_MPP = self.MPP_search(u0=u0,
N_max=100,
err_g_max=err_g_max)
if conv:
k += 1
U_MPP.append(u_MPP)
if k >= n_MPP: break
return np.array(U_MPP)
def generate_random_large_scale_field(self):
""" mg is a gmg object """
from scipy import random
# level on which the random field is generated
# this controls the scale of the field
# current limitation: this has to be done on a level for which
# each node has the whole domain
flev = self.nlevs-1#min(6,self.nlevs-1)
# gaussian noise parameters
mu = 0.
sigma = 1.
# generate it on rank==0 then broadcast it
# so that every rank has the same field
if (self.myrank == 0):
forc = random.normal(mu, sigma, (self.grid[flev].mv,self.grid[flev].nv))
forc = forc*self.grid[flev].msk
else:
forc = None
forc = MPI.COMM_WORLD.bcast(forc,root=0)
# interpolate it on the finest grid
self.x[flev][:,:] = forc
for lev in range(flev-1,-1,-1):
if self.grid[lev].flag=='peak':
coarsetofine(self.grid[lev+1],self.grid[lev],self.x[lev+1],self.x[lev])
else:
coarsetofine(self.grid[lev+1],self.grid[lev],self.x[lev+1],self.r[lev])
self.x[lev]+= self.r[lev]
self.grid[lev].smooth(self.x[lev],self.b[lev],2)#15oct changed ,1 to ,2
return self.x[0]
def initialize_x(N, init_type='normal'):
'''
Initialized an array of length N filled with probability parameter.
init_type: str
Accepts 'equal', 'normal', and 'uniform'
'''
x = np.zeros(N)
initialize = True
while initialize:
if init_type == 'normal':
x = random.normal(p, min(p, (1 - p)) / 2, N)
elif init_type == 'uniform':
x = random.uniform(pmin, pmax, N)
elif init_type == 'equal':
x = np.full(N, p)
else:
print('init_type is wrong')
exit()
if np.all(x <= pmax) and np.all(x >= pmin):
initialize = False
else:
initialize = True
return x
def generate_random_small_scale_field(self):
""" mg is a gmg object """
from scipy import random
# level on which the random field is generated
# this controls the scale of the field
# current limitation: this has to be done on a level for which
# each node has the whole domain
lev = 0 # min(6,self.nlevs-1)
# gaussian noise parameters
mu = 0.
sigma = 1.
# generate it on rank==0 then broadcast it
# so that every rank has the same field
forc = random.normal(mu, sigma, (self.grid[lev].mv, self.grid[lev].nv))
# smooth twice on the finest grid
self.x[lev][:, :] = forc
self.grid[lev].smooth(self.x[lev], self.b[lev],
2) # 15oct changed ,1 to ,2
return self.x[0]
def Run_MC(self, N_MC):
"""
Crude Monte Carlo
TODO: if N_MC = None -> run until cov is acceptable
Output:
beta - Reliability index (for comparison with FORM)
pof - Probability of failure
cov - Coefficient of variation
"""
# Sample in U space
U = random.normal(size=(N_MC, self.X_dist.dim))
# Trasform to X space
X = self.X_dist.U_to_X(U)
# Compute limit state and pof
g = self.G(X)
I = (g < 0) * 1
pof = I.mean()
# Coefficient of variation
if pof > 0:
var = pof * (1 - pof) / N_MC
cov = np.sqrt(var) / pof
else:
cov = 1
# Reliability index
beta = -stats.norm.ppf(pof)
return beta, pof, cov
def newEpisode(self):
if self.learning:
params = ravel(self.explorationlayer.module.params)
target = ravel(sum(self.history.getSequence(self.history.getNumSequences()-1)[2]) / 500)
if target != 0.0:
self.gp.addSample(params, target)
if len(self.gp.trainx) > 20:
self.gp.trainx = self.gp.trainx[-20:, :]
self.gp.trainy = self.gp.trainy[-20:]
self.gp.noise = self.gp.noise[-20:]
self.gp._calculate()
# get new parameters where mean was highest
max_cov = diag(self.gp.pred_cov).max()
indices = where(diag(self.gp.pred_cov) == max_cov)[0]
pick = indices[random.randint(len(indices))]
new_param = self.gp.testx[pick]
# check if that one exists already in gp training set
if len(where(self.gp.trainx == new_param)[0]) > 0:
# add some normal noise to it
new_param += random.normal(0, 1, len(new_param))
self.explorationlayer.module._setParameters(new_param)
else:
self.explorationlayer.drawRandomWeights()
# don't call StateDependentAgent.newEpisode() because it randomizes the params
LearningAgent.newEpisode(self)
def step(self):
self.sensors = random.normal(loc=self.sensors * self.A +
self.action * self.b,
scale=0.001).flatten()
if self.hasRenderer():
self.getRenderer().updateData(self.sensors)
if self.delay:
time.sleep(self.tau)
def drop_object(self):
"""Drops a random object (box, sphere) into the scene."""
# choose between boxes and spheres
if random.uniform() > 0.5:
(body, geom) = self._create_sphere(self.space, 10, 0.4)
else:
(body, geom) = self._create_box(self.space, 10, 0.5, 0.5, 0.5)
# randomize position slightly
body.setPosition((random.normal(-6.5, 0.5), 6.0, random.normal(-6.5, 0.5)))
# body.setPosition( (0.0, 3.0, 0.0) )
# randomize orientation slightly
#theta = random.uniform(0,2*pi)
#ct = cos (theta)
#st = sin (theta)
# rotate body and append to (body,geom) tuple list
# body.setRotation([ct, 0., -st, 0., 1., 0., st, 0., ct])
self.body_geom.append((body, geom))
def drop_object(self):
"""Drops a random object (box, sphere) into the scene."""
# choose between boxes and spheres
if random.uniform() > 0.5:
(body,geom) = self._create_sphere(self.space, 10, 0.4)
else:
(body,geom) = self._create_box(self.space, 10, 0.5,0.5,0.5)
# randomize position slightly
body.setPosition( (random.normal(-6.5, 0.5), 6.0, random.normal(-6.5, 0.5)) )
# body.setPosition( (0.0, 3.0, 0.0) )
# randomize orientation slightly
#theta = random.uniform(0,2*pi)
#ct = cos (theta)
#st = sin (theta)
# rotate body and append to (body,geom) tuple list
# body.setRotation([ct, 0., -st, 0., 1., 0., st, 0., ct])
self.body_geom.append((body,geom))
def keplerSim(tau, e, T0, K, w, sig, tlo, thi, n):
dt = (thi-tlo)/(n-1)
data = zeros((n,2), Float)
data[:,0] = r.uniform(tlo, thi, (n))
# for i in range(n):
# data[i,0] = tlo + i*dt
data[:,1] = v_rad(K, w, tau, e, T0, data[:,0])+r.normal(0.,sig,(n))
print "Created data."
return data
def keplerSim(tau, e, T0, K, w, sig, tlo, thi, n):
dt = (thi - tlo) / (n - 1)
data = zeros((n, 2), Float)
data[:, 0] = r.uniform(tlo, thi, (n))
# for i in range(n):
# data[i,0] = tlo + i*dt
data[:, 1] = v_rad(K, w, tau, e, T0, data[:, 0]) + r.normal(0., sig, (n))
print "Created data."
return data
def GaussianRandomInitializer(gridShape, sigma=0.2, seed=None, slipSystem=None, slipPlanes=None, slipDirections=None, vacancy=None, smectic=None):
oldgrid = copy.copy(gridShape)
if len(gridShape) == 1:
gridShape = (128,)
if len(gridShape) == 2:
gridShape = (128,128)
if len(gridShape) == 3:
gridShape = (128,128,128)
""" Returns a random initial set of fields of class type PlasticityState """
if slipSystem=='gamma':
state = SlipSystemState.SlipSystemState(gridShape,slipPlanes=slipPlanes,slipDirections=slipDirections)
elif slipSystem=='betaP':
state = SlipSystemBetaPState.SlipSystemState(gridShape,slipPlanes=slipPlanes,slipDirections=slipDirections)
else:
if vacancy is not None:
state = VacancyState.VacancyState(gridShape,alpha=vacancy)
elif smectic is not None:
state = SmecticState.SmecticState(gridShape)
else:
state = PlasticityState.PlasticityState(gridShape)
field = state.GetOrderParameterField()
Ksq_prime = FourierSpaceTools.FourierSpaceTools(gridShape).kSq * (-sigma**2/4.)
if seed is None:
seed = 0
n = 0
random.seed(seed)
Ksq = FourierSpaceTools.FourierSpaceTools(gridShape).kSq.numpy_array()
for component in field.components:
temp = random.normal(scale=gridShape[0],size=gridShape)
ktemp = fft.rfftn(temp)*(sqrt(pi)*sigma)**len(gridShape)*exp(-Ksq*sigma**2/4.)
field[component] = numpy.real(fft.irfftn(ktemp))
#field[component] = GenerateGaussianRandomArray(gridShape, temp ,sigma)
n += 1
"""
t, s = LoadState("2dstate32.save", 0)
for component in field.components:
for j in range(0,32):
field[component][:,:,j] = s.betaP[component].numpy_array()
"""
## To make seed consistent across grid sizes and convergence comparison
gridShape = copy.copy(oldgrid)
if gridShape[0] != 128:
state = ResizeState(state,gridShape[0],Dim=len(gridShape))
state = ReformatState(state)
state.ktools = FourierSpaceTools.FourierSpaceTools(gridShape)
return state
def fill_region(l,r,sigma,v):
if (l == r or l == r-1):
pass
else:
m = int(round((r+l)*0.5))
a = v[l] + (v[r]-v[l])*(m - l)/float(r - l)
s = sigma*sqrt((m-l)*(r-m)/float(r-l))
v[m] = a + s * random.normal()
fill_region(l,m,sigma,v)
fill_region(m,r,sigma,v)
def drawSample(self):
sum = 0.0
rndFakt = random.random()
for g in range(self.numOGaus):
sum += self.sigmo(self.alpha[g])
if rndFakt < sum:
if self.sigma[g] < self.minSig: self.sigma[g] = self.minSig
x = random.normal(self.mue[g], self.sigma[g])
break
return x
def drawSample(self):
sum = 0.0
rndFakt = random.random()
for g in range(self.numOGaus):
sum += self.sigmo(self.alpha[g])
if rndFakt < sum:
if self.sigma[g] < self.minSig: self.sigma[g] = self.minSig
x = random.normal(self.mue[g], self.sigma[g])
break
return x
def perturbation(self):
""" Generate a difference vector with the given standard deviations """
#print self.sigList
#print "_*_*_*_*_*_*_*_"
#raw_input("Press Enter to continue")
#time.sleep(3)
return random.normal(0., self.sigList)
def generate_data(N=100, true_params=secret_true_params, seed=42):
x = np.linspace(-2.5, 2.5, N)
y1 = my_model(x, *true_params)
y2 = 1.0 * random.normal(size=N)
# Create the data
data = np.array([x, y1 + y2]).T
# Shuffle the data
permuted_data = random.permutation(data)
# Save the data
np.savetxt("dataN%d.txt" % N, data)
return data
def add_noise(self, temp): """ Add per-pixel Gaussian random noise. """ self.noise = random.normal(0,temp,[self.npix,self.npix]) self.Fnoise = ft.fftshift(ft.fft2(self.noise)) self.Txy = self.Txy + self.noise self.Fxy = ft.fftshift(ft.fft2(self.Txy)) self.Clnoise = ((temp*self.mapsize_rad/self.npix)*self.Bl)**-2.e0 self.Pknoise = np.interp(self.modk, self.k, self.Clnoise)
def generate_lin_regression(n, d, sigma):
"""
See cgd.pdf
"""
X = random.randn(n, d)
for i in xrange(d):
X[:, i] /= numpy.max(numpy.abs(X[:, i]))
beta = random.uniform(low=0, high=1, size=d)
e = numpy.array(random.normal(0, sigma, n))
y = X.dot(beta) + e.T
return (X, y, beta, e)
def generate_lin_regression_nikolaenko(n, d):
"""
Generates a synthetic linear regression instance as in
"Privacy-Preserving Ridge Regression on Hundreds of Millions of Records"
"""
X = random.uniform(low=-1, high=1, size=(n, d))
beta = random.uniform(low=-1, high=1, size=d)
mu, sigma = 0, 1 # mean and standard deviation
e = numpy.array(random.normal(mu, sigma, n))
y = X.dot(beta) + e.T
return (X, y, beta, e)
def run(self):
self.households.reset_reading()
counter = 0
for h in self.households:
counter += 1
wtp = max(0.0, random.normal(7.348656, 9.407043))
h.SetField("wtp_extreme_heat", wtp)
if counter % 100000 == 0:
self.households.sync()
self.__container.set_next_by_index(counter)
self.households.finalise()
def generate_data(N=100, true_params=secret_true_params,
seed = 42):
x = np.linspace(-2.5, 2.5, N)
y1 = my_model(x, *true_params)
y2 = 1.0 * random.normal(size=N)
# Create the data
data = np.array([x,y1+y2]).T
# Shuffle the data
permuted_data = random.permutation(data)
# Save the data
np.savetxt("dataN%d.txt"%N, data)
return data
def sample(self, N):
"""
Generate N samples
"""
# Standard normal samples
U = random.normal(size=(N, self.dim))
# Sample random means with equal probability
random_means = self.means[list(random.randint(self.m, size=N)), :]
return U + random_means
def __init__(self, statedim, actiondim, sigma= -2.):
Explorer.__init__(self, actiondim, actiondim)
self.statedim = statedim
self.actiondim = actiondim
# initialize parameters to sigma
ParameterContainer.__init__(self, actiondim, stdParams=0)
self.sigma = [sigma] * actiondim
# exploration matrix (linear function)
self.explmatrix = random.normal(0., expln(self.sigma), (statedim, actiondim))
# store last state
self.state = None
def drawSample(self, dm):
sum = 0.0
rndFakt = random.random()
if dm == "max":
for g in range(self.numOGaus):
sum += self.sigmo(self.alpha[g])
if rndFakt < sum:
if self.sigma[g] < self.minSig: self.sigma[g] = self.minSig
x = random.normal(self.mue[g], self.sigma[g])
break
return x
if dm == "dist":
return rndFakt * self.distRange + self.rangeMin
return 0.0
def drawSample(self, dm):
sum = 0.0
rndFakt = random.random()
if dm == "max":
for g in range(self.numOGaus):
sum += self.sigmo(self.alpha[g])
if rndFakt < sum:
if self.sigma[g] < self.minSig: self.sigma[g] = self.minSig
x = random.normal(self.mue[g], self.sigma[g])
break
return x
if dm == "dist":
return rndFakt * self.distRange + self.rangeMin
return 0.0
def __init__(self, statedim, actiondim, sigma= -2.):
Explorer.__init__(self, actiondim, actiondim)
self.statedim = statedim
self.actiondim = actiondim
# initialize parameters to sigma
ParameterContainer.__init__(self, actiondim, stdParams=0)
self.sigma = [sigma] * actiondim
# exploration matrix (linear function)
self.explmatrix = random.normal(0., expln(self.sigma), (statedim, actiondim))
# store last state
self.state = None
def Run_MCIS(self, N_MC, u0=None):
"""
MC with importance sampling
TODO: if N_MC = None -> run until cov is acceptable
Output:
beta - Reliability index (for comparison with FORM)
pof - Probability of failure
cov - Coefficient of variation
"""
# Get MPP in U-space
if u0 is None:
conv, MPP_u = self.MPP_search()
else:
conv, MPP_u = True, u0
# Sample in U space
U = random.normal(size=(N_MC, self.X_dist.dim))
pdf_U = np.prod(stats.norm.pdf(U), 1)
# Shift samples to design point
U_shifted = U + MPP_u
pdf_U_shifted = np.prod(stats.norm.pdf(U_shifted), 1)
# Trasform to X space
X = self.X_dist.U_to_X(U_shifted)
# Evaluate limit state
g = self.G(X).flatten()
I = (g < 0) * 1
# Estimate pof
q = I * (pdf_U_shifted / pdf_U)
pof = (1 / N_MC) * q.sum()
# .. and CoV
if pof > 0:
var = (1 / N_MC) * (1 / (N_MC - 1)) * ((q - pof)**2).sum()
cov = np.sqrt(var) / pof
else:
cov = 1
# Reliability index
beta = -stats.norm.ppf(pof)
return beta, pof, cov
def randomlist(self,mode=1,size=1000,low=0,high=100):
"generate a list followed given distribution"
"IN:distribution model code which refer to randomlist method; sequence size; sequence range"
"OUT:a sequence followed distribution like"
x = []
if mode == 1:
x = random.randint(low,high,size=size)
if mode == 2:
x = map(float,random.normal(loc=(low+high)/2.0, scale=(high-low)/6.0, size=size))
if mode == 3:
x = map(long,random.exponential(scale=1, size=size)+low)
if mode == 4:
x = map(long,random.pareto(1,size=size)+low)
if mode == 5:
x = map(long,random.poisson(lam=(low+high)/2.0, size=size))
# x = random.choice(x,size=100)
return x
def model(times):
t_fold, t_fold_model = self.period_folding(times, available, m, m_err, out_dict)
data = empty(0)
rms = empty(0)
for time in t_fold_model:
# we're going to create a window around the desired time and sample a gaussian distribution around that time
period = 1.0 / f
assert (
period < available.ptp() * 1.5
), (
"period is greater than ####SEE VARIABLE CONTSTRAINT#### of the duration of available data"
) # alterring this. originally 1/3
# window is 2% of the period
passed = False
for x in arange(0.01, 0.1, 0.01):
t_min = time - x * period
t_max = time + x * period
window = logical_and(
(t_fold < t_max), (t_fold > t_min)
) # picks the available times that are within that window
try:
# there must be more than # points in the window for this to work:
assert window.sum() >= 2, str(time) # jhiggins changed sum from 5 to 2
except AssertionError:
continue
else:
passed = True
break
assert passed, "No adequate window found"
m_window = m[window]
mean_window = mean(m_window)
std_window = std(m_window)
# now we're ready to sample that distribution and create our point
new = (random.normal(loc=mean_window, scale=std_window, size=1))[0]
data = append(data, new)
rms = append(rms, std_window)
period_folded_model_file = file("period_folded_model.txt", "w")
# model_file = file("model.txt", "w")
for n in range(len(t_fold_model)):
period_folded_model_file.write("%f\t%f\t%f\n" % (t_fold_model[n], data[n], rms[n]))
# model_file.write("%f\t%f\t%f\n" % (available[n], data[n], rms[n]))
# model_file.close()
period_folded_model_file.close()
return {"flux": data, "rms": rms}
def __init__(self, mapsize=10.e0, pixels=1024, cosm=Cosmology()):
"""
Constructor.
Default will create a 10x10 degree FOV with 1024 pixels and
a WMAP7 Cosmology.
"""
self.cosm = cosm
self.mapsize_deg = mapsize # map size in np.real domain
self.mapsize_rad = np.deg2rad(self.mapsize_deg)
self.fsky = (mapsize**2.e0) / 41253.e0
self.npix = pixels
self.Fmapsize = 1.e0 / self.mapsize_rad # map size in Fourier domain
self.pixsize = self.mapsize_rad / self.npix # pixel size in radians
self.pixsize_deg = self.mapsize_deg / self.npix # pixel size in degrees
self.mapaxis = (
(self.mapsize_deg / self.npix) * # range of axes
np.arange(-self.mapsize_deg / 2.e0, self.mapsize_deg / 2.e0, 1))
self.Fmapaxis = 1.e0 / self.mapaxis
self.krange = (
self.Fmapsize * # define k-space
np.arange(-self.npix / 2.e0, self.npix / 2.e0, 1))
self.kx, self.ky = np.meshgrid(self.krange, self.krange)
self.modk = sqrt(self.kx**2.e0 + self.ky**2.e0)
self.Txy = random.normal(
0, 1, [self.npix, self.npix]) # Gaussian random field
self.Txy = self.Txy - np.mean(self.Txy)
self.Fxy = ft.fftshift(ft.fft2(self.Txy)) # Fourier domain GRF
self.Fxy = self.Fxy / sqrt(np.var(self.Fxy))
self.build_Pk(self.cosm) # Get flat-sky P(k) for cosmology
self.Fxy = self.Fxy * self.Pk # Apply the power spectrum
self.Txy = np.real(ft.ifft2(ft.fftshift(self.Fxy)))
self.ymap = np.zeros([self.npix, self.npix])
def model(times):
t_fold, t_fold_model = self.period_folding(times, available, m, m_err, out_dict)
data = empty(0)
rms = empty(0)
for time in t_fold_model:
# we're going to create a window around the desired time and sample a gaussian distribution around that time
period = 1./f
assert period < available.ptp()/3, "period is greater than one third of the duration of available data"
# window is 2% of the period
passed = False
for x in arange(0.01, 0.1, 0.01):
t_min = time - x * period
t_max = time + x * period
window = logical_and((t_fold < t_max), (t_fold > t_min)) # picks the available times that are within that window
try:
# there must be more than 3 points in the window for this to work:
assert (window.sum() > 5), str(time)
except AssertionError:
continue
else:
passed = True
break
assert passed, "No adequate window found"
m_window = m[window]
mean_window = mean(m_window)
std_window = std(m_window)
# now we're ready to sample that distribution and create our point
new = (random.normal(loc=mean_window, scale = std_window, size = 1))[0]
data = append(data,new)
rms = append(rms, std_window)
period_folded_model_file = file("period_folded_model.txt", "w")
# model_file = file("model.txt", "w")
for n in range(len(t_fold_model)):
period_folded_model_file.write("%f\t%f\t%f\n" % (t_fold_model[n], data[n], rms[n]))
# model_file.write("%f\t%f\t%f\n" % (available[n], data[n], rms[n]))
# model_file.close()
period_folded_model_file.close()
return {'flux':data, 'rms': rms}
def step(self):
""" integrate state using simple rectangle rule """
thrust = float(self.action[0])
rudder = float(self.action[1])
h, hdot, v = self.sensors
rnd = random.normal(0, 1.0, size=3)
thrust = min(max(thrust, -1), +2)
rudder = min(max(rudder, -90), +90)
drag = 5 * h + (rudder**2 + rnd[0])
force = 30.0 * thrust - 2.0 * v - 0.02 * v * drag + rnd[1] * 3.0
v = v + self.dt * force / self.mass
v = min(max(v, -10), +40)
torque = -v * (rudder + h + 1.0 * hdot + rnd[2] * 10.)
last_hdot = hdot
hdot += torque / self.I
hdot = min(max(hdot, -180), 180)
h += (hdot + last_hdot) / 2.0
if h > 180.:
h -= 360.
elif h < -180.:
h += 360.
self.sensors = (h, hdot, v)
def step(self):
""" integrate state using simple rectangle rule """
thrust = float(self.action[0])
rudder = float(self.action[1])
h, hdot, v = self.sensors
rnd = random.normal(0,1.0, size=3)
thrust = min(max(thrust,-1),+2)
rudder = min(max(rudder,-90),+90)
drag = 5*h + (rudder**2 + rnd[0])
force = 30.0*thrust - 2.0*v - 0.02*v*drag + rnd[1]*3.0
v = v + self.dt*force/self.mass
v = min(max(v,-10),+40)
torque = -v*(rudder + h + 1.0*hdot + rnd[2]*10.)
last_hdot = hdot
hdot += torque / self.I
hdot = min(max(hdot,-180),180)
h += (hdot + last_hdot) / 2.0
if h>180.:
h -= 360.
elif h<-180.:
h += 360.
self.sensors = (h,hdot,v)
def SmecticInitializer(gridShape, sigma=0.2, seed=None):
if seed is None:
seed = 0
random.seed(seed)
state = SmecticState.SmecticState(gridShape)
field = state.GetOrderParameterField()
Ksq = FourierSpaceTools.FourierSpaceTools(gridShape).kSq.numpy_array()
for component in field.components:
temp = random.normal(scale=gridShape[0],size=gridShape)
ktemp = fft.rfftn(temp)*(sqrt(pi)*sigma)**len(gridShape)*exp(-Ksq*sigma**2/4.)
field[component] = numpy.real(fft.irfftn(ktemp))
## To make seed consistent across grid sizes and convergence comparison
gridShape = copy.copy(oldgrid)
if gridShape[0] != 128:
state = ResizeState(state,gridShape[0],Dim=len(gridShape))
state = ReformatState(state)
state.ktools = FourierSpaceTools.FourierSpaceTools(gridShape)
return state
def update(self):
self.state = [s + 0.1 * a for s, a in zip(self.state, self.action)]
if self.noise:
self.state += random.normal(0, self.noise, self.dim)
import pyqtgraph as pg
from pyqtgraph import MultiPlotWidget
try:
from pyqtgraph.metaarray import *
except:
print("MultiPlot is only used with MetaArray for now (and you do not have the metaarray package)")
exit()
app = QtGui.QApplication([])
mw = QtGui.QMainWindow()
mw.resize(800,800)
pw = MultiPlotWidget()
mw.setCentralWidget(pw)
mw.show()
data = random.normal(size=(3, 1000)) * np.array([[0.1], [1e-5], [1]])
ma = MetaArray(data, info=[
{'name': 'Signal', 'cols': [
{'name': 'Col1', 'units': 'V'},
{'name': 'Col2', 'units': 'A'},
{'name': 'Col3'},
]},
{'name': 'Time', 'values': linspace(0., 1., 1000), 'units': 's'}
])
pw.plot(ma)
## Start Qt event loop unless running in interactive mode.
if __name__ == '__main__':
import sys
if (sys.flags.interactive != 1) or not hasattr(QtCore, 'PYQT_VERSION'):
QtGui.QApplication.instance().exec_()
def newEpisode(self):
""" Randomize the matrix values for exploration during one episode. """
self.explmatrix = random.normal(0., expln(self.sigma), self.explmatrix.shape)
def make_brownian_path(mean, sigma, numpts):
xn = sigma * sqrt(numpts)*random.normal()
result = [ 0.0 for x in range(0,numpts)]
result[len(result)-1] = xn;
fill_region(0,len(result)-1,sigma,result)
return [result[i]+mean*i for i in range (0,numpts)]
def _forwardImplementation(self, inbuf, outbuf):
outbuf[:] = random.normal(inbuf, expln(self.sigma))
def genDifVect(self):
# generates a difference vector with the given standard deviations
self.deltas=random.normal(0.0, self.sigList)
def drawRandomWeights(self):
self.module._setParameters(random.normal(0, expln(self.params), self.module.paramdim))
def run(self):
self.households.reset_reading()
for h in self.households:
wtp = max(0.0, random.normal(7.348656, 9.407043))
h.SetField("wtp_extreme_heat", wtp)
self.households.finalise()
# Définition des paramètres
NomFichier = 'MESURES1.CSV'
# ------------------------------------------------------------------------
# Début du programme
# ------------------------------------------------------------------------
# Création d'une liste de mesures avec des erreurs aléatoires
# contruite autour de la valeur de référence de la tension
U = 3.992 # tension de référence
NbMesures = 1000
ListeMesures = []
for i in range(NbMesures):
ListeMesures.append(random.normal(U, 0.002))
# Calcul des paramètres de la liste
NbMesures = len(ListeMesures)
MinListe = min(ListeMesures)
MaxListe = max(ListeMesures)
Moyenne = mean(ListeMesures)
EcartType = std(ListeMesures)
# Affichage des paramètres statistiques
print "Expression du résultat : ", Moyenne, " +- ", EcartType
# Définition des classes de l'histogramme
NbClasses = 10
ClasseRange = 0.002
def _forwardImplementation(self, inbuf, outbuf):
if not self.enabled:
outbuf[:] = inbuf
else:
outbuf[:] = random.normal(inbuf, expln(self.params))
def sampler(self, probabilities):
return random.normal(probabilities, self.visibleVariances)
def sample(self):
""" Sample with mean mu and variance sigma """
return random.normal(self.mu, self.sigma, 1)
def main():
"""
Today's agenda:
i) generate initial matrices
ii) simulate
iii) learn gauss
iv) simulate
v) plot & compare
"""
W = random.normal(0, sigma, [q, q])
WI = random.uniform(-sigma, sigma, [q, 1])
X = random.uniform(-1, 1, [q])
a = ones([q])
b = zeros([q])
S = zeros([q, ITERATIONS])
S2 = zeros([q, ITERATIONS])
ahist = zeros([q, ITERATIONS])
# i?) simulate
U = random.uniform(-1, 1, [ITERATIONS])
for it in range(ITERATIONS):
net = dot(WI, U[it].reshape(1)) + dot(W, X)
X = tanh( a * net + b)
S[:, it] = X
# iii) learn
U = random.uniform(-1, 1, [ITERATIONS])
for it in range(ITERATIONS):
net = dot(WI, U[it].reshape(1)) + dot(W, X)
Y = tanh( a * net + b)
a, b = ipgauss(net, Y, a, b)
ahist[:, it] = a
X = Y
# i?) simulate2
U = random.uniform(-1, 1, [ITERATIONS])
for it in range(ITERATIONS):
net = dot(WI, U[it].reshape(1)) + dot(W, X)
X = tanh( a * net + b)
S2[:, it] = X
# iv) view histogram
BINCNT=10
def show_histograms():
for yplt in range(gridy):
print("\r {}/{}".format(yplt, gridy), end="")
for xplt in range(gridx):
indx = yplt*gridx + xplt
pyplot.subplot(gridy, gridx, indx)
std1 = std(S[indx, :])
std2 = std(S2[indx, :])
pyplot.hist(S[indx,:], bins=BINCNT, normed=True, label="{}:bfr std1={:6.4f}".format(indx,std1))
pyplot.hist(S2[indx,:], bins=BINCNT, normed=True, label="{}:atr std2={:6.4f}".format(indx,std2))
pyplot.grid(True)
pyplot.legend()
print("std1={0}, std2={1}".format(std1, std2))
#pyplot.legend()
pyplot.show()
show_histograms()
for ciara in range(q):
pyplot.plot(range(ITERATIONS), ahist[ciara, :], label="%d"%ciara)
pyplot.legend()
pyplot.show()
print("a = %s" % a)
print("b = %s" % b)
print("done.")
#mue learning
sigmoA = self.sigmo(self.alpha)
self.mue += self.alphaM * fakt * (x - self.mue) * sigmoA * norm
#sigma learning
if fakt > 0.0:
self.sigma += self.alphaS * fakt * ((x - self.mue) ** 2 - self.sigma ** 2) / self.sigma * sigmoA * norm
def sigmo(self, a):
return 1.0 / (1.0 + exp(-1.0 * a))
def invSigmo(self, a):
return - log(1.0 / a - 1.0)
def getSample(self):
sampleX = self.drawSample()
return sampleX
if __name__ == '__main__':
m = MixtureOfGaussians()
for i in range(10000):
x = m.getSample()
n = x / m.distRange * 10.0
if abs(n) > 5.0: n = 0.0
y = (20.0 + n ** 2 - 10.0 * cos(2.0 * 3.1416 * n)) / 55.0 + random.normal(0, 0.2) #one dimensional rastrigin
m.learn(x, y)
print(m.alpha)
print(m.mue)
print(m.sigma)
band_specific_names = observed_apparent_mag_names[observed_apparent_mag_band_mapping==m]
fig = plt.figure(figsize = (12, 12))
ax1 = subplot(111)
# with some dust, poor color excess approximation
dust_corrected_abs_mags = (apparent_mags - 0.85*prior_ebvs*(const_R_V*extinction_ccm_a[m] + extinction_ccm_b[m]) ) - prior_mus
dust_corrected_abs_mag_errs = sqrt(apparent_mag_errs**2 + (0.85*prior_ebv_errs)**2 + prior_mu_errs**2)
linear_period = (10**period_terms) * P_0
ax1.errorbar(log10(linear_period), dust_corrected_abs_mags, dust_corrected_abs_mag_errs, linestyle="none", marker="s", color="blue")
polyfit_slope = []
polyfit_intercept = []
for iter in range(1000):
fit_params = polyfit(period_terms, random.normal(dust_corrected_abs_mags, dust_corrected_abs_mag_errs), 1)
polyfit_slope.append(fit_params[0])
polyfit_intercept.append(fit_params[1])
polyfit_slope = array(polyfit_slope)
polyfit_intercept = array(polyfit_intercept)
best_fit_line = polyfit_intercept.mean() + polyfit_slope.mean()*logper_grid
squared_m_errs = ((dust_corrected_abs_mags) - (polyfit_intercept.mean() + polyfit_slope.mean()*period_terms))**2
sig_m = sqrt(squared_m_errs.mean())
ci_err_grid = []
for logper_val in logper_grid:
ci_err_grid.append(sqrt(sig_m**2 + std(polyfit_intercept + polyfit_slope * logper_val)**2))
ci_err_grid = array(ci_err_grid)
