def test_skewed():
from ctapipe.image.toymodel import SkewedGaussian
# test if the parameters we calculated for the skew normal
# distribution produce the correct moments
np.random.seed(0)
geom = CameraGeometry.from_name('LSTCam')
x, y = u.Quantity([0.2, 0.3], u.m)
width = 0.05 * u.m
length = 0.15 * u.m
intensity = 50
psi = '30d'
skewness = 0.3
model = SkewedGaussian(
x=x, y=y, width=width,
length=length, psi=psi, skewness=skewness
)
image, signal, _ = model.generate_image(
geom, intensity=intensity, nsb_level_pe=5,
)
a, loc, scale = model._moments_to_parameters()
mean, var, skew = skewnorm(a=a, loc=loc, scale=scale).stats(moments='mvs')
assert np.isclose(mean, 0)
assert np.isclose(var, length.to_value(u.m)**2)
assert np.isclose(skew, skewness)
def plotpdf(mean=0.0,stdev=1.0,skew=0.0,npts=250):
x = np.linspace(-5,5,100)
pdf = skewnorm(convert_to_alpha(skew),loc=mean,scale=stdev)
y = pdf.pdf(x)
data = pdf.rvs(npts)
data = realign_data(data,mean,stdev)
mn,var=pdf.stats(moments='mv')
xtrans = x-mn
xtrans = mean+(xtrans*stdev/np.sqrt(var))
plt.figure(1,figsize=(12,5))
plt.subplot(121)
nbins=np.min([npts//10,50])
(N,xbins,_)=plt.hist(data,bins=nbins)
midx = xbins[:-1]+(np.diff(xbins)/2)
midy = pdf.pdf(midx)
mult=np.sum(np.diff(xbins)*N)/np.sum(np.diff(xbins*stdev/np.sqrt(var))*midy)
plt.plot(xtrans,y*mult,'k-')
mline=plt.axvline(np.mean(data),color='r',linestyle='--',linewidth=2,label='Mean')
dline=plt.axvline(np.median(data),color='k',linestyle='--',linewidth=2,label='Median')
plt.xlim(-4.5,4.5)
plt.ylim(0,npts//8)
plt.legend()
plt.title('Histogram of data')
plt.subplot(122)
plt.plot(data[::5],'k.-')
plt.axhline(np.mean(data),color='r',linestyle='--')
plt.ylim(-5,5)
plt.title('Sample of randomly-generated data\n with the given parameters')
return
def pdf(self, x, y):
'''2d probability for photon electrons in the camera plane'''
mu = u.Quantity([self.x, self.y]).to_value(u.m)
rotation = linalg.rotation_matrix_2d(-Angle(self.psi))
pos = np.column_stack([x.to_value(u.m), y.to_value(u.m)])
long, trans = rotation @ (pos - mu).T
trans_pdf = norm(loc=0, scale=self.width).pdf(trans)
a, loc, scale = self._moments_to_parameters()
return trans_pdf * skewnorm(a=a, loc=loc, scale=scale).pdf(long)
def demo():
# hide module load time from Timer
from sklearn.neighbors import NearestNeighbors
## Bootstrap didn't help, but leave the test code in place for now
#D = Dirichlet(alpha=[0.02]*20)
#theta = D.rvs(size=1000)
#S, Serr = wnn_bootstrap(D.rvs(size=200000))
#print("bootstrap", S, D.entropy())
#return
if False:
# Multivariate T distribution
D = stats.t(df=4)
_show_entropy("T;df=4", D, N=20000)
D = MultivariateT(sigma=np.diag([1]), df=4)
_show_entropy("MT[1];df=4", D, N=20000)
D = MultivariateT(sigma=np.diag([1, 12, 0.2])**2, df=4)
_show_entropy("MT[1,12,0.2];df=4", D, N=10000)
D = MultivariateT(sigma=np.diag([1]*10), df=4)
_show_entropy("MT[1]*10;df=4", D, N=10000)
D = MultivariateT(sigma=np.diag([1, 12, 0.2, 1e2, 1e-2, 1])**2, df=4)
_show_entropy("MT[1,12,0.2,1e3,1e-3,1];df=4", D, N=10000)
return
if False:
# Multivariate skew normal distribution
D = stats.skewnorm(5)
_show_entropy("skew=5 N[1]", D, N=20000)
D = Joint(stats.skewnorm(5, 0, s) for s in [1, 12, 0.2])
_show_entropy("skew=5 N[1,12,0.2]", D, N=10000)
D = Joint(stats.skewnorm(5, 0, s) for s in [1]*10)
_show_entropy("skew=5 N[1]*10", D, N=10000)
D = Joint(stats.skewnorm(5, 0, s) for s in [1, 12, 0.2, 1e2, 1e-2, 1])
_show_entropy("skew=5 N[1,12,0.2,1e3,1e-3,1]", D, N=10000)
#print("double check entropy", D.entropy()/LN2, entropy_mc(D)/LN2)
return
D = Box(center=[100]*10, width=np.linspace(1, 10, 10))
_show_entropy("Box 10!", D, N=10000)
D = stats.norm(10, 8)
#_show_entropy("N[100,8]", D, N=100)
#_show_entropy("N[100,8]", D, N=200)
#_show_entropy("N[100,8]", D, N=500)
#_show_entropy("N[100,8]", D, N=1000)
#_show_entropy("N[100,8]", D, N=2000)
#_show_entropy("N[100,8]", D, N=5000)
_show_entropy("N[100,8]", D, N=10000)
#_show_entropy("N[100,8]", D, N=20000)
#_show_entropy("N[100,8]", D, N=50000)
#_show_entropy("N[100,8]", D, N=100000)
D = stats.multivariate_normal(cov=np.diag([1, 12, 0.2])**2)
#_show_entropy("MVN[1,12,0.2]", D)
D = stats.multivariate_normal(cov=np.diag([1]*10)**2)
#_show_entropy("MVN[1]*10", D, N=1000)
_show_entropy("MVN[1]*10", D, N=10000)
#_show_entropy("MVN[1]*10", D, N=100000)
#_show_entropy("MVN[1]*10", D, N=200000, N_entropy=20000)
D = stats.multivariate_normal(cov=np.diag([1, 12, 0.2, 1, 1, 1])**2)
#_show_entropy("MVN[1,12,0.2,1,1,1]", D, N=100)
#_show_entropy("MVN[1,12,0.2,1,1,1]", D, N=1000)
_show_entropy("MVN[1,12,0.2,1,1,1]", D, N=10000)
#_show_entropy("MVN[1,12,0.2,1,1,1]", D, N=100000)
D = stats.multivariate_normal(cov=np.diag([1, 12, 0.2, 1e2, 1e-2, 1])**2)
#_show_entropy("MVN[1,12,0.2,1e3,1e-3,1]", D, N=100)
#_show_entropy("MVN[1,12,0.2,1e3,1e-3,1]", D, N=1000)
_show_entropy("MVN[1,12,0.2,1e3,1e-3,1]", D, N=10000)
#_show_entropy("MVN[1,12,0.2,1e3,1e-3,1]", D, N=100000)
D = GaussianMixture([1,10], mu=[[0]*10, [100]*10], sigma=[[10]*10, [0.1]*10])
_show_entropy("bimodal mixture", D)
D = Dirichlet(alpha=[0.02]*20)
#_show_entropy("Dirichlet[0.02]*20", D, N=1000)
#_show_entropy("Dirichlet[0.02]*20", D, N=2000)
#_show_entropy("Dirichlet[0.02]*20", D, N=5000)
#_show_entropy("Dirichlet[0.02]*20", D, N=10000)
_show_entropy("Dirichlet[0.02]*20", D, N=20000)