def Gs(i, j):
return lambda: random.gauss(Qs[0][i, j], math.sqrt(Qs[1][i, j]))
import Pymatr.synthesis as Syn
from Pymatr.utils import numerical
L = red.dEigen
nsyn = 100
Gen = Syn.MatrixRngOpt(numerical(A), numerical(E / L), Gs, nsyn)
def average():
s = sum(Gen())
av = s / nsyn
# print(" \n sum {}, average: {}\n".format(r, av) )
return av
lln = red.lln()
import Pymatr.byPieces as Bp
Bp.plot(lln)
import Pymatr.histogram as H
nsample = 1000
H.plot(nsample, average)
import matplotlib.pyplot as plt
#plt.xticks( [ Q1r[0].evalf() ], ["µ"] )
plt.show()
\end{equation}
for our example, we have
''')
llnLaw = Lim.llnLimit(Q1r, paths, probP)
__latex__(r'''%
\begin{equation}
p \p{ \frac{S(\vec{X})}{N} = s } = ''')
__pynclusion__(llnLaw.latex('s'))
__latex__(r'''
\end{equation}
''')
plt.figure(figsize=Pl.fig_center)
import Pymatr.byPieces as Bp
Pl.limitTicks(5, 4)
Bp.plot(llnLaw, plot=lambda x, y: plt.plot(x, y, "k--"))
import Pymatr.Histogram as H
import math
def sample():
s = sum(GenLLN())
return s / nsyn
H.plot(nhist, sample, lambda x, y: plt.plot(x, y, "b-"))
plt.xlabel("$s$")
plt.ylabel("$\Psi(s)$")
plt.tight_layout()
plt.savefig("Figs/LLN.pdf")
return lambda : random.gauss( Qs[0][i,j], math.sqrt(Qs[1][i,j]) )
import Pymatr.synthesis as Syn
from Pymatr.utils import numerical
L= red.dEigen
nsyn=100
Gen = Syn.MatrixRngOpt(numerical(A),numerical(E/L), Gs, nsyn)
def average():
s= sum(Gen())
av= s /nsyn
# print(" \n sum {}, average: {}\n".format(r, av) )
return av
lln=red.lln()
import Pymatr.byPieces as Bp
Bp.plot(lln)
import Pymatr.histogram as H
nsample=1000
H.plot(nsample, average)
import matplotlib.pyplot as plt
#plt.xticks( [ Q1r[0].evalf() ], ["µ"] )
plt.show()
\end{equation}
for our example, we have
''')
llnLaw=Lim.llnLimit(Q1r,paths,probP)
__latex__(r'''%
\begin{equation}
p \p{ \frac{S(\vec{X})}{N} = s } = ''')
__pynclusion__(llnLaw.latex('s'))
__latex__(r'''
\end{equation}
''')
plt.figure(figsize=Pl.fig_center )
import Pymatr.byPieces as Bp
Pl.limitTicks(5,4)
Bp.plot(llnLaw, plot=lambda x,y : plt.plot(x,y,"k--"))
import Pymatr.Histogram as H
import math
def sample():
s= sum(GenLLN())
return s/nsyn
H.plot(nhist, sample, lambda x,y : plt.plot(x,y,"b-") )
plt.xlabel("$s$")
plt.ylabel("$\Psi(s)$" )
plt.tight_layout()
plt.savefig("Figs/LLN.pdf")
plt.savefig("Figs/LLN.svg")
__latex__(r'''%