red = Mod.reduced(A, E, Qs)
import random
import math
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
def GsCLT(i, j):
return lambda: random.gauss(0, math.sqrt(Qs[1][i, j]))
import Pymatr.synthesis as Syn
nsyn = 500
nhist = 1000
from Pymatr.utils import numerical
E0n = numerical(E0)
A0n = numerical(A0)
GenLLN = Syn.MatrixRngOpt(A0n, E0n, GsLLN, nsyn)
GenCLT = Syn.MatrixRngOpt(A0n, E0n, GsCLT, nsyn)
__latex__(r'''%
\begin{equation}
\mEx = ''')
__pynclusion__(pr.mat(E0, spacing="0.1cm"))
__latex__(r''', \quad \mAx_{i,j} = 1
\end{equation}
\section{Strongly connected classes $\Xi_i$}
The first step is to identify the irreducible classes (called strongly connected components in graph theory) of $\mE$.
In order to do so, an interesting method is to compute a connectivity matrix $\Conn$
\begin{equation}
\Conn \equiv \sum_{k=0}^{+\infty} (\epsilon\mE)^k = (\mId- \epsilon\mE )^{-1} .
\end{equation}