Generate a multiplicative cascade process
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I am trying to simulate a multiplicative cascade process. At the first iteration i call four random numbers (between 0 and 1); these numbers are the initial probabilities. In the following step, i call again four random numbers and then multiply them by the parent probabilities as shown in the figure. I repeat the process 6 times. At each iteration, i want the four probabilities (x, y, z, and w) to satisfy the following conditions:
(1) x^2+y^2+z^2+w^2== m, where m is a constant
(2) x+y+z+w==1
I have tried to use the "solve" and "vapsolve" tools in matlab, but the problem is that i am getting negative numbers and zero values. I have also tried to set x and y so that i only have two unknowns, but it didn't help.
I will appreciate any help.
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darova
am 31 Mai 2019
Probably should think about initial m, w, z
m = 0.2;
z = rand;
w = rand;
syms x
y = -x-z-w+1;
eq = x^2+y^2+z^2+w^2 -m;
X = solve(eq,x);
x = double(X)
Y = matlabFunction(y);
Y(x)
6 Kommentare
darova
am 3 Jun. 2019
I made a mistake before
Z2(imag(Z2)~=0) = inf; % remove complex numbers
% should be
Z2(imag(Z2)~=0) = NaN; % remove complex numbers
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