I am running simulations in which I solve a system of 3 equations and 3 unknowns for n values of a parameter, with m random guesses in the solver for each of the n parameter values. The solutions array is nxmx3. I want to separate the solutions along the second dimension into m nx3 matrices and stack them into a 2 dimensional matrix (n*m)x3 where I am effectively displaying all possible solutions, sorted by the parameter value. Here are the 3 equations:
if true
function F=equations(a,S)
F(1)=2*((a(3))^2-(a(1))^2 )^0.5-((1-2*a(1)))/((1-2*a(1))^2+...
(1-2*a(2))^2 )^0.5*((a(3))^2-0.25*((1-2*a(1))^2+(1-2*a(2))^2 ))^0.5;
F(2)=2*((a(3))^2-(a(2))^2 )^0.5-((1-2*a(2)))/((1-2*a(1))^2+...
(1-2*a(2))^2 )^0.5*((a(3))^2-0.25*((1-2*a(1))^2+(1-2*a(2))^2 ))^0.5;
F(3)=acos(0.5*((1-2*a(1))^2+(1-2*a(2))^2)^0.5/a(3))+...
acos((a(1))/(a(3)))+acos((a(2))/(a(3)))+(0.5*((1-2*a(1))^2+...
(1-2*a(2))^2)^0.5*((a(3))^2-0.25*((1-2*a(1))^2+(1-2*a(2))^2 ))^0.5)...
/((S-2*(a(3))^2))+(a(1)*((a(3))^2-(a(1))^2 )^0.5)/((S-2*(a(3))^2))...
+(a(2)*((a(3))^2-(a(2))^2)^0.5)/((S-2*(a(3))^2))-pi;
end
end
Here is my code for solving the system.
if true
clear;
clc;
n=10;
m=5;
draw=100;
S=zeros(n,1);
guess=zeros(n,m,3);
b=zeros(n,m,1);
c=zeros(n,m,1);
d=zeros(n,m,1);
solutions=zeros(n,m,3);
for t=1:n;
S(t)=(t+n/(3+2^1.5))/n;
for k=1:m;
b(t,k)=randsample(draw,1);
c(t,k)=randsample(draw,1);
d(t,k)=randsample(draw,1);
guess(t,k,1)=b(t)/(2*draw+1);
guess(t,k,2)=c(t)/(2*draw+1);
guess(t,k,3)=d(t)*1.2/(2*draw+1);
system = @(a)equations(a,S(t));
solutions(t,k,:)=fsolve(system,guess(t,k,:));
end
end
end
Now that I have the nxmx3 solutions matrix, I want to remove the second dimension and somehow "stack" the m nx3 matrices into one big (n*m)x3 matrix. I tried using a for loop and cat() but I don't think that is a good way. Here is how I started. Please advise. Your help is GREATLY appreciated!
if true
sols2d=zeros(m*n,3);
for k=1:m
submat(k)=solutions(:,k,:);
rsubmat(k)=reshape(submat(k),[n,3]);
cat(1,[]);
end
end
Thank you!
