Hi. How I can write this formula with Matlab code?

[Rik]

That depends on what psi is, but with a nested loop this is trivial. What did you try?

[Aynur Resulzade]

psi is 2x2 matrix which is depend on n psi(n)=(A11(n) A12(n);A21(n) A22(n))

Answer 1

[Bruno Luong]

n=10;
psi=rand(1,n-2);

chi = 0;
for k=1:n-2
    i = nchoosek(1:n-2,k);
    j = 1:k;
    l = k+1-j;
    il = i(:,l);
    chi = chi+sum(prod(psi(il),2));
end
chi

chi = 11.2726

% Or remove some of the unecessary indexing with j and l
chi = 0;
for k=1:n-2
    chi = chi+sum(prod(psi(nchoosek(1:n-2,k)),2));
end
chi

chi = 11.2726

[Aynur Resulzade]

what is error calculated xi?

clear all
clc
a=3;
b=1;
%alf=1.6995;
alf=5/3;
% a=3
%f=1;
L=5;
n=4;
n1=n
l=10;
h=(1-0.1)/l;
x=0.1:h:1;
sizex=size(x);
delta=h;
y0=0;
n=n-1;
k=n;
%in here if k=n
A_11n=-1+(-h*(((a*(x(2*n-2+1)-x(2*n-4+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*n-4+1)))...
    +2*h*((((a*(x(2*n-2+1)-x(2*n-3+1))^(1-alf))/gamma(alf)))+b*(x(2*n-2+1)-x(2*n-3+1))));
A_12n=2+(-h*(((a*(x(2*n-2+1)-x(2*n-3+1))^(1-alf)/gamma(alf)))+b*(x(2*n-2+1)-x(2*n-3+1))))  ;
A_21n=-2-2*h*((a*(x(2*n-2+1)-x(2*n-4+1))^(1-alf)/gamma(alf))+b*(x(2*n-2+1)-x(2*n-4+1)))+...
    +4*h*((a*(x(2*n-2+1)-x(2*n-3+1))^ (1-alf)/gamma(alf))+b*(x(2*n-2+1)-x(2*n-3+1)))...
    +h^2*(((a*(x(2*n-1+1)-x(2*n-2+1))^ (1-alf)/gamma(alf))+b*(x(2*n-1+1)-x(2*n-2+1)))* ...
    (((a*(x(2*n-2+1)-x(2*n-4+1))^ (1-alf)/gamma(alf))+b*(x(2*n-2+1)-x(2*n-4+1)))))...
    -(2*h^2*((a*(x(2*n-1+1)-x(2*n-2+1))^ (1-alf)/gamma(alf))+b*(x(2*n-1+1)-x(2*n-2+1)))*...
    (((a*(x(2*n-2+1)-x(2*n-3+1))^ (1-alf)/gamma(alf))))+b*(x(2*n-2+1)-x(2*n-3+1)))...
    -h*((a*(x(2*n-1+1)-x(2*n-4+1))^ (1-alf)/gamma(alf))+b*(x(2*n-1+1)-x(2*n-4+1)))...
    +2*h*((a*(x(2*n-1+1)-x(2*n-3+1))^ (1-alf)/gamma(alf))+b*(x(2*n-1+1)-x(2*n-3+1)));

A_22n=3-2*h*((a*(x(2*n-2+1)-x(2*n-3+1))^(1-alf)/gamma(alf))+b*(x(2*n-2+1)-x(2*n-3+1)))...
    -h*((a*(x(2*n-1+1)-x(2*n-3+1))^(1-alf)/gamma(alf))+b*(x(2*n-1+1)-x(2*n-3+1)))...    
    +h*h*((a*(x(2*n-1+1)-x(2*n-2+1))^(1-alf)/gamma(alf))+b*(x(2*n-1+1)-x(2*n-2+1)))*...
    ((a*(x(2*n-2+1)-x(2*n-3+1))^(1-alf)/gamma(alf))+b*(x(2*n-2+1)-x(2*n-3+1)));
An=[A_11n A_12n; A_21n A_22n];
%in here if k=0
k=0;
A110=-h*(((a*(x(2*n-2+1)-x(0+1))^(1-alf)/gamma(alf)))+b*(x(2*n-2+1)-x(0+1)));
A120=2*h*(((a*(x(2*n-2+1)-x(0+1) )^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(0+1) ))...
    -h*(((a*(x(2*n-2+1)-x(1+1) )^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(1+1)));
A210=(-2*h+h*h*(((a*(x(2*n-1+1)-x(2*n-2+1) )^(1-alf)/gamma(alf))))+b*((x(2*n-1+1)-x(2*n-2+1))))*...
    (a*(((x(2*n-2+1)-x(0+1))^(1-alf))/gamma(alf))+b*((x(2*n-2+1)-x(0+1))))-...
    -h*(((a*(x(2*n-1+1)-x(0+1))^(1-alf)/gamma(alf)))+b*(x(2*n-1+1)-x(0+1)));
A220=(4*h*(((a*(x(2*n-2+1)-x(0+1) )^(1-alf))/gamma(alf)))+b*(x(2*n-2+1)-x(0+1) ))...
    +2*h*(((a*(x(2*n-2+1)-x(0+1) )^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(0+1) ))-...
    -2*h*(((a*(x(2*n-2+1)-x(1+1) )^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(1+1) ))...
    -h*((a*((x(2*n-1+1)-x(1+1) )^(1-alf))/gamma(alf))+b*(x(2*n-1+1)-x(1+1) ))...
    -2*h*h*(((a*(x(2*n-1+1)-x(2*n-2+1) )^(1-alf))/gamma(alf))+b*(x(2*n-1+1)-x(2*n-2+1) ))...
    *(((a*(x(2*n-2+1)-x(0+1) )^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(0+1) ))+...
    +h*h*(((a*(x(2*n-1+1)-x(2*n-2+1) )^(1-alf))/gamma(alf))+b*(x(2*n-1+1)-x(2*n-2+1) ))...
    *(((a*(x(2*n-2+1)-x(1+1) )^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(1+1)))

A0=[A110 A120; A210 A220];
Ak(1:2,1:2)=A0
%in here if k=1,2,...,n-2
for k=1:n1-2;
    
    A11k=-h*(((a*(x(2*n-2+1)-x(2*k-2+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-2+1)))...
        +2*h*(((a*(x(2*n-2+1)-x(2*k-1+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-1+1)))...
        -h*(((a*(x(2*n-2+1)-x(2*k+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k+1)));
    A12k=-h*(((a*(x(2*n-2+1)-x(2*k-1+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-1+1)))...
        +2*h*(((a*(x(2*n-2+1)-x(2*k+1) )^(1-alf))/gamma(alf))+b*(a*(x(2*n-2+1)-x(2*k+1))))...
        -h*(((a*(x(2*n-2+1)-x(2*k+1+1) )^ (1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k+1+1) ));
    A21k=-2*h*(((a*(x(2*n-2+1)-x(2*k-2+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-2+1)))...
        +4*h*(((a*(x(2*n-2+1)-x(2*k-1+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-1+1)))-...
        -2*h*(((a*(x(2*n-2+1)-x(2*k+1))^(1-alf))/gamma(alf))+b*((x(2*n-2+1)-x(2*k+1)))-...
        -h*(((a*(x(2*n-1+1)-x(2*k-2+1))^(1-alf))/gamma(alf))+b*(x(2*n-1+1)-x(2*k-2+1)))+...
        +2*h*(((a*(x(2*n-2+1)-x(2*k-1+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-1+1)))-...
        -h*(((a*(x(2*n-1+1)-x(2*k+1))^(1-alf))/gamma(alf))+b*(x(2*n-1+1)-x(2*k+1)))+...
        (h*h*(((a*(x(2*n-1+1)-x(2*n-2+1))^(1-alf))/gamma(alf))+b*(x(2*n-1+1)-x(2*n-2+1)))*((a*(x(2*n-2+1)-x(2*k-2+1))^(1-alf))/gamma(alf)))+b*(x(2*n-2+1)-x(2*k-2+1)))...
        -(2*h*h*(((a*(x(2*n-1+1)-x(2*n-2+1))^(1-alf))/gamma(alf)))+b*(a*(x(2*n-1+1)-x(2*n-2+1)))*((a*(x(2*n-2+1)-x(2*k-1+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-1+1)))+...
        ((h*h*(((a*(x(2*n-1+1)-x(2*n-2+1))^(1-alf))/gamma(alf)))+b*(x(2*n-1+1)-x(2*n-2+1)))*...
        ((a*(x(2*n-2+1)-x(2*k+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k+1)));
    
    A22k=(-2*h*(((a*(x(2*n-2+1)-x(2*k-1+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k-1+1)))...
        +4*h*(((a*(x(2*n-2+1)-x(2*k+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k+1)))...
        -2*h*(((a*(x(2*n-2+1)-x(2*k+1+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k+1+1)))-...
        -h*(((a*(x(2*n-1+1)-x(2*k-1+1))^(1-alf))/gamma(alf))+b*(x(2*n-1+1)-x(2*k-1+1)))...
        +2*h*(((a*(x(2*n-2+1)-x(2*k+1))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k+1)))...
        -h*(((a*(x(2*n-1+1)-x(2*k+1+1))^(1-alf))/gamma(alf)))+b*(x(2*n-1+1)-x(2*k+1+1)))+...
        (h*h*(((a*(x(2*n-1+1)-x(2*n-2+1))^(1-alf))/gamma(alf)))+b*(x(2*n-1+1)-x(2*n-2+1)))*((((a*(x(2*n-2+1)-x(2*k-1+1))^(1-alf))/gamma(alf)))+b*(x(2*n-2+1)-x(2*k-1+1)))...
        -(2*h*h*(((a*((x(2*n-1+1)-x(2*n-2+1))^(1-alf))/gamma(alf))))+b*((x(2*n-1+1)-x(2*n-2+1))))...
        *((((a*(x(2*n-2+1)-x(2*k+1))^(1-alf))/gamma(alf)))+b*(x(2*n-2+1)-x(2*k+1)))+...
        +(h*h*(((a*(x(2*n-1+1)-x(2*n-2+1))^(1-alf))/gamma(alf)))+b*(x(2*n-1+1)-x(2*n-2+1)))*((((a*(x(2*n-2+1)-x(2*k+1+1)))^(1-alf))/gamma(alf))+b*(x(2*n-2+1)-x(2*k+1+1)));
    Akk=[A11k A12k; A21k A22k] ;
    %Collected all Ak in one matrix
    Ak(1:2,1:2)=An
    t=k
    2*t+1:2*t+2;
    Ak(1:2,2*t+1:2*t+2)= Akk;
    Ak
end

%   A1=Ak(1:2,1:2)
%   A2=Ak(1:2,1:2)+Ak(1:2,3:4)*Ak(1:2,1:2)
%   A3=(Ak(1:2,1:2)+Ak(1:2,3:4)*Ak(1:2,1:2)+Ak(1:2,5:6)*Ak(1:2,1:2)+Ak(1:2,5:6)*Ak(1:2,3:4)*Ak(1:2,1:2))
s1(1:2,1:2)=[0 0;0 0]
s(1:2,1:2)=[0 0;0 0]
pr=[1 1;1 1]
n1=4
k=n1-2
n=n1
for k=1:n-2
    s1=s1+sum(1:2,2*k+1:2*k+2)
    sum1(1:2,2*k+1:2*k+2)=s1
    
    i=nchoosek(1:n-2,k)
    
    for j=1:k
        j=k+1-j
        pr=pr*Ak(1:2,2*j+1:2*j+2);
        
        s=s+prod(1:2,2*i+1:2*i+2);
        sum(1:2,2*i+1:2*i+2)=s;
        
    end
end 
s1

[Aynur Resulzade]

[Bruno Luong]

@Aynur Resulzade You must kidding me. I'll delete my answer

[Aynur Resulzade]

@Bruno Luong please excecuse me

Sorry I ask second time this question for 2x2 matrix where fi

admin say that you must ask for this in after question and didnt accept answer

that is way I unaccept ((((((

please help me for this problem and don't angry)))