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

20 Jan 2023
1 Answer
Updated 23 Jan 2023
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Rik
Rik on 21 Jan 2023
That depends on what psi is, but with a nested loop this is trivial. What did you try?
Aynur Resulzade
Aynur Resulzade on 22 Jan 2023
Edited: Aynur Resulzade on 22 Jan 2023
psi is 2x2 matrix which is depend on n psi(n)=(A11(n) A12(n);A21(n) A22(n))

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Answers (1)

Bruno Luong
Bruno Luong on 21 Jan 2023
Ran in:

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Ran in:
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

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Aynur Resulzade
Aynur Resulzade on 23 Jan 2023
Edited: Rik on 23 Jan 2023
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
Bruno Luong
Bruno Luong on 23 Jan 2023
Edited: Bruno Luong on 23 Jan 2023
@Aynur Resulzade You must kidding me. I'll delete my answer
Aynur Resulzade
Aynur Resulzade on 23 Jan 2023
Edited: Aynur Resulzade on 23 Jan 2023
@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)))

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Aynur Resulzade
Aynur Resulzade
on 20 Jan 2023

Edited:

Aynur Resulzade
Aynur Resulzade
on 23 Jan 2023

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