Is there a way to come up with all the combination between 0 and 1 that sum up to equal 1?

Is there a way to come up with all the combination between 0 and 1 that sum up to equal 1?

1. All combination between 0 and 1. y4 = [Ny4 Hy4 Ay4 Cy4] , if sum(y4) = 1
2. Put Them into sum(((K-1).*y4)./(1+(K-1)*v)) = 0 to solve for v.
3. Then x5 = y4./(1+(K-1).*v), if sum(x5) = 1
4. finally y6 = K.*x5, if sum(y6) = 1

When I used nchoosek([0:1/10000:1],4) I get error.

Error using zeros

Maximum variable size allowed by the program is exceeded.

Error in nchoosek>combs (line 164)

P = zeros(total, k, 'like', v);

Error in nchoosek (line 123)

c = combs(v,k);

I solved this using excel solver, that is how I got the values.

% guess mole fraction for stream 4 the feed into the flash separator.
% the sum of all 4 must equal 1.
Ny4 = 0.108536069;
Hy4 = 0.772457477;
Ay4 = 0.117147745;
Cy4 = 0.001858709;
y4 = [Ny4 Hy4 Ay4 Cy4];
% K-value given
NK = 4.8;
HK = 70;
AK = .051;
CK = .32;
K = [NK HK AK CK];
% guess ratio
% v is want I want to solve for when t(v) = 0
v =.925028796;
t = sum(((K-1).*y4)./(1+(K-1)*v));
% mole fraction for stream 5 the liquid out the flash separator.
% the sum of all 4 must equal 1.
x5 = y4./(1+(K-1).*v)
testx5= sum(x5)
% mole fraction for stream 6 the vapor out the flash separator.
% the sum of all 4 must equal 1.
y6 = K.*x5
testy6 = sum(y6)

Answer 1

[KSSV]

x = 0:1/100:1 ; 

id = nchoosek(1:length(x),4) ; 
thesum = sum(x(id),2) ; 
% find sum == 1 
idx = thesum==1 ;
iwant = x(id(idx,:)) ;  

[A C]

Ny4 = 0.108536069;

Hy4 = 0.772457477;

Ay4 = 0.117147745;

Cy4 = 0.001858709;

I at least need it to pick up 10^-4 because Cy4 is a smaller number than the rest. x = 0:1/10000:1; or more.

Is there a way to make condition with nchoosek because I know that Hy4 will be the biggest number,and Cy4 will be the smallest, and all the four numbers will never equal 0 or 1 by themselves.

Thank you for your help.

[KSSV]

Yes you can make a condition.

x = 0:1/10000:1 ; 
id = nchoosek(1:length(x),4) ; 
x = x(id) ;   % nx4 array of all x's 

In the above, apply your condition to x, Cy4 i.e column 4 should be less than 0.002 (say)

id_c1 = x(:,4)<0.002 ; % condition on 4th column 
x = x(id_c1,:) ;       % this will give fourth column only < 0.002 

Now you can get the sum on x and follow. If you want, you can apply condition on the first column also.

[A C]

I am sorry that I did not explain my problem. When I use 1/10000 it gives me a error.

Do you get the same errors?

x = 0:1/10000:1 ;

id = nchoosek(1:length(x),4) ;

x = x(id) ; % nx4 array of all x's

Error using zeros

Maximum variable size allowed by the program is exceeded.

Error in nchoosek>combs (line 164)

P = zeros(total, k, 'like', v);

Error in nchoosek (line 123)

c = combs(v,k);

[KSSV]

It might be dude to x is large and posing memory issues. You can split x into multiple parts, and get the job done.