Vector decomposition with Matlab

Hello !

I want to split a vector b, in two parts, b1 and b2, like that:

b= [2; 1; 2; 1; 0; 1; 2; 1; 2]

b1=[2; 1; 1; 1; 0; 0; 1; 0; 0]

b2=[0; 0; 1; 0; 0; 1; 1; 1; 2]

But my code, work only for n=4; for n>4, don't work fine.

n=4;

b=zeros((n-1)^2,1);
b(1)=2;
b(2:(n-2))=ones(n-3,1);
b(n-1)=2;
for i=1:n-3
    b((n-1)*i+1)=1;
    b((n-1)*(i+1))=1;
end
b((n-1)*(n-2)+1)=2;
b((n-1)*(n-2)+2:(n-1)*(n-2)+n-2)=ones(n-3,1);
b((n-1)^2)=2;

b1(1)=2;
b1(2:(n-2))=1;
b1(n-1)=1;
for i=1:n-3
    b1((n-1)*i+1)=1;
    b1((n-1)*(i+1))=0;
end
b1((n-1)*(n-2)+1)=1;
b1(n*2:(n-1)*(n-2))=0;
  
b1((n-1)*(n-2)+2:(n-1)*(n-2)+n-2)=zeros(n-3,1);
b1((n-1)^2)=0;
b2(1)=0;

b2(2:(n-2))=0;
b2(n-1)=1;
b2((n-1)*(n-2))=1;
b2((n-1)*(n-2)+1)=1;
b2((n-1)*(n-2)+2:(n-1)*(n-2)+n-2)=ones(n-3,1);
b2((n-1)^2)=2;

[Torsten]

One can split a vector in two vectors in many ways. What are the rules ?

[Gogu]

b=b1+b2

For the first half of elements, the rules are:

the first 2 keep in b1; 1 keep in b1; 2 split in two values of 1; 1 keep in b1

For the second half of elements, the rules are:

1 move to b2; 2 split in two; the last 2, move to b2

Answer 1

[Bruno Luong]

b= [2; 1; 2; 1; 0; 1; 2; 1; 2]

b1=min(b,1);
b1([find(b==2,1,'first'),find(b==2,1,'last')])=2;
b2=b-b1;
n=length(b);
tail=floor(n/2)+1:n; %or ceil?
[b1(tail),b2(tail)]=deal(b2(tail),b1(tail));

b1
b2

[Gogu]

Unfortunately, one rule for the second half of elements, are not met (1 move to b2) :

b1 =

   2   1   1   1   0   1   1   1   0

b2 =

   0   0   1   0   0   0   1   0   2

[Gogu]

Solved !!!

lx = (length(b));
half = ceil(lx/2);

b1(1)=2;
b2(1)=0;
b1((n-1)^2)=0;
b2((n-1)^2)=2;

j=(n-1)^2;

for i=2:j-1
  if b(i)==2
    b1(i)=1;
    b2(i)=1;
  end
end

for i=2:half
  
  if find(b(i)==1)
    b1(i)=1;
    b2(i)=0;
  end
  
end

for i= half + 1 : j-1
  if find(b(i)==1)
    b1(i)=0;
    b2(i)=1;
  end
end

b1'
b2'