-----------------------------------------------------------------------
drop extension if exists flow cascade;
NOTICE:  extension "flow" does not exist, skipping
create extension flow;
select '[]'::flow;
 flow 
------
 []
(1 row)

-- id,nr,qtt_prov,qtt_requ,sid,own,qtt,np
select '[(1,2,3,4,5,6,7,8)]'::flow as flow;
            flow            
----------------------------
 [(1, 2, 3, 4, 5, 6, 7, 8)]
(1 row)

select '[(1,2,3,4,5,6,7,8),(9,8,11,12,13,14,15,16)]'::flow as flow;
                           flow                            
-----------------------------------------------------------
 [(1, 2, 3, 4, 5, 6, 7, 8),(9, 8, 11, 12, 13, 14, 15, 16)]
(1 row)

select flow_status('[(1,2,3,4,5,6,7,8)]'::flow);
 flow_status 
-------------
 noloop
(1 row)

select flow_omega('[(1,2,3,4,5,6,7,8)]'::flow);
 flow_omega 
------------
       0.75
(1 row)

select flow_omegax('[(1,2,3,4,5,6,7,8)]'::flow,2,1);
 flow_omegax 
-------------
         1.5
(1 row)

select flow_cat('[(1,2,3,4,5,6,7,8)]'::flow,9,8,11,12,13,14,15,16);
                         flow_cat                          
-----------------------------------------------------------
 [(1, 2, 3, 4, 5, 6, 7, 8),(9, 8, 11, 12, 13, 14, 15, 16)]
(1 row)

select flow_proj('[(1,2,3,4,5,6,7,8),(9,8,11,12,13,14,15,16)]'::flow,1);
 flow_proj 
-----------
 {1,9}
(1 row)

select flow_proj('[(1,2,3,4,5,6,7,8),(9,8,11,12,13,14,15,16)]'::flow,2);
 flow_proj 
-----------
 {2,8}
(1 row)

select flow_proj('[(1,2,3,4,5,6,7,8),(9,8,11,12,13,14,15,16)]'::flow,9);
 flow_proj 
-----------
 {0,0}
(1 row)

select flow_dim('[(1,2,3,4,5,6,7,8),(9,8,11,12,13,14,15,16)]'::flow);
 flow_dim 
----------
        2
(1 row)

select flow_to_matrix('[(1,2,3,4,5,6,7,8),(9,8,11,12,13,14,15,16)]'::flow);
                 flow_to_matrix                  
-------------------------------------------------
 {{1,2,3,4,5,6,7,8,0},{9,8,11,12,13,14,15,16,0}}
(1 row)

-- cycle 3 nodes, 3 stocks,3 owners
-- id,nr,qtt_prov,qtt_requ,sid,own,qtt,np
-- result {20,80,40}
select flow_proj('[(1,3,1,1,1,1,20,1),(2,1,8,1,2,2,80,2),(3,2,1,1,3,3,120,3)]'::flow,9);
 flow_proj  
------------
 {20,80,40}
(1 row)

-- cycle 3 nodes, 3 stocks,3 owners - all stock exhausted
-- id,nr,qtt_prov,qtt_requ,sid,own,qtt,np
-- result {20,80,40}
select flow_proj('[(1,3,1,1,1,1,20,1),(2,1,8,1,2,2,80,2),(3,2,1,1,3,3,40,3)]'::flow,9);
 flow_proj  
------------
 {20,80,40}
(1 row)

-- idem with pivot.id=0 - lastIgnore
--result {10,80,10} even if the last stock has qtt=1
select flow_proj('[(1,3,1,1,1,1,20,1),(2,1,8,1,2,2,80,2),(0,2,1,1,0,3,1,3)]'::flow,9);
 flow_proj  
------------
 {10,80,10}
(1 row)

-- cycle 3 nodes, 3 stocks,2 owners
-- id,nr,qtt_prov,qtt_requ,sid,own,qtt,np
-- result {10,80,40}
select flow_proj('[(1,3,1,1,1,1,40,1),(2,1,16,1,2,2,80,2),(3,2,1,1,3,2,120,3)]'::flow,9);
 flow_proj  
------------
 {10,80,40}
(1 row)

-- cycle 2 nodes, 2 stocks,2 owners
-- id,nr,qtt_prov,qtt_requ,sid,own,qtt,np
-- result {20,20}
select flow_proj('[(1,2,2,1,1,1,20,1),(2,1,2,1,2,2,120,2)]'::flow,9);
 flow_proj 
-----------
 {20,20}
(1 row)

-- cycle 4 nodes, 3 stocks,3 owners
-- id,nr,qtt_prov,qtt_requ,sid,own,qtt,np
-- result {80,80,80,80}
select flow_proj('[
(1,4,1,1,1,1,240,1),
(2,1,1,1,2,2, 80,2),
(3,2,1,1,1,1,240,1),
(4,1,1,1,3,3,120,4)]'::flow,9);
   flow_proj   
---------------
 {80,80,80,80}
(1 row)

-- cycle 4 nodes, 3 stocks,3 owners
-- id,nr,qtt_prov,qtt_requ,sid,own,qtt,np
-- result {80,80,80,80}
select flow_proj('[
(1,4,2,1,1,1,240,1),
(2,1,4,1,2,2, 80,2),
(3,2,2,1,1,1,240,1),
(4,1,4,1,3,3,120,4)]'::flow,9);
   flow_proj   
---------------
 {80,80,80,80}
(1 row)

-- flow_get_fim1_fi
select flow_proj('[(1,3,1,1,1,1,40,1),(2,1,16,1,2,2,80,2),(3,2,1,1,3,2,120,3)]'::flow,9);
 flow_proj  
------------
 {10,80,40}
(1 row)

-- result {10,80,40}
select flow_get_fim1_fi('[(1,3,1,1,1,1,40,1),(2,1,16,1,2,2,80,2),(3,2,1,1,3,2,120,3)]'::flow,0);
 flow_get_fim1_fi 
------------------
 {40,10}
(1 row)

select flow_get_fim1_fi('[(1,3,1,1,1,1,40,1),(2,1,16,1,2,2,80,2),(3,2,1,1,3,2,120,3)]'::flow,1);
 flow_get_fim1_fi 
------------------
 {10,80}
(1 row)

select flow_get_fim1_fi('[(1,3,1,1,1,1,40,1),(2,1,16,1,2,2,80,2),(3,2,1,1,3,2,120,3)]'::flow,2);
 flow_get_fim1_fi 
------------------
 {80,40}
(1 row)

-- flow 8 nodes, 8 stocks, 8 owners
select flow_proj('[
(1,8,1,1,1,1, 10,1),
(2,1,1,1,2,2, 10,2),
(3,2,1,1,3,3, 10,3),
(4,3,1,1,4,4, 10,4),
(5,4,1,1,5,5, 10,5),
(6,5,1,1,6,6, 10,6),
(7,6,1,1,7,7, 10,7),
(8,7,1,1,8,8, 10,8)]'::flow,9);
         flow_proj         
---------------------------
 {10,10,10,10,10,10,10,10}
(1 row)

/* flow 9 nodes produces an error
select flow_proj('[
(1,9,1,1,1,1, 10,1),
(2,1,1,1,2,2, 10,2),
(3,2,1,1,3,3, 10,3),
(4,3,1,1,4,4, 10,4),
(5,4,1,1,5,5, 10,5),
(6,5,1,1,6,6, 10,6),
(7,6,1,1,7,7, 10,7),
(8,7,1,1,8,8, 10,8),
(9,8,1,1,9,9, 10,9)]'::flow,9); */