Scilab function
Last update : August 1997

pipe_network - solves the pipe network problem

### Calling Sequence

  `[x,pi] = pipe_network(g)`

### Parameters

- `g`: graph list
- `x`: row vector of the value of the flow on the arcs
- `pi`: row vector of the value of the potential on the nodes

### Description

`pipe_network` returns the value of the flows and of the potentials for the pipe network problem: flow problem with two Kirchhoff laws. The graph must be directed. The problem must be feasible (the sum of the node demands must be equal to 0). The resistances on the arcs must be strictly positive and are given as the values of the element 'edge_weight' of the graph list.

The problem is solved by using sparse matrices LU factorization.

### Examples

    ta=[1 1 2 2 3 3 4 4 5 5 5 5 6 6 6 7 7 15 15 15 15 15 15];
    ta=[ta, 15 8 9 10 11 12 13 14];
    he=[10 13 9 14 8 11 9 11 8 10 12 13 8 9 12 8 11 1 2 3 4];
    he=[he, 5 6 7 16 16 16 16 16 16 16];
    n=16;
    g=make_graph('foo',1,n,ta,he);
    g('node_x')=[42 615 231 505 145 312 403 233 506 34 400 312 142 614 260 257];
    g('node_y')=[143 145 154 154 147 152 157 270 273 279 269 273 273 274 50 376];
    show_graph(g);
    g('node_demand')=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 -100 100];
    w = [1 3 2 6 4 7 8 1 2 2 2 4 7 8 9 2 3 5 7 3 2 5 8 2 5 8];
    g('edge_weight')=[w, 6 4 3 5 6];
    [x,pi] = pipe_network(g)