/// <summary>
/// Creates a Linear Programming problem instance for creating divergence free flows using a tiling method.
/// The instance is stored in <see cref="LpModel"/>.
/// </summary>
/// <param name="minXFlux">Minimum flux in X direction as an integer</param>
/// <param name="maxXFlux">Maximum flux in X direction as an integer</param>
/// <param name="minYFlux">Minimum flux in Y direction as an integer</param>
/// <param name="maxYFlux">Maximum flux in Y direction as an integer</param>
/// <param name="currentTileGrid"></param>
public static void BuildInitialModel(int minXFlux, int maxXFlux, int minYFlux, int maxYFlux,
TileGrid currentTileGrid, int?[, ][] boundaryConditions)
{
int gridDimension = currentTileGrid.Dimension;
//Number of variables is 2*n*(n+1) for n x n - grid
LpModel = lpsolve.make_lp(0, 2 * gridDimension * (gridDimension + 1));
//We always have four variables in the constraint
int[] tileEdges = new int[4];
//Improves performance when adding rows to model
lpsolve.set_add_rowmode(LpModel, 1);
lpsolve.set_obj_fn(LpModel, new double[2 * gridDimension * (gridDimension + 1)]);
//Add incompressibility constraint to all cells which don't already have a flowtile on them.
for (int row = 0; row < gridDimension; row++)
{
for (int column = 0; column < gridDimension; column++)
{
if (!currentTileGrid.HasTile(row, column))
{
tileEdges = TileEdgeIndices(row, column, gridDimension);
lpsolve.add_constraintex(LpModel, 4, new double[] { -1, -1, 1, 1 }, tileEdges,
lpsolve.lpsolve_constr_types.EQ, 0);
}
}
}
//Add row mode has to be turned off before continuing with other operations, if not then program crashes.
lpsolve.set_add_rowmode(LpModel, 0);
bool[] edgeSetFlag = new bool[2 * gridDimension * (gridDimension + 1) + 1];
//Iterate over all rows and columns in the grid and set bounds on variables.
for (int row = 0; row < gridDimension; row++)
{
for (int column = 0; column < gridDimension; column++)
{
tileEdges = TileEdgeIndices(row, column, gridDimension);
if (!currentTileGrid.HasTile(row, column))
{
//Set the bounds for each edge flow. Zero if it is a boundary edge.
if (!edgeSetFlag[tileEdges[(int)Direction.Top]])
{
int?boundaryCondition = boundaryConditions[row, column][(int)Direction.Top];
if (boundaryCondition != null)
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Top], (double)boundaryCondition, (double)boundaryCondition);
edgeSetFlag[tileEdges[(int)Direction.Top]] = true;
}
else
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Top], minYFlux, maxYFlux);
}
}
if (!edgeSetFlag[tileEdges[(int)Direction.Right]])
{
int?boundaryCondition = boundaryConditions[row, column][(int)Direction.Right];
if (boundaryCondition != null)
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Right], (double)boundaryCondition, (double)boundaryCondition);
edgeSetFlag[tileEdges[(int)Direction.Right]] = true;
}
else
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Right], minXFlux, maxXFlux);
}
}
if (!edgeSetFlag[tileEdges[(int)Direction.Bottom]])
{
int?boundaryCondition = boundaryConditions[row, column][(int)Direction.Bottom];
if (boundaryCondition != null)
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Bottom], (double)boundaryCondition, (double)boundaryCondition);
edgeSetFlag[tileEdges[(int)Direction.Bottom]] = true;
}
else
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Bottom], minYFlux, maxYFlux);
}
}
if (!edgeSetFlag[tileEdges[(int)Direction.Left]])
{
int?boundaryCondition = boundaryConditions[row, column][(int)Direction.Left];
if (boundaryCondition != null)
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Left], (double)boundaryCondition, (double)boundaryCondition);
edgeSetFlag[tileEdges[(int)Direction.Left]] = true;
}
else
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Left], minXFlux, maxXFlux);
}
}
}
//Else there is a tile on the slot and the values are bounded by the flows from that tile
else
{
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Top],
currentTileGrid.GetFlowTile(row, column).Flux.TopEdge,
currentTileGrid.GetFlowTile(row, column).Flux.TopEdge);
//Sets a flag that the edge flux has been set so that the value isn't overridden later.
edgeSetFlag[tileEdges[(int)Direction.Top]] = true;
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Right],
currentTileGrid.GetFlowTile(row, column).Flux.RightEdge,
currentTileGrid.GetFlowTile(row, column).Flux.RightEdge);
//Sets a flag that the edge flux has been set so that the value isn't overridden later.
edgeSetFlag[tileEdges[(int)Direction.Right]] = true;
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Bottom],
currentTileGrid.GetFlowTile(row, column).Flux.BottomEdge,
currentTileGrid.GetFlowTile(row, column).Flux.BottomEdge);
//Sets a flag that the edge flux has been set so that the value isn't overridden later.
edgeSetFlag[tileEdges[(int)Direction.Bottom]] = true;
lpsolve.set_bounds(LpModel, tileEdges[(int)Direction.Left],
currentTileGrid.GetFlowTile(row, column).Flux.LeftEdge,
currentTileGrid.GetFlowTile(row, column).Flux.LeftEdge);
//Sets a flag that the edge flux has been set so that the value isn't overridden later.
edgeSetFlag[tileEdges[(int)Direction.Left]] = true;
}
}
}
lpsolve.set_verbose(LpModel, 0);
}