void ConstructLinearSystemFromMajorization(out SparseMatrix Lw, out SparseMatrix Lx)
{
int numEdges = GetNumberOfEdges(NodeVotings);
#if SHARPKIT //SharpKit/Colin: multidimensional arrays not supported in JavaScript - https://code.google.com/p/sharpkit/issues/detail?id=340
var edgesDistance = new double[numEdges];
var edgesWeight = new double[numEdges];
#else
var edges = new double[numEdges, 2];
#endif
// list of undirected (symmetric) edges: [,0]=distance, [,1]=weight , every edge must be symmetric (thus exist once in each direction).
//each element in the array corresponds to a node, the list corresponds to the adjacency list of that node.
//int[0]: node id of adjacent node, int[1]: edge id of this edge
var adjLists = new List <int[]> [NodeVotings.Count];
int row = 0;
int edgeId = 0;
foreach (NodeVoting nodeVoting in NodeVotings)
{
int targetId = nodeVoting.VotedNodeIndex;
int numAdj = 0;
nodeVoting.VotingBlocks.ForEach(block => numAdj += block.Votings.Count);
var currentAdj = new List <int[]>(numAdj);
if (row != targetId)
{
throw new ArgumentOutOfRangeException("VotedNodeIndex must be consecutive starting from 0");
}
adjLists[row] = currentAdj;
foreach (VoteBlock block in nodeVoting.VotingBlocks)
{
foreach (Vote voting in block.Votings)
{
//corresponds to an edge or an entry in the corresponding matrix
int sourceId = voting.VoterIndex;
#if SHARPKIT
edgesDistance[edgeId] = voting.Distance;
edgesWeight[edgeId] = voting.Weight * block.BlockWeight;
#else
edges[edgeId, 0] = voting.Distance;
edges[edgeId, 1] = voting.Weight * block.BlockWeight;
#endif
currentAdj.Add(new[] { sourceId, edgeId });
edgeId++;
}
}
row++;
}
//TODO check if sorting can be removed to make it faster.
//sort the adjacency lists, so that we can create a sparse matrix where the ordering is important
for (int rowC = 0; rowC < adjLists.Length; rowC++)
{
List <int[]> adjList = adjLists[rowC];
//add self loop, since there will be an entry in the matrix too.
adjList.Add(new[] { rowC, -1 });
adjList.Sort((a, b) => a[0].CompareTo(b[0]));
}
numEdges += adjLists.Length; //self loop added to every node, so number of edges has increased by n.
var diagonalPos = new int[adjLists.Length];
// points to the position of the i-th diagonal entry in the flatened value array
Lw = new SparseMatrix(numEdges, adjLists.Length, adjLists.Length);
Lx = new SparseMatrix(numEdges, adjLists.Length, adjLists.Length);
int valPos = 0;
for (int rowId = 0; rowId < adjLists.Length; rowId++)
{
List <int[]> adjList = adjLists[rowId];
double sumLw = 0;
double sumLx = 0;
foreach (var node in adjList)
{
int colId = node[0];
Lw.ColInd()[valPos] = colId;
Lx.ColInd()[valPos] = colId;
if (rowId == colId)
{
//on diagonal of matrix
diagonalPos[rowId] = valPos; //we will fill in the value later with the sum of all row entries
}
else
{
#if SHARPKIT
double distance = edgesDistance[node[1]]; // distance(rowId,colId)
double weight = edgesWeight[node[1]]; // weight(rowId,colId)
#else
double distance = edges[node[1], 0]; // distance(rowId,colId)
double weight = edges[node[1], 1]; // weight(rowId,colId)
#endif
// weighted laplacian fill
Lw.Values()[valPos] = -weight;
sumLw += weight;
// Lx, which is similar to weighted laplacian but takes the distance into account
//TODO extract the distance computation outside of this step to make the procedure faster
double euclid = (Positions[rowId] - Positions[colId]).Length;
double entry = -weight * distance / euclid;
Lx.Values()[valPos] = entry;
sumLx += entry;
}
valPos++;
}
//set the diagonal to the sum of all other entries in row
Lw.Values()[diagonalPos[rowId]] = sumLw;
Lx.Values()[diagonalPos[rowId]] = -sumLx;
//mark row end in flatened list
Lw.RowPtr()[rowId + 1] = valPos;
Lx.RowPtr()[rowId + 1] = valPos;
}
}