void PrecomputeDistanceMatrix2D(int W, int H, bool show = true)
{
int N = area_cnt;
////////////////////////////////////////////////////////////
// step III-1. build matrix A for distance computation
// [CAUTION] this is NEGATED matrix to use Cholesky decomp.
////////////////////////////////////////////////////////////
var C_dist = new CoordinateStorage <double>(N, N, 5 * N); // banded matrix without exception
for (int matid_this = 0; matid_this < N; matid_this++)
{
List <int> matid_neighbor;
if (!MatrixNeighbors.TryGetValue(matid_this, out matid_neighbor))
{
continue;
}
double A_diag = -1e-6; // small value to use Cholesky decomposition
Action <int> CheckNeighbor = (id) =>
{
int matid_next = matid_neighbor[id];
if (matid_next != -1)
{
A_diag += -1.0;
C_dist.At(matid_this, matid_next, -1.0);
}
};
CheckNeighbor(0);
CheckNeighbor(1);
CheckNeighbor(2);
CheckNeighbor(3);
C_dist.At(matid_this, matid_this, -A_diag);
}
var A_dist = Converter.ToCompressedColumnStorage(C_dist) as SparseMatrix;
////////////////////////////////////////////////////////////
// step III-2. build matrix A for heat diffusion
////////////////////////////////////////////////////////////
#if USE_3RDPARTY
solver_dist = new SuperLU(A_dist);
var options = solver_dist.Options;
options.SymmetricMode = true;
solver_dist.Factorize();
#else
solver_dist = SparseCholesky.Create(A_dist, ColumnOrdering.MinimumDegreeAtPlusA);
#endif
}
void PrecomputeHeatMatrix2D(double dt)
{
int N = area_cnt;
////////////////////////////////////////////////////////////
// step I-1. build matrix A for heat diffusion
////////////////////////////////////////////////////////////
var C_heat = new CoordinateStorage <double>(N, N, 5 * N); // banded matrix without exception
for (int matid_this = 0; matid_this < N; matid_this++)
{
List <int> matid_neighbor;
if (!MatrixNeighbors.TryGetValue(matid_this, out matid_neighbor))
{
continue;
}
if (matid_neighbor[0] != -1)
{
C_heat.At(matid_this, matid_neighbor[0], -1.0 * dt);
}
if (matid_neighbor[1] != -1)
{
C_heat.At(matid_this, matid_neighbor[1], -1.0 * dt);
}
if (matid_neighbor[2] != -1)
{
C_heat.At(matid_this, matid_neighbor[2], -1.0 * dt);
}
if (matid_neighbor[3] != -1)
{
C_heat.At(matid_this, matid_neighbor[3], -1.0 * dt);
}
C_heat.At(matid_this, matid_this, 1.0 + 4.0 * dt);
}
var A_heat = Converter.ToCompressedColumnStorage(C_heat) as SparseMatrix;
////////////////////////////////////////////////////////////
// step I-2. build matrix A for heat diffusion
////////////////////////////////////////////////////////////
#if USE_3RDPARTY
solver_heat = new SuperLU(A_heat);
var options = solver_heat.Options;
options.SymmetricMode = true;
solver_heat.Factorize();
#else
solver_heat = SparseCholesky.Create(A_heat, ColumnOrdering.MinimumDegreeAtPlusA);
#endif
}
protected override IDisposableSolver <Complex> CreateSolver(SparseMatrix matrix, bool symmetric)
{
var solver = new SuperLU(matrix);
if (symmetric)
{
var options = solver.Options;
options.SymmetricMode = true;
options.ColumnOrderingMethod = OrderingMethod.MinimumDegreeAtPlusA;
options.DiagonalPivotThreshold = 0.001;
}
return(solver);
}