/// <summary>
/// Compress Z submatrix with multilevel subdivision
/// </summary>
/// <param name="basicFuncBoxes">Information about the location of basis functions in boxes at different levels</param>
/// <param name="ix_s">x-index of source box at level l</param>
/// <param name="iy_s">y-index of source box at level l</param>
/// <param name="iz_s">z-index of source box at level l</param>
/// <param name="ix_f">x-index of field box at level l</param>
/// <param name="iy_f">y-index of field box at level l</param>
/// <param name="iz_f">z-index of field box at level l</param>
/// <param name="l">Current level</param>
/// <param name="L">Maximum level to end multilevel subdivion</param>
/// <param name="ACA_thres">Relative error threshold to stop adding rows and columns in ACA iteration</param>
/// <param name="Z_comp">compressed matrix</param>
public static void MultilevelCompres(BasicFuncBoxes basicFuncBoxes, double ix_s, double iy_s, double iz_s, double ix_f, double iy_f, double iz_f, int l, double L, double ACA_thres,ref NewSparseMatrix Z_comp)
{
bool sym_source_field = true;
//NewSparseMatrix Z_comp = new NewSparseMatrix();
for (double xchs = 0; xchs <= 1; xchs++)
{
for (double ychs = 0; ychs <= 1; ychs++)
{
for (double zchs = 0; zchs <= 1; zchs++)
{
// x-index of source child box at level l+1
double ix_chs = ix_s * 2 + xchs;
// y-index of source child box at level l+1
double iy_chs = iy_s * 2 + ychs;
// z-index of source child box at level l+1
double iz_chs = iz_s * 2 + zchs;
//Find indices of basis functions in source child box
List<int> m = new List<int>();
for (int i = 0; i < basicFuncBoxes.X.RowCount; i++)
{
if (basicFuncBoxes.X[i, l] == ix_chs && basicFuncBoxes.Y[i, l] == iy_chs && basicFuncBoxes.Z[i, l] == iz_chs)
{
m.Add(i);
}
}
if (m.Count == 0)
{
continue;
}
//Subdivide field box and process children
for (double xchf = 0; xchf <= 1; xchf++)
{
for (double ychf = 0; ychf <= 1; ychf++)
{
for (double zchf = 0; zchf <= 1; zchf++)
{
//x-index of field child box at level l+1
double ix_chf = ix_f * 2 + xchf;
// y-index of field child box at level l+1
double iy_chf = iy_f * 2 + ychf;
// z-index of field child box at level l+1
double iz_chf = iz_f * 2 + zchf;
//Find indices of testing functions in field child box
List<int> n = new List<int>();
for (int i = 0; i < basicFuncBoxes.X.RowCount; i++)
{
if (basicFuncBoxes.X[i, l] == ix_chf && basicFuncBoxes.Y[i, l] == iy_chf && basicFuncBoxes.Z[i, l] == iz_chf)
{
n.Add(i);
}
}
if (n.Count == 0)
{
continue;
}
// Here we have a pair of non-empty source and field boxes
if (Math.Abs(ix_chs - ix_chf) > 1 || Math.Abs(iy_chs - iy_chf) > 1 || Math.Abs(iz_chs - iz_chf) > 1)
{// Far-field boxes
if (sym_source_field == true)
{
// Symmetric source-field field-source
// interactions are only computed once.
if (ix_chs - ix_chf > 0 || ix_chs - ix_chf == 0 && iy_chs - iy_chf > 0 || ix_chs - ix_chf == 0 && iy_chs - iy_chf == 0 && iz_chs - iz_chf > 0)
{
//[U,V] = ACA(ACA_thres, m,n, OG_data,EM_data);
DenseMatrix U = new DenseMatrix(1, 1);
DenseMatrix V = new DenseMatrix(1, 1);
Tuple<Matrix,Matrix> r = Aca(ACA_thres, m, n, U, V);
//Z_comp{length(Z_comp)+1} = struct('m',m,'n',n,'comp',1,'self',0,'Z',[] ,'U',U,'V',V);
Z_comp.Add(new ACAStruct(m,n,new DenseMatrix(1,1),r.Item1,r.Item2,1,0));
}
}
else
{
// We need to compute all because there is
// not symmetric interactions
DenseMatrix U = new DenseMatrix(1, 1);
DenseMatrix V = new DenseMatrix(1, 1);
//[U,V] = ACA(ACA_thres, m,n, OG_data,EM_data);
Tuple<Matrix, Matrix> r = Aca(ACA_thres, m, n, U, V);
//Z_comp{length(Z_comp)+1} = struct('m',m,'n',n,'comp',1,'self',0,'Z',[] ,'U',U,'V',V);
Z_comp.Add(new ACAStruct(m, n, new DenseMatrix(1, 1), r.Item1, r.Item2, 1, 0));
}
}
else // Near-field boxes
{
double self = 0;
if (l + 1 == L)
{
if (sym_source_field == true)
{
// Symmetric source-field field-source
// interactions are only computed once.
if (ix_chs - ix_chf == 0 && iy_chs - iy_chf == 0 && iz_chs - iz_chf == 0)
{
// Self-interactions
self = 1;
// Z_comp{length(Z_comp)+1} = struct('m',m,'n',n,'comp',0,'self',self,'Z', user_impedance(m,n,OG_data,EM_data),'U',[],'V',[]);
Z_comp.Add(new ACAStruct(m, n, UserImpedance(m, n), new DenseMatrix(1, 1), new DenseMatrix(1, 1), 0, self));
}
if (ix_chs - ix_chf > 0 || ix_chs - ix_chf == 0 && iy_chs - iy_chf > 0 || ix_chs - ix_chf == 0 && iy_chs - iy_chf == 0 && iz_chs - iz_chf > 0)
{
//Z_comp{length(Z_comp)+1} = struct('m',m,'n',n,'comp',0,'self',self,'Z', user_impedance(m,n,OG_data,EM_data),'U',[],'V',[]);
Z_comp.Add(new ACAStruct(m, n, UserImpedance(m, n), new DenseMatrix(1, 1), new DenseMatrix(1, 1), 0, self));
}
}
else
{
// We need to compute all because there are
// not symmetric interactions
if (ix_chs - ix_chf == 0 && iy_chs - iy_chf == 0 && iz_chs - iz_chf == 0)
{
// Self-interactions
self = 1;
}
//Z_comp{length(Z_comp)+1} = struct('m',m,'n',n,'comp',0,'self',self,'Z', user_impedance(m,n,OG_data,EM_data),'U',[],'V',[]);
Z_comp.Add(new ACAStruct(m, n, UserImpedance(m, n), new DenseMatrix(1, 1), new DenseMatrix(1, 1), 0, (int)self));
}
}
else
{
//Z_comp = [Z_comp multilevel_compress(basis_func_boxes,ix_chs,iy_chs,iz_chs,ix_chf,iy_chf,iz_chf,l+1,L,ACA_thres,OG_data,EM_data)];
//multilevel_compress(basis_func_boxes,ix_s,iy_s,iz_s,ix_f,iy_f,iz_f,l,L,ACA_thres,OG_data,EM_data)
MultilevelCompres(basicFuncBoxes,ix_chs,iy_chs,iz_chs,ix_chf,iy_chf,iz_chf,l+1,L,ACA_thres,ref Z_comp);
}
}
}
}
}
}
}
}
//return Z_comp;
}
/// <summary>
/// Compute indices of boxes at all levels for each basis function
/// </summary>
/// <param name="rcx">x-coordinates of basis functions centers</param>
/// <param name="rcy">y-coordinates of basis functions centers</param>
/// <param name="rcz">z-coordinates of basis functions centers</param>
/// <param name="N">Number of basis functions (length of rcx, rcy, and rcz)</param>
/// <param name="finest_level_size">size of finest level in multilevel subdivision</param>
/// <returns>
/// Matrix with one column per level in multilevel subdivision
/// Columns contain the box index in which a basis function is located Row index is the basis function index
/// </returns>
public static BasicFuncBoxes PrepareMultilevel(Vector rcx, Vector rcy, Vector rcz, int N, double finest_level_size)
{
double xmax = rcx.Max(); double xmin = rcx.Min();
double ymax = rcy.Max(); double ymin = rcy.Min();
double zmax = rcz.Max(); double zmin = rcz.Min();
int Lx = (int)Math.Ceiling(Math.Log((xmax - xmin) / (finest_level_size)) / Math.Log(2));
int Ly = (int)Math.Ceiling(Math.Log((ymax - ymin) / (finest_level_size)) / Math.Log(2));
int Lz = (int)Math.Ceiling(Math.Log((zmax - zmin) / (finest_level_size)) / Math.Log(2));
int L = (int)Math.Max(Lx, Math.Max(Ly, Lz));
double box_size_x = (xmax - xmin) * (1 + 1e-3);
double box_size_y = (ymax - ymin) * (1 + 1e-3);
double box_size_z = (zmax - zmin) * (1 + 1e-3);
double box_size = Math.Max(box_size_x, Math.Max(box_size_y, box_size_z));
BasicFuncBoxes basicFuncBoxes = new BasicFuncBoxes(N, L);
for (int i = 0; i < L; i++)
{
box_size = box_size / 2;
Vector tempVx = new DenseVector(rcx.Count);
for (int j = 0; j < rcx.Count; j++)
{
tempVx[j] = Math.Floor((rcx[j] - xmin) / box_size);
}
Vector tempVy = new DenseVector(rcy.Count);
for (int j = 0; j < rcy.Count; j++)
{
tempVy[j] = Math.Floor((rcy[j] - ymin) / box_size);
}
Vector tempVz = new DenseVector(rcz.Count);
for (int j = 0; j < rcz.Count; j++)
{
tempVz[j] = Math.Floor((rcz[j] - zmin) / box_size);
}
basicFuncBoxes.X.SetColumn(i, tempVx);
basicFuncBoxes.Y.SetColumn(i, tempVy);
basicFuncBoxes.Z.SetColumn(i, tempVz);
}
return basicFuncBoxes;
}
static void Main(string[] args)
{
BasicFuncBoxes b = new BasicFuncBoxes(10, 10);
double finest_level_size = 0.25; // Size of finest level (lambdas) of multilevel subdivision
double ACA_thres = 1e-3; // Relative error threshold to stop adding rows and columns in ACA iteration
double precon_radius = 0.15; // Precondioner size (meters): elements of Z with R < precon_radius
double tol = 1e-2; // Convergence tolerance in iterative solver
double maxN_Z = 5000;
StreamReader xRead = new StreamReader("X.txt");
StreamReader yRead = new StreamReader("Y.txt");
StreamReader zRead = new StreamReader("Z.txt");
StreamReader jRead = new StreamReader("J.txt");
Vector rcx;
Vector rcy;
Vector rcz;
String str = xRead.ReadToEnd();
List<double> lst = new List<double>();
foreach (string s in str.Split('\t'))
{
lst.Add(double.Parse(s));
}
rcx = new DenseVector(lst.ToArray());
str = yRead.ReadToEnd();
lst.Clear();
foreach (string s in str.Split('\t'))
{
lst.Add(double.Parse(s));
}
rcy = new DenseVector(lst.ToArray());
str = zRead.ReadToEnd();
lst.Clear();
foreach (string s in str.Split('\t'))
{
lst.Add(double.Parse(s));
}
rcz = new DenseVector(lst.ToArray());
int N = 3072;
//Fill Z matrix
if( N <= maxN_Z)
{
//Z = user_impedance(1:N, 1:N, OG_data,EM_data);
List<int> n = new List<int>(N);
for (int i = 0; i < N; i++)
{
n.Add(i);
}
Matrix Z = ACA.UserImpedance(n,n);
// Copy of uncompressed Z for iterative solver
//Z_uncomp = cell(1,1);
NewSparseMatrix Z_uncomp = new NewSparseMatrix();
Z_uncomp.Add(new ACAStruct(n, n, Z, new DenseMatrix(1, 1), new DenseMatrix(1, 1), 0, 1));
}
//CHECKED - OK everything before works well
BasicFuncBoxes bfb = ACA.PrepareMultilevel(rcx, rcy, rcz, N, finest_level_size);
NewSparseMatrix Z_comp = new NewSparseMatrix();
ACA.MultilevelCompres(bfb, 0, 0, 0, 0, 0, 0, 0, bfb.L, ACA_thres, ref Z_comp);
//testing Multiply(matvec in mathlab)
Vector J = new DenseVector(3072);
int k = 0;
while (jRead.EndOfStream == false)
{
string s = jRead.ReadLine();
string[] a = s.Split(' ');
int p = 3;
if (a.Length == 5) p = 2;
J[k] = double.Parse(a[p].Replace('.',','));
k++;
}
Vector r = Z_comp.Multiply(J, true);
}
