public static SparseMatrix CreateMatrixATA(ref SparseMatrix A,ref NonManifoldMesh mesh)
{
// assume A is sorted
// assume values in parameter adj is in order
if (A == null)
throw new Exception("A matrix is null");
int[][] adj = MeshOperators.BuildTwoRingVV(ref mesh).GetRowIndex();
int n = A.ColumnSize;
SparseMatrix ATA = new SparseMatrix(n, n);
for (int i = 0; i < n; i++)
{
List<SparseMatrix.Element> col1 = A.GetColumn(i);
foreach (int j in adj[i])
{
List<SparseMatrix.Element> col2 = A.GetColumn(j);
int c1 = 0, c2 = 0;
double sum = 0.0;
bool used = false;
while (c1 < col1.Count && c2 < col2.Count)
{
if (col1[c1].i < col2[c2].i) { c1++; continue; }
if (col1[c1].i > col2[c2].i) { c2++; continue; }
sum += col1[c1].value * col2[c2].value;
used = true;
c1++;
c2++;
}
if (used)
ATA.AddElement(i, j, sum);
}
}
if (ATA.IsSymmetric() == false) throw new Exception("ATA is not symmetric!!");
return ATA;
}
public SparseMatrix ConvertToSparse(double[,] i, double[,] j,double[,] value,int row,int col)
{
SparseMatrix sparse = new SparseMatrix(row, col);
for(int k=0;k<i.Length;k++)
{
int r = (int)i[k, 0] - 1;
int c = (int)j[k, 0] - 1;
sparse.AddElement(r,c, value[k,0]);
// Console.WriteLine("{0}--{1}--{2}", r,c, value[k, 0]);
}
return sparse;
}
public SparseMatrix Convert()
{
SparseMatrix result = new SparseMatrix(this.RowCount, this.ColumnCount);
foreach (KeyValuePair<Pair, double> item in this.mapData)
{
Pair pair = item.Key;
double value = item.Value;
result.AddElement(pair.Key,pair.Value, value);
}
return result;
}
private SparseMatrix BuildMatrixA_old(List <VertexRecord> records, int[] faceIndex, double[] lapWeight, double[] posWeight)
{
// build backward map
int[] map = new int[mesh.VertexCount];
for (int i = 0; i < records.Count; i++)
{
map[records[i].index] = i;
}
int n = records.Count;
int fn = faceIndex.Length / 3;
SparseMatrix A = new SparseMatrix(2 * n, n);
for (int i = 0, j = 0; i < fn; i++, j += 3)
{
int c1 = faceIndex[j];
int c2 = faceIndex[j + 1];
int c3 = faceIndex[j + 2];
Vector3d v1 = new Vector3d(mesh.VertexPos, c1 * 3);
Vector3d v2 = new Vector3d(mesh.VertexPos, c2 * 3);
Vector3d v3 = new Vector3d(mesh.VertexPos, c3 * 3);
double cot1 = (v2 - v1).Dot(v3 - v1) / (v2 - v1).Cross(v3 - v1).Length();
double cot2 = (v3 - v2).Dot(v1 - v2) / (v3 - v2).Cross(v1 - v2).Length();
double cot3 = (v1 - v3).Dot(v2 - v3) / (v1 - v3).Cross(v2 - v3).Length();
//cot1 = cot2 = cot3 = 1.0;
if (double.IsNaN(cot1))
{
throw new Exception();
}
if (double.IsNaN(cot2))
{
throw new Exception();
}
if (double.IsNaN(cot3))
{
throw new Exception();
}
c1 = map[c1];
c2 = map[c2];
c3 = map[c3];
A.AddValueTo(c2, c2, -cot1); A.AddValueTo(c2, c3, cot1);
A.AddValueTo(c3, c3, -cot1); A.AddValueTo(c3, c2, cot1);
A.AddValueTo(c3, c3, -cot2); A.AddValueTo(c3, c1, cot2);
A.AddValueTo(c1, c1, -cot2); A.AddValueTo(c1, c3, cot2);
A.AddValueTo(c1, c1, -cot3); A.AddValueTo(c1, c2, cot3);
A.AddValueTo(c2, c2, -cot3); A.AddValueTo(c2, c1, cot3);
}
for (int i = 0; i < n; i++)
{
double tot = 0;
foreach (SparseMatrix.Element e in A.Rows[i])
{
if (e.i != e.j)
{
tot += e.value;
}
}
if (tot > 10000)
{
foreach (SparseMatrix.Element e in A.Rows[i])
{
e.value /= (tot / 10000);
}
}
foreach (SparseMatrix.Element e in A.Rows[i])
{
e.value *= lapWeight[records[i].index];
}
}
// positional constraints
for (int i = 0; i < n; i++)
{
A.AddElement(i + n, i, posWeight[records[i].index]);
}
A.SortElement();
return(A);
}
private ColMatrix BuildMatrixA(Resolution r, double[] lapWeight, double[] posWeight)
{
// build backward map
int[] map = new int[mesh.VertexCount];
for (int i = 0; i < r.vertexList.Length; i++)
{
map[r.vertexList[i]] = i;
}
int n = r.vertexList.Length;
int fn = r.faceList.Length / 3;
SparseMatrix A = new SparseMatrix(2 * n, n);
for (int i = 0, j = 0; i < fn; i++, j += 3)
{
int c1 = r.faceList[j];
int c2 = r.faceList[j + 1];
int c3 = r.faceList[j + 2];
Vector3d v1 = new Vector3d(mesh.VertexPos, c1 * 3);
Vector3d v2 = new Vector3d(mesh.VertexPos, c2 * 3);
Vector3d v3 = new Vector3d(mesh.VertexPos, c3 * 3);
double cot1 = (v2 - v1).Dot(v3 - v1) / (v2 - v1).Cross(v3 - v1).Length();
double cot2 = (v3 - v2).Dot(v1 - v2) / (v3 - v2).Cross(v1 - v2).Length();
double cot3 = (v1 - v3).Dot(v2 - v3) / (v1 - v3).Cross(v2 - v3).Length();
//cot1 = cot2 = cot3 = 1.0;
if (double.IsNaN(cot1))
{
throw new Exception();
}
if (double.IsNaN(cot2))
{
throw new Exception();
}
if (double.IsNaN(cot3))
{
throw new Exception();
}
c1 = map[c1];
c2 = map[c2];
c3 = map[c3];
A.AddValueTo(c2, c2, -cot1); A.AddValueTo(c2, c3, cot1);
A.AddValueTo(c3, c3, -cot1); A.AddValueTo(c3, c2, cot1);
A.AddValueTo(c3, c3, -cot2); A.AddValueTo(c3, c1, cot2);
A.AddValueTo(c1, c1, -cot2); A.AddValueTo(c1, c3, cot2);
A.AddValueTo(c1, c1, -cot3); A.AddValueTo(c1, c2, cot3);
A.AddValueTo(c2, c2, -cot3); A.AddValueTo(c2, c1, cot3);
}
for (int i = 0; i < n; i++)
{
double tot = 0;
foreach (SparseMatrix.Element e in A.Rows[i])
{
if (e.i != e.j)
{
tot += e.value;
}
}
if (tot > 10000)
{
foreach (SparseMatrix.Element e in A.Rows[i])
{
e.value /= (tot / 10000);
}
}
foreach (SparseMatrix.Element e in A.Rows[i])
{
e.value *= lapWeight[r.vertexList[i]];
}
}
// positional constraints
for (int i = 0; i < n; i++)
{
A.AddElement(i + n, i, posWeight[r.vertexList[i]]);
}
A.SortElement();
ColMatrixCreator cmA = new ColMatrixCreator(2 * n, n);
foreach (List <SparseMatrix.Element> row in A.Rows)
{
foreach (SparseMatrix.Element e in row)
{
cmA.AddValueTo(e.i, e.j, e.value);
}
}
return(cmA);
}