public static SparseMatrixComplex operator -(SparseMatrixComplex left, SparseMatrixComplex right)
{
SparseMatrixComplex result = new SparseMatrixComplex(right.rowCount, right.columnCount);
foreach (KeyValuePair <Pair, Complex> item in left.mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
result.mapData.Add(pair, value);
}
foreach (KeyValuePair <Pair, Complex> item in right.mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
if (result.mapData.ContainsKey(pair))
{
Complex temp = result.mapData[pair] -= item.Value;
if (temp.Equals(Complex.Zero))
{
result.mapData.Remove(pair);
}
}
else
{
result.mapData.Add(pair, value);
}
}
return(result);
}
public SparseMatrixComplex BuildEnergy()
{
//Build Laplace matrix
SparseMatrixDouble d0 = DECDouble.Instance.BuildExteriorDerivative0Form(mesh);;
SparseMatrixDouble star1 = DECDouble.Instance.BuildHodgeStar1Form(mesh);
SparseMatrixDouble L = d0.Transpose() * star1 * d0;
SparseMatrixComplex A = SparseMatrixComplex.Copy(ref L);
//Iterate faces
foreach (TriMesh.Face face in mesh.Faces)
{
//Iterate each halfedge in face
foreach (TriMesh.HalfEdge hf in face.Halfedges)
{
int i = hf.ToVertex.Index;
int j = hf.FromVertex.Index;
Complex value = 0.5 * DDGConstant;
A[i, j] -= value;
A[j, i] += value;
}
}
return(A);
}
public SparseMatrixComplex cBuildExteriorDerivative1Form(TriMesh mesh)
{
SparseMatrixComplex d1 = new SparseMatrixComplex(mesh.Faces.Count, mesh.Edges.Count);
foreach (TriMesh.Face face in mesh.Faces)
{
foreach (TriMesh.HalfEdge hf in face.Halfedges)
{
double s = 0;
if (hf.Edge.HalfEdge0 == hf)
{
s = -1;
}
else
{
s = 1;
}
d1[face.Index, hf.Edge.Index] = new Complex(s, 0);
}
}
return d1;
}
public static CholmodInfo cConverter(ref SparseMatrixComplex A, CholmodInfo.CholmodMatrixStorage storage)
{
CholmodInfo info = new CholmodInfo();
info.MatrixType = CholmodInfo.CholmodMatrixType.Sparse;
info.MatrixStorageType = storage;
info.MatrixStorageMethod = CholmodInfo.CholmodMatrixStoageMethod.Normal;
info.MatrixItemType = CholmodInfo.CholmodMatrixItemType.Complex;
info.RowCount = A.RowCount;
info.ColumnCount = A.ColumnCount;
switch (storage)
{
case CholmodInfo.CholmodMatrixStorage.CRS:
A.ToCRS(out info.colIndex, out info.rowIndex, out info.values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.CCS:
A.ToCCS(out info.colIndex, out info.rowIndex, out info.values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.Triplet:
A.ToTriplet(out info.colIndex, out info.rowIndex, out info.values, out info.z, out info.nnz);
break;
default:
A.ToTriplet(out info.colIndex, out info.rowIndex, out info.values, out info.z, out info.nnz);
break;
}
return(info);
}
/*
* For Complex Calculation
*/
public void FactorizationLU(ref SparseMatrixComplex A)
{
CholmodInfo cholmodA = CholmodConverter.cConverter(ref A,
CholmodInfo.CholmodMatrixStorage.CCS);
m = A.RowCount;
n = A.ColumnCount;
fixed(int *Index = cholmodA.rowIndex, Pt = cholmodA.colIndex)
fixed(double *val = cholmodA.values)
{
solver = CreateSolverLUUMFPACK_CCS_Complex(cholmodA.RowCount,
cholmodA.ColumnCount,
cholmodA.nnz,
Index,
Pt,
val
);
}
if (solver == null)
{
throw new Exception("Create Solver Fail");
}
}
public double cResidual(ref SparseMatrixComplex A, ref DenseMatrixComplex b, ref DenseMatrixComplex x)
{
DenseMatrixComplex errors = (A * x - b);
double norm = errors.InifnityNorm() / x.InifnityNorm();
return(norm);
}
public DenseMatrixComplex smallestEigPositiveDefinite(ref SparseMatrixComplex A, ref SparseMatrixComplex B, ref DenseMatrixComplex x)
{
LinearSystemGenericByLib.Instance.FactorizationLU(ref A);
int n = A.Length();
DenseMatrixComplex e = new DenseMatrixComplex(n, 1);
e.Fill(new Complex(1, 0));
Complex dot = e.Dot(B * e);
double norm = Math.Sqrt(dot.Norm());
e /= new Complex(norm, 0);
//Iteratation
for (int i = 0; i < MaxEigIter; i++)
{
x = B * x;
x = LinearSystemGenericByLib.Instance.SolveByFactorizedLU(ref x);
x -= x.Dot(B * e) * e;
double newNorm = Math.Sqrt(x.Dot(B * x).Norm());
x /= new Complex(newNorm, 0);
}
LinearSystemGenericByLib.Instance.FreeSolverLUComplex();
return(x);
}
public DenseMatrixComplex SolveLinerSystem(ref SparseMatrixComplex A, ref DenseMatrixComplex b)
{
if (A.RowCount != b.RowCount)
{
throw new Exception("The dimension of A and b must be agree");
}
CholmodInfo cholmodb = CholmodConverter.cConverter(ref b);
CholmodInfo cholmodA = CholmodConverter.cConverter(ref A, CholmodInfo.CholmodMatrixStorage.CCS);
double[] x = new double[2 * A.ColumnCount];
fixed(int *Index = cholmodA.rowIndex, Pt = cholmodA.colIndex)
fixed(double *val = cholmodA.values, bp = cholmodb.values, xx = x)
{
SolveRealByQR_CCS_Complex(cholmodA.RowCount,
cholmodA.ColumnCount,
cholmodA.nnz,
Pt, //Column Pointer
Index, //Row Index
val,
xx,
bp);
}
DenseMatrixComplex unknown = CholmodConverter.cConvertArrayToDenseMatrix(ref x, x.Length, 1);
cholmodA = null;
cholmodb = null;
GC.Collect();
return(unknown);
}
public SparseMatrixComplex cBuildExteriorDerivative1Form(TriMesh mesh)
{
SparseMatrixComplex d1 = new SparseMatrixComplex(mesh.Faces.Count, mesh.Edges.Count);
foreach (TriMesh.Face face in mesh.Faces)
{
foreach (TriMesh.HalfEdge hf in face.Halfedges)
{
double s = 0;
if (hf.Edge.HalfEdge0 == hf)
{
s = -1;
}
else
{
s = 1;
}
d1[face.Index, hf.Edge.Index] = new Complex(s, 0);
}
}
return(d1);
}
public void FlattenProcess()
{
SparseMatrixComplex Lc = BuildEnergy();
SparseMatrixComplex star0 = DECComplex.Instance.cBuildHodgeStar0Form(mesh);
Lc += new Complex(1.0e-8, 0) * star0; //[Reconsider: Complex(1.0e-8)]
//Compute parameterization
DenseMatrixComplex x = new DenseMatrixComplex(Lc.RowCount, 1);
x.Randomize(); //Initial guesses
DenseMatrixComplex result = LinearSystemDEC.Instance.smallestEigPositiveDefinite(ref Lc, ref star0, ref x);
//Assign sultion
foreach (TriMesh.Vertex v in mesh.Vertices)
{
Complex value = result[v.Index, 0];
v.Traits.Position.x = value.RealPart;
v.Traits.Position.y = value.ImagePart;
v.Traits.Position.z = 0;
}
TriMeshUtil.ScaleToUnit(mesh, 1.0);
TriMeshUtil.MoveToCenter(mesh);
}
public DenseMatrixComplex smallestEigPositiveDefinite(ref SparseMatrixComplex A, bool ignoreConstantVector)
{
ignoreConstantVector = true;
DenseMatrixComplex x = new DenseMatrixComplex();
return(x);
}
public static SparseMatrixComplex Copy(ref SparseMatrixComplex B)
{
Dictionary <Pair, Complex> newData = new Dictionary <Pair, Complex>(B.mapData);
SparseMatrixComplex newMatrix = new SparseMatrixComplex(B.rowCount, B.columnCount);
newMatrix.mapData = newData;
return(newMatrix);
}
public SparseMatrixComplex SubMatrix(int rowStart, int rowEnd, int columnStart, int columnEnd)
{
if (rowEnd < rowStart || columnEnd < columnStart)
{
throw new ArgumentOutOfRangeException();
}
int rows = rowEnd - rowStart + 1;
int columns = columnEnd - columnStart + 1;
SparseMatrixComplex subMatrix = new SparseMatrixComplex(rows, columns);
int subMatrixEntiries = rows * columns;
if (subMatrixEntiries < mapData.Count)
{
for (int i = 0; i < rows; i++)
{
int rowInx = i + rowStart;
for (int j = 0; j < columns; j++)
{
int columnInx = j + columnStart;
Pair pair = new Pair(rowInx, columnInx);
if (!mapData.ContainsKey(pair))
{
continue;
}
Pair subPair = new Pair(i, j);
subMatrix.mapData[subPair] = mapData[pair];
}
}
}
else if (subMatrixEntiries >= mapData.Count)
{
foreach (KeyValuePair <Pair, Complex> item in mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
int m = pair.Key;
int n = pair.Value;
if ((m >= rowStart && m <= rowEnd) && (n >= columnStart && m <= columnEnd))
{
int i = m - rowStart;
int j = n - columnStart;
subMatrix.mapData[new Pair(i, j)] = value;
}
}
}
return(subMatrix);
}
public static SparseMatrixComplex Identity(int N)
{
SparseMatrixComplex identity = new SparseMatrixComplex(N, N);
for (int i = 0; i < N; i++)
{
identity.mapData.Add(new Pair(i, i), Complex.Identity);
}
return(identity);
}
public SparseMatrixComplex cBuildHodgeStar0Form(TriMesh mesh)
{
SparseMatrixComplex star0 = new SparseMatrixComplex(mesh.Vertices.Count, mesh.Vertices.Count);
foreach (TriMesh.Vertex vertex in mesh.Vertices)
{
Complex value = new Complex(ComputeVertexDualArea(vertex), 0);
star0[vertex.Index, vertex.Index] = value;
}
return(star0);
}
public static SparseMatrixComplex operator *(Complex left, SparseMatrixComplex right)
{
SparseMatrixComplex result = new SparseMatrixComplex(right.rowCount, right.columnCount);
foreach (KeyValuePair <Pair, Complex> item in right.mapData)
{
Pair pair = item.Key;
Complex value = left * item.Value;
result.mapData.Add(pair, value);
}
return(result);
}
public SparseMatrixComplex cBuildHodgeStar2Form(TriMesh mesh)
{
SparseMatrixComplex star2 = new SparseMatrixComplex(mesh.Faces.Count, mesh.Faces.Count);
foreach (TriMesh.Face face in mesh.Faces)
{
Complex value = new Complex(1 / TriMeshUtil.ComputeAreaFace(face), 0);
star2[face.Index, face.Index] = value;
}
return(star2);
}
public static SparseMatrixComplex operator *(Complex left, SparseMatrixComplex right)
{
SparseMatrixComplex result = new SparseMatrixComplex(right.rowCount, right.columnCount);
foreach (KeyValuePair<Pair, Complex> item in right.mapData)
{
Pair pair = item.Key;
Complex value = left * item.Value;
result.mapData.Add(pair, value);
}
return result;
}
public SparseMatrixComplex Transpose()
{
SparseMatrixComplex trMatrix = new SparseMatrixComplex(this.columnCount, this.rowCount);
foreach (KeyValuePair <Pair, Complex> item in mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
trMatrix.mapData[new Pair(pair.Value, pair.Key)] = value;
}
return(trMatrix);
}
public SparseMatrixComplex cBuildExteriorDerivative0Form(TriMesh mesh)
{
SparseMatrixComplex d0 = new SparseMatrixComplex(mesh.Edges.Count, mesh.Vertices.Count);
foreach (TriMesh.Edge edge in mesh.Edges)
{
int ci = edge.HalfEdge0.FromVertex.Index;
int cj = edge.HalfEdge0.ToVertex.Index;
d0[edge.Index, ci] = new Complex(1, 0);
d0[edge.Index, cj] = new Complex(-1, 0);
}
return(d0);
}
public SparseMatrixComplex cBuildExteriorDerivative0Form(TriMesh mesh)
{
SparseMatrixComplex d0 = new SparseMatrixComplex(mesh.Edges.Count, mesh.Vertices.Count);
foreach (TriMesh.Edge edge in mesh.Edges)
{
int ci = edge.HalfEdge0.FromVertex.Index;
int cj = edge.HalfEdge0.ToVertex.Index;
d0[edge.Index, ci] = new Complex(1, 0);
d0[edge.Index, cj] = new Complex(-1, 0);
}
return d0;
}
public SparseMatrixComplex cBuildHodgeStar1Form(TriMesh mesh)
{
SparseMatrixComplex star1 = new SparseMatrixComplex(mesh.Edges.Count, mesh.Edges.Count);
foreach (TriMesh.Edge edge in mesh.Edges)
{
double cotAlpha = ComputeTan(edge.HalfEdge0);
double cotBeta = ComputeTan(edge.HalfEdge1);
Complex value = new Complex((cotAlpha + cotBeta) / 2, 0);
star1[edge.Index, edge.Index] = value;
}
return(star1);
}
public static SparseMatrixComplex Copy(ref SparseMatrixDouble B)
{
//We only copy of realpart
Dictionary <Pair, Complex> newData = new Dictionary <Pair, Complex>();
foreach (KeyValuePair <Pair, double> e in B.Datas)
{
Pair pair = e.Key;
double value = e.Value;
newData.Add(pair, new Complex(value, 0));
}
SparseMatrixComplex newMatrix = new SparseMatrixComplex(B.RowCount, B.ColumnCount);
newMatrix.mapData = newData;
return(newMatrix);
}
public SparseMatrixComplex cBuildHodgeStar2Form(TriMesh mesh)
{
SparseMatrixComplex star2 = new SparseMatrixComplex(mesh.Faces.Count, mesh.Faces.Count);
foreach (TriMesh.Face face in mesh.Faces)
{
Complex value = new Complex(1 / TriMeshUtil.ComputeAreaFace(face), 0);
star2[face.Index, face.Index] = value;
}
return star2;
}
public static CholmodInfo cConverter(ref SparseMatrixComplex A, CholmodInfo.CholmodMatrixStorage storage)
{
CholmodInfo info = new CholmodInfo();
info.MatrixType = CholmodInfo.CholmodMatrixType.Sparse;
info.MatrixStorageType = storage;
info.MatrixStorageMethod = CholmodInfo.CholmodMatrixStoageMethod.Normal;
info.MatrixItemType = CholmodInfo.CholmodMatrixItemType.Complex;
info.RowCount = A.RowCount;
info.ColumnCount = A.ColumnCount;
switch (storage)
{
case CholmodInfo.CholmodMatrixStorage.CRS:
A.ToCRS(out info.colIndex, out info.rowIndex, out info.values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.CCS:
A.ToCCS(out info.colIndex, out info.rowIndex, out info.values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.Triplet:
A.ToTriplet(out info.colIndex, out info.rowIndex, out info.values, out info.z, out info.nnz);
break;
default:
A.ToTriplet(out info.colIndex, out info.rowIndex, out info.values, out info.z, out info.nnz);
break;
}
return info;
}
public static CholmodInfo cConverter(ref SparseMatrixComplex A, CholmodInfo.CholmodMatrixStorage storage, CholmodInfo.CholmodMatrixStoageMethod method)
{
CholmodInfo info = new CholmodInfo();
info.MatrixType = CholmodInfo.CholmodMatrixType.Sparse;
info.MatrixStorageType = storage;
info.MatrixStorageMethod = method;
info.MatrixItemType = CholmodInfo.CholmodMatrixItemType.Complex;
info.RowCount = A.RowCount;
info.ColumnCount = A.ColumnCount;
double[] values = null;
switch (storage)
{
case CholmodInfo.CholmodMatrixStorage.CRS:
A.ToCRS(out info.colIndex, out info.rowIndex, out values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.CCS:
A.ToCCS(out info.colIndex, out info.rowIndex, out values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.Triplet:
A.ToTriplet(out info.colIndex, out info.rowIndex, out values, out info.z, out info.nnz);
break;
default:
A.ToTriplet(out info.colIndex, out info.rowIndex, out values, out info.z, out info.nnz);
break;
}
switch (method)
{
case CholmodInfo.CholmodMatrixStoageMethod.Normal:
info.values = values;
break;
case CholmodInfo.CholmodMatrixStoageMethod.Divided:
double[] realParts = new double[info.nnz];
double[] imgParts = new double[info.nnz];
for (int i = 0; i < info.nnz; i++)
{
realParts[i] = values[2 * i];
imgParts[i] = values[2 * i + 1];
}
info.values = realParts;
info.z = imgParts;
values = null;
break;
default:
break;
}
GC.Collect();
return info;
}
public static SparseMatrixComplex operator *(SparseMatrixComplex left, SparseMatrixComplex right)
{
//Make sure matrix dimensions are equal
if (left.columnCount != right.rowCount)
{
throw new Exception("The dimension of two matrix must be equal");
}
SparseMatrixComplex result = new SparseMatrixComplex(left.rowCount, right.columnCount);
int leftNNZ = left.mapData.Count;
int rightNNZ = right.mapData.Count;
#region Left < Right
//We use right as stardand sight
//if (leftNNZ < rightNNZ)
//{
//Connection nonezero for each row of matrix a
List <KeyValuePair <int, Complex> >[] bRows = new List <KeyValuePair <int, Complex> > [right.rowCount];
for (int i = 0; i < bRows.Length; i++)
{
bRows[i] = new List <KeyValuePair <int, Complex> >();
}
foreach (KeyValuePair <Pair, Complex> item in right.mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
bRows[pair.Key].Add(new KeyValuePair <int, Complex>(pair.Value, value));
}
//Compute C = A*B
foreach (KeyValuePair <Pair, Complex> item in left.mapData)
{
Pair pair = item.Key;
int mA = pair.Key;
int nA = pair.Value;
Complex value = item.Value;
List <KeyValuePair <int, Complex> > bRow = bRows[nA];
for (int i = 0; i < bRow.Count; i++)
{
int k = bRow[i].Key;
Pair pair2 = new Pair(mA, k);
if (result.mapData.ContainsKey(pair2))
{
result.mapData[pair2] += value * bRow[i].Value;
}
else
{
result.mapData.Add(pair2, value * bRow[i].Value);
}
}
}
//}
#endregion
#region Right < Left
//else if (leftNNZ > rightNNZ)
//{
// //Connection nonezero for each row of matrix a
// List<KeyValuePair<int, double>>[] aCols = new List<KeyValuePair<int, double>>[left.columnCount];
// for (int i = 0; i < aCols.Length; i++)
// {
// aCols[i] = new List<KeyValuePair<int, double>>();
// }
// foreach (KeyValuePair<Pair, double> item in left.mapData)
// {
// Pair pair = item.Key;
// double value = item.Value;
// aCols[pair.Value].Add(new KeyValuePair<int, double>(pair.Key, value));
// }
// //Compute C = A*B
// foreach (KeyValuePair<Pair, double> item in right.mapData)
// {
// Pair pair = item.Key;
// int mA = pair.Key;
// int nA = pair.Value;
// double value = item.Value;
// List<KeyValuePair<int, double>> aCol = aCols[mA];
// for (int i = 0; i < aCol.Count; i++)
// {
// int k = aCol[i].Key;
// Pair pair2 = new Pair(k, nA);
// if (result.mapData.ContainsKey(pair2))
// {
// result.mapData[pair2] += value * aCol[i].Value;
// }
// else
// {
// result.mapData.Add(pair2, value * aCol[i].Value);
// }
// }
// }
//}
#endregion
return(result);
}
public SparseMatrixComplex(SparseMatrixComplex matrix)
{
mapData = new Dictionary <Pair, Complex>(matrix.mapData);
this.rowCount = matrix.rowCount;
this.columnCount = matrix.columnCount;
}
public SparseMatrixComplex(SparseMatrixComplex matrix)
{
mapData = new Dictionary<Pair, Complex>(matrix.mapData);
this.rowCount = matrix.rowCount;
this.columnCount = matrix.columnCount;
}
public static SparseMatrixComplex operator *(SparseMatrixComplex left, SparseMatrixComplex right)
{
//Make sure matrix dimensions are equal
if (left.columnCount != right.rowCount)
{
throw new Exception("The dimension of two matrix must be equal");
}
SparseMatrixComplex result = new SparseMatrixComplex(left.rowCount, right.columnCount);
int leftNNZ = left.mapData.Count;
int rightNNZ = right.mapData.Count;
#region Left < Right
//We use right as stardand sight
//if (leftNNZ < rightNNZ)
//{
//Connection nonezero for each row of matrix a
List<KeyValuePair<int, Complex>>[] bRows = new List<KeyValuePair<int, Complex>>[right.rowCount];
for (int i = 0; i < bRows.Length; i++)
{
bRows[i] = new List<KeyValuePair<int, Complex>>();
}
foreach (KeyValuePair<Pair, Complex> item in right.mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
bRows[pair.Key].Add(new KeyValuePair<int, Complex>(pair.Value, value));
}
//Compute C = A*B
foreach (KeyValuePair<Pair, Complex> item in left.mapData)
{
Pair pair = item.Key;
int mA = pair.Key;
int nA = pair.Value;
Complex value = item.Value;
List<KeyValuePair<int, Complex>> bRow = bRows[nA];
for (int i = 0; i < bRow.Count; i++)
{
int k = bRow[i].Key;
Pair pair2 = new Pair(mA, k);
if (result.mapData.ContainsKey(pair2))
{
result.mapData[pair2] += value * bRow[i].Value;
}
else
{
result.mapData.Add(pair2, value * bRow[i].Value);
}
}
}
//}
#endregion
#region Right < Left
//else if (leftNNZ > rightNNZ)
//{
// //Connection nonezero for each row of matrix a
// List<KeyValuePair<int, double>>[] aCols = new List<KeyValuePair<int, double>>[left.columnCount];
// for (int i = 0; i < aCols.Length; i++)
// {
// aCols[i] = new List<KeyValuePair<int, double>>();
// }
// foreach (KeyValuePair<Pair, double> item in left.mapData)
// {
// Pair pair = item.Key;
// double value = item.Value;
// aCols[pair.Value].Add(new KeyValuePair<int, double>(pair.Key, value));
// }
// //Compute C = A*B
// foreach (KeyValuePair<Pair, double> item in right.mapData)
// {
// Pair pair = item.Key;
// int mA = pair.Key;
// int nA = pair.Value;
// double value = item.Value;
// List<KeyValuePair<int, double>> aCol = aCols[mA];
// for (int i = 0; i < aCol.Count; i++)
// {
// int k = aCol[i].Key;
// Pair pair2 = new Pair(k, nA);
// if (result.mapData.ContainsKey(pair2))
// {
// result.mapData[pair2] += value * aCol[i].Value;
// }
// else
// {
// result.mapData.Add(pair2, value * aCol[i].Value);
// }
// }
// }
//}
#endregion
return result;
}
/*
* For Complex Calculation
*/
public void FactorizationLU(ref SparseMatrixComplex A)
{
CholmodInfo cholmodA = CholmodConverter.cConverter(ref A,
CholmodInfo.CholmodMatrixStorage.CCS);
m = A.RowCount;
n = A.ColumnCount;
fixed (int* Index = cholmodA.rowIndex, Pt = cholmodA.colIndex)
fixed (double* val = cholmodA.values)
{
solver = CreateSolverLUUMFPACK_CCS_Complex(cholmodA.RowCount,
cholmodA.ColumnCount,
cholmodA.nnz,
Index,
Pt,
val
);
}
if (solver == null) throw new Exception("Create Solver Fail");
}
public DenseMatrixComplex SolveLinerSystem(ref SparseMatrixComplex A, ref DenseMatrixComplex b)
{
if (A.RowCount != b.RowCount)
{
throw new Exception("The dimension of A and b must be agree");
}
CholmodInfo cholmodb = CholmodConverter.cConverter(ref b);
CholmodInfo cholmodA = CholmodConverter.cConverter(ref A, CholmodInfo.CholmodMatrixStorage.CCS);
double[] x = new double[2 * A.ColumnCount];
fixed (int* Index = cholmodA.rowIndex, Pt = cholmodA.colIndex)
fixed (double* val = cholmodA.values, bp = cholmodb.values, xx = x)
{
SolveRealByQR_CCS_Complex(cholmodA.RowCount,
cholmodA.ColumnCount,
cholmodA.nnz,
Pt, //Column Pointer
Index, //Row Index
val,
xx,
bp);
}
DenseMatrixComplex unknown = CholmodConverter.cConvertArrayToDenseMatrix(ref x, x.Length, 1);
cholmodA = null;
cholmodb = null;
GC.Collect();
return unknown;
}
public static CholmodInfo cConverter(ref SparseMatrixComplex A, CholmodInfo.CholmodMatrixStorage storage, CholmodInfo.CholmodMatrixStoageMethod method)
{
CholmodInfo info = new CholmodInfo();
info.MatrixType = CholmodInfo.CholmodMatrixType.Sparse;
info.MatrixStorageType = storage;
info.MatrixStorageMethod = method;
info.MatrixItemType = CholmodInfo.CholmodMatrixItemType.Complex;
info.RowCount = A.RowCount;
info.ColumnCount = A.ColumnCount;
double[] values = null;
switch (storage)
{
case CholmodInfo.CholmodMatrixStorage.CRS:
A.ToCRS(out info.colIndex, out info.rowIndex, out values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.CCS:
A.ToCCS(out info.colIndex, out info.rowIndex, out values, out info.nnz);
break;
case CholmodInfo.CholmodMatrixStorage.Triplet:
A.ToTriplet(out info.colIndex, out info.rowIndex, out values, out info.z, out info.nnz);
break;
default:
A.ToTriplet(out info.colIndex, out info.rowIndex, out values, out info.z, out info.nnz);
break;
}
switch (method)
{
case CholmodInfo.CholmodMatrixStoageMethod.Normal:
info.values = values;
break;
case CholmodInfo.CholmodMatrixStoageMethod.Divided:
double[] realParts = new double[info.nnz];
double[] imgParts = new double[info.nnz];
for (int i = 0; i < info.nnz; i++)
{
realParts[i] = values[2 * i];
imgParts[i] = values[2 * i + 1];
}
info.values = realParts;
info.z = imgParts;
values = null;
break;
default:
break;
}
GC.Collect();
return(info);
}
public static SparseMatrixComplex Copy(ref SparseMatrixComplex B)
{
Dictionary<Pair, Complex> newData = new Dictionary<Pair, Complex>(B.mapData);
SparseMatrixComplex newMatrix = new SparseMatrixComplex(B.rowCount, B.columnCount);
newMatrix.mapData = newData;
return newMatrix;
}
public static SparseMatrixComplex Copy(ref SparseMatrixDouble B)
{
//We only copy of realpart
Dictionary<Pair, Complex> newData = new Dictionary<Pair, Complex>();
foreach (KeyValuePair<Pair, double> e in B.Datas)
{
Pair pair = e.Key;
double value = e.Value;
newData.Add(pair, new Complex(value, 0));
}
SparseMatrixComplex newMatrix = new SparseMatrixComplex(B.RowCount, B.ColumnCount);
newMatrix.mapData = newData;
return newMatrix;
}
public static SparseMatrixComplex Identity(int N)
{
SparseMatrixComplex identity = new SparseMatrixComplex(N, N);
for (int i = 0; i < N; i++)
{
identity.mapData.Add(new Pair(i, i), Complex.Identity);
}
return identity;
}
public SparseMatrixComplex cBuildHodgeStar0Form(TriMesh mesh)
{
SparseMatrixComplex star0 = new SparseMatrixComplex(mesh.Vertices.Count, mesh.Vertices.Count);
foreach (TriMesh.Vertex vertex in mesh.Vertices)
{
Complex value = new Complex(ComputeVertexDualArea(vertex), 0);
star0[vertex.Index, vertex.Index] = value;
}
return star0;
}
public static SparseMatrixComplex operator -(SparseMatrixComplex left, SparseMatrixComplex right)
{
SparseMatrixComplex result = new SparseMatrixComplex(right.rowCount, right.columnCount);
foreach (KeyValuePair<Pair, Complex> item in left.mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
result.mapData.Add(pair, value);
}
foreach (KeyValuePair<Pair, Complex> item in right.mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
if (result.mapData.ContainsKey(pair))
{
Complex temp = result.mapData[pair] -= item.Value;
if (temp.Equals(Complex.Zero))
{
result.mapData.Remove(pair);
}
}
else
{
result.mapData.Add(pair, value);
}
}
return result;
}
public SparseMatrixComplex SubMatrix(int rowStart, int rowEnd, int columnStart, int columnEnd)
{
if (rowEnd < rowStart || columnEnd < columnStart)
{
throw new ArgumentOutOfRangeException();
}
int rows = rowEnd - rowStart + 1;
int columns = columnEnd - columnStart + 1;
SparseMatrixComplex subMatrix = new SparseMatrixComplex(rows, columns);
int subMatrixEntiries = rows * columns;
if (subMatrixEntiries < mapData.Count)
{
for (int i = 0; i < rows; i++)
{
int rowInx = i + rowStart;
for (int j = 0; j < columns; j++)
{
int columnInx = j + columnStart;
Pair pair = new Pair(rowInx, columnInx);
if (!mapData.ContainsKey(pair))
{
continue;
}
Pair subPair = new Pair(i, j);
subMatrix.mapData[subPair] = mapData[pair];
}
}
}
else if (subMatrixEntiries >= mapData.Count)
{
foreach (KeyValuePair<Pair, Complex> item in mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
int m = pair.Key;
int n = pair.Value;
if ((m >= rowStart && m <= rowEnd) && (n >= columnStart && m <= columnEnd))
{
int i = m - rowStart;
int j = n - columnStart;
subMatrix.mapData[new Pair(i, j)] = value;
}
}
}
return subMatrix;
}
public SparseMatrixComplex cBuildHodgeStar1Form(TriMesh mesh)
{
SparseMatrixComplex star1 = new SparseMatrixComplex(mesh.Edges.Count, mesh.Edges.Count);
foreach (TriMesh.Edge edge in mesh.Edges)
{
double cotAlpha = ComputeTan(edge.HalfEdge0);
double cotBeta = ComputeTan(edge.HalfEdge1);
Complex value = new Complex((cotAlpha + cotBeta) / 2, 0);
star1[edge.Index, edge.Index] = value;
}
return star1;
}
public SparseMatrixComplex Transpose()
{
SparseMatrixComplex trMatrix = new SparseMatrixComplex(this.columnCount, this.rowCount);
foreach (KeyValuePair<Pair, Complex> item in mapData)
{
Pair pair = item.Key;
Complex value = item.Value;
trMatrix.mapData[new Pair(pair.Value, pair.Key)] = value;
}
return trMatrix;
}