public static void test_SparseCG()
{
int N = 10;
SymmetricSparseMatrix M = new SymmetricSparseMatrix();
double[] B = new double[N];
for (int i = 0; i < N; ++i)
{
for (int j = i; j < N; ++j)
{
if (i == j)
{
M.Set(i, j, 1);
}
else
{
M.Set(i, j, (double)(i + j) / 100.0);
}
}
B[i] = i + 1;
}
double[] X = new double[N];
SparseSymmetricCG Solver = new SparseSymmetricCG()
{
B = B, MultiplyF = M.Multiply
};
Solver.Solve();
string s = "";
for (int i = 0; i < N; ++i)
{
s += " " + Solver.X[i];
}
System.Console.WriteLine(s);
}
// Result must be as large as Mesh.MaxVertexID
public bool Solve(Vector3D[] Result)
{
UpdateForSolve();
// use initial positions as initial solution.
Array.Copy(Px, Sx, N);
Array.Copy(Py, Sy, N);
Array.Copy(Pz, Sz, N);
Action <double[], double[]> CombinedMultiply = (X, B) => {
M.Multiply(X, B);
for (int i = 0; i < N; ++i)
{
B[i] += WeightsM[i, i] * X[i];
}
};
SparseSymmetricCG SolverX = new SparseSymmetricCG()
{
B = Bx, X = Sx,
MultiplyF = CombinedMultiply, PreconditionMultiplyF = Preconditioner.Multiply,
UseXAsInitialGuess = true
};
SparseSymmetricCG SolverY = new SparseSymmetricCG()
{
B = By, X = Sy,
MultiplyF = CombinedMultiply, PreconditionMultiplyF = Preconditioner.Multiply,
UseXAsInitialGuess = true
};
SparseSymmetricCG SolverZ = new SparseSymmetricCG()
{
B = Bz, X = Sz,
MultiplyF = CombinedMultiply, PreconditionMultiplyF = Preconditioner.Multiply,
UseXAsInitialGuess = true
};
SparseSymmetricCG[] solvers = new SparseSymmetricCG[3] {
SolverX, SolverY, SolverZ
};
bool[] ok = new bool[3];
int[] indices = new int[3] {
0, 1, 2
};
// preconditioned solve is slower =\
//Action<int> SolveF = (i) => { ok[i] = solvers[i].SolvePreconditioned(); };
Action <int> SolveF = (i) => { ok[i] = solvers[i].Solve(); };
gParallel.ForEach(indices, SolveF);
if (ok[0] == false || ok[1] == false || ok[2] == false)
{
return(false);
}
for (int i = 0; i < N; ++i)
{
int vid = ToMeshV[i];
Result[vid] = new Vector3D(Sx[i], Sy[i], Sz[i]);
}
// apply post-fixed constraints
if (HavePostFixedConstraints)
{
foreach (var constraint in SoftConstraints)
{
if (constraint.Value.PostFix)
{
int vid = constraint.Key;
Result[vid] = constraint.Value.Position;
}
}
}
return(true);
}
public static void test_SparseCG_Precond()
{
// A test case where Jacobi preconditioner (ie M = diag(A)) provides some improvement
// described in http://www.math.iit.edu/~fass/477577_Chapter_16.pdf
int N = 10000;
SymmetricSparseMatrix M = new SymmetricSparseMatrix();
double[] B = new double[N];
for (int i = 0; i < N; ++i)
{
for (int j = i; j < N; ++j)
{
if (i == j)
{
M.Set(i, i, 0.5 + Math.Sqrt(i));
}
else if (Math.Abs(i - j) == 1)
{
M.Set(i, j, 1);
}
else if (Math.Abs(i - j) == 100)
{
M.Set(i, j, 1);
}
}
B[i] = 1;
}
SparseSymmetricCG Solver = new SparseSymmetricCG()
{
B = B, MultiplyF = M.Multiply
};
Solver.Solve();
double[] BTest = new double[N];
M.Multiply(Solver.X, BTest);
double diff = BufferUtil.DistanceSquared(B, BTest);
if (diff > MathUtil.ZeroTolerance)
{
System.Console.WriteLine("test_SparseCG: initial solve failed!");
}
PackedSparseMatrix PackedM = new PackedSparseMatrix(M);
PackedM.Sort();
SparseSymmetricCG Solver_PackedM = new SparseSymmetricCG()
{
B = B, MultiplyF = PackedM.Multiply
};
Solver_PackedM.Solve();
PackedM.Multiply(Solver_PackedM.X, BTest);
double diff_packed = BufferUtil.DistanceSquared(B, BTest);
if (diff_packed > MathUtil.ZeroTolerance)
{
System.Console.WriteLine("test_SparseCG: Packed solve failed!");
}
#if false
SparseCholeskyDecomposition cholDecomp = new SparseCholeskyDecomposition(PackedM);
cholDecomp.ComputeIncomplete();
// factorization is filled with NaNs!! doing something wrong.
double[] TmpX = new double[N], Y = new double[N];
cholDecomp.Solve(BTest, TmpX, Y);
// note: can also try just lower-triangular matrix - this is (L+D), Gauss-Seidel preconditioner?
// see http://www.math.iit.edu/~fass/477577_Chapter_16.pdf
Action <double[], double[]> cholPrecond = (R, Z) => {
cholDecomp.Solve(R, Z, Y);
};
SymmetricSparseMatrix diagPrecond = new SymmetricSparseMatrix(N);
for (int k = 0; k < N; ++k)
{
diagPrecond[k, k] = 1.0 / M[k, k];
}
SparseSymmetricCG Solver_Precond = new SparseSymmetricCG()
{
B = B, MultiplyF = PackedM.Multiply, PreconditionMultiplyF = diagPrecond.Multiply
};
//SparseSymmetricCG Solver_Precond = new SparseSymmetricCG() { B = B, MultiplyF = PackedM.Multiply, PreconditionMultiplyF = cholPrecond };
Solver_Precond.SolvePreconditioned();
PackedM.Multiply(Solver_Precond.X, BTest);
double diff_precond = BufferUtil.DistanceSquared(B, BTest);
if (diff_precond > MathUtil.ZeroTolerance)
{
System.Console.WriteLine("test_SparseCG: cholesky-preconditioned solve failed!");
}
System.Console.WriteLine("Iterations regular {0} precond {1}", Solver_PackedM.Iterations, Solver_Precond.Iterations);
System.Console.WriteLine("Tol regular {0} precond {1}", diff_packed, diff_precond);
#endif
}
public static void test_SparseCG()
{
Random r = new Random(31337);
int N = 100;
var pts = TestUtil.RandomScalars(N, r, new Interval1d(1, 10));
SymmetricSparseMatrix M = new SymmetricSparseMatrix();
double[] B = new double[N];
for (int i = 0; i < N; ++i)
{
for (int j = i; j < N; ++j)
{
if (i == j)
{
M.Set(i, j, pts[i]);
}
else
{
M.Set(i, j, (double)(i + j) / 10.0);
}
}
B[i] = i + 1;
}
SparseSymmetricCG Solver = new SparseSymmetricCG()
{
B = B, MultiplyF = M.Multiply
};
Solver.Solve();
double[] BTest = new double[N];
M.Multiply(Solver.X, BTest);
double diff = BufferUtil.DistanceSquared(B, BTest);
if (diff > MathUtil.ZeroTolerance)
{
System.Console.WriteLine("test_SparseCG: initial solve failed!");
}
PackedSparseMatrix PackedM = new PackedSparseMatrix(M);
PackedM.Sort();
SparseSymmetricCG Solver_PackedM = new SparseSymmetricCG()
{
B = B, MultiplyF = PackedM.Multiply
};
Solver_PackedM.Solve();
PackedM.Multiply(Solver_PackedM.X, BTest);
double diff_packed = BufferUtil.DistanceSquared(B, BTest);
if (diff_packed > MathUtil.ZeroTolerance)
{
System.Console.WriteLine("test_SparseCG: Packed solve failed!");
}
#if false
SparseCholeskyDecomposition decomp = new SparseCholeskyDecomposition(PackedM);
decomp.ComputeIncomplete();
PackedSparseMatrix choleskyPrecond = decomp.L.Square();
SymmetricSparseMatrix diagPrecond = new SymmetricSparseMatrix(N);
for (int k = 0; k < N; ++k)
{
diagPrecond[k, k] = 1.0 / M[k, k];
}
SparseSymmetricCG Solver_Precond = new SparseSymmetricCG()
{
B = B, MultiplyF = PackedM.Multiply, PreconditionMultiplyF = diagPrecond.Multiply
};
Solver_Precond.SolvePreconditioned();
PackedM.Multiply(Solver_Precond.X, BTest);
double diff_precond = BufferUtil.DistanceSquared(B, BTest);
if (diff_precond > MathUtil.ZeroTolerance)
{
System.Console.WriteLine("test_SparseCG: cholesky-preconditioned solve failed!");
}
System.Console.WriteLine("Iterations regular {0} precond {1}", Solver_PackedM.Iterations, Solver_Precond.Iterations);
System.Console.WriteLine("Tol regular {0} precond {1}", diff_packed, diff_precond);
#endif
}
// [RMS] this only tests some basic cases...
public static void test_Laplacian()
{
// compact version
DMesh3 mesh = new DMesh3(TestUtil.MakeRemeshedCappedCylinder(1.0), true);
Debug.Assert(mesh.IsCompact);
AxisAlignedBox3d bounds = mesh.GetBounds();
TestUtil.WriteDebugMesh(mesh, "___CG_before.obj");
List <IMesh> result_meshes = new List <IMesh>();
// make uniform laplacian matrix
int N = mesh.VertexCount;
SymmetricSparseMatrix M = new SymmetricSparseMatrix();
//DenseMatrix M = new DenseMatrix(N, N);
double[] Px = new double[N], Py = new double[N], Pz = new double[N];
int[] nbr_counts = new int[N];
for (int vid = 0; vid < N; ++vid)
{
nbr_counts[vid] = mesh.GetVtxEdgeCount(vid);
}
int ti = MeshQueries.FindNearestTriangle_LinearSearch(mesh, new Vector3d(2, 5, 2));
int v_pin = mesh.GetTriangle(ti).a;
List <int> constraints = new List <int>()
{
v_pin
};
double consW = 10;
double consBottom = 10;
foreach (int vid in constraints)
{
result_meshes.Add(TestUtil.MakeMarker(mesh.GetVertex(vid), (vid == 0) ? 0.2f : 0.1f, Colorf.Red));
}
for (int vid = 0; vid < N; ++vid)
{
int n = nbr_counts[vid];
Vector3d v = mesh.GetVertex(vid), c = Vector3d.Zero;
Px[vid] = v.x; Py[vid] = v.y; Pz[vid] = v.z;
bool bottom = (v.y - bounds.Min.y) < 0.01f;
double sum_w = 0;
foreach (int nbrvid in mesh.VtxVerticesItr(vid))
{
int n2 = nbr_counts[nbrvid];
// weight options
//double w = -1;
double w = -1.0 / Math.Sqrt(n + n2);
//double w = -1.0 / n;
M.Set(vid, nbrvid, w);
c += w * mesh.GetVertex(nbrvid);
sum_w += w;
}
sum_w = -sum_w;
M.Set(vid, vid, sum_w);
// add soft constraints
if (constraints.Contains(vid))
{
M.Set(vid, vid, sum_w + consW);
}
else if (bottom)
{
M.Set(vid, vid, sum_w + consBottom);
}
}
// compute laplacians
double[] MLx = new double[N], MLy = new double[N], MLz = new double[N];
M.Multiply(Px, MLx);
M.Multiply(Py, MLy);
M.Multiply(Pz, MLz);
DiagonalMatrix Preconditioner = new DiagonalMatrix(N);
for (int i = 0; i < N; i++)
{
Preconditioner.Set(i, i, 1.0 / M[i, i]);
}
MLy[v_pin] += consW * 0.5f;
MLx[v_pin] += consW * 0.5f;
MLz[v_pin] += consW * 0.5f;
bool useXAsGuess = true;
// preconditioned
SparseSymmetricCG SolverX = new SparseSymmetricCG()
{
B = MLx, X = Px, MultiplyF = M.Multiply, PreconditionMultiplyF = Preconditioner.Multiply, UseXAsInitialGuess = useXAsGuess
};
// initial solution
SparseSymmetricCG SolverY = new SparseSymmetricCG()
{
B = MLy, X = Py, MultiplyF = M.Multiply, UseXAsInitialGuess = useXAsGuess
};
// neither of those
SparseSymmetricCG SolverZ = new SparseSymmetricCG()
{
B = MLz, MultiplyF = M.Multiply
};
bool bx = SolverX.Solve();
bool by = SolverY.Solve();
bool bz = SolverZ.Solve();
for (int vid = 0; vid < mesh.VertexCount; ++vid)
{
Vector3d newV = new Vector3d(SolverX.X[vid], SolverY.X[vid], SolverZ.X[vid]);
mesh.SetVertex(vid, newV);
}
result_meshes.Add(mesh);
TestUtil.WriteDebugMeshes(result_meshes, "___CG_result.obj");
}