public double[] bucketedCS01FromCreditCurve(
CDS cds,
double cdsCoupon,
CDS[] bucketCDSs,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve)
{
int n = bucketCDSs.Length;
Vector <double> vLambda = Vector <double> .Build.Random(n);
for (int i = 0; i < n; i++)
{
vLambda[i] = _pricer.pvCreditSensitivity(cds, yieldCurve, creditCurve, cdsCoupon, i);
}
Matrix <double> jacT = Matrix <double> .Build.Random(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
jacT[i, j] = _pricer.parSpreadCreditSensitivity(bucketCDSs[j], yieldCurve, creditCurve, i);
}
}
LU <double> LUResult = jacT.LU();
Vector <double> vS = LUResult.Solve(vLambda);
return(vS.ToArray());
}
/// <inheritdoc />
public IEnumerable <double> LowerUpperFactorizeAndSolve(IEnumerable <double> colleyRatings)
{
LU <double> lowerUpper = _sparseMatrix.LU();
Vector ratingsVector = new DenseVector(colleyRatings.ToArray());
Vector <double> solvedVector = lowerUpper.Solve(ratingsVector);
return(solvedVector.AsArray());
}
public Vector3D MinError()
{
var lu = new LU(Derivative(), 4);
lu.Decompose();
var x = new double[4];
lu.Solve(new double[] { 0.0, 0.0, 0.0, 1.0 }, ref x);
return(new Vector3D(x[0], x[1], x[2]));
}
public double[] getHedgeRatios(double[] cdsSensitivities, LU <double> luRes)
{
int n = cdsSensitivities.Length;
Vector <double> vLambda = Vector <double> .Build.Random(n);
for (int i = 0; i < n; i++)
{
vLambda[i] = cdsSensitivities[i];
}
double[] w = luRes.Solve(vLambda).ToArray();
return(w);
}
void Test03()
{
var A = new double[] {
-1, 1, 1,
1, -1, 1,
1, 1, -1
};
var lu = new LU(A, 3);
var b = new double[] { -3, 1, 1 };
var refX = new double[] { 1, -1, -1 };
var x = new double[3];
lu.Solve(b, ref x);
AssertX(b, refX);
}
public void ShouldRegress()
{
var X = new Matrix(new double[, ]
{
{ 13.0, 12.0, 0.0 },
{ 15.0, 19.0, 0.0 },
{ 12.0, 23.0, 0.0 },
{ 13.0, 30.0, 1.0 },
{ 13.0, 22.0, 1.0 },
{ 16.0, 11.0, 0.0 },
{ 15.0, 13.0, 1.0 },
{ 16.0, 28.0, 1.0 },
{ 15.0, 10.0, 1.0 },
{ 16.0, 11.0, 1.0 }
});
var Y = new Vector(new double[]
{
34.12,
40.94,
33.58,
38.95,
35.42,
32.12,
28.57,
40.47,
32.06,
30.55
});
Debug.WriteLine($"Data:\n{X.ConcatColumns(Y):F2}");
var Xdesign = new Vector(X.Rows).Fill(1).ConcatColumns(X);
Debug.WriteLine($"Design:\n{Xdesign:F2}");
var coef = LU.Solve(Xdesign, Y);
var r2 = X.ConcatColumns(Y).RSquared(coef);
Debug.Print($"R2={r2}");
var y = MatrixMath.Predict(new double[] { 14, 12, 0 }, coef);
Debug.Print($"Prediction is {y}");
}
void Test01()
{
var A = new double[] {
1, 2, 3, 4,
2, 3, 4, 1,
3, 4, 1, 2,
4, 1, 2, 3,
};
var lu = new LU(A, 4);
var b = new double[] { 16, 14, 16, 14 };
var x = new double[4];
lu.Solve(b, ref x);
var refX = new double[] { 1, 2, 1, 2 };
AssertX(x, refX);
}
void Test02()
{
var A = new double[] {
0, 1, 2,
2, 0, 1,
1, 2, 0
};
var lu = new LU(A, 3);
var refLu = new double[] {
2f, 0f, 1f,
1f / 2, 2f, -1f / 2,
0f, 1f / 2, 9f / 4
};
AssertLU(lu, refLu);
var b = new double[] { 8, 5, 5 };
var x = new double[3];
var refX = new double[] { 1, 2, 3 };
lu.Solve(b, ref x);
AssertX(x, refX);
}
public double[][] bucketedCS01FromCreditCurve(
CDS[] cds,
double[] cdsCoupon,
CDS[] bucketCDSs,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve)
{
int m = cds.Length;
LUDecompositionCommons decomp = new LUDecompositionCommons();
int n = bucketCDSs.Length;
Matrix <double> jacT = Matrix <double> .Build.Random(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
jacT[i, j] = _pricer.parSpreadCreditSensitivity(bucketCDSs[j], yieldCurve, creditCurve, i);
}
}
Vector <double> vLambda = Vector <double> .Build.Random(n);
double[][] res = new double[m][];
LU <double> LUResult = jacT.LU();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
vLambda[j] = _pricer.pvCreditSensitivity(cds[i], yieldCurve, creditCurve, cdsCoupon[i], j);
}
res[i] = LUResult.Solve(vLambda).ToArray();
}
return(res);
}
private void Solve()
{
Stopwatch stopwatch = new Stopwatch();
stopwatch.Start();
double[] h = new double[Codend.dof];
double PrevTowSpeed = Codend.towSpeed;
int PrevCatch = Codend.GetMeshesBlocked();
SparseLU LU;
var LUorder = ColumnOrdering.MinimumDegreeAtPlusA;
double LUtolerance = 1.0;
bool hasConverged = false; // convergence flag
bool correctSolution = false; // correctness of solution flag
bool hasDiverged = false; // restart flag
bool usePrecalc = CheckPrecalc();
int restartsCount = 0;
int iter = 0;
double hNorm = 1;
double addStiff = SolverSettings.DiagStiffness;
double addStiff0 = SolverSettings.DiagStiffness;
double tolStiff = SolverSettings.StiffnessTol;
//=============================
// Start calculation
//=============================
for (int stage = 1; stage <= 2; stage++)
{
//===========================
// Restarts loop
//===========================
while (!correctSolution)
{
// Set initial shape depending on whether it is precalculated from previous stage or not
Codend.ClearState();
SetStageInitialShape(stage);
Codend.UpdateTotalForces(IncludeBC: true);
Codend.UpdateResidual();
if (addStiff0 == 0 && restartsCount > 0) // if the scheme doesnt work without extra stiffness
{
addStiff0 = 1;
}
addStiff = addStiff0;
tolStiff = SolverSettings.StiffnessTol;
//===========================
// Newton-Raphson loop
//===========================
while (!hasConverged)
{
// check if diverged
if (Codend.R > SolverSettings.ResidualMax)
{
hasDiverged = true;
break;
}
// check whether to add less diagonal stiffness
if (Codend.R < tolStiff)
{
addStiff *= SolverSettings.ReduceStiffnessBy;
tolStiff *= SolverSettings.ReduceStiffnessBy;
}
// check if converged and no stiffness is added
if (Codend.R < SolverSettings.ResidualTol && hNorm < SolverSettings.DisplacementTol)
{
break;
}
Codend.UpdateTotalJacobian(kDiag: -addStiff, IncludeBC: true);
LU = SparseLU.Create(Codend.J, LUorder, LUtolerance);
LU.Solve(Codend.F, h);
hNorm = DisplacmentNorm(h);
Codend.UpdatePosition(h, 1);
Codend.UpdateTotalForces(IncludeBC: true);
Codend.UpdateResidual();
iter++; // display iteration status
Console.WriteLine(
PrintIter(iter, 0, addStiff, Codend.R, hNorm));
}
//===================
// Restart routine
//===================
if (hasDiverged || IsIncorrectSolution())
{
restartsCount += 1;
addStiff0 *= SolverSettings.IncreaseStiffnessBy;
ReportRestartCause(hasDiverged);
hasDiverged = false;
}
else
{
correctSolution = true; // correct solution found
Console.WriteLine("\nConvergence acheived in {0} iterations and {1} restarts in {2} [ms]\n",
iter, restartsCount, stopwatch.ElapsedMilliseconds);
}
}
if (usePrecalc)
{
Codend.X.CopyTo(precalcX, 0);
Codend.ApplyCatch(PrevCatch);
Codend.ApplyTowing(PrevTowSpeed);
Console.WriteLine("\nInitial shape is precalculated. Moiving to and actual case.\n");
correctSolution = false;
usePrecalc = false;
hasConverged = false;
}
else
{
break;
}
}
}
public static void SolveSparseLU(this SparseMatrix matrix, Vector <double> result, Vector <double> rhs, double tol = 1.0)
{
LU lu = matrix.SparseLU(tol: tol);
lu.Solve(rhs, result);
}
public List <Vector <double> > CalculateARAPMesh(Vector3 targetPosition, int vertexIndex)
{
// A temporary vector to hold all the edge products for all the vertices.
// This is the S matrix in equation (5).
List <Matrix <double> > edge_product = new List <Matrix <double> >();
for (int i = 0; i < mesh_vertices.Count; i++)
{
Matrix <double> edge_product_ = Matrix <double> .Build.Dense(3, 3);
foreach (int j in neighbors[i])
{
double weight = weights[i, j];
Matrix <double> edge = mesh_vertices[i].ToRowMatrix() - mesh_vertices[j].ToRowMatrix();
Matrix <double> edge_update =
deformed_vertices[i].ToRowMatrix() - deformed_vertices[j].ToRowMatrix();
edge_product_ += weight * edge.Transpose() * edge_update;
edge_product.Add(edge_product_);
}
}
for (int v = 0; v < mesh_vertices.Count; ++v)
{
Svd <double> svd = edge_product[v].Svd(true);
Matrix <double> rotation = svd.U.Transpose() * svd.VT.Transpose();
rotations[v] = rotation;
}
// Step 2: compute the rhs in equation (9).
// The right hand side of equation (9). The x, y and z coordinates are
// computed separately.
Matrix <double> rhs = Matrix <double> .Build.Dense(free_indices.Count, 3);
for (int i = 0; i < free_indices.Count; ++i)
{
int i_pos = free_indices[i];
foreach (int j_pos in neighbors[i_pos])
{
double weight = weights[i_pos, j_pos];
Matrix <double> vec = weight * 0.5d
* (rotations[i_pos] + rotations[j_pos])
* (mesh_vertices[i_pos] - mesh_vertices[j_pos]).ToRowMatrix().Transpose();
rhs.SetRow(i, rhs.Row(i) + vec.Column(0));
if (fixed_indices.Exists(x => x == j_pos))
{
rhs.SetRow(i, rhs.Row(i) + weight * deformed_vertices[j_pos]);
}
}
}
// Solve for free_vertices.
Matrix <double> solution = solver.Solve(rhs);
for (int i = 0; i < free_indices.Count; ++i)
{
int pos = free_indices[i];
deformed_vertices[pos] = solution.Row(i);
}
return(deformed_vertices);
}
public void DeformationPreprocess(Vector3 target_position, int target_idx)
{
//free_indices.Remove(target_idx);
//fixed_indices.Add(target_idx);
Matrix <double> meshMatrix = Matrix <double> .Build.Dense(
mesh_vertices.Count, 3);
Matrix <double> fixedMatrix = Matrix <double> .Build.Dense(
fixed_indices.Count, 3);
Matrix <double> deformedMatrix = Matrix <double> .Build.Dense(mesh_vertices.Count, 3);
for (int i = 0; i < mesh_vertices.Count; i++)
{
meshMatrix.SetRow(i, mesh_vertices[i]);
deformedMatrix.SetRow(i, mesh_vertices[i]);
if (i < fixed_indices.Count)
{
fixedMatrix.SetRow(i, mesh_vertices[fixed_indices[i]]);
}
}
fixedMatrix.SetRow(fixed_indices.Count - 1,
Utilities.ConvertFromUVectorToMNVector(target_position));
Matrix <double> A = Matrix <double> .Build.Sparse(mesh_vertices.Count,
free_indices.Count);
Matrix <double> B = Matrix <double> .Build.Sparse(mesh_vertices.Count,
fixed_indices.Count);
for (int i = 0; i < mesh_vertices.Count; i++)
{
for (int j = 0; j < free_indices.Count; j++)
{
A[i, j] = weights[i, free_indices[j]];
}
for (int j = 0; j < fixed_indices.Count; j++)
{
B[i, j] = weights[i, fixed_indices[j]];
}
}
Matrix <double> left = A.Transpose() * A;
LU <double> naive_lap_solver = left.LU();
for (int c = 0; c < 3; c++)
{
Vector <double> b = weights * meshMatrix.Column(c) - B * fixedMatrix.Column(c);
Vector <double> right = A.Transpose() * b;
Vector <double> x = naive_lap_solver.Solve(right);
for (int i = 0; i < free_indices.Count; ++i)
{
deformedMatrix[free_indices[i], c] = x[i];
}
}
//// simple initial guess
//List<Vector<double>> def_vertices = mesh_vertices;
//Vector<double> targetDistance = Utilities.ConvertFromUVectorToMNVector(target_position) - def_vertices[target_idx];
//Vector<double> startPosition = def_vertices[target_idx];
//double maxDistance = 0.0f;
//for (int i = 0; i < def_vertices.Count; i++)
//{
// double dist = (def_vertices[i] - def_vertices[target_idx]).L2Norm() *
// (def_vertices[i] - def_vertices[target_idx]).L2Norm();
// if (dist > maxDistance)
// {
// maxDistance = (def_vertices[i] - def_vertices[target_idx]).L2Norm();
// }
//}
//for (int i = 0; i < def_vertices.Count; i++)
//{
// double dist = (def_vertices[i] - startPosition).L2Norm() *
// (def_vertices[i] - startPosition).L2Norm();
// double originalDistance = dist / maxDistance;
// def_vertices[i] += targetDistance * (1 - originalDistance);
// for (int c = 0; c < 3; c++)
// {
// deformedMatrix[i, c] = def_vertices[i][c];
// }
//}
// initial rotation
deformed_vertices = new List <Vector <double> >();
for (int i = 0; i < mesh_vertices.Count; i++)
{
deformed_vertices.Add(deformedMatrix.Row(i));
}
for (int i = 0; i < fixed_indices.Count; i++)
{
deformed_vertices[fixed_indices[i]] = fixedMatrix.Row(i);
}
List <Matrix <double> > edge_product = new List <Matrix <double> >();
for (int i = 0; i < mesh_vertices.Count; i++)
{
Matrix <double> edge_product_ = Matrix <double> .Build.Dense(3, 3);
foreach (int j in neighbors[i])
{
double weight = weights[i, j];
Matrix <double> edge = mesh_vertices[i].ToRowMatrix() - mesh_vertices[j].ToRowMatrix();
Matrix <double> edge_update =
deformed_vertices[i].ToRowMatrix() - deformed_vertices[j].ToRowMatrix();
edge_product_ += weight * edge.Transpose() * edge_update;
edge_product.Add(edge_product_);
}
}
rotations = new List <Matrix <double> >();
for (int v = 0; v < mesh_vertices.Count; ++v)
{
Svd <double> svd = edge_product[v].Svd(true);
Matrix <double> rotation = svd.U.Transpose() * svd.VT.Transpose();
rotations.Add(rotation);
}
}
/// <summary>
/// Perform one iteration of training.
/// </summary>
public void Iteration()
{
int rowCount = _trainingData.Count;
int coeffCount = _algorithm.LongTermMemory.Length;
var working = new double[rowCount, coeffCount];
var errors = new double[rowCount];
var weights = new double[rowCount];
for (int i = 0; i < rowCount; i++)
{
BasicData element = _trainingData[i];
working[i, 0] = 1;
for (int j = 0; j < element.Input.Length; j++)
{
working[i, j + 1] = element.Input[j];
}
}
for (int i = 0; i < rowCount; i++)
{
BasicData element = _trainingData[i];
double y = _algorithm.ComputeRegression(element.Input)[0];
errors[i] = y - element.Ideal[0];
weights[i] = y * (1.0 - y);
}
for (int i = 0; i < coeffCount; i++)
{
_gradient[i, 0] = 0;
for (int j = 0; j < coeffCount; j++)
{
_hessian[i, j] = 0;
}
}
for (int j = 0; j < rowCount; j++)
{
for (int i = 0; i < coeffCount; i++)
{
_gradient[i, 0] += working[j, i] * errors[j];
}
}
for (int k = 0; k < weights.Length; k++)
{
for (int j = 0; j < coeffCount; j++)
{
for (int i = 0; i < coeffCount; i++)
{
_hessian[j, i] += working[k, i] * working[k, j] * weights[k];
}
}
}
LU <double> lu = _hessian.LU();
Matrix <double> deltas = lu.Solve(_gradient);
var prev = (double[])_algorithm.LongTermMemory.Clone();
for (int i = 0; i < _algorithm.LongTermMemory.Length; i++)
{
_algorithm.LongTermMemory[i] -= deltas[i, 0];
}
double max = 0;
for (int i = 0; i < deltas.ColumnCount; i++)
{
max = Math.Max(Math.Abs(deltas[i, 0]) / Math.Abs(prev[i]), max);
}
_error = max;
}
public void Init()
{
decomposition.Solve(new DenseVector(Columns, 0));
}