private SparseLU lu; //Initialize the LU factorizaation
/// <summary>
/// This is a small routine call to initialize the Neuron Cell
/// this will initialize the solution vectors which are <c>U</c>, <c>M</c>, <c>N</c>, and <c>H</c>
/// </summary>
protected override void PreSolve()
{
InitializeNeuronCell();
///<c>R</c> this is the reaction vector for the reaction solve
R = Vector.Build.Dense(Neuron.nodes.Count);
///<c>reactConst</c> this is a small list for collecting the conductances and reversal potential which is sent to the reaction solve routine
reactConst = new List <double> {
gk, gna, gl, ek, ena, el
};
/// this sets the target time step size
timeStep = SetTargetTimeStep(cap, 2 * Neuron.MaxRadius, Neuron.TargetEdgeLength, gna, gk, res, Rmemscf, cfl);
///UnityEngine.Debug.Log("Target Time Step = " + timeStep);
///<c>List<CoordinateStorage<double>> sparse_stencils = makeSparseStencils(Neuron, res, cap, k);</c> Construct sparse RHS and LHS in coordinate storage format, no zeros are stored \n
/// <c>sparse_stencils</c> this is a list which contains only two matrices the LHS and RHS matrices for the Crank-Nicolson solve
sparse_stencils = makeSparseStencils(Neuron, res, cap, timeStep);
///<c>CompressedColumnStorage</c> call Compresses the sparse matrices which are stored in <c>sparse_stencils[0]</c> and <c>sparse_stencils[1]</c>
r_csc = CompressedColumnStorage <double> .OfIndexed(sparse_stencils[0]); //null;
l_csc = CompressedColumnStorage <double> .OfIndexed(sparse_stencils[1]); //null;
///<c>double [] b</c> we define storage for the diffusion solve part
b = new double[Neuron.nodes.Count];
///<c>var lu = SparseLU.Create(l_csc, ColumnOrdering.MinimumDegreeAtA, 0.1);</c> this creates the LU decomposition of the HINES matrix which is defined by <c>l_csc</c>
lu = SparseLU.Create(l_csc, ColumnOrdering.MinimumDegreeAtA, 0.1);
}
public static Vector SolveLU(CompressedColumnStorage <double> A, Vector x, Vector b, out bool status, out string algorithm)
{
var orderings = new[] { CSparse.ColumnOrdering.MinimumDegreeAtPlusA, CSparse.ColumnOrdering.MinimumDegreeAtA, CSparse.ColumnOrdering.MinimumDegreeStS, CSparse.ColumnOrdering.Natural };
status = false;
algorithm = "LU";
try
{
status = true;
if (A.RowCount == A.ColumnCount)
{
var lu = new SparseLU(A, CSparse.ColumnOrdering.MinimumDegreeAtA, 1.0);
var xc = x.Clone();
var bc = b.Clone();
lu.Solve(bc.ToDouble(), xc.ToDouble());
algorithm = "LU/" + CSparse.ColumnOrdering.MinimumDegreeAtPlusA;
status = true;
return(xc);
}
}
catch (Exception e)
{
status = false;
}
return(x);
}
public void TestEmptyFactorize()
{
var A = new SparseMatrix(0, 0, 0);
var lu = SparseLU.Create(A, ColumnOrdering.MinimumDegreeAtPlusA, 1.0);
Assert.NotNull(lu);
Assert.IsTrue(lu.NonZerosCount == 0);
}
private double[] SolveSparseSystem(double[] h)
{
var order = ColumnOrdering.MinimumDegreeAtPlusA;
double tolerance = 1.0;
var lu = SparseLU.Create(Converter.ToCompressedColumnStorage(globalK), order, tolerance);
lu.Solve(globalF, h);
return(h);
}
public SparseLUSolver(int totalCases, double[,] matrix, double[] vector)
{
TotalCases = totalCases;
CompressedColumnStorage <double> e = CompressedColumnStorage <double> .OfArray(matrix);
SparseLUMatrix = SparseLU.Create(e, CSparse.ColumnOrdering.MinimumDegreeAtPlusA, 1.0);
SparseLUVector = vector;
SparseLUResultVector = Vector.Create(vector.Length, 1.0);
SparseLUMethod();
}
/// <summary>
/// Performs the LU factorization: A = L * U of a ssquare matrix A. The matrix A is provided in CSC format by
/// <paramref name="cscValues"/>, <paramref name="cscRowIndices"/> and <paramref name="cscColOffsets"/>.
/// </summary>
/// <param name="order">The number of rows/columns of the square matrix.</param>
/// <param name="numNonZeros">The number of explicitly stored entries of the matrix before the factorization.</param>
/// <param name="cscValues">
/// Contains the non-zero entries of the upper triangle. Its length must be equal to <paramref name="numNonZeros"/>.
/// The non-zero entries of each row must appear consecutively in <paramref name="cscValues"/>. They should also be
/// sorted in increasing order of their row indices, to speed up subsequent the factorization.
/// </param>
/// <param name="cscRowIndices">
/// Contains the row indices of the non-zero entries. Its length must be equal to <paramref name="numNonZeros"/>.
/// There is an 1 to 1 matching between these two arrays: <paramref name="cscRowIndices"/>[i] is the row index of the
/// entry <paramref name="cscValues"/>[i]. Also: 0 <= <paramref name="cscRowIndices"/>[i] <
/// <paramref name="order"/>.
/// </param>
/// <param name="cscColOffsets">
/// Contains the index of the first entry of each column into the arrays <paramref name="cscValues"/> and
/// <paramref name="cscRowIndices"/>. Its length must be <paramref name="order"/> + 1. The last entry must be
/// <paramref name="numNonZeros"/>.
/// </param>
/// <param name="pivotTolerance">The partial pivoting tolerance (from 0.0 to 1.0).</param>
/// <exception cref="SingularMatrixException">Thrown if the original matrix is not positive definite.</exception>
public static LUCSparseNet Factorize(int order, int numNonZeros, double[] cscValues, int[] cscRowIndices,
int[] cscColOffsets, double pivotTolerance = defaultPivotTolelance)
{
try
{
var matrixCSparse = new SparseMatrix(order, order, cscValues, cscRowIndices, cscColOffsets);
var factorization = SparseLU.Create(matrixCSparse, ColumnOrdering.Natural, pivotTolerance);
return(new LUCSparseNet(order, factorization));
}
catch (Exception ex) //TODO: how can I make sure this exception was thrown because of an indefinite matrix?
{
throw new SingularMatrixException(ex.Message);
}
}
public void TestSolve()
{
// Load matrix from a file.
var A = ResourceLoader.Get <Complex>("general-40x40.mat");
// Create test data.
var x = Helper.CreateTestVector(A.ColumnCount);
var b = Helper.Multiply(A, x);
var r = Vector.Clone(b);
// Create LU factorization.
var lu = SparseLU.Create(A, ColumnOrdering.MinimumDegreeAtPlusA, 1.0);
// Solve Ax = b.
lu.Solve(b, x);
// Compute residual r = b - Ax.
A.Multiply(-1.0, x, 1.0, r);
Assert.IsTrue(Vector.Norm(r.Length, r) < EPS);
}
/// <inheritdoc />
public void Initialize()
{
var matrix = A;
var sp = new Stopwatch();
sp.Start();
lu =
SparseLU.Create(matrix, ColumnOrdering.MinimumDegreeAtPlusA, 0.01);
IsInitialized = true;
sp.Stop();
if (Target != null)
{
Target.Trace.Write(TraceRecord.Create(BriefFiniteElementNet.Common.TraceLevel.Info,
string.Format(CultureInfo.CurrentCulture, "LU decomposition of matrix took about {0:#,##0} ms",
sp.ElapsedMilliseconds)));
}
}
public static Vector SolveLU(CompressedColumnStorage <double> A, Vector x, Vector b, out bool status, out string error)
{
var orderings = new[] { CSparse.ColumnOrdering.MinimumDegreeAtPlusA, CSparse.ColumnOrdering.MinimumDegreeAtA, CSparse.ColumnOrdering.MinimumDegreeStS, CSparse.ColumnOrdering.Natural };
status = false;
error = null;
try
{
status = true;
if (A.RowCount == A.ColumnCount)
{
var lu = SparseLU.Create(A, CSparse.ColumnOrdering.MinimumDegreeAtPlusA, 1.0);
lu.Solve(b.ToDouble(), x.ToDouble());
status = true;
return(x);
}
}
catch (Exception e)
{
error = e.Message;
status = false;
}
return(x);
}
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 void mosek2(List<leaf> _listLeaf, List<branch> _listBranch, List<node> _listNode, double force)
{
//variable settings
ShoNS.Array.SparseDoubleArray mat = new SparseDoubleArray(_listNode.Count * 3, _listNode.Count * 3);
ShoNS.Array.SparseDoubleArray F = new SparseDoubleArray(_listNode.Count * 3, 1);
ShoNS.Array.SparseDoubleArray xx = new SparseDoubleArray(_listNode.Count*3,1);
ShoNS.Array.SparseDoubleArray shift = new SparseDoubleArray(_listNode.Count*3, _listNode.Count*3);
for (int k = 0; k < _listNode.Count;k++ )
{
var node = _listNode[k];
xx[k * 3 + 0, 0] = node.x;
xx[k * 3 + 1, 0] = node.y;
xx[k * 3 + 2, 0] = node.z;
/* if (node.nodeType == node.type.fx)
{
for (int i = 0; i < node.shareB.Count; i++)
{
var branch = node.shareB[i];
var index = node.numberB[i];
if (branch.branchType == branch.type.fix)
{
node.x = branch.crv.Points[index].Location.X;
node.y = branch.crv.Points[index].Location.Y;
node.z = branch.slice2.height;
xx[k * 3 + 0, 0] = node.x;
xx[k * 3 + 1, 0] = node.y;
xx[k * 3 + 2, 0] = node.z;
}
}
}*/
}
List<int> series=new List<int>();
List<Point3d> origin = new List<Point3d>();
for(int i=0;i<_listNode.Count;i++)
{
series.Add(i);
}
int L1=0;
int L2=_listNode.Count;
for(int i=0;i<_listNode.Count;i++)
{
var node=_listNode[i];
if(node.nodeType==node.type.fx)
{
L2--;
series[i]=L2;
}else{
series[i]=L1;
origin.Add(new Point3d(node.x, node.y, node.z));
L1++;
}
}
for (int i = 0; i < _listNode.Count; i++)
{
shift[i * 3 + 0, series[i] * 3 + 0] = 1;
shift[i * 3 + 1, series[i] * 3 + 1] = 1;
shift[i * 3 + 2, series[i] * 3 + 2] = 1;
F[i * 3 + 2, 0] = -force;//force
}
foreach (var leaf in _listLeaf)
{
foreach (var tup in leaf.tuples)
{
var det = tup.SPK[0, 0] * tup.SPK[1, 1] - tup.SPK[0, 1] * tup.SPK[0, 1];
if (det > 0)
{
for (int i = 0; i < tup.nNode; i++)
{
for (int j = 0; j < tup.nNode; j++)
{
for (int k = 0; k < 3; k++)
{
for (int l = 0; l < 2; l++)
{
for (int m = 0; m < 2; m++)
{
var val = tup.B[l, m, i * 3 + k, j * 3 + k] * tup.SPK[l, m] * tup.refDv * tup.area;
mat[leaf.globalIndex[tup.internalIndex[i]] * 3 + k, leaf.globalIndex[tup.internalIndex[j]] * 3 + k] += val;
}
}
}
}
}
}
}
}
foreach (var branch in _listBranch)
{
foreach (var tup in branch.tuples)
{
for (int i = 0; i < tup.nNode; i++)
{
for (int j = 0; j < tup.nNode; j++)
{
for (int k = 0; k < 3; k++)
{
//if (tup.SPK[0, 0] > 0)
{
var val = tup.B[0, 0, i * 3 + k, j * 3 + k] * tup.SPK[0, 0] * tup.refDv * tup.area;
for (int l = 0; l < 1; l++)
{
for (int m = 0; m < 1; m++)
{
var val2 = tup.B[l, m, i * 3 + k, j * 3 + k] * tup.SPK[l, m] * tup.refDv * tup.area;
mat[branch.globalIndex[tup.internalIndex[i]] * 3 + k, branch.globalIndex[tup.internalIndex[j]] * 3 + k] += val2;
}
}
}
}
}
}
}
}
var reactionForce = mat * xx as SparseDoubleArray;
double max1 = 0;
double max2 = 0;
for (int i = 0; i < _listNode.Count; i++)
{
if (_listNode[i].nodeType == node.type.fr)
{
var nx = reactionForce[i * 3 + 0, 0];
var ny = reactionForce[i * 3 + 1, 0];
var norm = Math.Sqrt(nx * nx + ny * ny);
if (norm > max1) max1 = norm;
}
else
{
var nx = reactionForce[i * 3 + 0, 0];
var ny = reactionForce[i * 3 + 1, 0];
var norm = Math.Sqrt(nx * nx + ny * ny);
if (norm > max2) max2 = norm;
}
}
//System.Windows.Forms.MessageBox.Show(max1.ToString() + ".-." + max2.ToString());
var newMat = (shift.T.Multiply(mat) as SparseDoubleArray).Multiply(shift) as SparseDoubleArray;
var newxx = shift.T.Multiply(xx) as SparseDoubleArray;
var newF = shift.T.Multiply(F) as SparseDoubleArray;
var T = newMat.GetSliceDeep(0, L1 * 3 - 1, 0, L1 * 3 - 1);
var D = newMat.GetSliceDeep(0, L1 * 3 - 1, L1 * 3, _listNode.Count * 3 - 1);
var fx = newxx.GetSliceDeep(L1 * 3, _listNode.Count * 3 - 1, 0, 0);
newF = newF.GetSliceDeep(0, L1 * 3 - 1, 0, 0);
var solve = new SparseLU(T);
//var solve = new SparseSVD(T);
//var _U = solve.U;
//var _V = solve.V;
//var _D = solve.D;
//double tol=0.00000000001;
//for (int i = 0; i < L1*3; i++)
//{
// if (_D[i, i] > tol) _D[i, i] = 1d / _D[i, i];
// else if (_D[i, i] < -tol) _D[i, i] = 1d / _D[i, i];
// else _D[i, i] = 0d;
//}
var df = D * fx as SparseDoubleArray;
var b = DoubleArray.From((-newF - df));
var sol=solve.Solve(b);
//var sol = _V * _D * _U.T*b;
var exSol = new SparseDoubleArray(sol.GetLength(0)+fx.GetLength(0),1);
for (int i = 0; i < L1; i++)
{
exSol[i * 3 + 0, 0] = sol[i * 3 + 0, 0];
exSol[i * 3 + 1, 0] = sol[i * 3 + 1, 0];
exSol[i * 3 + 2, 0] = sol[i * 3 + 2, 0];
}
for (int i = L1; i < _listNode.Count; i++)
{
exSol[i * 3 + 0, 0] = fx[(i - L1) * 3 + 0, 0];
exSol[i * 3 + 1, 0] = fx[(i - L1) * 3 + 1, 0];
exSol[i * 3 + 2, 0] = fx[(i - L1) * 3 + 2, 0];
}
exSol = shift.Multiply(exSol) as SparseDoubleArray;
foreach (var branch in _listBranch)
{
branch.shellCrv = branch.crv.Duplicate() as NurbsCurve;
for (int i = 0; i < branch.N; i++)
{
var P = branch.shellCrv.Points[i].Location;
branch.shellCrv.Points.SetPoint(i, new Point3d(exSol[branch.globalIndex[i] * 3 + 0, 0], exSol[branch.globalIndex[i] * 3 + 1, 0], exSol[branch.globalIndex[i] * 3 + 2, 0]));
//if you don't want to allow movements of x and y coordinates, use the following instead of the above.
//branch.shellCrv.Points.SetPoint(i, new Point3d(P.X, P.Y, exSol[branch.globalIndex[i] * 3 + 2, 0]));
}
}
foreach (var leaf in _listLeaf)
{
leaf.shellSrf = leaf.srf.Duplicate() as NurbsSurface;
for (int i = 0; i < leaf.nU; i++)
{
for (int j = 0; j < leaf.nV; j++)
{
var P = leaf.shellSrf.Points.GetControlPoint(i, j).Location;
leaf.shellSrf.Points.SetControlPoint(i, j, new ControlPoint(exSol[leaf.globalIndex[i + j * leaf.nU] * 3 + 0, 0], exSol[leaf.globalIndex[i + j * leaf.nU] * 3 + 1, 0], exSol[leaf.globalIndex[i + j * leaf.nU] * 3 + 2, 0]));
//if you don't want to allow movements of x and y coordinates, use the following instead of the above.
//leaf.shellSrf.Points.SetControlPoint(i, j, new ControlPoint(P.X, P.Y, exSol[leaf.globalIndex[i + j * leaf.nU] * 3 + 2, 0]));
}
}
}
}
public DisposableSparseLU(SparseMatrix matrix)
{
lu = SparseLU.Create(matrix, ColumnOrdering.MinimumDegreeAtPlusA, 0.1);
}
private LUCSparseNet(int order, SparseLU factorization)
{
this.Order = order;
this.factorization = factorization;
}