private float getOptimalTau(PointInfo goalPointInfo, PointInfo startPointInfo,
/*params for Newton*/ float t0 = 20, int max_n = 10, float r = 2.0f)
{
float p_x0 = startPointInfo.pos.x;
float p_y0 = startPointInfo.pos.z;
float v_x0 = startPointInfo.vel.x;
float v_y0 = startPointInfo.vel.z;
float p_x1 = goalPointInfo.pos.x;
float p_y1 = goalPointInfo.pos.z;
float v_x1 = goalPointInfo.vel.x;
float v_y1 = goalPointInfo.vel.z;
float a = ((24 * r * v_x1 * v_x0) + (12 * r * v_x1 * (v_x1 - v_x0)) - (4 * r * Mathf.Pow(2 * (v_x1 - v_x0) - 3 * v_x0, 2)) - (4 * r * Mathf.Pow(2 * (v_y1 - v_y0) - 3 * v_y0, 2)));
float b = (-24 * r * v_x1 * (p_x1 - p_x0) + 24 * r * (2 * (v_x1 - v_x0) - 3 * v_x0) * (p_x1 - p_x0) + 24 * r * (2 * (v_y1 - v_y0) - 3 * v_y0) * (p_y1 - p_y0));
float c = -36 * r * ((p_x1 - p_x0) * (p_x1 - p_x0) + (p_y1 - p_y0) * (p_y1 - p_y0));
float[] coefficients = new float[5];
coefficients [0] = c;
coefficients [1] = b;
coefficients [2] = a;
coefficients [3] = 0;
coefficients [4] = 1;
return(NewtonSolver.Newton(coefficients, t0, max_n));
}
public double GetTangentModulus(double ratio)
{
double stress = ratio * SoilModel.GetFailureStress();
var solver = new NewtonSolver(x => SoilModel.GetDeviatoricStress(x) - stress, 0);
double eps = solver.Solve();
var derivative = new Derivative(x => SoilModel.GetDeviatoricStress(x), DerivativeAccuracy);
return(derivative.GetFirstDerivative(eps));
}
public static double CalculateImpliedVolCall(double C, double S, double k, double r, double T, double x0 = 0.5, double maxErr = 1e-6, int N = 10000)
{
Func <double, double> F = (x) =>
{
return(C - BlackScholesFormula.CalculateCallOptionPrice(x, S, k, r, T));
};
NewtonSolver s = new NewtonSolver(maxErr, N);
return(s.Solve(F, null, x0));
}
public double GetSecantModulus(double ratio)
{
double stress = ratio * SoilModel.GetFailureStress();
var solver = new NewtonSolver(x => SoilModel.GetDeviatoricStress(x) - stress, 0);
double eps = solver.Solve();
if (eps == 0)
{
throw new Exception();
}
return(stress / eps);
}
private static List <ISolver> DeafaultSolvers()
{
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver = new NewtonSolver(opts);
return(new List <ISolver>()
{
solver
});
}
public static double CalculateImpliedVolCall(double C, double S, double K, double r, double T, double x0 = 0.5, double maxErr = 1e-6, int N = 10000)
{
if (C <= 0 || T <= 0 || K <= 0 || S <= 0 || maxErr <= 0 || N <= 0)
{
throw new System.ArgumentException("Need C > 0, T > 0, K > 0, S > 0, maxErr > 0, N > 0.");
}
Func <double, double> F = (x) => {
return(C - BlackScholesFormula.CalculateCallOptionPrice(x, S, K, r, T));
};
NewtonSolver s = new NewtonSolver(maxErr, N);
return(s.Solve(F, null, x0));
}
/// <summary>
/// Provides the revesed model, according to the specified variables
/// </summary>
public WorkflowReversedModel Reverse(List <Data> inputs, List <Data> outputs)
{
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver = new NewtonSolver(opts);
string reversedName = GetReversedName(inputs, outputs);
var reversedModel = new WorkflowReversedModel(reversedName, Description, inputs, outputs, this, new List <ISolver>()
{
solver
});
reversedModel.Rename(FullName + new string(reversedName.SkipWhile(c => c != ':').ToArray()));
return(reversedModel);
}
private static List <ISolver> DeafaultSolversSCC()
{
var solver = new FixedPointSolver()
{
MaxEvals = 20
};
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver2 = new NewtonSolver(opts);
return(new List <ISolver>()
{
solver, solver2
});
}
/// <summary>
/// This function identifies the Modified models (from imMatrixi and imMatrif) in the modelObjects, then creates a 'modified model subprocess' for each modified model,
/// and therafter combines it with other models in the modelObjects and return it in a object array
/// </summary>
/// <param name="IMi"></param>
/// <param name="IMf"></param>
/// <param name="components"></param>
/// <param name="data"></param>
/// <param name="clusters"></param>
/// <param name="name"></param>
/// <returns></returns>
private static WorkflowComponent[] CreateReversedModels(IncidenceMatrix IMi, IncidenceMatrix IMf, List <WorkflowComponent> components, List <Data> data, List <Cluster> clusters, string name)
{
var processedComponents = new WorkflowComponent[IMf.RowCount];
for (int r = 0; r < IMi.RowCount; r++)
{
WorkflowComponent component = components[r];
Vector <double> row = IMi.Row(r);
if (!IMf.Row(r).CompareAssigned(row))
{
List <int> inputIndices = row.FindLocations(IN);
List <int> outputIndices = row.FindLocations(OUT);
var inputs = inputIndices.Select(i => data[i]).ToList();
var outputs = outputIndices.Select(i => data[i]).ToList();
if (component is Model model)
{
processedComponents[r] = model.Reverse(inputs, outputs);
}
else if (component is Workflow workflow)
{
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver = new NewtonSolver(opts);
processedComponents[r] = new WorkflowGlobal($"{name}#GlobalWorkflow#{workflow.Name}", "", inputs, outputs, workflow.Components, workflow.Components, new List <ISolver>()
{
solver
});
}
}
else
{
processedComponents[r] = components[r];
}
}
return(processedComponents);
}
public void Circlify(List <TreemapData> data)
{
//IL faut commencer par les 2 plus gros cercles, le milieu du cercle final étant le centre du segment reliant les extrémités de ces cercles.
double a1 = GetInnerCircleArea() * data[0].Size / Size;
double a2 = GetInnerCircleArea() * data[1].Size / Size;
double r1 = Math.Sqrt(a1 / Math.PI);
double r2 = Math.Sqrt(a2 / Math.PI);
var items = new Dictionary <TreemapItem, List <TreemapItem> >();
Geometric.Point center = GetCenter();
TreemapItem item1 = AddItem(data[0], center.AddX(-r2), r1);
TreemapItem item2 = AddItem(data[1], center.AddX(r1), r2);
items.Add(item1, new List <TreemapItem> {
item2
});
items.Add(item2, new List <TreemapItem> {
item1
});
for (int d = 2; d < data.Count; d++)
{
double a = GetInnerCircleArea() * data[d].Size / Size;
double r = Math.Sqrt(a / Math.PI);
var results = new List <Tuple <TreemapItem, TreemapItem, Geometric.Point, double> >();
foreach (var kvp in items)
{
TreemapItem i1 = kvp.Key;
foreach (TreemapItem i2 in kvp.Value)
{
Triangle t = Triangle.FromTwoPointsAndTwoLengths(i1.GetCenter(), i2.GetCenter(),
i1.GetRadius() + r, i2.GetRadius() + r);
double distance = center.Distance(t.Point3);
if (Items.All(item => item.GetCenter().Distance(t.Point3) - (item.GetRadius() + r) >= -0.0001))
{
results.Add(Tuple.Create(i1, i2, t.Point3, distance));
}
}
}
var result = results.OrderBy(t => t.Item4).First();
TreemapItem newItem = AddItem(data[d], result.Item3, r);
items[result.Item1].Add(newItem);
items[result.Item2].Add(newItem);
items.Add(newItem, new List <TreemapItem> {
result.Item1, result.Item2
});
}
//Identify the item farther from the center and expand the chart so that this item becomes adjacent to external circle
var max = Items
.Select(i => new { Item = i, Distance = i.GetCenter().Distance(center) + i.GetRadius() })
.OrderByDescending(o => o.Distance)
.First();
Homothety homothety = new Homothety(center, GetRadius() / max.Distance);
foreach (var item in Items)
{
item.Rectangle = homothety.Transform(item.Rectangle);
item.InnerRectangle = homothety.Transform(item.InnerRectangle);
item.Empty = homothety.Transform(item.Empty);
}
//Homothety from contact point
Vector vector = new Segment(center, max.Item.GetCenter()).ToVector();
Geometric.Point contact = max.Item.GetCenter()
.AddX(max.Item.GetRadius() / vector.Length * vector.X)
.AddY(max.Item.GetRadius() / vector.Length * vector.Y);
NewtonSolver solver = new NewtonSolver((c) =>
{
Homothety h = new Homothety(contact, c);
double min = Items
.Except(new List <TreemapItem> {
max.Item
})
.Select(i => h.Transform(i.InnerRectangle))
.Select(r => new
{
Center = new Geometric.Point(r.Left + r.Width / 2, r.Top + r.Height / 2),
Radius = r.Width / 2
})
.Min(r => GetRadius() - (r.Center.Distance(center) + r.Radius));
return(min);
})
.Solve(1);
homothety = new Homothety(contact, solver.Solution);
foreach (var item in Items)
{
item.Rectangle = homothety.Transform(item.Rectangle);
item.InnerRectangle = homothety.Transform(item.InnerRectangle);
item.Empty = homothety.Transform(item.Empty);
}
}
public ViscoElasticKnot(Knot _knot, GetBetaFunction getElasticBeta)
: base(_knot.core_node, _knot.current_time)
{
int L = nodes.GetLength(0);
lumen_sq_old = new double[L];
chrt_func = new MDFunction[L];
energy_conservation_func = new MDFunction[L - 1];
funcs = new MDFunction[2 * L];
wall_thickhess = new double[L];
lumen_sq_0 = new double[L];
beta_1 = new double[L];
chrt_b = new double[L];
chrt_f = new double[L];
c_dst = new double[L];
dep_matrix = new bool[2 * L, 2 * L];
prev_velocity = new double[L];
#if FAST
nl_system = new NewtonSolver(2 * L);
#endif
for (int i = 0; i < L; i++)
{
for (int j = 0; j < L; j++)
{
dep_matrix[i, j] = false;
}
}
for (int i = 0; i < L; i++)
{
double R0 = Math.Sqrt(nodes[i].lumen_sq_0 / Math.PI);
beta_1[i] = getElasticBeta(R0, nodes[i].elasticity) / nodes[i].lumen_sq_0;
wall_thickhess[i] = GlobalDefs.getBoileauWallThickness(R0, nodes[i].elasticity);
lumen_sq_0[i] = nodes[i].lumen_sq_0;
prev_velocity[i] = nodes[i].velocity;
chrt_b[i] = 0;
chrt_f[i] = 0;
c_dst[i] = Math.Pow(nodes[i].lumen_sq_0, 0.25f) * Math.Sqrt(beta_1[i] / 2.0f / GlobalDefs.BLOOD_DENSITY);
lumen_sq_old[i] = lumen_sq_0[i];
}
for (int i = 0; i < L; i++)
{
pressure[i] = GlobalDefs.DIASTOLIC_PRESSURE;
}
int count = 0;
unsafe
{
for (int i = 0; i < L; i++)
{
int I = i;
#if FAST
MDFunction_del f1_del = delegate(double *args)
{
double v = args[0 + I * 2];
double l = args[1 + I * 2];
if (v > 0)
{
return(Math.Abs(v) + 4 * (Math.Sqrt(Math.Sqrt(l)) * Math.Sqrt(beta_1[I] / 2.0f / GlobalDefs.BLOOD_DENSITY) - c_dst[I]) - chrt_f[I]);
}
else
{
return(Math.Abs(v) - 4 * (Math.Sqrt(Math.Sqrt(l)) * Math.Sqrt(beta_1[I] / 2.0f / GlobalDefs.BLOOD_DENSITY) - c_dst[I]) - chrt_b[I]);
}
};
baseMDFunction f1 = new delegateMDFunc(f1_del);
nl_system.addFunc(f1);
nl_system.setDetMatrixEl(count, 2 * I, true);
nl_system.setDetMatrixEl(count, 2 * I + 1, true);
#endif
chrt_func[i] = delegate(double[] args) //v1,l1; v2,l2 ...
{
double v = args[0 + I * 2];
double l = args[1 + I * 2];
if (v > 0)
{
return(Math.Abs(v) + 4 * (Math.Pow(l, 0.25f) * Math.Sqrt(beta_1[I] / 2.0f / GlobalDefs.BLOOD_DENSITY) - c_dst[I]) - chrt_f[I]);
}
else
{
return(Math.Abs(v) - 4 * (Math.Pow(l, 0.25f) * Math.Sqrt(beta_1[I] / 2.0f / GlobalDefs.BLOOD_DENSITY) - c_dst[I]) - chrt_b[I]);
}
};
funcs[count] = chrt_func[i];
dep_matrix[count, 2 * I] = true;
dep_matrix[count, 2 * I + 1] = true;
count++;
}
}
unsafe
{
#if FAST
MDFunction_del f1_del = delegate(double *args)
{
double summ_flux = 0;
for (int i = 0; i < L; i++)
{
summ_flux += args[0 + i * 2] * args[1 + i * 2];
}
return(summ_flux);
};
baseMDFunction f1 = new delegateMDFunc(f1_del);
nl_system.addFunc(f1);
for (int i = 0; i < 2 * L; i++)
{
nl_system.setDetMatrixEl(count, i, true);
}
#endif
mass_conservation_func = delegate(double[] args)
{
double summ_flux = 0;
for (int i = 0; i < L; i++)
{
double v = args[0 + i * 2];
double l = args[1 + i * 2];
summ_flux += v * l;
}
return(summ_flux);
};
funcs[count] = mass_conservation_func;
for (int i = 0; i < 2 * L; i++)
{
dep_matrix[count, i] = true;
}
};
count++;
unsafe
{
for (int i = 1; i < L; i++)
{
int I = i;
#if FAST
MDFunction_del f1_del = delegate(double *args)
{
double v0 = args[0];
double p0 = calcPressureV(0, args[1]);
double v = args[0 + I * 2];
double p = calcPressureV(I, args[1 + 2 * I]);
return(GlobalDefs.BLOOD_DENSITY * (v0 * v0 - v * v) / 2 + p0 - p);
};
baseMDFunction f1 = new delegateMDFunc(f1_del);
nl_system.addFunc(f1);
nl_system.setDetMatrixEl(count, 0, true);
nl_system.setDetMatrixEl(count, 1, true);
nl_system.setDetMatrixEl(count, 2 * I, true);
nl_system.setDetMatrixEl(count, 2 * I + 1, true);
#endif
energy_conservation_func[i - 1] = delegate(double[] args)
{
double v0 = args[0];
double p0 = calcPressureV(0, args[1]);
double v = args[0 + I * 2];
double p = calcPressureV(I, args[1 + 2 * I]);
return(GlobalDefs.BLOOD_DENSITY * (v0 * v0 - v * v) / 2 + p0 - p);
};
funcs[count] = energy_conservation_func[I - 1];
dep_matrix[count, 0] = true;
dep_matrix[count, 1] = true;
dep_matrix[count, 2 * I] = true;
dep_matrix[count, 2 * I + 1] = true;
count++;
}
#if FAST
us_init_X = (double *)Marshal.AllocHGlobal(2 * L * sizeof(double));
us_solution = (double *)Marshal.AllocHGlobal(2 * L * sizeof(double));
for (int i = 0; i < 2 * L; i += 2)
{
us_init_X[i] = nodes[i / 2].velocity * v_sign[i / 2];
us_init_X[i + 1] = nodes[i / 2].lumen_sq;
nl_system.setDxVectorEl(i, 1e-12f);
nl_system.setDxVectorEl(i + 1, 1e-12f);
}
#endif
}
dX = new double[2 * L];
for (int i = 0; i < 2 * L; i += 2)
{
dX[i] = 1e-12f;
dX[i + 1] = 1e-12f;
}
}
