/// <summary>
/// 計算Tsquare
/// </summary>
/// <param name="item">a observation</param>
/// <param name="mean">mean vector</param>
/// <param name="invS">inverse of covariance matrix</param>
/// <returns></returns>
public static double CalculateTSquare(LinearAlgebra.Matrix <double> item, LinearAlgebra.Matrix <double> mean, LinearAlgebra.Matrix <double> invS)
{
if (item.ColumnCount != mean.ColumnCount || item.ColumnCount != invS.ColumnCount || mean.ColumnCount != invS.ColumnCount)
{
throw new ArgumentException("矩陣的維度無法計算");
}
LinearAlgebra.Matrix <double> diff = item - mean;
var t2 = diff.Multiply(invS).Multiply(diff.Transpose());
return(t2.At(0, 0));
}
/// <summary>
/// 計算數列各元素的累積和
/// </summary>
/// <param name="x">要處理的陣列，合法的輸入是 double[]</param>
/// <returns></returns>
public static double[] PartialSum(double[] x)
{
LinearAlgebra.Vector <double> vx
= LinearAlgebra.Double.DenseVector.OfArray(x);
int row = vx.Count;
int col = row;
LinearAlgebra.Matrix <double> lmat
= LinearAlgebra.Matrix <double> .Build.Dense(row, col, 1);
lmat = lmat.LowerTriangle();
LinearAlgebra.Vector <double> result
= lmat.Multiply(vx);
return(result.ToArray());
}
public LinearAlgebra.Matrix <double> ComputeStiffnessMatrix()
{
LinearAlgebra.Matrix <double> K = LinearAlgebra.Matrix <double> .Build.Dense(2, 2);
double x1 = Nodes[0].Point.X;
double y1 = Nodes[0].Point.Y;
double z1 = Nodes[0].Point.Z;
double x2 = Nodes[1].Point.X;
double y2 = Nodes[1].Point.Y;
double z2 = Nodes[1].Point.Z;
ElemLength = Math.Sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1) + (z2 - z1) * (z2 - z1));
K[0, 0] = Area * StiffnessModulus / ElemLength;
K[0, 1] = -Area * StiffnessModulus / ElemLength;
K[1, 0] = -Area * StiffnessModulus / ElemLength;
K[1, 1] = Area * StiffnessModulus / ElemLength;
// Tranform to global element stiffness matrix using transformation matrix G
double nxx = (x2 - x1) / ElemLength;
double nyx = (y2 - y1) / ElemLength;
double nzx = (z2 - z1) / ElemLength;
G[0, 0] = nxx;
G[0, 1] = nyx;
G[0, 2] = nzx;
G[1, 3] = nxx;
G[1, 4] = nyx;
G[1, 5] = nzx;
LinearAlgebra.Matrix <double> GT = G.Transpose();
LinearAlgebra.Matrix <double> KGlobal = (GT.Multiply(K)).Multiply(G);
return(KGlobal);
}
public double ComputeStress(List <double> elemDisplacements)
{
LinearAlgebra.Vector <double> elemDispVector = LinearAlgebra.Vector <double> .Build.Dense(elemDisplacements.ToArray());
double N = StiffnessModulus * Area / ElemLength * LinearAlgebra.Vector <double> .Build.Dense(new double[] { -1, 1 }).DotProduct(G.Multiply(elemDispVector));
return(N / Area);
}
public LinearAlgebra.Vector <double> solveEquations(LinearAlgebra.Matrix <double> stiffnessMatrix, LinearAlgebra.Vector <double> forceVector, List <int> boundaryDofs, List <double> boundaryConstraints)
{
int nDof = forceVector.Count;
// Find all dofs where force is known
List <int> allDofs = Enumerable.Range(0, nDof).ToList();
List <int> unknownDofs = allDofs.Except(boundaryDofs).ToList();
// Add the know displacements to the result
LinearAlgebra.Vector <double> displacementVector = LinearAlgebra.Vector <double> .Build.Dense(nDof);
for (int i = 0; i < boundaryDofs.Count; i++)
{
displacementVector[boundaryDofs[i]] = boundaryConstraints[i];
}
// Pick out part of matrix corresponding to known forces
int nrUnknownDofs = unknownDofs.Count;
LinearAlgebra.Matrix <double> unknownK = LinearAlgebra.Matrix <double> .Build.Dense(nrUnknownDofs, nrUnknownDofs);
LinearAlgebra.Vector <double> knownForces = LinearAlgebra.Vector <double> .Build.Dense(unknownDofs.Count);
for (int i = 0; i < unknownDofs.Count; i++)
{
for (int j = 0; j < unknownDofs.Count; j++)
{
unknownK[i, j] = stiffnessMatrix[unknownDofs[i], unknownDofs[j]];
}
knownForces[i] = forceVector[unknownDofs[i]];
}
LinearAlgebra.Matrix <double> unkownKnownK = LinearAlgebra.Matrix <double> .Build.Dense(nrUnknownDofs, boundaryDofs.Count);
for (int i = 0; i < unknownDofs.Count; i++)
{
for (int j = 0; j < boundaryDofs.Count; j++)
{
unkownKnownK[i, j] = stiffnessMatrix[unknownDofs[i], boundaryDofs[j]];
}
knownForces[i] = forceVector[unknownDofs[i]];
}
// Solve for the unknown displacements
LinearAlgebra.Vector <double> unknownDisplacements = unknownK.Inverse().Multiply(knownForces.Subtract(unkownKnownK.Multiply(LinearAlgebra.Vector <double> .Build.Dense(boundaryConstraints.ToArray()))));
// Insert the calculated displacements
for (int i = 0; i < unknownDofs.Count; i++)
{
displacementVector[unknownDofs[i]] = unknownDisplacements[i];
}
return(displacementVector);
}