/// <summary>
/// 計算多變量管制圖的 Tsquare decomposition
/// </summary>
/// <param name="data"></param>
/// <param name="mean"></param>
/// <param name="S"></param>
/// <returns></returns>
public static LinearAlgebra.Matrix <double> T2Decomposition(LinearAlgebra.Matrix <double> data, LinearAlgebra.Matrix <double> mean, LinearAlgebra.Matrix <double> S)
{
//mean 的 #column = #columns of data = #columns of covariance
if (data.ColumnCount != mean.ColumnCount || data.ColumnCount != S.ColumnCount || mean.ColumnCount != S.ColumnCount)
{
throw new ArgumentException("矩陣的維度無法計算");
}
LinearAlgebra.Matrix <double> invS = S.Inverse();
List <double> tsquare = new List <double>();
for (int i = 0; i < data.RowCount; i++)
{
tsquare.Add(CalculateTSquare(data.Row(i).ToRowMatrix(), mean, invS));
}
List <double> decoValue = new List <double>();
for (int c = 0; c < data.ColumnCount; c++)
{
LinearAlgebra.Matrix <double> subData = data.RemoveColumn(c);
LinearAlgebra.Matrix <double> subMean = mean.RemoveColumn(c);
LinearAlgebra.Matrix <double> subS = S.RemoveColumn(c).RemoveRow(c);
LinearAlgebra.Matrix <double> invSubS = subS.Inverse();
for (int r = 0; r < data.RowCount; r++)
{
decoValue.Add(tsquare[r] - CalculateTSquare(subData.Row(r).ToRowMatrix(), subMean, invSubS));
}
}
LinearAlgebra.Matrix <double> m = LinearAlgebra.Matrix <double> .Build.DenseOfColumnMajor(data.RowCount, data.ColumnCount, decoValue);
return(m);
}
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);
}