public static void LU(Matrix matrix, out Matrix lowerMatrix, out Matrix upperMatrix)
{
if (!matrix.IsSquare())
{
throw new NonSquareMatrixException();
}
lowerMatrix = new Matrix(matrix.NumberOfRows, matrix.NumberOfColumns);
lowerMatrix.SetColumn(0, matrix.GetColumn(0));
upperMatrix = Matrix.Identity(matrix.NumberOfRows);
for (int i = 0; i < matrix.NumberOfRows; i++)
{
for (int j = i + 1; j < matrix.NumberOfColumns; j++)
{
for (int k = 0; k <= i - 1; k++)
{
upperMatrix[i, j] += lowerMatrix[i, k] * upperMatrix[k, j];
}
upperMatrix[i, j] = (matrix[i, j] - upperMatrix[i, j]) / lowerMatrix[i, i];
}
if (i == matrix.NumberOfColumns - 1)
{
continue;
}
for (int j = i + 1; j < matrix.NumberOfColumns; j++)
{
for (int k = 0; k <= i + 1 - 1; k++)
{
lowerMatrix[j, i + 1] += lowerMatrix[j, k] * upperMatrix[k, i + 1];
}
lowerMatrix[j, i + 1] = matrix[j, i + 1] - lowerMatrix[j, i + 1];
}
}
}
public EigenvaluesEigenvectors GetEigenvaluesEigenvectors()
{
if (!IsSymmetric())
{
throw new NotImplementedException();
}
//Q=wT * this * w
Matrix Q = this.Clone();
Matrix eigenvectors = Identity(this.NumberOfColumns);;
double threshold = Q.CalculateSumOfNonDiagonalElemets();
do
{
DoSweep(ref Q, ref eigenvectors);
threshold = Q.CalculateAbsoluteSumOfNonDiagonalElements();
} while (threshold > 0.0000000001);
//return W;
double[] eigenvalues = new double[eigenvectors.NumberOfColumns];
for (int i = 0; i < eigenvectors.NumberOfColumns; i++)
{
Matrix tempEigenvector = new Matrix(NumberOfRows, 1);
tempEigenvector.SetColumn(0, eigenvectors.GetColumn(i));
Matrix tempMultiplication = this * tempEigenvector;
eigenvalues[i] = tempMultiplication[0, 0] / tempEigenvector[0, 0];
}
return(new EigenvaluesEigenvectors(eigenvalues, eigenvectors));
}