/// <summary>
/// Determines whether the matrix is diagonal.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns><c>true</c> if the matrix is both lower and upper triangular; otherwise, <c>false</c>.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
public static Boolean IsDiagonal(this Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException(nameof(matrix));
}
return(MatrixComputations.IsUpperTriangular(matrix) && MatrixComputations.IsLowerTriangular(matrix));
}
/// <summary>
/// Initializes a new instance of the <see cref="CholeskyDecomposition" /> class.
/// </summary>
/// <param name="matrix">The matrix of which the decomposition is computed.</param>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="System.ArgumentException">The matrix is not symmetric.</exception>
public CholeskyDecomposition(Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException(nameof(matrix));
}
if (!MatrixComputations.IsSymmetric(matrix))
{
throw new ArgumentException(NumericsMessages.MatrixIsNotSymmetric, nameof(matrix));
}
this.matrix = matrix;
}
/// <summary>
/// Tridiagonalizes the specified matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>The tridiagonalization of the <paramref name="matrix" />.</returns>
/// <exception cref="System.ArgumentNullException">The matrix is null.</exception>
/// <exception cref="System.ArgumentException">
/// The matrix is not square.
/// or
/// The matrix is not symmetric.
/// </exception>
public static Matrix Tridiagonalize(Matrix matrix)
{
if (matrix == null)
{
throw new ArgumentNullException(nameof(matrix));
}
if (!matrix.IsSquare)
{
throw new ArgumentException(NumericsMessages.MatrixIsNotSquare, nameof(matrix));
}
if (!MatrixComputations.IsSymmetric(matrix))
{
throw new ArgumentException(NumericsMessages.MatrixIsNotSymmetric, nameof(matrix));
}
Matrix tridiagonalMatrix = new Matrix(matrix);
for (Int32 columnIndex = 0; columnIndex < matrix.NumberOfColumns - 2; columnIndex++)
{
Double[] column = tridiagonalMatrix.GetColumn(columnIndex);
Double sum = 0;
for (Int32 index = columnIndex + 1; index < column.Length; index++)
{
sum += column[index] * column[index];
}
Double alpha = -Math.Sign(column[columnIndex + 1]) * Math.Sqrt(sum);
Double r = Math.Sqrt(0.5 * (alpha * alpha - column[columnIndex + 1] * alpha));
Vector v = new Vector(column.Length);
v[columnIndex + 1] = (column[columnIndex + 1] - alpha) / 2 / r;
for (Int32 j = columnIndex + 2; j < column.Length; j++)
{
v[j] = column[j] / 2 / r;
}
Matrix p = MatrixFactory.CreateIdentity(column.Length) - 2 * v * v.Transpose();
tridiagonalMatrix = p * tridiagonalMatrix * p;
}
return(tridiagonalMatrix);
}
