/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Cholesky_decomposition">Cholesky decomposition</seealso>
public void Run()
{
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create square, symmetric, positive definite matrix
var matrix = new DenseMatrix(new[,] { { 2.0, 1.0 }, { 1.0, 2.0 } });
Console.WriteLine(@"Initial square, symmetric, positive definite matrix");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Perform Cholesky decomposition
var cholesky = matrix.Cholesky();
Console.WriteLine(@"Perform Cholesky decomposition");
// 1. Lower triangular form of the Cholesky matrix
Console.WriteLine(@"1. Lower triangular form of the Cholesky matrix");
Console.WriteLine(cholesky.Factor.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Reconstruct initial matrix: A = L * LT
var reconstruct = cholesky.Factor * cholesky.Factor.Transpose();
Console.WriteLine(@"2. Reconstruct initial matrix: A = L*LT");
Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Get determinant of the matrix
Console.WriteLine(@"3. Determinant of the matrix");
Console.WriteLine(cholesky.Determinant);
Console.WriteLine();
// 4. Get log determinant of the matrix
Console.WriteLine(@"4. Log determinant of the matrix");
Console.WriteLine(cholesky.DeterminantLn);
Console.WriteLine();
}
public void CholeskyFailsWithNonSquareMatrix()
{
var matrix = new DenseMatrix(3, 2);
Assert.That(() => matrix.Cholesky(), Throws.ArgumentException);
}