/// <summary>
/// Solves a system of linear equations, <b>Ax = b</b>.
/// </summary>
/// <param name="factor">A coefficient matrix A.</param>
/// <param name="right">A right-hand vector b.</param>
/// <returns>
/// Returns a vector x that is a solution of the system of linear equations, <b>Ax = b</b>.
/// </returns>
public Vector Solve(Matrix factor, Vector right)
{
if (factor == null)
{
throw new ArgumentNullException("Factor matrix cannot be null.");
}
if (right == null)
{
throw new ArgumentNullException("Right vector cannot be null.");
}
if (factor.Rows != right.Size)
{
throw new ArgumentException("Factor matrix and right vector have inconsistence size.");
}
var decomposition = new CholeskyDecomposition();
var(l, lt) = decomposition.Decompose(factor);
var y = SolveLower(l, right);
var x = SolveUpper(lt, y);
return(x);
}
public void CholeskyDecomposition_CalculateLLtMatrices_ReturnsAsExpected()
{
var choleskyDecomposition = new CholeskyDecomposition();
var matrix = new Matrix(3, 3, new double[, ] {
{ 81, -45, 45 }, { -45, 50, -15 }, { 45, -15, 38 }
});
var expectedL = new Matrix(3, 3, new double[, ] {
{ 9, 0, 0 }, { -5, 5, 0 }, { 5, 2, 3 }
});
var expectedLt = new Matrix(3, 3, new double[, ] {
{ 9, -5, 5 }, { 0, 5, 2 }, { 0, 0, 3 }
});
var(l, lt) = choleskyDecomposition.Decompose(matrix);
Assert.AreEqual(expectedL, l);
Assert.AreEqual(expectedLt, lt);
}