/// <summary>
/// Computes the BFGS correction formula for inverse hessiana approximation.
/// </summary>
/// <param name="func">Function to find it the hessiana approximation.</param>
/// <param name="b">Current inverse approximation of the hessiana.</param>
/// <param name="x">Current vector of the minimization Quasi-Newton algorithm.</param>
/// <param name="x1">Next vector of the minimization Quasi-Newton algorithm.</param>
/// <returns>Returns a matrix representing the next step in inverse hessiana approximation.s</returns>
public static Matrix Bfgs(CompiledFunc func, Matrix b, Vector x, Vector x1)
{
var sk = new Matrix(x1 - x);
var yk = new Matrix(func.Differentiate(x1) - func.Differentiate(x));
var t = b.Dot(sk.Transpose()).Dot(sk).Dot(b)/sk.Dot(b).Dot(sk.Transpose())[0,0];
var t1 = yk.Transpose().Dot(yk)/yk.Dot(sk.Transpose())[0,0];
return b - t + t1;
}
public void DotValues()
{
var m1 = new Matrix(new[] {1, 2, 3}, new[] {1, 2, 3});
var m2 = new Matrix(new[] { 4, 5 }, new[] { 4, 5 }, new []{4, 5});
var res = m1.Dot(m2);
Assert.AreEqual(2, res.Rows);
Assert.AreEqual(2, res.Columns);
Assert.AreEqual(24, res[0, 0]);
Assert.AreEqual(30, res[0, 1]);
Assert.AreEqual(24, res[1, 0]);
Assert.AreEqual(30, res[1, 1]);
}
