public void TestInverse2x2b()
{
const int n = 2;
float[,] a = new float[n, n] {
{ 1, 2 },
{ 3, 4 }
};
float[,] aInv = (float[, ])a.Clone();
Lapack.Inverse(aInv, n);
float[,] eye = new float[n, n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
eye[i, j] += a[i, k] * aInv[k, j];
}
}
}
AssertArray.AreAlmostEqual(1f, eye[0, 0]);
AssertArray.AreAlmostEqual(0f, eye[0, 1]);
AssertArray.AreAlmostEqual(0f, eye[1, 0]);
AssertArray.AreAlmostEqual(1f, eye[1, 1]);
}
public static Array <float> PowerMethod(Array <float> a)
{
// https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse
// init A(0) = (A*A + dI)-1.A*
var d = 1e-6f;
var result = a.T.Dot(a) + d * NN.Eye(a.Shape[1]);
Lapack.Inverse(result.Values, result.Shape[0]);
result = result.Dot(a.T);
// iterate: A(i+1) = 2A(i) - A(i).A.A(i)
for (int i = 0; i < 2; i++)
{
result = 2 * result - result.Dot(a).Dot(result);
}
return(result);
}
