internal static T DeterminantLaplace(GenTensor <T, TWrapper> t, int diagLength)
{
if (diagLength == 1)
{
return(t.GetValueNoCheck(0, 0));
}
var det = default(TWrapper).CreateZero();
var sign = default(TWrapper).CreateOne();
var temp = SquareMatrixFactory <T, TWrapper> .GetMatrix(diagLength - 1);
for (int i = 0; i < diagLength; i++)
{
Inversion <T, TWrapper> .GetCofactorMatrix(t, temp, 0, i, diagLength);
det = default(TWrapper).Add(det,
default(TWrapper).Multiply(
sign,
default(TWrapper).Multiply(
t.GetValueNoCheck(0, i),
DeterminantLaplace(temp, diagLength - 1)
))
);
sign = default(TWrapper).Negate(sign);
}
return(det);
}
public static GenTensor <T, TWrapper> Adjoint(GenTensor <T, TWrapper> t)
{
#if ALLOW_EXCEPTIONS
if (!t.IsSquareMatrix)
{
throw new InvalidShapeException("Matrix should be square");
}
#endif
var diagLength = t.Shape.shape[0];
if (diagLength is 1)
{
return(GenTensor <T, TWrapper> .CreateIdentityMatrix(1));
}
var res = GenTensor <T, TWrapper> .CreateSquareMatrix(diagLength);
var temp = SquareMatrixFactory <T, TWrapper> .GetMatrix(diagLength - 1);
if (diagLength == 1)
{
res.SetValueNoCheck(default(TWrapper).CreateOne(), 0, 0);
return(res);
}
var toNegate = false;
for (int x = 0; x < diagLength; x++)
{
for (int y = 0; y < diagLength; y++)
{
GetCofactorMatrix(t, temp, x, y, diagLength);
var cofactor = Determinant <T, TWrapper> .DeterminantGaussianSafeDivision(temp, diagLength - 1);
// TODO: is this statement correct?
toNegate = (x + y) % 2 == 1;
var minor = toNegate ? default(TWrapper).Negate(cofactor) : cofactor;
res.SetValueNoCheck(minor, y, x);
}
}
return(res);
}