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);
}
public static void InvertMatrix(GenTensor <T, TWrapper> t)
{
#if ALLOW_EXCEPTIONS
if (!t.IsSquareMatrix)
{
throw new InvalidShapeException("this should be a square matrix");
}
#endif
var diagLength = t.Shape.shape[0];
if (diagLength is 1)
{
t.SetValueNoCheck(
default(TWrapper).Divide(
default(TWrapper).CreateOne(),
t.GetValueNoCheck(0, 0)
), 0, 0);
return;
}
var det = Determinant <T, TWrapper> .DeterminantGaussianSafeDivision(t);
#if ALLOW_EXCEPTIONS
if (default(TWrapper).IsZero(det))
{
throw new InvalidDeterminantException("Cannot invert a singular matrix");
}
#endif
var adj = Adjoint(t);
for (int x = 0; x < diagLength; x++)
{
for (int y = 0; y < diagLength; y++)
{
t.SetValueNoCheck(
default(TWrapper).Divide(
adj.GetValueNoCheck(x, y),
det
),
x, y
);
}
}
}