internal T DeterminantLaplace(int diagLength)
{
if (diagLength == 1)
{
return(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(0, 0)));
}
var det = ConstantsAndFunctions <T> .CreateZero();
var sign = ConstantsAndFunctions <T> .CreateOne();
var temp = SquareMatrixFactory <T> .GetMatrix(diagLength);
for (int i = 0; i < diagLength; i++)
{
GetCofactor(this, temp, 0, i, diagLength);
det = ConstantsAndFunctions <T> .Add(det,
ConstantsAndFunctions <T> .Multiply(
sign,
ConstantsAndFunctions <T> .Multiply(
this.GetValueNoCheck(0, i),
temp.DeterminantLaplace(diagLength - 1)
))
);
sign = ConstantsAndFunctions <T> .Negate(sign);
}
return(det);
}
/// <summary>
/// Returns adjugate matrix
///
/// O(N^5)
/// </summary>
public GenTensor <T> Adjoint()
{
#if ALLOW_EXCEPTIONS
if (!IsSquareMatrix)
{
throw new InvalidShapeException("Matrix should be square");
}
#endif
var diagLength = Shape.shape[0];
var res = GenTensor <T> .CreateSquareMatrix(diagLength);
var temp = SquareMatrixFactory <T> .GetMatrix(diagLength);
if (diagLength == 1)
{
res.SetValueNoCheck(ConstantsAndFunctions <T> .CreateOne(), 0, 0);
return(res);
}
var toNegate = false;
for (int x = 0; x < diagLength; x++)
{
for (int y = 0; y < diagLength; y++)
{
GetCofactor(this, temp, x, y, diagLength);
toNegate = (x + y) % 2 == 1;
var det = temp.DeterminantGaussianSafeDivision(diagLength - 1);
if (toNegate)
{
res.SetValueNoCheck(ConstantsAndFunctions <T> .Negate(det), y, x);
}
else
{
res.SetValueNoCheck(det, y, x);
}
}
}
return(res);
}
internal static GenTensor <int, IntWrapper> TestGetMatrixExposed(int diagLength) => SquareMatrixFactory <int, IntWrapper> .GetMatrix(diagLength);
