internal static T DeterminantGaussianSafeDivision(GenTensor <T, TWrapper> t, int diagLength)
{
#if ALLOW_EXCEPTIONS
if (!t.IsMatrix)
{
throw new InvalidShapeException("this should be matrix");
}
if (t.Shape[0] != t.Shape[1])
{
throw new InvalidShapeException("this should be square matrix");
}
#endif
if (t.Shape[0] == 1)
{
return(t.GetValueNoCheck(0, 0));
}
var n = diagLength;
var elemMatrix = EchelonForm <T, TWrapper> .InnerGaussianEliminationSafeDivision(t, n, n, out var swapCount);
var det = default(EchelonForm <T, TWrapper> .WrapperSafeDivisionWrapper <T, TWrapper>).CreateOne();
for (int i = 0; i < n; i++)
{
det = default(EchelonForm <T, TWrapper> .WrapperSafeDivisionWrapper <T, TWrapper>).Multiply(det, elemMatrix.GetValueNoCheck(i, i));
}
if (default(TWrapper).IsZero(det.den))
{
return(default(TWrapper).CreateZero());
}
return(swapCount % 2 is 0 ? det.Count() : default(TWrapper).Negate(det.Count()));
}
internal static GenTensor <SafeDivisionWrapper <T, TWrapper>, WrapperSafeDivisionWrapper <T, TWrapper> > InnerGaussianEliminationSafeDivision(GenTensor <T, TWrapper> t, int m, int n, out int swapCount)
{
var elemMatrix = t.SimpleToSafeDivision();
swapCount = 0;
EchelonForm <SafeDivisionWrapper <T, TWrapper>, WrapperSafeDivisionWrapper <T, TWrapper> > .InnerGaussianEliminationSimple(elemMatrix, 0, ref swapCount);
return(elemMatrix);
}
