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);
}
// TODO: how to avoid code duplication?
/// <summary>
/// Performs simple Gaussian elimination method on a tensor
///
/// O(N^3)
/// </summary>
public T DeterminantGaussianSimple()
{
#if ALLOW_EXCEPTIONS
if (!IsMatrix)
{
throw new InvalidShapeException("this should be matrix");
}
if (Shape[0] != Shape[1])
{
throw new InvalidShapeException("this should be square matrix");
}
#endif
if (Shape[0] == 1)
{
return(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(0, 0)));
}
var n = Shape[0];
var elemMatrix = this.Forward();
for (int k = 1; k < n; k++)
{
for (int j = k; j < n; j++)
{
var m = ConstantsAndFunctions <T> .Divide(
ConstantsAndFunctions <T> .Forward(elemMatrix.GetValueNoCheck(j, k - 1)),
ConstantsAndFunctions <T> .Forward(elemMatrix.GetValueNoCheck(k - 1, k - 1))
);
for (int i = 0; i < n; i++)
{
var curr = ConstantsAndFunctions <T> .Forward(elemMatrix.GetValueNoCheck(j, i));
elemMatrix.SetValueNoCheck(ConstantsAndFunctions <T> .Subtract(
curr,
ConstantsAndFunctions <T> .Multiply(
m,
elemMatrix.GetValueNoCheck(k - 1, i)
)
), j, i);
}
}
}
var det = ConstantsAndFunctions <T> .CreateOne();
for (int i = 0; i < n; i++)
{
det = ConstantsAndFunctions <T> .Multiply(det, elemMatrix.GetValueNoCheck(i, i));
}
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);
}
/// <summary>
/// Finds Determinant with possible overflow
/// because it uses fractions for avoiding division
///
/// O(N^3)
/// </summary>
internal T DeterminantGaussianSafeDivision(int diagLength)
{
InitIfNotInitted();
#if ALLOW_EXCEPTIONS
if (!IsMatrix)
{
throw new InvalidShapeException("this should be matrix");
}
if (Shape[0] != Shape[1])
{
throw new InvalidShapeException("this should be square matrix");
}
#endif
if (Shape[0] == 1)
{
return(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(0, 0)));
}
var n = diagLength;
var elemMatrix = InnerGaussianEliminationSafeDivision(n);
var det =
ConstantsAndFunctions <SafeDivisionWrapper <T> > .CreateOne();
for (int i = 0; i < n; i++)
{
det = ConstantsAndFunctions <SafeDivisionWrapper <T> > .Multiply(det, elemMatrix.GetValueNoCheck(i, i));
}
if (ConstantsAndFunctions <T> .IsZero(det.den))
{
return(ConstantsAndFunctions <T> .CreateZero());
}
return(det.Count());
}
public SafeDivisionWrapper(W val)
{
num = val;
den = ConstantsAndFunctions <W> .CreateOne();
}
private static void InitIfNotInitted()
{
if (isFracInitted)
{
return;
}
isFracInitted = true;
ConstantsAndFunctions <SafeDivisionWrapper <T> > .Add =
(a, b) =>
new SafeDivisionWrapper <T>(
ConstantsAndFunctions <T> .Add(
ConstantsAndFunctions <T> .Multiply(a.num, b.den),
ConstantsAndFunctions <T> .Multiply(a.den, b.num)
),
ConstantsAndFunctions <T> .Multiply(a.den, b.den)
);
ConstantsAndFunctions <SafeDivisionWrapper <T> > .Subtract =
(a, b) =>
new SafeDivisionWrapper <T>(
ConstantsAndFunctions <T> .Subtract(
ConstantsAndFunctions <T> .Multiply(a.num, b.den),
ConstantsAndFunctions <T> .Multiply(a.den, b.num)
),
ConstantsAndFunctions <T> .Multiply(a.den, b.den)
);
ConstantsAndFunctions <SafeDivisionWrapper <T> > .Multiply =
(a, b) =>
new SafeDivisionWrapper <T>(
ConstantsAndFunctions <T> .Multiply(a.num, b.num),
ConstantsAndFunctions <T> .Multiply(a.den, b.den)
);
ConstantsAndFunctions <SafeDivisionWrapper <T> > .Divide =
(a, b) =>
new SafeDivisionWrapper <T>(
ConstantsAndFunctions <T> .Multiply(a.num, b.den),
ConstantsAndFunctions <T> .Multiply(a.den, b.num)
);
ConstantsAndFunctions <SafeDivisionWrapper <T> > .CreateOne = () =>
new SafeDivisionWrapper <T>(ConstantsAndFunctions <T> .CreateOne());
}
