private GenTensor <SafeDivisionWrapper <T> > InnerGaussianEliminationSafeDivision(int n)
{
InitIfNotInitted();
var elemMatrix = GenTensor <SafeDivisionWrapper <T> >
.CreateMatrix(n, n,
(x, y) => new SafeDivisionWrapper <T>(ConstantsAndFunctions <T> .Forward(this.GetValueNoCheck(x, y)))
);
for (int k = 1; k < n; k++)
{
for (int j = k; j < n; j++)
{
var m = ConstantsAndFunctions <SafeDivisionWrapper <T> > .Divide(
elemMatrix.GetValueNoCheck(j, k - 1),
elemMatrix.GetValueNoCheck(k - 1, k - 1)
);
for (int i = 0; i < n; i++)
{
var curr = elemMatrix.GetValueNoCheck(j, i);
elemMatrix.SetValueNoCheck(ConstantsAndFunctions <SafeDivisionWrapper <T> > .Subtract(
curr,
ConstantsAndFunctions <SafeDivisionWrapper <T> > .Multiply(
m,
elemMatrix.GetValueNoCheck(k - 1, i)
)
), j, i);
}
}
}
return(elemMatrix);
}
/// <summary>
/// Finds a perpendicular vector to two given
/// TODO: So far only implemented for 3D vectors
/// </summary>
public static GenTensor <T> VectorCrossProduct(GenTensor <T> a,
GenTensor <T> b)
{
#if ALLOW_EXCEPTIONS
if (!a.IsVector || !b.IsVector)
{
throw new InvalidShapeException($"Both {nameof(a)} and {nameof(b)} should be vectors");
}
if (a.Shape[0] != b.Shape[0])
{
throw new InvalidShapeException($"Length of {nameof(a)} and {nameof(b)} should be equal");
}
if (a.Shape[0] != 3)
{
throw new NotImplementedException("Other than vectors of the length of 3 aren't supported for VectorCrossProduct yet");
}
#endif
return(GenTensor <T> .CreateVector(
ConstantsAndFunctions <T> .Subtract(
ConstantsAndFunctions <T> .Multiply(a[1], b[2]),
ConstantsAndFunctions <T> .Multiply(a[2], b[1])),
ConstantsAndFunctions <T> .Subtract(
ConstantsAndFunctions <T> .Multiply(a[2], b[0]),
ConstantsAndFunctions <T> .Multiply(a[0], b[2])),
ConstantsAndFunctions <T> .Subtract(
ConstantsAndFunctions <T> .Multiply(a[0], b[1]),
ConstantsAndFunctions <T> .Multiply(a[1], b[0]))
));
}
// 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);
}
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());
}
public static GenTensor <T> PiecewiseSubtract(
T a, GenTensor <T> b)
=> CreateTensor(b.Shape, ind =>
ConstantsAndFunctions <T> .Subtract(a, b[ind]));
public static GenTensor <T> PiecewiseSubtract(GenTensor <T> a,
T b)
=> CreateTensor(a.Shape, ind =>
ConstantsAndFunctions <T> .Subtract(a[ind], b));