/// <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]))
));
}
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);
}
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 matrix multiplication result
/// a and b are matrices
/// a.Shape[1] should be equal to b.Shape[0]
/// the resulting matrix is [a.Shape[0] x b.Shape[1]] shape
///
/// O(N^3)
/// </summary>
public static GenTensor <T> MatrixMultiply(GenTensor <T> a,
GenTensor <T> b)
{
#if ALLOW_EXCEPTIONS
if (!a.IsMatrix || !b.IsMatrix)
{
throw new InvalidShapeException($"Both {nameof(a)} and {nameof(b)} should be matrices");
}
if (a.Shape[1] != b.Shape[0])
{
throw new InvalidShapeException($"{nameof(a)}'s height must be equal to {nameof(b)}'s width");
}
#endif
var width = a.Shape[0];
var height = b.Shape[1];
var row = a.Shape[1];
var res = CreateMatrix(width, height);
for (int x = 0; x < width; x++)
{
for (int y = 0; y < height; y++)
{
var s = ConstantsAndFunctions <T> .CreateZero();
for (int i = 0; i < row; i++)
{
var v1 = a.GetValueNoCheck(x, i);
var v2 = b.GetValueNoCheck(i, y);
s = ConstantsAndFunctions <T> .Add(s, ConstantsAndFunctions <T> .Multiply(v1, v2));
}
res.SetValueNoCheck(s, x, y);
}
}
return(res);
}
// 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());
}
/// <summary>
/// Finds the scalar product of two vectors
///
/// O(N)
/// </summary>
public static T VectorDotProduct(GenTensor <T> a,
GenTensor <T> b)
{
#if ALLOW_EXCEPTIONS
if (!a.IsVector || !b.IsVector)
{
throw new InvalidShapeException($"{nameof(a)} and {nameof(b)} should be vectors");
}
if (a.Shape[0] != b.Shape[0])
{
throw new InvalidShapeException($"{nameof(a)}'s length should be the same as {nameof(b)}'s");
}
#endif
var res = ConstantsAndFunctions <T> .CreateZero();
for (int i = 0; i < a.Shape[0]; i++)
{
res = ConstantsAndFunctions <T> .Add(res,
ConstantsAndFunctions <T> .Multiply(a.GetValueNoCheck(i), b.GetValueNoCheck(i)));
}
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 static GenTensor <T> PiecewiseMultiply(GenTensor <T> a,
T b)
=> CreateTensor(a.Shape, ind =>
ConstantsAndFunctions <T> .Multiply(a[ind], b));