/// <summary>
/// Inverts a matrix A to B so that A * B = I
/// Borrowed from here: https://www.geeksforgeeks.org/adjoint-inverse-matrix/
///
/// O(N^5)
/// </summary>
public void InvertMatrix()
{
#if ALLOW_EXCEPTIONS
if (!IsSquareMatrix)
{
throw new InvalidShapeException("this should be a square matrix");
}
#endif
var diagLength = Shape.shape[0];
var det = DeterminantGaussianSafeDivision();
#if ALLOW_EXCEPTIONS
if (ConstantsAndFunctions <T> .IsZero(det))
{
throw new InvalidDeterminantException("Cannot invert a singular matrix");
}
#endif
var adj = Adjoint();
for (int x = 0; x < diagLength; x++)
{
for (int y = 0; y < diagLength; y++)
{
this.SetValueNoCheck(
ConstantsAndFunctions <T> .Divide(
adj.GetValueNoCheck(x, y),
det
),
x, y
);
}
}
}
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);
}
// 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);
}
public W Count() => ConstantsAndFunctions <W> .Divide(num, den);
public static GenTensor <T> PiecewiseDivide(
T a, GenTensor <T> b)
=> CreateTensor(b.Shape, ind =>
ConstantsAndFunctions <T> .Divide(a, b[ind]));
public static GenTensor <T> PiecewiseDivide(GenTensor <T> a,
T b)
=> CreateTensor(a.Shape, ind =>
ConstantsAndFunctions <T> .Divide(a[ind], b));