/// <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
);
}
}
}
/// <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());
}
