Currently IsSymmetric() is implemented as a generic method on IComparable. It would be good if it accepted a tolerance. For large symmetric matrices, it feels restrictive if a tiny floating point error caused this to return false.

Will need to be a T4 template job (or just a few special cases like double and float) as IComparable does not allow difference comparisons (AFAIK). I imagine it is faster if it's not generic. Proposed API:

/// Some lovely comments...
/// param isRelative: whether matrix is symmetric based on the relative or absolute error
public static double IsSymmetric(this double[,] a, double tol = 0, bool isRelativeError = false)

so you could say, M[i,j] cannot be different to M[j,i] by more than 0.0001% or maybe 1e-12 etc.

Question

@cesarsouza Is this useful or am I being paranoid (I want it for #832)? Can you envisage any scenario where a matrix that should be symmetric is not exactly symmetric because of tiny rounding errors? if you can, assign this to me, if you can't, feel free to close this issue.

Thanks!
Alex