Move invert3x3 out of general purpose utils.hxx header

[ZedThree]

Only used in Coordinates, so make private implementation detail

Also return bool instead of int

[dschwoerer]

The negative small value is only used in tests.

As this is private, we can remove this usage.

Then the checks on the caller can be removed, making the code cleaner. Unfortunately I cannot suggest this, so I can push a commit if you agree, @ZedThree

[dschwoerer]

Suggested change

	// Non-default small
	input = 0.;
	input(0, 0) = 1.0e-12;
	input(1, 1) = 1.0;
	input(2, 2) = 1.0;
	EXPECT_NO_THROW(invert3x3(input, -1.0e-10));

[dschwoerer]

Suggested change

	/// If small is less than zero then instead of throwing we return false.
	/// This is ugly but can be used to support some use cases.

[dschwoerer]

Suggested change

	if (small >= 0) {
	throw BoutException("Determinant of matrix < {:e} --> Poorly conditioned", small);
	}
	return false;
	throw BoutException("Determinant of metric component {:e} < {:e} --> Poorly conditioned", std::abs(det), small);

[dschwoerer]

Suggested change

	bool invert3x3(Matrix<T>& a, T small = 1.0e-15) {
	void invert3x3(Matrix<T>& a, T small = 1.0e-15) {

[dschwoerer]

Suggested change

	return true;

[ZedThree]

Yes, I was tempted to do the same thing, although I realised the error message in Coordinates is actually more specific. We could rewrite the interface even further, we calculate all 9 elements and we only need 6!

So maybe we just remove the throw from invert3x3 but still return bool and do the error handling in Coordinates?

[dschwoerer]

Right now the error is thrown from invert3x3 - so the more specific error is actually not used.

We can throw a more specific error, as it is only used to invert the metric tensor.

[ZedThree]

Yes, exactly

[dschwoerer]

We could rewrite the interface even further, we calculate all 9 elements and we only need 6!

Introduce a new SymmetricMatrix<T> type :-)

[dschwoerer]

Looks good, thanks @ZedThree

[dschwoerer]

This could be 3D compatible:

Suggested change

	"\tERROR: metric tensor is singular at ({:d}, {:d}), determinant: {:d}\n",
	i.x(), i.y(), det.value());
	"\tERROR: metric tensor is singular at {}, determinant: {:d}\n",
	i, det.value());

[ZedThree]

Nice, good catch, thanks!

[dschwoerer]

same:

Suggested change

	"\tERROR: metric tensor is singular at ({:d}, {:d}), determinant: {:d}\n",
	i.x(), i.y(), det.value());
	"\tERROR: metric tensor is singular at {}, determinant: {:d}\n",
	i, det.value());

[dschwoerer]

Is the explicit constructor really needed? Could this not be:

Suggested change

	return std::optional<BoutReal>{det};
	return det;

[ZedThree]

Not sure, will check