SmallMatrix: Matrix class with compile time size

[WeiqunZhang]

Add amrex::SmallMatrix class with compile time size.

Useful for, e.g.:

• [Draft] Transport and Covariance Matrices ECP-WarpX/impactx#714
• Add beam eigenemittances to reduced diagnostics. ECP-WarpX/impactx#702

[zingale]

it would be good to have a .setVal() method to set all elements to a value.

[WeiqunZhang]

Notes on why SmallMatrix matrix{} is zero initialized.

SmallMatrix is not an aggregate, because it has a user declared default
constructor. The rule is that, for SmallMatrix matrix{} with an empty
brace-enclosed initializer list, value-initialization is performed. The
effects of value-initialization of SmallMatrix (which has a user-declared
but not user-provided default constructor) are that the matrix object is
first zero-initialized and then the object's default constructor is
applied. Since the default constructor does nothing, the final result is
the object is zero-initialized.

Why is SmallMatrix's default constructor user-declared not user-provided?
It's because we first declare it with SmallMatrix () = default.

Reference:
https://en.cppreference.com/w/cpp/language/list_initialization
https://en.cppreference.com/w/cpp/language/value_initialization
https://en.cppreference.com/w/cpp/language/zero_initialization

[ax3l]

Is SmallMatrix<Real, N, M> m; also zero-defined then or is it allocated but values are undefined?

[ax3l]

FYI @cemitch99

[WeiqunZhang]

It's uninitialized by default.

/**
 * \brief Default constructor
 *
 * The data are uninitialized by default. If you want to initialize
 * to zero, you can do `SmallMatrix<T,NRows,NCols> M{};`.
 */
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
constexpr SmallMatrix () = default;

[ax3l]

That is super useful, I think that is all we currently need 🚀 ✨

[ax3l]

Nice, very useful!