Add Parser

[AlexanderSinn]

This PR is based on #594

The use of amrex::Parser allows for expressions to be parsed from the input file instead of just numbers. In this PR all input Parameters, even the ones queried by AMReX, are obtained with this Parser, except for string.
It is possible to define user constants in the input script with my_constants. Some Physical constants are already provided.

my_constants.kp_inv = 10e-6
my_constants.kp = 1 / kp_inv
my_constants.wp = clight * kp
my_constants.ne = wp^2 * m_e * epsilon0 / q_e^2
plasma.density = ne

Already implemented but currently unused is the ability to define functions in the input script which can be evaluated in the GPU.

• Small enough (< few 100s of lines), otherwise it should probably be split into smaller PRs
• Tested (describe the tests in the PR description)
• Runs on GPU (basic: the code compiles and run well with the new module)
• Contains an automated test (checksum and/or comparison with theory)
• Documented: all elements (classes and their members, functions, namespaces, etc.) are documented
• Constified (All that can be const is const)
• Code is clean (no unwanted comments, )
• Style and code conventions are respected at the bottom of https://github.com/Hi-PACE/hipace
• Proper label and GitHub project, if applicable

[MaxThevenet]

Excellent, thanks a lot for this great PR!! You will find a few minor comments below.
As you mentioned in the description, the capability to read a function is implemented in getFunctionWithParser, but not used. I think the most useful one would be for <plasma>.density. Do you think you could implement that in a separate PR? I would suggest to read e.g.

<plasma>.density(x,y,z) = ne*(1.+(x^2+y*2)/R^2)

where we explicitly add (x,y,z) to the name of the queried parameter, just to inform the user that a function of space can be read here, and that the coordinates are called x, y and z.

[MaxThevenet]

Suggested change

	{"true", 1.},
	{"false", 0.}
	{"true", 1},
	{"false", 0}

[MaxThevenet]

Suggested change

//amrex::Parser parser(parse_function);

[MaxThevenet]

Why do you need to return the parser instead of only modifying the input argument? Could you do

void
initParser (amrex::Parser& parser, amrex::Vector<std::string> const& varnames) {

and call

initParser(parser, {}).compileHost<0>()();

instead of

val = initParser(parser, {}).compileHost<0>()();

?

[MaxThevenet]

Would that work too? Just to remind users that an int and a float are written differently. This also applies below.

Suggested change

	my_constants.kp_inv = 10e-6
	my_constants.kp = 1 / kp_inv
	my_constants.wp = clight * kp
	my_constants.ne = wp^2 * m_e * epsilon0 / q_e^2
	my_constants.kp_inv = 10.e-6
	my_constants.kp = 1. / kp_inv
	my_constants.wp = clight * kp
	my_constants.ne = wp^2 * m_e * epsilon0 / q_e^2

Also, while this is exactly how we convert between the SI and normalised input files, this is not what a new user would do (typically, they would set the electron density ne, and calculate kp etc. from it). Could you check this with @SeverinDiederichs?

[AlexanderSinn]

True, but no dot also works because the parser always uses double internally.

blowout_wake/inputs_ionization_SI calculates kp_inv from ne. Should another file do this too?

[MaxThevenet]

Let us keep this discussion for later. I think that examples/blowout_wake/inputs_SI is the first example people would look at, because it is the most usual use case, so we should make it meaningful. But let's keep it as is for now.

[MaxThevenet]

Suggested change

	geometry.prob_lo = -8*kp_inv -8*kp_inv -6*kp_inv # physical domain
	geometry.prob_hi = 8*kp_inv 8*kp_inv 6*kp_inv
	geometry.prob_lo = -8.*kp_inv -8.*kp_inv -6.*kp_inv # physical domain
	geometry.prob_hi = 8.*kp_inv 8.*kp_inv 6.*kp_inv

[MaxThevenet]

Lovely. Do you know when double-quotes "3*ne" are required? I assume it is at least the case for multi-line expressions, but apart from that does this always work without double quotes?

[AlexanderSinn]

Quotes are needed around the individual expressions of an array type like geometry.prob_lo if the expressions contain spaces. I also found that quotes can help if the expression uses functions like exp(x) and is inside a bash script.