added NPRK trees functionality in src/NPRKTrees.jl and tests in test/…

[btranmath]

+ src/NPRKTrees.jl
+ test/nprktrees_test.jl

adding functionality for NPRK trees in NPRKTrees module and tests in test/nprktrees_test.jl including:

src/NPRKTrees.jl

• ARKTreeIterator: returns a Vector of ColoredRootedTrees containing all (non-equivalent) ARK trees of a given number of colors and given order

• NPRKTreeIterator: returns a Vector of ColoredRootedTrees containing all (non-equivalent) NPRK trees of a given number of colors and given order

• isMultiColored: determines whether a ColoredRootedTree (either ARK or NPRK tree specified as a Bool in the argument) contains multiple colors

• GetParentIndex: given a node in a tree, returns the index in the level sequence of the parent node

• isColorBranching: determines whether an NPRK tree is color branching, i.e., contains at least one node with two outward edges of differing colors

• elementaryWeightNPRK2: given an NPRK tableau $A$ (cubic 3-tensor) and $b$ (square matrix) and an NPRK tree $\tau$ corresponding to 2 partitions (i.e., 2 colors), returns the elementary weight of that tree, $\Phi(\tau)$, i.e., the LHS of the order condition

• residualNPRK2: computes the residual of the order condition with the same as input as above, i.e., $|\Phi(\tau) - 1/\gamma(\tau)|$ (where $\gamma(\tau)$ denotes the tree density).

test/nprktrees_test.jl

• tests to confirm that these functions work

[ranocha]

Thanks a lot for your contribution. Please find below some general comments that also apply to other parts of the code. Please let me know if I can help you with that.

[ranocha]

Suggested change

	function isMultiColored(colored_tree::ColoredRootedTree, root_color_fixed::Bool)::Bool
	function is_multi_colored(colored_tree::ColoredRootedTree, root_color_fixed::Bool)

In Julia, the general convention is to use snake_case for function and variable names, see https://docs.julialang.org/en/v1/manual/variables/#Stylistic-Conventions. Moreover, it's not typical to assert the return type.

[btranmath]

Thanks Hendrik for your comments; I am not too familiar with Julia conventions so I appreciate the suggestions. I will revise when I get the chance.

[ranocha]

Suggested change

	return ~allequal(colorseq)
	else
	return ~allequal(colored_tree.color_sequence)
	return !allequal(colorseq)
	else
	return !allequal(colored_tree.color_sequence)

~ is bitwise not, while ! is the general not operation that is more common in Julia code.

[ranocha]

Suggested change

	function GetParentIndex(levelseq::Vector, nodeindex::Int64)::Int64
	toReturn = 0
	for i in reverse(1:length(levelseq))
	if levelseq[i] == levelseq[nodeindex]-1
	toReturn = i
	break
	end
	end
	return toReturn
	end
	function get_parent_index(levelseq::AbstractVector, nodeindex::Integer)
	to_return = 0
	for i in reverse(eachindex(levelseq))
	if levelseq[i] == levelseq[nodeindex] - 1
	to_return = i
	break
	end
	end
	return to_return
	end

See the comments on the style above. In general, Julia does not require strict type constraints in function arguments; see, e.g., https://docs.julialang.org/en/v1/manual/style-guide/#Avoid-writing-overly-specific-types

[ranocha]

This is again too restrictive - we would like to be able to compute with Float32, rational numbers, symbolic expressions etc. as well.

[ranocha]

Could you please add using Test and add some @test statements explicitly to this file so that test results do not need to be checked manually but are checked automatically?