General Helpers

General utility functions that are used throughout Mantis.

All docstrings from Mantis.GeneralHelpers

Mantis.GeneralHelpers.export_path Method

export_path(output_directory_tree::Vector{String}, filename::String)

Create a directory (if needed) and return the path to the output file.

Arguments

• output_directory_tree::Vector{String}: A vector of strings representing the directory tree.

• filename::String: The name of the output file.

Example

output_file = export_path(["examples", "data", "output"], "output.vtk") # "examples/data/output/output.vtk"

source

Mantis.GeneralHelpers.get_derivative_idx Function

get_derivative_idx(der_key::Vector{Int})

Convert the given derivative key to a linear index corresponding to its storage location.

If local_basis corresponds to basis evaluations for some manifold_dim-variate function space, then its k-th derivatives will all be stored in the location local_basis[k+1]. Moreover, the k-th derivative corresponding to the key [i₁,i₂,...,iₙ] in the location local_basis[k+1][m] where:

• m = 1 when iⱼ = 0 for all j, i.e., for basis function values;

• m = 1+r when iⱼ = 0 for all j except for j = r and iⱼ = 1, i.e., for the first derivative w.r.t. the j-th canonical coordinate;

• in all other cases (i.e., when k>1), the value of m is equal to l if [i₁,i₂,...,iₙ] is the l-th key returned by the function integer_sums(k, manifold_dim).

As an example, consider the first derivative with respect to x₁ (∂/∂x₁) in 2D, which has key [1, 0]. In 3D, this same derivative has key [1, 0, 0]. In 3D, the derivative ∂³/∂x₁²∂x₂ thus has key [2, 1, 0].

Arguments

• der_key::Vector{Int}: A key for the desired derivative order.

Returns

• ::Int: The linear index corresponding to the derivative's storage location in basis evaluations.

source

Mantis.GeneralHelpers.integer_sums Function

integer_sums(sum_indices::Int, num_indices::Int)

Generates all possible combinations of non-negative integers that sum up to a given value, where each combination has a specified number of elements.

Arguments

• sum_indices::Int: The target sum of the integers in each combination.

• num_indices::Int: The number of integers in each combination.

Returns

• ::Vector{Vector{Int}}: Each inner vector represents a combination of integers that sum up to sum_indices. If no valid combinations exist, the vectors are empty.

source