Adjacency
This handles adjacency matrices between entities of polyhedral complexes, e.g. nodes, cells, edges etc.
An adjacency is described by an Adjacency matrix, which is a sparse matrix whose entries a 0 or 1. While such a matrix always can be stored as a SparseMatrixCSC, in general this would be a waste of storage.
For the general case, it is sufficient to only store the column start indieces and the column entries (row numbers), and to implicitly assume that nonzero entries are 1. This kind of storage is realised in a VariableTargetAdjacency.
In many cases, this can be compressed even more, if each column has the same length. In that case, a Matrix is sufficient to store the data. This is the usual base for implementing FEM/FVM assembly, and the interface for the general case should be similar.
From these ideas we develop the following interface for an adjacency a.
In order to avoid name confusion, we introduce the following notation which should be consistent with the use in assembly loops.
source: source of adjacency link
target: target of adjacency linkE.g. the cell-node adjacency for FEM assembly links a number of cells with a collection of nodes. The cells are the sources, and the targets are the nodes.
getindex(a,i,isource) aka a[i,isource]: return i-th target of source j
num_sources(a): overall number of sources, e.g. number of cells
num_targets(a): overall number of targets
num_targets(a,isource): number of targets for source given by isource
num_links(a): number of links aka nonzero entries of adjacency matrix
show(a): print stuffFurther API ideas:
- Convert between Matrix and Variable target stuff using 0 entries as "padding"
API
ExtendableGrids.Adjacency — Type
Adjacency{T}Adjacency type as union of FixedTargetAdjacency and VariableTargetAdjacency
ExtendableGrids.Adjacency — Method
Constructors for Adjacency
ExtendableGrids.FixedTargetAdjacency — Type
mutable struct Array{T, 2} <: DenseArray{T, 2}Use Matrix to store fixed target adjacency
ExtendableGrids.SerialVariableTargetAdjacency — Method
SerialVariableTargetAdjacency(
) -> SerialVariableTargetAdjacency{Int64}
Create an empty SerialVariableTargetAdjacency with default type
ExtendableGrids.SerialVariableTargetAdjacency — Method
SerialVariableTargetAdjacency(
t::Type{T}
) -> SerialVariableTargetAdjacency
Create an empty SerialVariableTargetAdjacency
ExtendableGrids.VariableTargetAdjacency — Type
struct VariableTargetAdjacency{T}Adjacency struct. Essentially, this is the sparsity pattern of a matrix whose nonzero elements all have the same value in the CSC format.
ExtendableGrids.VariableTargetAdjacency — Method
VariableTargetAdjacency() -> VariableTargetAdjacency{Int64}
Create an empty VariableTargetAdjacency with default type
ExtendableGrids.VariableTargetAdjacency — Method
VariableTargetAdjacency(
m::Array{T, 2}
) -> VariableTargetAdjacency
Create a VariableTargetAdjacency from Matrix
ExtendableGrids.VariableTargetAdjacency — Method
VariableTargetAdjacency(
m::SparseArrays.SparseMatrixCSC{Tv<:Integer, Ti<:Integer}
) -> VariableTargetAdjacency{Ti} where Ti<:Integer
Create variable target adjacency from adjacency matrix
ExtendableGrids.VariableTargetAdjacency — Method
VariableTargetAdjacency(
t::Type{T}
) -> VariableTargetAdjacency
Create an empty VariableTargetAdjacency
Base.:(==) — Method
==(a, b)
Comparison of two adjacencies
Base.:(==) — Method
==(a, b)
Comparison of two adjacencies
Base.append! — Method
append!(adj::SerialVariableTargetAdjacency, len) -> Vector
Append a column to adjacency.
Base.append! — Method
append!(adj::VariableTargetAdjacency, column) -> Vector
Append a column to adjacency.
Base.getindex — Method
getindex(
adj::SerialVariableTargetAdjacency,
i,
isource
) -> Any
Access adjacency as if it is a 2D Array
Base.getindex — Method
getindex(adj::VariableTargetAdjacency, i, isource) -> Any
Access adjacency as if it is a 2D Array
Base.maximum — Method
maximum(adj::VariableTargetAdjacency) -> Any
Maximum for VariableTargetAdjacency
Base.minimum — Method
minimum(adj::VariableTargetAdjacency) -> Any
Minimum for VariableTargetAdjacency
Base.show — Method
show(io::IO, adj::SerialVariableTargetAdjacency)
Show adjacency (in transposed form; preliminary)
Base.show — Method
show(io::IO, adj::VariableTargetAdjacency)
Show adjacency (in transposed form; preliminary)
ExtendableGrids.asparse — Method
asparse(a::Matrix) -> SparseArrays.SparseMatrixCSC{Int64}
Create sparse incidence matrix from adjacency
ExtendableGrids.asparse — Method
asparse(
a::VariableTargetAdjacency
) -> SparseArrays.SparseMatrixCSC{Int64}
Create sparse incidence matrix from adjacency
ExtendableGrids.atranspose — Method
atranspose(adj::Adjacency{T}) where {T}Transpose adjacency
ExtendableGrids.makevar — Method
makevar(a::Array{T, 2}) -> VariableTargetAdjacency
Turn fixed target adjacency into variable target adjacency
ExtendableGrids.max_num_targets_per_source — Method
max_num_targets_per_source(
adj::SerialVariableTargetAdjacency
) -> Any
Maximum number of targets per source
ExtendableGrids.max_num_targets_per_source — Method
max_num_targets_per_source(
adj::VariableTargetAdjacency
) -> Any
Maximum number of targets per source
ExtendableGrids.num_links — Method
ExtendableGrids.num_links — Method
num_links(adj::VariableTargetAdjacency) -> Int64
Number of links
ExtendableGrids.num_sources — Method
ExtendableGrids.num_sources — Method
num_sources(adj::SerialVariableTargetAdjacency) -> Int64
Number of sources in adjacency
ExtendableGrids.num_sources — Method
num_sources(adj::VariableTargetAdjacency) -> Int64
Number of sources in adjacency
ExtendableGrids.num_targets — Method
ExtendableGrids.num_targets — Method
ExtendableGrids.num_targets — Method
num_targets(
adj::SerialVariableTargetAdjacency,
isource
) -> Any
Number of targets for given source
ExtendableGrids.num_targets — Method
num_targets(adj::VariableTargetAdjacency, isource) -> Any
Number of targets for given source
ExtendableGrids.num_targets — Method
num_targets(adj::VariableTargetAdjacency) -> Any
Number of targeta
ExtendableGrids.tryfix — Method
tryfix(
a::Union{Array{T, 2}, VariableTargetAdjacency{T}}
) -> Any
Try to turn variable target adjacency into fixed target adjacency