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refactor: change Bareiss pivot selection algorithm #131

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Merged
AayushSabharwal merged 1 commit into from
Jul 9, 2026
Merged

refactor: change Bareiss pivot selection algorithm #131

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98 changes: 39 additions & 59 deletions src/singularity_removal.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -59,98 +59,78 @@ end
"""
$(SIGNATURES)

Find the first linear variable such that `𝑠neighbors(adj, i)[j]` is true given
the `constraint`.
Find a variable (column) and its coefficient (value) in `M` among equations (rows) in `range`,
filtering out equations for which `mask` is `false` (`mask` can be `nothing` to avoid masking).
In case of a tie, `var_priorities` is used to choose a variable with lower priority. In case
priorities are tied, it will prefer the row with fewer elements.
"""
@inline function find_first_linear_variable(M::SparseMatrixCLIL,
range,
mask,
constraint, ::Nothing = nothing)
eadj = M.row_cols
@inbounds for i in range
vertices = eadj[i]
if constraint(length(vertices))
for (j, v) in enumerate(vertices)
if (mask === nothing || mask[v])
return (CartesianIndex(i, v), M.row_vals[i][j])
end
end
end
end
return nothing
end

@inline function find_first_linear_variable(
M::SparseMatrixCLIL,
range,
mask,
constraint, var_priorities::AbstractVector{Int}
var_priorities = nothing
)
eadj = M.row_cols
candidate_i = 0
candidate_v = 0
candidate_val = 0
candidate_nnz = 0
@inbounds for i in range
vertices = eadj[i]
constraint(length(vertices)) || continue
candidate_v = 0
candidate_val = 0
nnz = length(vertices)
if !iszero(candidate_v) && var_priorities === nothing && nnz >= candidate_nnz
continue
end
for (j, v) in enumerate(vertices)
mask === nothing || mask[v] || continue
iszero(candidate_v) || var_priorities[v] < var_priorities[candidate_v] || continue
candidate_v = v
candidate_val = M.row_vals[i][j]
# Prefer, in order
# 1. Lower priority pivots
# 2. Rows with fewer elements
if iszero(candidate_v) || var_priorities === nothing && nnz < candidate_nnz ||
var_priorities !== nothing && (
var_priorities[v] < var_priorities[candidate_v] ||
var_priorities[v] == var_priorities[candidate_v] && nnz < candidate_nnz
)
candidate_i = i
candidate_v = v
candidate_val = M.row_vals[i][j]
candidate_nnz = nnz
end
end
iszero(candidate_v) || return CartesianIndex(i, candidate_v), candidate_val
end
iszero(candidate_v) || return CartesianIndex(candidate_i, candidate_v), candidate_val
return nothing
end

@inline function find_first_linear_variable(M::AbstractMatrix,
range,
mask,
constraint, ::Nothing = nothing)
var_priorities = nothing)
candidate_i = 0
candidate_v = 0
candidate_val = 0
candidate_nnz = 0
@inbounds for i in range
row = @view M[i, :]
if constraint(count(!iszero, row))
for (v, val) in enumerate(row)
if mask === nothing || mask[v]
return CartesianIndex(i, v), val
end
end
nnz = count(!izero, row)
if !izero(candidate_v) && var_priorities === nothing && nnz >= candidate_nnz
continue
end
end
return nothing
end

@inline function find_first_linear_variable(
M::AbstractMatrix,
range,
mask,
constraint, var_priorities::AbstractVector{Int}
)
@inbounds for i in range
row = @view M[i, :]
constraint(count(!iszero, row)) || continue
candidate_v = 0
candidate_val = 0
for (v, val) in enumerate(row)
mask === nothing || mask[v] || continue
if iszero(candidate_v) || var_priorities[v] < var_priorities[candidate_v]
if iszero(candidate_v) || (var_priorities === nothing && nnz < candidate_nnz || var_priorities !== nothing && (var_priorities[v] < var_priorities[candidate_v] || var_priorities[v] == var_priorities[candidate_v] && nnz < candidate_nnz))
candidate_i = i
candidate_v = v
candidate_val = val
candidate_nnz = nnz
end
end
iszero(candidate_v) && return nothing
return CartesianIndex(i, candidate_v), candidate_val
end
return nothing
end

function find_masked_pivot(variables, M, k, var_priorities)
r = find_first_linear_variable(M, k:size(M, 1), variables, isequal(1), var_priorities)
r !== nothing && return r
r = find_first_linear_variable(M, k:size(M, 1), variables, isequal(2), var_priorities)
r !== nothing && return r
r = find_first_linear_variable(M, k:size(M, 1), variables, _ -> true, var_priorities)
return r
return find_first_linear_variable(M, k:size(M, 1), variables, var_priorities)
end

count_nonzeros(a::AbstractArray) = count(!iszero, a)
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