fix

.github/workflows/examples.yml

@@ -9,9 +9,7 @@ jobs:
  strategy:
  matrix:
  version:
- - '1.6'
  - '1'
- - 'nightly'
  os:
  - ubuntu-latest
  arch:
@@ -35,7 +33,7 @@ jobs:
  ${{ runner.os }}-test-${{ env.cache-name }}-
  ${{ runner.os }}-test-
  ${{ runner.os }}-
- - name: Example project instantiation
+ - name: Examples project instantiation
  shell: julia --project=examples {0}
  run: |
  using Pkg
@@ -46,21 +44,25 @@ jobs:
  - name: Example C₂ linear action
  shell: julia --project=examples {0}
  run: |
- include("examples/preamble.jl");
- include("examples/ex_C2.linear.jl")
+ wd = walkdir(pwd())
+ @info first(wd)
+ @info isdir("examples")
+ @info isfile("examples/preamble.jl")
+ include(joinpath(pwd(), "examples/preamble.jl"))
+ include(joinpath(pwd(), "examples/ex_C2.linear.jl"))
  - name: Example a polynomial with Sym(4)-symmetry
  shell: julia --project=examples {0}
  run: |
- include("examples/preamble.jl");
- include("examples/ex_S4.jl")
+ include("./examples/preamble.jl");
+ include("./examples/ex_S4.jl")
  - name: Example Motzkin polynomial
  shell: julia --project=examples {0}
  run: |
- include("examples/preamble.jl");
- include("examples/ex_motzkin.jl")
+ include("./examples/preamble.jl");
+ include("./examples/ex_motzkin.jl")
  - name: Example Robinson Form
  shell: julia --project=examples {0}
  run: |
- include("examples/preamble.jl");
- include("examples/ex_robinson_form.jl")
+ include("./examples/preamble.jl");
+ include("./examples/ex_robinson_form.jl")
 

bareiss.jl

@@ -0,0 +1,91 @@
+# Bareiss algorithm
+function bareiss_update!(zero!, M::Matrix, k, swapto, pivot, prev_pivot)
+ for i in k+1:size(M, 2), j in k+1:size(M, 1)
+ M[j,i] = exactdiv(M[j,i]*pivot - M[j,k]*M[k,i], prev_pivot)
+ end
+ zero!(M, k+1:size(M, 1), k)
+end
+
+function bareiss_update!(zero!, M::AbstractMatrix, k, swapto, pivot, prev_pivot)
+ V = @view M[k+1:end, k+1:end]
+ V .= exactdiv.(V * pivot - M[k+1:end, k] * M[k, k+1:end]', prev_pivot)
+ zero!(M, k+1:size(M, 1), k)
+end
+
+function bareiss_update_virtual_colswap!(zero!, M::AbstractMatrix, k, swapto, pivot, prev_pivot)
+ V = @view M[k+1:end, :]
+ V .= exactdiv.(V * pivot - M[k+1:end, swapto[2]] * M[k, :]', prev_pivot)
+ zero!(M, k+1:size(M, 1), swapto[2])
+end
+
+bareiss_zero!(M, i, j) = M[i,j] .= zero(eltype(M))
+
+function find_pivot_col(M, i)
+ p = findfirst(!iszero, @view M[i,i:end])
+ p === nothing && return nothing
+ idx = CartesianIndex(i, p + i - 1)
+ (idx, M[idx])
+end
+
+function find_pivot_any(M, i)
+ p = findfirst(!iszero, @view M[i:end,i:end])
+ p === nothing && return nothing
+ idx = p + CartesianIndex(i - 1, i - 1)
+ (idx, M[idx])
+end
+
+const bareiss_colswap = (Base.swapcols!, Base.swaprows!, bareiss_update!, bareiss_zero!)
+const bareiss_virtcolswap = ((M,i,j)->nothing, Base.swaprows!, bareiss_update_virtual_colswap!, bareiss_zero!)
+
+"""
+ bareiss!(M)
+Perform Bareiss's fraction-free row-reduction algorithm on the matrix `M`.
+Optionally, a specific pivoting method may be specified.
+"""
+function bareiss!(M::AbstractMatrix,
+ (swapcols!, swaprows!, update!, zero!) = bareiss_colswap;
+ find_pivot=find_pivot_any)
+ prev = one(eltype(M))
+ n = size(M, 1)
+ for k in 1:n
+ r = find_pivot(M, k)
+ r === nothing && return k - 1
+ (swapto, pivot) = r
+ if CartesianIndex(k, k) != swapto
+ swapcols!(M, k, swapto[2])
+ swaprows!(M, k, swapto[1])
+ end
+ update!(zero!, M, k, swapto, pivot, prev)
+ prev = pivot
+ end
+ return n
+end
+
+"""
+ det_bareiss!(M)
+Calculates the determinant of a matrix using the
+[Bareiss Algorithm](https://en.wikipedia.org/wiki/Bareiss_algorithm) using
+inplace operations.
+# Examples
+```jldoctest
+julia> M = [1 0; 2 2]
+2×2 Matrix{Int64}:
+ 1 0
+ 2 2
+julia> LinearAlgebra.det_bareiss!(M)
+2
+```
+"""
+function det_bareiss!(M)
+ n = checksquare(M)
+ parity = true
+ swaprows!(M, i, j) = (i != j && (parity = !parity); Base.swaprows!(M, i, j))
+ swapcols!(M, i, j) = (i != j && (parity = !parity); Base.swapcols!(M, i, j))
+ # We only look at the last entry, so we don't care that the sub-diagonals are
+ # garbage.
+ zero!(M, i, j) = nothing
+ rank = bareiss!(M, (swapcols!, swaprows!, bareiss_update!, zero!);
+ find_pivot=find_pivot_col)
+ rank != n && return zero(eltype(M))
+ return parity ? M[n,n] : -M[n, n]
+end