Merge branch 'st/remove_chol_copy' of github.com:st--/LinearAlgebra.jl into st/remove_chol_copy

Author: st--

.ci/Manifest.toml

@@ -52,7 +52,7 @@ version = "1.11.0"
 
 [[deps.JuliaSyntaxHighlighting]]
 deps = ["StyledStrings"]
-uuid = "dc6e5ff7-fb65-4e79-a425-ec3bc9c03011"
+uuid = "ac6e5ff7-fb65-4e79-a425-ec3bc9c03011"
 version = "1.12.0"
 
 [[deps.LazyArtifacts]]
@@ -93,7 +93,7 @@ version = "1.11.0"
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 path = ".."
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-version = "1.11.0"
+version = "1.12.0"
 
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

src/dense.jl

@@ -1587,24 +1587,25 @@ factorize(A::Transpose) = transpose(factorize(parent(A)))
 factorize(a::Number)    = a # same as how factorize behaves on Diagonal types
 
 function getstructure(A::StridedMatrix)
+    require_one_based_indexing(A)
     m, n = size(A)
     if m == 1 return A[1] end
     utri    = true
     utri1   = true
     herm    = true
     sym     = true
-    for j = 1:n-1, i = j+1:m
-        if utri1
+    for j = 1:n, i = j:m
+        if (j < n) && (i > j) && utri1 # indices are off-diagonal
             if A[i,j] != 0
                 utri1 = i == j + 1
                 utri = false
             end
         end
         if sym
-            sym &= A[i,j] == A[j,i]
+            sym &= A[i,j] == transpose(A[j,i])
         end
         if herm
-            herm &= A[i,j] == conj(A[j,i])
+            herm &= A[i,j] == adjoint(A[j,i])
         end
         if !(utri1|herm|sym) break end
     end
@@ -1617,10 +1618,12 @@ function getstructure(A::StridedMatrix)
     if ltri1
         for i = 1:n-1
             if A[i,i+1] != 0
-                ltri &= false
+                ltri = false
                 break
             end
         end
+    else
+        ltri = false
     end
     return (utri, utri1, ltri, ltri1, sym, herm)
 end
@@ -1779,6 +1782,10 @@ Condition number of the matrix `M`, computed using the operator `p`-norm. Valid
 """
 function cond(A::AbstractMatrix, p::Real=2)
     if p == 2
+        if isempty(A)
+            checksquare(A)
+            return zero(real(eigtype(eltype(A))))
+        end
         v = svdvals(A)
         maxv = maximum(v)
         return iszero(maxv) ? oftype(real(maxv), Inf) : maxv / minimum(v)

test/dense.jl

@@ -56,6 +56,18 @@ Random.seed!(1234323)
         @test cond(Mars, 2)   ≈ 6.181867355918493
         @test cond(Mars, Inf) ≈ 7.1
     end
+    @testset "Empty matrices" begin
+        for p in (1,2,Inf)
+            # zero for square (i.e. 0×0) matrices
+            @test cond(zeros(Int, 0, 0), p) === 0.0
+            @test cond(zeros(0, 0), p) === 0.0
+            @test cond(zeros(ComplexF64, 0, 0), p) === 0.0
+            # error for non-square matrices
+            for size in ((10,0), (0,10))
+                @test_throws DimensionMismatch cond(zeros(size...), p)
+            end
+        end
+    end
 end
 
 areal = randn(n,n)/2
@@ -1347,4 +1359,11 @@ end
     end
 end
 
+@testset "structure of dense matrices" begin
+    # A is neither triangular nor symmetric/Hermitian
+    A = [1 im 2; -im 0  3; 2 3 im]
+    @test factorize(A) isa LU{ComplexF64, Matrix{ComplexF64}, Vector{Int}}
+    @test !any(LinearAlgebra.getstructure(A))
+end
+
 end # module TestDense