Make generic cholesky throw on non-psd input (#49417)

stdlib/LinearAlgebra/src/cholesky.jl

@@ -206,7 +206,7 @@ function _chol!(A::AbstractMatrix, ::Type{UpperTriangular})
             A[k,k] = Akk
             Akk, info = _chol!(Akk, UpperTriangular)
             if info != 0
-                return UpperTriangular(A), info
+                return UpperTriangular(A), convert(BlasInt, k)
             end
             A[k,k] = Akk
             AkkInv = inv(copy(Akk'))
@@ -233,7 +233,7 @@ function _chol!(A::AbstractMatrix, ::Type{LowerTriangular})
             A[k,k] = Akk
             Akk, info = _chol!(Akk, LowerTriangular)
             if info != 0
-                return LowerTriangular(A), info
+                return LowerTriangular(A), convert(BlasInt, k)
             end
             A[k,k] = Akk
             AkkInv = inv(Akk)
@@ -251,11 +251,12 @@ function _chol!(A::AbstractMatrix, ::Type{LowerTriangular})
 end
 
 ## Numbers
-function _chol!(x::Number, uplo)
+function _chol!(x::Number, _)
     rx = real(x)
+    iszero(rx) && return (rx, convert(BlasInt, 1))
     rxr = sqrt(abs(rx))
     rval =  convert(promote_type(typeof(x), typeof(rxr)), rxr)
-    rx == abs(x) ? (rval, convert(BlasInt, 0)) : (rval, convert(BlasInt, 1))
+    return (rval, convert(BlasInt, rx != abs(x)))
 end
 
 ## for StridedMatrices, check that matrix is symmetric/Hermitian

stdlib/LinearAlgebra/test/cholesky.jl

@@ -260,29 +260,32 @@ end
     end
 end
 
-@testset "behavior for non-positive definite matrices" for T in (Float64, ComplexF64)
+@testset "behavior for non-positive definite matrices" for T in (Float64, ComplexF64, BigFloat)
     A = T[1 2; 2 1]
     B = T[1 2; 0 1]
+    C = T[2 0; 0 0]
     # check = (true|false)
-    for M in (A, Hermitian(A), B)
+    for M in (A, Hermitian(A), B, C)
         @test_throws PosDefException cholesky(M)
         @test_throws PosDefException cholesky!(copy(M))
         @test_throws PosDefException cholesky(M; check = true)
         @test_throws PosDefException cholesky!(copy(M); check = true)
         @test !LinearAlgebra.issuccess(cholesky(M; check = false))
         @test !LinearAlgebra.issuccess(cholesky!(copy(M); check = false))
     end
-    for M in (A, Hermitian(A), B)
-        @test_throws RankDeficientException cholesky(M, RowMaximum())
-        @test_throws RankDeficientException cholesky!(copy(M), RowMaximum())
-        @test_throws RankDeficientException cholesky(M, RowMaximum(); check = true)
-        @test_throws RankDeficientException cholesky!(copy(M), RowMaximum(); check = true)
-        @test !LinearAlgebra.issuccess(cholesky(M, RowMaximum(); check = false))
-        @test !LinearAlgebra.issuccess(cholesky!(copy(M), RowMaximum(); check = false))
-        C = cholesky(M, RowMaximum(); check = false)
-        @test_throws RankDeficientException chkfullrank(C)
-        C = cholesky!(copy(M), RowMaximum(); check = false)
-        @test_throws RankDeficientException chkfullrank(C)
+    if T !== BigFloat # generic pivoted cholesky is not implemented
+        for M in (A, Hermitian(A), B)
+            @test_throws RankDeficientException cholesky(M, RowMaximum())
+            @test_throws RankDeficientException cholesky!(copy(M), RowMaximum())
+            @test_throws RankDeficientException cholesky(M, RowMaximum(); check = true)
+            @test_throws RankDeficientException cholesky!(copy(M), RowMaximum(); check = true)
+            @test !LinearAlgebra.issuccess(cholesky(M, RowMaximum(); check = false))
+            @test !LinearAlgebra.issuccess(cholesky!(copy(M), RowMaximum(); check = false))
+            C = cholesky(M, RowMaximum(); check = false)
+            @test_throws RankDeficientException chkfullrank(C)
+            C = cholesky!(copy(M), RowMaximum(); check = false)
+            @test_throws RankDeficientException chkfullrank(C)
+        end
     end
     @test !isposdef(A)
     str = sprint((io, x) -> show(io, "text/plain", x), cholesky(A; check = false))