From 25ee4ea48a93df072aacbc3d523f0ba60323db36 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mos=C3=A8=20Giordano?=
 <765740+giordano@users.noreply.github.com>
Date: Sun, 6 Oct 2024 23:10:51 +0100
Subject: [PATCH] [LinearAlgebra] Remove unreliable doctests (#56011)

The exact textual representation of the output of these doctests depend
on the specific kernel used by the BLAS backend, and can vary between
versions of OpenBLAS (as it did in #41973), or between different CPUs,
which makes these doctests unreliable.

Fix #55998.

(cherry picked from commit c2a2e38079c1b540e93e8524cf53da4153358481)
---
 stdlib/LinearAlgebra/src/LinearAlgebra.jl | 26 ++++-------------------
 stdlib/LinearAlgebra/src/hessenberg.jl    |  2 +-
 2 files changed, 5 insertions(+), 23 deletions(-)

diff --git a/stdlib/LinearAlgebra/src/LinearAlgebra.jl b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
index 7b3ff8f0db53d..2557a207455a7 100644
--- a/stdlib/LinearAlgebra/src/LinearAlgebra.jl
+++ b/stdlib/LinearAlgebra/src/LinearAlgebra.jl
@@ -299,17 +299,8 @@ julia> Y = zero(X);
 
 julia> ldiv!(Y, qr(A), X);
 
-julia> Y
-3-element Vector{Float64}:
-  0.7128099173553719
- -0.051652892561983674
-  0.10020661157024757
-
-julia> A\\X
-3-element Vector{Float64}:
-  0.7128099173553719
- -0.05165289256198333
-  0.10020661157024785
+julia> Y ≈ A\\X
+true
 ```
 """
 ldiv!(Y, A, B)
@@ -340,17 +331,8 @@ julia> Y = copy(X);
 
 julia> ldiv!(qr(A), X);
 
-julia> X
-3-element Vector{Float64}:
-  0.7128099173553719
- -0.051652892561983674
-  0.10020661157024757
-
-julia> A\\Y
-3-element Vector{Float64}:
-  0.7128099173553719
- -0.05165289256198333
-  0.10020661157024785
+julia> X ≈ A\\Y
+true
 ```
 """
 ldiv!(A, B)
diff --git a/stdlib/LinearAlgebra/src/hessenberg.jl b/stdlib/LinearAlgebra/src/hessenberg.jl
index 6f5efd1c42d16..8dc4b4896d60a 100644
--- a/stdlib/LinearAlgebra/src/hessenberg.jl
+++ b/stdlib/LinearAlgebra/src/hessenberg.jl
@@ -440,7 +440,7 @@ This is useful because multiple shifted solves `(F + μ*I) \\ b`
 Iterating the decomposition produces the factors `F.Q, F.H, F.μ`.
 
 # Examples
-```jldoctest
+```julia-repl
 julia> A = [4. 9. 7.; 4. 4. 1.; 4. 3. 2.]
 3×3 Matrix{Float64}:
  4.0  9.0  7.0