Backports release 1.12 (#1353)

Backported PRs:
- [x] #1209 <!-- Remove `LinearAlgebra` qualifications in `cholesky.jl`
-->
- [x] #1230 <!-- Avoid materializing `diag` in `Diagonal` `kron` -->
- [x] #1240 <!-- Reduce `stable_muladdmul` branches in `generic
matvecmul!` -->
- [x] #1247 <!-- fix dispatch to herk -->
- [x] #1255 <!-- use smaller matrix size in `peakflops` on 32-bit -->
- [x] #1310 <!-- Only `@noinline` error path in `matmul_size_check` -->
- [x] #1267 <!-- Refine column ranges in `_isbanded_impl` -->
- [x] #1320 <!-- Copy matrices in `triu`/`tril` if no zero exists for
the `eltype` -->
- [x] #1324 <!-- Fix empty `Tridiagonal` broadcast -->
- [x] #1327 <!-- `iszero` check in hessenberg setindex -->
- [x] #1326 <!-- Fix multiplication with empty `HessenbergQ` -->
- [x] #1332 <!-- Unwrap triangular matrices in broadcast -->
- [x] #1337 <!-- Change `1:size` to `axes` in bidiag mul -->
- [x] #1342 <!-- `Char` uplo in `Bidiagonal` constructor -->
- [x] #1344 <!-- Update the docstring of ldiv! -->
- [x] #1335 <!-- Test: prune old LA based on ENV variable -->
- [x] #1346 <!-- Fix scaling unit triangular matrices -->
- [x] #1355 <!-- Add compat notice for `diagview` -->
- [x] #1349 <!-- Prune `LinearAlgebra` module in ambiguity test -->

Contains multiple commits, manual intervention needed:
- [x] #1238 <!-- Ensure positive-definite matrix in lapack posv test -->
- [x] #1298 <!-- Add `diagm` example -->
- [x] #1312 <!-- WIP: Try use method deletion instead of custom sysimage
-->
- [x] #1333 <!-- Make `fillstored!` public -->
- [x] #1331 <!-- Document SingularException throw for
inv(::AbstractMatrix) -->
- [x] #1350 <!-- Fix copy for partly initialized unit triangular -->

Non-merged PRs with backport label:
- [x] #1352 <!-- log for dense diagonal matrix with negative elements
-->
- [ ] #1305 <!-- Bounds-checking in triangular indexing branches -->

---------

Co-authored-by: Mateus Araújo <[email protected]>
Co-authored-by: Jeff Bezanson <[email protected]>
Co-authored-by: Steven G. Johnson <[email protected]>
Co-authored-by: WalterMadelim <[email protected]>
Co-authored-by: Kristoffer Carlsson <[email protected]>
Co-authored-by: Daniel Karrasch <[email protected]>
Co-authored-by: Michael Abbott <[email protected]>

Author: 8 people

.buildkite/runtests.yml

@@ -16,8 +16,7 @@ steps:
           version: "nightly"
           arch: "i686"
     command: |
-      julia --color=yes --project=.ci -e 'using Pkg; Pkg.instantiate()'
-      julia --color=yes --project=.ci .ci/create_sysimage_and_run_tests.jl
+      julia --color=yes --code-coverage=@ .ci/run_tests.jl
     agents:
       queue: "julia"
       os: "linux"
@@ -40,8 +39,7 @@ steps:
       - JuliaCI/julia#v1:
           version: "nightly"
     command: |
-      julia --color=yes --project=.ci --code-coverage=@ -e 'using Pkg; Pkg.instantiate()'
-      julia --color=yes --project=.ci --code-coverage=@ .ci/create_sysimage_and_run_tests.jl
+      julia --color=yes --code-coverage=@ .ci/run_tests.jl
     agents:
       queue: "julia"
       os: "linux"
@@ -55,8 +53,7 @@ steps:
       - JuliaCI/julia-coverage#v1:
           codecov: true
     command: |
-      julia --color=yes --project=.ci --code-coverage=@ -e 'using Pkg; Pkg.instantiate()'
-      julia --color=yes --project=.ci --code-coverage=@ .ci/create_sysimage_and_run_tests.jl
+      julia --color=yes --code-coverage=@ .ci/run_tests.jl
     agents:
       queue: "julia"
       os: "macos"
@@ -69,8 +66,7 @@ steps:
       - JuliaCI/julia-coverage#v1:
           codecov: true
     command: |
-      julia --color=yes --project=.ci --code-coverage=@ -e 'using Pkg; Pkg.instantiate()'
-      julia --color=yes --project=.ci --code-coverage=@ .ci/create_sysimage_and_run_tests.jl
+      julia --color=yes --code-coverage=@ .ci/run_tests.jl
     agents:
       queue: "julia"
       os: "windows"

.ci/Manifest.toml

@@ -0,0 +1,10 @@
+if haskey(ENV, "BUILDKITE")
+    ncores = Sys.CPU_THREADS
+else
+    ncores = ceil(Int, Sys.CPU_THREADS / 2)
+end
+
+proj = abspath(joinpath(@__DIR__, ".."))
+cmd = """Base.runtests(["LinearAlgebra"]; propagate_project=true, ncores=$ncores)"""
+run(addenv(`$(Base.julia_cmd()) --project=$proj --compiled-modules=existing -e $cmd`,
+    "JULIA_NUM_THREADS" => 1, "JULIA_PRUNE_OLD_LA" => true))

.ci/Project.toml

@@ -21,9 +21,8 @@ jobs:
           version: 'nightly'
       - name: Generate docs
         run: |
-          julia --color=yes --project=.ci -e 'using Pkg; Pkg.instantiate()'
           julia --color=yes --project=docs -e 'using Pkg; Pkg.instantiate()'
-          julia --color=yes --project=.ci .ci/create_sysimage_and_run_docs.jl
+          julia --color=yes --project=docs --compiled-modules=existing docs/make.jl
         env:
           DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }}
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}

.ci/create_sysimage.jl

@@ -37,10 +37,37 @@ This package performs some type piracy and is also included in the sysimage, whi
 To use a development version of this package, you can choose one of the following methods:
 
 1. **Change the UUID in the project file and load the package:**
-   This approach will produce warnings and may lead to method ambiguities between the development version and the one in the sysimage, but it can be used for basic experimentation.
+
+   Change the UUID line in `Project.toml` as
+   ```diff
+   - uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+   + uuid = "27e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+   ```
+
+   Start `julia` as
+   ```console
+   JULIA_PRUNE_OLD_LA=true julia +nightly --compiled-modules=existing --project
+   ```
+   where it is assumed that one is already within the `LinearAlgebra` directory (otherwise, adjust
+   the project path accordingly). The `julia +nightly` command above assumes that `juliaup` is being used
+   to launch `julia`, but one may substitute this with the path to the julia executable.
+
+   Within the `julia` session, load the `LinearAlgebra` module after pruning the one in the sysimage. This may be done as
+   ```julia
+   include("test/prune_old_LA.jl") && using LinearAlgebra
+   ```
+
+   Note that loading the test files in the REPL will automatically carry out the pruning to ensure that the development version of the package is used in the tests.
+
+   If you are contributing to the repo using this method, it may be convenient to ignore the local changes to `Project.toml` by running
+   ```console
+   git update-index --skip-worktree Project.toml
+   ```
 
 2. **Build Julia with the custom `LinearAlgebra` commit:**
-   Modify the commit in `stdlib/LinearAlgebra.version` and build Julia.
+
+   Modify the commit in [`stdlib/LinearAlgebra.version`](https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra.version) and build Julia. This requires one to push the development branch
+   to `GitHub` or an equivalent platform.
 
 3. **Build a custom sysimage with the new `LinearAlgebra`:**
    - Install `PackageCompiler`.

.ci/create_sysimage_and_run_docs.jl

@@ -1,3 +1,7 @@
+withenv("JULIA_PRUNE_OLD_LA" => "true") do
+    include("../test/prune_old_LA.jl")
+end
+
 using LinearAlgebra
 using Documenter: DocMeta, makedocs, deploydocs, HTML