Stop cg_lanczos! resolving to the shifted workspace (#1251)

`get_KrylovJL_solver` tested `KrylovAlg === Krylov.cg_lanczos!` twice. The
first branch returned `CgLanczosShiftWorkspace`, so it won, and the second
branch returning `CgLanczosWorkspace` was unreachable.

`cg_lanczos!` is listed in the `KrylovJL` docstring as a supported
`KrylovAlg`, so this is reachable from documented usage:

    solve(LinearProblem(A, b), KrylovJL(KrylovAlg = Krylov.cg_lanczos!))
    MethodError: no method matching CgLanczosShiftWorkspace(::Matrix{Float64}, ::Vector{Float64})

Dropping the first branch lets it fall through to the right workspace. The
solve then succeeds, to a relative error of 5.9e-9 on a symmetric positive
definite system.

`cg_lanczos_shift!` and `cgls_lanczos_shift!` are deliberately left
unmapped. Both exist in Krylov 0.10, but they take a `shifts` argument that
this wrapper never passes, and neither appears in the docstring's list, so
they keep hitting "Invalid Krylov method detected" rather than being
advertised and broken.

Spotted in #554, which is otherwise superseded: block GMRES and MINRES are
already interfaced through `BlockGmresWorkspace` and `BlockMinresWorkspace`
for a matrix right-hand side.

Author: AJ0070

src/iterative_wrappers.jl

@@ -373,8 +373,6 @@ function get_KrylovJL_solver(KrylovAlg)
         Krylov.CrmrWorkspace
     elseif (KrylovAlg === Krylov.cg!)
         Krylov.CgWorkspace
-    elseif (KrylovAlg === Krylov.cg_lanczos!)
-        Krylov.CgLanczosShiftWorkspace
     elseif (KrylovAlg === Krylov.cgls!)
         Krylov.CglsWorkspace
     elseif (KrylovAlg === Krylov.cg_lanczos!)

test/Core/nonsquare.jl

@@ -345,3 +345,33 @@ end
         end
     end
 end
+
+# `get_KrylovJL_solver` matched `cg_lanczos!` twice. The first branch handed back the
+# *shifted* workspace, so the documented `KrylovAlg = Krylov.cg_lanczos!` threw a
+# `MethodError` out of the workspace constructor, and the second branch, the correct
+# one, was unreachable. See SciML/LinearSolve.jl#554.
+@testset "documented KrylovAlg values map to their own workspace" begin
+    for (f, W) in (
+            (Krylov.cg!, Krylov.CgWorkspace),
+            (Krylov.cg_lanczos!, Krylov.CgLanczosWorkspace),
+            (Krylov.cgls!, Krylov.CglsWorkspace),
+            (Krylov.minres!, Krylov.MinresWorkspace),
+            (Krylov.gmres!, Krylov.GmresWorkspace),
+        )
+        @test LinearSolve.get_KrylovJL_solver(f) === W
+    end
+
+    # The shifted variants need a `shifts` argument that this wrapper never passes, and
+    # the docstring does not list them, so they stay unmapped rather than advertised.
+    @test_throws ErrorException LinearSolve.get_KrylovJL_solver(Krylov.cg_lanczos_shift!)
+
+    # `cg_lanczos!` wants a symmetric positive definite system.
+    Random.seed!(554)
+    nl = 24
+    Xl = rand(nl, nl)
+    Al = Xl' * Xl + nl * I
+    bl = rand(nl)
+    sol = solve(LinearProblem(Al, bl), KrylovJL(KrylovAlg = Krylov.cg_lanczos!))
+    @test SciMLBase.successful_retcode(sol)
+    @test sol.u ≈ Al \ bl rtol = 1.0e-6
+end