Add tests with LinearOperators.jl (#863)

* Add tests with LinearOperators.jl

* Update block_gmres for complex numbers

* Update block_gmres.jl

.buildkite/pipeline.yml

@@ -98,3 +98,17 @@ steps:
         Pkg.instantiate()
         include("test/cpu/component_arrays.jl")'
     timeout_in_minutes: 30
+
+  - label: "CPUs -- LinearOperators.jl"
+    plugins:
+      - JuliaCI/julia#v1:
+          version: "1.10"
+    agents:
+      queue: "juliaecosystem"
+    command: |
+      julia --color=yes --project -e '
+        using Pkg
+        Pkg.add("LinearOperators")
+        Pkg.instantiate()
+        include("test/cpu/linear_operators.jl")'
+    timeout_in_minutes: 30

src/block_gmres.jl

@@ -148,6 +148,7 @@ kwargs_block_gmres = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rto
     # Define the blocks D1 and D2
     D1 = view(D, 1:p, :)
     D2 = view(D, p+1:2p, :)
+    trans = FC <: AbstractFloat ? 'T' : 'C'
 
     # Coefficients for mul!
     α = -one(FC)
@@ -263,7 +264,7 @@ kwargs_block_gmres = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rto
         for i = 1 : inner_iter-1
           D1 .= R[nr+i]
           D2 .= R[nr+i+1]
-          @kormqr!('L', 'T', H[i], τ[i], D)
+          @kormqr!('L', trans, H[i], τ[i], D)
           R[nr+i] .= D1
           R[nr+i+1] .= D2
         end
@@ -276,7 +277,7 @@ kwargs_block_gmres = (:M, :N, :ldiv, :restart, :reorthogonalization, :atol, :rto
         # Update Zₖ = (Qₖ)ᴴΓE₁ = (Λ₁, ..., Λₖ, Λbarₖ₊₁)
         D1 .= Z[inner_iter]
         D2 .= zero(FC)
-        @kormqr!('L', 'T', H[inner_iter], τ[inner_iter], D)
+        @kormqr!('L', trans, H[inner_iter], τ[inner_iter], D)
         Z[inner_iter] .= D1
 
         # Update residual norm estimate.

test/cpu/linear_operators.jl

@@ -0,0 +1,16 @@
+using LinearAlgebra, SparseArrays, Test
+using Krylov, LinearOperators
+
+@testset "LinearOperators" begin
+  n = 50
+  p = 5
+
+  for T in (Float64, ComplexF64)
+    A = rand(T, n, n)
+    B = rand(T, n, p)
+
+    opA = LinearOperator(A)
+    x, stats = block_gmres(opA, B)
+    @test stats.solved
+  end
+end