Extend KrylovKit.eigsolve by allowing the initial guess x₀ to be a Tensor

ext/TenetKrylovKitExt.jl

@@ -25,9 +25,28 @@ function eigsolve_prehook_tensor_reshape(A::Tensor, left_inds, right_inds)
     return Amat, left_sizes, right_sizes
 end
 
-function KrylovKit.eigselector(A::Tensor, T::Type; left_inds=Symbol[], right_inds=Symbol[], kwargs...)
-    Amat, _, _ = eigsolve_prehook_tensor_reshape(A, left_inds, right_inds)
-    return KrylovKit.eigselector(Amat, T; kwargs...)
+function eigsolve_prehook_tensor_reshape(A::Tensor, x₀::Tensor, left_inds, right_inds)
+    left_inds, right_inds = Tenet.factorinds(A, left_inds, right_inds)
+
+    Amat, left_sizes, right_sizes = eigsolve_prehook_tensor_reshape(A, left_inds, right_inds)
+    prod_left_sizes = prod(left_sizes)
+
+    inds(x₀) != left_inds && throw(
+        ArgumentError(
+            "The initial guess must have the same left indices as the tensor, but got $(inds(x₀)) and $left_inds."
+        ),
+    )
+    prod(size.((x₀,), left_inds)) != prod_left_sizes && throw(
+        ArgumentError(
+            "The initial guess must have the same size as the left indices, but got sizes $prod_x₀_sizes and $prod_left_sizes.",
+        ),
+    )
+
+    # Permute and reshape the tensor
+    x₀ = permutedims(x₀, left_inds)
+    x₀vec = reshape(parent(x₀), prod_left_sizes)
+
+    return Amat, left_sizes, right_sizes, x₀vec
 end
 
 function KrylovKit.eigsolve(
@@ -50,20 +69,6 @@ function KrylovKit.eigsolve(
     return vals, Avecs, info
 end
 
-function KrylovKit.eigsolve(
-    f::Tensor, x₀, howmany::Int=1, which::KrylovKit.Selector=:LM; left_inds=Symbol[], right_inds=Symbol[], kwargs...
-)
-    Amat, left_sizes, right_sizes = eigsolve_prehook_tensor_reshape(A, left_inds, right_inds)
-
-    # Compute eigenvalues and eigenvectors
-    vals, vecs, info = KrylovKit.eigsolve(Amat, x₀, howmany, which; kwargs...)
-
-    # Tensorify the eigenvectors
-    Avecs = [Tensor(reshape(vec, left_sizes...), left_inds) for vec in vecs]
-
-    return vals, Avecs, info
-end
-
 """
     KrylovKit.eigsolve(tensor::Tensor; left_inds, right_inds, kwargs...)
 
@@ -95,4 +100,25 @@ function KrylovKit.eigsolve(
     return vals, Avecs, info
 end
 
+function KrylovKit.eigsolve(
+    A::Tensor,
+    x₀::Tensor,
+    howmany::Int,
+    which::KrylovKit.Selector,
+    alg::Algorithm;
+    left_inds=inds(x₀),
+    right_inds=Symbol[],
+    kwargs...,
+) where {Algorithm<:KrylovKit.Lanczos} # KrylovKit.KrylovAlgorithm}
+    Amat, left_sizes, right_sizes, x₀vec = eigsolve_prehook_tensor_reshape(A, x₀, left_inds, right_inds)
+
+    # Compute eigenvalues and eigenvectors
+    vals, vecs, info = KrylovKit.eigsolve(Amat, x₀vec, howmany, which, alg; kwargs...)
+
+    # Tensorify the eigenvectors
+    Avecs = [Tensor(reshape(vec, left_sizes...), left_inds) for vec in vecs]
+
+    return vals, Avecs, info
+end
+
 end

test/integration/KrylovKit_test.jl

@@ -55,8 +55,24 @@
     @test parent(reconstructed_tensor) ≈ parent(transpose(reconstructed_tensor_perm))
 
     @testset "Lanczos" begin
-        vals_lanczos, vecs_lanczos = eigsolve(
-            tensor, rand(ComplexF64, 4), 1, :SR, Lanczos(; krylovdim=2, tol=1e-16); left_inds=[:i], right_inds=[:j]
+        @test_throws ArgumentError eigsolve(
+            tensor,
+            Tensor(rand(ComplexF64, 4), (:j,)),
+            1,
+            :SR,
+            Lanczos(; krylovdim=2, tol=1e-16);
+            left_inds=[:i],
+            right_inds=[:j],
+        )
+
+        vals_lanczos, vecs_lanczos, info = eigsolve(
+            tensor,
+            Tensor(rand(ComplexF64, 4), (:i,)),
+            1,
+            :SR,
+            Lanczos(; krylovdim=2, tol=1e-16);
+            left_inds=[:i],
+            right_inds=[:j],
         )
 
         @test length(vals_lanczos) == 1