diff --git a/test/ctmrg/fixediter.jl b/test/ctmrg/fixediter.jl
new file mode 100644
index 00000000..3e8a634c
--- /dev/null
+++ b/test/ctmrg/fixediter.jl
@@ -0,0 +1,75 @@
+using Test
+using Random
+using TensorKit
+using PEPSKit
+using PEPSKit:
+    FixedSVD,
+    ctmrg_iter,
+    gauge_fix,
+    fix_relative_phases,
+    fix_global_phases,
+    check_elementwise_convergence
+
+# initialize parameters
+χbond = 2
+χenv = 16
+svd_algs = [SVDAdjoint(; fwd_alg=TensorKit.SVD()), SVDAdjoint(; fwd_alg=IterSVD())]
+unitcells = [(1, 1), (3, 4)]
+
+# test for element-wise convergence after application of FixedIter step
+@testset "$unitcell unit cell with $(typeof(svd_alg.fwd_alg))" for (unitcell, svd_alg) in
+                                                                   Iterators.product(
+    unitcells, svd_algs
+)
+    ctm_alg = CTMRG(; tol=1e-12, verbosity=1, ctmrgscheme=:AllSides, svd_alg)
+
+    # initialize states
+    Random.seed!(91283219347)
+    psi = InfinitePEPS(2, χbond; unitcell)
+    env_conv1 = leading_boundary(CTMRGEnv(psi; Venv=ComplexSpace(χenv)), psi, ctm_alg)
+
+    # do extra iteration to get SVD
+    env_conv2, info = ctmrg_iter(psi, env_conv1, ctm_alg)
+    env_fix, signs = gauge_fix(env_conv1, env_conv2)
+    @test check_elementwise_convergence(env_conv1, env_fix)
+
+    # fix gauge of SVD
+    U_fix, V_fix = fix_relative_phases(info.U, info.V, signs)
+    svd_alg_fix = SVDAdjoint(; fwd_alg=FixedSVD(U_fix, info.S, V_fix))
+    ctm_alg_fix = CTMRG(; svd_alg=svd_alg_fix, trscheme=notrunc(), ctmrgscheme=:AllSides)
+
+    # do iteration with FixedSVD
+    env_fixedsvd, = ctmrg_iter(psi, env_conv1, ctm_alg_fix)
+    env_fixedsvd = fix_global_phases(env_conv1, env_fixedsvd)
+    @test check_elementwise_convergence(env_conv1, env_fixedsvd)
+end
+
+##
+# ctm_alg = CTMRG(;
+#     tol=1e-12,
+#     miniter=4,
+#     maxiter=100,
+#     verbosity=1,
+#     ctmrgscheme=:AllSides,
+#     svd_alg=SVDAdjoint(; fwd_alg=IterSVD()),
+# )
+
+# # initialize states
+# Random.seed!(91283219347)
+# psi = InfinitePEPS(2, χbond)
+# env_conv1 = leading_boundary(CTMRGEnv(psi; Venv=ComplexSpace(χenv)), psi, ctm_alg);
+
+# # do extra iteration to get SVD
+# env_conv2, info = ctmrg_iter(psi, env_conv1, ctm_alg);
+# env_fix, signs = gauge_fix(env_conv1, env_conv2);
+# @test check_elementwise_convergence(env_conv1, env_fix)
+
+# # fix gauge of SVD
+# U_fix, V_fix = fix_relative_phases(info.U, info.V, signs);
+# svd_alg_fix = SVDAdjoint(; fwd_alg=FixedSVD(U_fix, info.S, V_fix));
+# ctm_alg_fix = CTMRG(; svd_alg=svd_alg_fix, trscheme=notrunc(), ctmrgscheme=:AllSides);
+
+# # do iteration with FixedSVD
+# env_fixedsvd, = ctmrg_iter(psi, env_conv1, ctm_alg_fix);
+# env_fixedsvd = fix_global_phases(env_conv1, env_fixedsvd);
+# @test check_elementwise_convergence(env_conv1, env_fixedsvd)
\ No newline at end of file
diff --git a/test/ctmrg/fixedsvd.jl b/test/ctmrg/fixedsvd.jl
deleted file mode 100644
index 9b0ec4d1..00000000
--- a/test/ctmrg/fixedsvd.jl
+++ /dev/null
@@ -1,60 +0,0 @@
-using Test
-using Random
-using TensorKit
-using PEPSKit
-using PEPSKit:
-    FixedSVD,
-    ctmrg_iter,
-    gauge_fix,
-    fix_relative_phases,
-    fix_global_phases,
-    check_elementwise_convergence
-
-# initialize parameters
-χbond = 2
-χenv = 16
-ctm_alg = CTMRG(; tol=1e-12, miniter=4, maxiter=100, verbosity=1, ctmrgscheme=:AllSides)
-
-@testset "(1, 1) unit cell" begin
-    # initialize states
-    Random.seed!(91283219347)
-    psi = InfinitePEPS(2, χbond)
-    env_conv1 = leading_boundary(CTMRGEnv(psi; Venv=ComplexSpace(χenv)), psi, ctm_alg)
-
-    # do extra iteration to get SVD
-    env_conv2, info = ctmrg_iter(psi, env_conv1, ctm_alg)
-    env_fix, signs = gauge_fix(env_conv1, env_conv2)
-    @test check_elementwise_convergence(env_conv1, env_fix)
-
-    # fix gauge of SVD
-    U_fix, V_fix = fix_relative_phases(info.U, info.V, signs)
-    svd_alg_fix = SVDAdjoint(; fwd_alg=FixedSVD(U_fix, info.S, V_fix))
-    ctm_alg_fix = CTMRG(; svd_alg=svd_alg_fix, trscheme=notrunc(), ctmrgscheme=:AllSides)
-
-    # do iteration with FixedSVD
-    env_fixedsvd, = ctmrg_iter(psi, env_conv1, ctm_alg_fix)
-    env_fixedsvd = fix_global_phases(env_conv1, env_fixedsvd)
-    @test check_elementwise_convergence(env_conv1, env_fixedsvd)
-end
-
-@testset "(3, 4) unit cell" begin
-    # initialize states
-    Random.seed!(91283219347)
-    psi = InfinitePEPS(2, χbond; unitcell=(3, 4))
-    env_conv1 = leading_boundary(CTMRGEnv(psi; Venv=ComplexSpace(χenv)), psi, ctm_alg)
-
-    # do extra iteration to get SVD
-    env_conv2, info = ctmrg_iter(psi, env_conv1, ctm_alg)
-    env_fix, signs = gauge_fix(env_conv1, env_conv2)
-    @test check_elementwise_convergence(env_conv1, env_fix)
-
-    # fix gauge of SVD
-    U_fix, V_fix = fix_relative_phases(info.U, info.V, signs)
-    svd_alg_fix = SVDAdjoint(; fwd_alg=FixedSVD(U_fix, info.S, V_fix))
-    ctm_alg_fix = CTMRG(; svd_alg=svd_alg_fix, trscheme=notrunc(), ctmrgscheme=:AllSides)
-
-    # do iteration with FixedSVD
-    env_fixedsvd, = ctmrg_iter(psi, env_conv1, ctm_alg_fix)
-    env_fixedsvd = fix_global_phases(env_conv1, env_fixedsvd)
-    @test check_elementwise_convergence(env_conv1, env_fixedsvd)
-end
diff --git a/test/ctmrg/gradients.jl b/test/ctmrg/gradients.jl
index 978d65e7..3e3a7070 100644
--- a/test/ctmrg/gradients.jl
+++ b/test/ctmrg/gradients.jl
@@ -17,9 +17,15 @@ models = [square_lattice_heisenberg(), square_lattice_pwave()]
 names = ["Heisenberg", "p-wave superconductor"]
 Random.seed!(42039482030)
 tol = 1e-8
-boundary_alg = CTMRG(; tol=tol, miniter=4, maxiter=100, verbosity=0)
+boundary_alg = CTMRG(; tol=tol, miniter=4, maxiter=100, verbosity=0, ctmrgscheme=:AllSides)
 gradmodes = [
-    nothing, GeomSum(; tol), ManualIter(; tol), KrylovKit.GMRES(; tol=tol, maxiter=10)
+    nothing,
+    GeomSum(; tol, iterscheme=:FixedIter),
+    GeomSum(; tol, iterscheme=:DiffGauge),
+    ManualIter(; tol, iterscheme=:FixedIter),
+    ManualIter(; tol, iterscheme=:DiffGauge),
+    LinSolve(; alg=KrylovKit.GMRES(; tol=tol, maxiter=10), iterscheme=:FixedIter),
+    LinSolve(; alg=KrylovKit.GMRES(; tol=tol, maxiter=10), iterscheme=:DiffGauge),
 ]
 steps = -0.01:0.005:0.01
 
diff --git a/test/runtests.jl b/test/runtests.jl
index 99810728..143e188b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -21,7 +21,7 @@ end
             include("ctmrg/svd_wrapper.jl")
         end
         @time @safetestset "SVD wrapper" begin
-            include("ctmrg/fixedsvd.jl")
+            include("ctmrg/fixediter.jl")
         end
         @time @safetestset "SVD wrapper" begin
             include("ctmrg/unitcell.jl")