diff --git a/src/algorithms.jl b/src/algorithms.jl
index d6996ea..b89dc8d 100644
--- a/src/algorithms.jl
+++ b/src/algorithms.jl
@@ -208,16 +208,19 @@ abstract type ProjectionAlgorithm end
         if als.check isa FitCheck
             if als.check.iter == 0
                 println("Warning: FitCheck is not enabled for $(als.mttkrp_alg) will run $(als.check.max_counter) iterations.")
+                if verbose
+                    println("Warning: Sampled fit will be provided")
+                end
             end
             als.check.iter += 1
             if verbose
-                inner_prod = real((had_contract([als.target, dag.(factors)...], cprank) * dag(λ))[])
-                partial_gram = [fact * dag(prime(fact; tags=tags(cprank))) for fact in factors];
-                fact_square = ITensorCPD.norm_factors(partial_gram, λ)
-                normResidual =
-                    sqrt(abs(als.check.ref_norm * als.check.ref_norm + fact_square - 2 * abs(inner_prod)))
-                elt = typeof(inner_prod)
-                println("$(dim(cprank))\t$(als.check.iter)\t$(one(elt) - normResidual / norm(als.check.ref_norm))")
+                cpd = CPD{ITensor}(factors, λ)
+                krpproj = had_contract(factors[1], λ, cprank) * compute_krp(als.mttkrp_alg, als, factors, cpd, cprank, 1)
+                tproj =  matricize_tensor(als.mttkrp_alg, als, factors, cpd, cprank, 1)
+
+                cpfit = one(real(eltype(krpproj))) - norm(tproj - krpproj) / norm(tproj)
+
+                println("$(dim(cprank))\t$(als.check.iter)\t$(cpfit)")
             end
             if als.check.iter == als.check.max_counter
                 als.check.iter = 0
@@ -258,14 +261,14 @@ abstract type ProjectionAlgorithm end
             sampled_cols = sample_factor_matrices(nsamps, fact, als.additional_items[:factor_weights])
             ## Write new samples to pivot tensor
             dRis = dims(inds(cp)[1:end .!= fact])
-            data(als.additional_items[:pivot_tensors][fact]) .= multi_coords_to_column(dRis, sampled_cols)
+            data(als.additional_items[:projects_tensors][fact]) .= multi_coords_to_column(dRis, sampled_cols)
             
-            return pivot_hadamard(factors, rank, sampled_cols, inds(als.additional_items[:pivot_tensors][fact])[end])
+            return pivot_hadamard(factors, rank, sampled_cols, inds(als.additional_items[:projects_tensors][fact])[end])
         end
 
         function matricize_tensor(::LevScoreSampled, als, factors, cp, rank::Index, fact::Int)
             ## I need to turn this into an ITensor and then pass it to the computed algorithm.
-            return fused_flatten_sample(als.target, fact, als.additional_items[:pivot_tensors][fact])
+            return fused_flatten_sample(als.target, fact, als.additional_items[:projects_tensors][fact])
         end
 
 
@@ -288,6 +291,7 @@ abstract type ProjectionAlgorithm end
         BlockLevScoreSampled(n::Int, m::Int) = BlockLevScoreSampled((n,), (m,))
         BlockLevScoreSampled(n::Tuple) = BlockLevScoreSampled{n, (1,)}()
         BlockLevScoreSampled(n::Int, m::Tuple) = BlockLevScoreSampled((n,), m)
+        BlockLevScoreSampled(n::Tuple, m::Int) = BlockLevScoreSampled(n, (m,))
 
         nsamples(alg::BlockLevScoreSampled) = alg.NSamples
         blocks(alg::BlockLevScoreSampled) = alg.Blocks
@@ -302,14 +306,14 @@ abstract type ProjectionAlgorithm end
             sampled_cols = block_sample_factor_matrices(nsamps, als.additional_items[:factor_weights], block_size, fact)
             ## Write new samples to pivot tensor
             dRis = dims(inds(cp)[1:end .!= fact])
-            data(als.additional_items[:pivot_tensors][fact]) .= multi_coords_to_column(dRis, sampled_cols)
+            data(als.additional_items[:projects_tensors][fact]) .= multi_coords_to_column(dRis, sampled_cols)
             
-            return pivot_hadamard(factors, rank, sampled_cols, inds(als.additional_items[:pivot_tensors][fact])[end])
+            return pivot_hadamard(factors, rank, sampled_cols, inds(als.additional_items[:projects_tensors][fact])[end])
         end
 
         function matricize_tensor(::BlockLevScoreSampled, als, factors, cp, rank::Index, fact::Int)
             ## I need to turn this into an ITensor and then pass it to the computed algorithm.
-            return fused_flatten_sample(als.target, fact, als.additional_items[:pivot_tensors][fact])
+            return fused_flatten_sample(als.target, fact, als.additional_items[:projects_tensors][fact])
         end
 
 
@@ -376,7 +380,7 @@ abstract type ProjectionAlgorithm end
         ## need to recompute the QR. This is a "dumb" algorithm because it resamples the full
         ## target tensor so a future algorithm should just modify the target to reduce the amount of work.
         ## reshuffle redoes the sampling of the pivots beyond the rank of the matrix.
-        function update_samples(als, new_num_end; reshuffle = false, new_num_start = 0)
+        function update_samples(target, als, new_num_end; reshuffle = false, new_num_start = 0)
             @assert(als.mttkrp_alg isa PivotBasedSolvers)
             
             ## Make an updated alg with correct new range
@@ -391,7 +395,7 @@ abstract type ProjectionAlgorithm end
                 ## This is reshuffling the indices
                 if reshuffle
                     p1 = p[1:meff]
-                    p_rest = p[m+1:end]
+                    p_rest = p[meff+1:end]
                     p2 = p_rest[randperm(length(p_rest))]
                     pshuff = vcat(p1, p2)
                     
@@ -415,7 +419,7 @@ abstract type ProjectionAlgorithm end
 
                 projectors[pos] =  itensor(tensor(Diag(pivots[pos][int_start:int_end]), (Ris..., piv_id)))
 
-                targets[pos] = fused_flatten_sample(als.target, pos, projectors[pos])
+                targets[pos] = fused_flatten_sample(target, pos, projectors[pos])
             end
 
             extra_args = Dict(
diff --git a/src/converge_checks/converge_checks.jl b/src/converge_checks/converge_checks.jl
index f16976b..cfe087b 100644
--- a/src/converge_checks/converge_checks.jl
+++ b/src/converge_checks/converge_checks.jl
@@ -10,6 +10,8 @@ function norm_factors(partial_gram::Vector, λ::ITensor)
     return real(had*(λ*dag(prime(λ))))[]
 end
 
+save_mttkrp(::ConvergeAlg, ::ITensor) = nothing
+
 include("no_check.jl")
 include("fit_check.jl")
 include("cp_diff_check.jl")
diff --git a/src/converge_checks/cp_angle_check.jl b/src/converge_checks/cp_angle_check.jl
index f200541..a339675 100644
--- a/src/converge_checks/cp_angle_check.jl
+++ b/src/converge_checks/cp_angle_check.jl
@@ -69,6 +69,4 @@ function check_converge(check::CPAngleCheck, factors, λ, partial_gram; verbose
     return false
 end
 
-CPDFit(check::CPAngleCheck) = check.final_fit
-
-function save_mttkrp(::CPAngleCheck, ::ITensor) end
\ No newline at end of file
+CPDFit(check::CPAngleCheck) = check.final_fit
\ No newline at end of file
diff --git a/src/converge_checks/cp_diff_check.jl b/src/converge_checks/cp_diff_check.jl
index e17edce..8be55b9 100644
--- a/src/converge_checks/cp_diff_check.jl
+++ b/src/converge_checks/cp_diff_check.jl
@@ -67,6 +67,4 @@ function check_converge(check::CPDiffCheck, factors, λ, partial_gram; verbose =
     return false
 end
 
-CPDFit(check::CPDiffCheck) = check.final_fit
-
-function save_mttkrp(::CPDiffCheck, ::ITensor) end
\ No newline at end of file
+CPDFit(check::CPDiffCheck) = check.final_fit
\ No newline at end of file
diff --git a/src/converge_checks/no_check.jl b/src/converge_checks/no_check.jl
index c1e88ae..1e31552 100644
--- a/src/converge_checks/no_check.jl
+++ b/src/converge_checks/no_check.jl
@@ -17,5 +17,3 @@ function check_converge(check::NoCheck, factors, λ, partial_gram; verbose = fal
     check.counter += 1
     return false
 end
-
-function save_mttkrp(::NoCheck, ::ITensor) end
\ No newline at end of file
diff --git a/src/math_tools/probability.jl b/src/math_tools/probability.jl
index 0f70266..ec5a038 100644
--- a/src/math_tools/probability.jl
+++ b/src/math_tools/probability.jl
@@ -4,9 +4,9 @@ function compute_leverage_score_probabilitiy(A, row::Index)
   ## This only works on matrices for now.
   @assert ndims(A) == 2
   q, _ = qr(A, row)
-  ITensors.hadamard_product!(q, q, q)
+  ITensors.hadamard_product!(q, q, dag(q))
   ni = dim(q, 1)
-  return [sum(array(q)[i,:])  for i in 1:ni] ./ minimum(dims(A))
+  return [real(sum(array(q)[i,:]))  for i in 1:ni] ./ minimum(dims(A))
 end
 
 function samples_from_probability_vector(PW::Vector, samples)
diff --git a/src/optimizers/ALS/als.jl b/src/optimizers/ALS/als.jl
index d9444fb..a58ac17 100644
--- a/src/optimizers/ALS/als.jl
+++ b/src/optimizers/ALS/als.jl
@@ -233,7 +233,7 @@ function compute_als(
     extra_args[:qr_factors] = qr_factors
     extra_args[:effective_ranks] = effective_ranks
     
-    return ALS(target, alg, extra_args, check)
+    return ALS(ITensor(inds(target)), alg, extra_args, check)
 end
 
 function compute_als(
@@ -317,7 +317,7 @@ function compute_als(
     extra_args[:qr_factors] = qr_factors
     extra_args[:effective_ranks] = effective_ranks
     
-    return ALS(target, alg, extra_args, check)
+    return ALS(ITensor(inds(target)), alg, extra_args, check)
 end
 
 function compute_als(
@@ -362,7 +362,7 @@ function compute_als(
 )
     ## For each factor matrix compute its weights
     extra_args[:factor_weights] = [compute_leverage_score_probabilitiy(cp[i], ind(cp, i)) for i in 1:length(cp)]
-    pivot_tensors = Vector{ITensor}()
+    projects_tensors = Vector{ITensor}()
     for fact in 1:length(cp)
         ## grab the tensor indices for all other factors but fact
         Ris = inds(cp)[1:end .!= fact]
@@ -380,9 +380,9 @@ function compute_als(
         piv_ind = Index(length(sampled_tensor_cols), "selector_$(fact)")
 
         ## make the canonical pivot tensor. This list of pivots will be overwritten each ALS iteration
-        push!(pivot_tensors, itensor(tensor(Diag(sampled_tensor_cols), (Ris..., piv_ind))))
+        push!(projects_tensors, itensor(tensor(Diag(sampled_tensor_cols), (Ris..., piv_ind))))
     end
-    extra_args[:pivot_tensors] = pivot_tensors
+    extra_args[:projects_tensors] = projects_tensors
     return ALS(target, alg, extra_args, check)
 end
 
@@ -396,7 +396,7 @@ function compute_als(
 )
     ## For each factor matrix compute its weights
     extra_args[:factor_weights] = [compute_leverage_score_probabilitiy(cp[i], ind(cp, i)) for i in 1:length(cp)]
-    pivot_tensors = Vector{ITensor}()
+    projects_tensors = Vector{ITensor}()
     for fact in 1:length(cp)
         ## grab the tensor indices for all other factors but fact
         Ris = inds(cp)[1:end .!= fact]
@@ -417,11 +417,11 @@ function compute_als(
         piv_ind = Index(length(sampled_tensor_cols), "selector_$(fact)")
 
         ## make the canonical pivot tensor. This list of pivots will be overwritten each ALS iteration
-        push!(pivot_tensors, itensor(tensor(Diag(sampled_tensor_cols), (Ris..., piv_ind))))
+        push!(projects_tensors, itensor(tensor(Diag(sampled_tensor_cols), (Ris..., piv_ind))))
     end
     ## Notice the pivot tensor is actually a low rank tensor it stores the diagonal pivot values
     ## in α form (rows of the matricized tensor) and the indices which are captured in the pivot.
     ## The order of indices are (indices which connect to the pivot, pivot_index).
-    extra_args[:pivot_tensors] = pivot_tensors
+    extra_args[:projects_tensors] = projects_tensors
     return ALS(target, alg, extra_args, check)
 end
diff --git a/test/standard_cpd.jl b/test/standard_cpd.jl
index 5b2cd5e..d64de6f 100644
--- a/test/standard_cpd.jl
+++ b/test/standard_cpd.jl
@@ -1,5 +1,4 @@
 @testset "Standard CPD-ALS, elt=$elt" for elt in [Float64, ComplexF64]
-    elt = Float64
     verbose = false
     i, j, k = Index.((20, 30, 40))
     r = Index(400, "CP_rank")
@@ -53,7 +52,7 @@
     alg = ITensorCPD.QRPivProjected(800)
     als = ITensorCPD.compute_als(A, cp_A; alg, check, trunc_tol=4);
     
-    als = ITensorCPD.update_samples(als, 900; reshuffle = false);
+    als = ITensorCPD.update_samples(A, als, 900; reshuffle = false);
     @test ITensorCPD.stop(als.mttkrp_alg) == 900
     @test ITensorCPD.start(als.mttkrp_alg) == 1
     @test typeof(als.mttkrp_alg) == ITensorCPD.QRPivProjected
@@ -68,7 +67,7 @@
     alg = ITensorCPD.SEQRCSPivProjected(1, 800, (1,2,3),(100,100,100))
     als = ITensorCPD.compute_als(A, cp_A; alg, check);
     
-    als = ITensorCPD.update_samples(als, 600; reshuffle = true);
+    als = ITensorCPD.update_samples(A, als, 600; reshuffle = true);
     @test ITensorCPD.stop(als.mttkrp_alg) == 600
     @test ITensorCPD.start(als.mttkrp_alg) == 1
     @test typeof(als.mttkrp_alg) == ITensorCPD.SEQRCSPivProjected
@@ -131,6 +130,25 @@
         min_val = val < min_val ? val : val
     end
      @test min_val < 0.1
+
+    ### Test for Leverage score sampling CPD 
+    alg = ITensorCPD.BlockLevScoreSampled((50, 50, 500), 1)
+    min_val = 1
+    for i in 1:3
+        cpd_opt = ITensorCPD.als_optimize(T, cpd; alg, check, verbose);
+        val = norm(reconstruct(cpd_opt) - T) / norm(T) 
+        min_val = val < min_val ? val : val
+    end
+     @test min_val < 0.1
+
+     alg = ITensorCPD.BlockLevScoreSampled((50, 50, 500), 12)
+    min_val = 1
+    for i in 1:3
+        cpd_opt = ITensorCPD.als_optimize(T, cpd; alg, check, verbose);
+        val = norm(reconstruct(cpd_opt) - T) / norm(T) 
+        min_val = val < min_val ? val : val
+    end
+     @test min_val < 0.1
 end
 
 @testset "Standard CPD-ALS, elt=$elt" for elt in [Float32, ComplexF32]
@@ -227,6 +245,14 @@ end
     alg = ITensorCPD.LevScoreSampled(100)
     cpd_opt = ITensorCPD.als_optimize(T, cpd; alg, check, verbose);
     @test norm(reconstruct(cpd_opt) - T) / norm(T) < 0.1
+
+    alg = ITensorCPD.BlockLevScoreSampled(100,1)
+    cpd_opt = ITensorCPD.als_optimize(T, cpd; alg, check, verbose);
+    @test norm(reconstruct(cpd_opt) - T) / norm(T) < 0.1
+
+    alg = ITensorCPD.BlockLevScoreSampled(100,3)
+    cpd_opt = ITensorCPD.als_optimize(T, cpd; alg, check, verbose);
+    @test norm(reconstruct(cpd_opt) - T) / norm(T) < 0.1
 end