diff --git a/Project.toml b/Project.toml
index de06d941..aa8ccaee 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "FeynmanDiagram"
 uuid = "e424a512-dbd9-41ff-9883-094748823e72"
 authors = ["Kun Chen", "Pengcheng Hou", "Daniel Cerkoney"]
-version = "1.0.1"
+version = "1.0.2"
 
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
diff --git a/src/backend/compiler_python.jl b/src/backend/compiler_python.jl
index 1efc40c9..0cf48816 100644
--- a/src/backend/compiler_python.jl
+++ b/src/backend/compiler_python.jl
@@ -6,28 +6,28 @@
 # Arguments:
 - `graphs`  vector of computational graphs
 """
-function to_python_str(graphs::AbstractVector{<:AbstractGraph})
+function to_python_str(graphs::AbstractVector{<:AbstractGraph};
+    root::AbstractVector{Int}=[id(g) for g in graphs], name::String="eval_graph", in_place::Bool=false)
     head = ""
     body = ""
     leafidx = 0
-    root = [id(g) for g in graphs]
     inds_visitedleaf = Int[]
     inds_visitednode = Int[]
-    gid_to_leafid = Dict{String,Int64}()
-    rootidx = 0
+    map_validx_leaf = Dict{Int,eltype(graphs)}()  # mapping from the index of the leafVal to the leaf graph 
     for graph in graphs
         for g in PostOrderDFS(graph) #leaf first search
             g_id = id(g)
             target = "g$(g_id)"
             isroot = false
             if g_id in root
+                target_root = "root[:, $(findfirst(x -> x == g_id, root)-1)]"
                 isroot = true
             end
             if isempty(subgraphs(g)) #leaf
                 g_id in inds_visitedleaf && continue
-                body *= "    $target = leaf[$(leafidx)]\n"
-                gid_to_leafid[target] = leafidx
+                body *= "    $target = leafVal[:, $(leafidx)]\n"
                 leafidx += 1
+                map_validx_leaf[leafidx] = g
                 push!(inds_visitedleaf, g_id)
             else
                 g_id in inds_visitednode && continue
@@ -35,23 +35,25 @@ function to_python_str(graphs::AbstractVector{<:AbstractGraph})
                 push!(inds_visitednode, g_id)
             end
             if isroot
-                body *= "    root$(rootidx) = $target\n"
-                rootidx += 1
+                body *= "    $target_root = $target\n"
             end
         end
     end
-    head *= "def graphfunc(leaf):\n"
-    output = ["root$(i)" for i in 0:rootidx-1]
-    output = join(output, ",")
-    tail = "    return $output\n\n"
-
-    expr = head * body * tail
+    if in_place
+        head *= "def $name(root, leafVal):\n"
+    else
+        head *= "import torch\n"
+        head *= "def $name(leafVal):\n"
+        head *= "    root = torch.empty(leafVal.shape[0], $(length(graphs)), dtype=leafVal.dtype, device=leafVal.device)\n"
+    end
+    tail = "    return root\n\n"
 
-    return expr, gid_to_leafid
+    return head * body * tail, map_validx_leaf
 end
-function compile_Python(graphs::AbstractVector{<:AbstractGraph}, filename::String="GraphFunc.py")
-    py_string, leafmap = to_python_str(graphs)
-    open(filename, "w") do f
+function compile_Python(graphs::AbstractVector{<:AbstractGraph}, filename::String;
+    root::AbstractVector{Int}=[id(g) for g in graphs], func_name="eval_graph")
+    py_string, leafmap = to_python_str(graphs, root=root, name=func_name)
+    open(filename, "a") do f
         write(f, py_string)
     end
     return leafmap