diff --git a/.gitignore b/.gitignore
index 3af67b1..1c02e5e 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,5 @@
 *.jl.*.cov
 *.jl.cov
 *.jl.mem
+Manifest.toml
 /docs/build/
diff --git a/Manifest.toml b/Manifest.toml
deleted file mode 100644
index 2f54168..0000000
--- a/Manifest.toml
+++ /dev/null
@@ -1,217 +0,0 @@
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diff --git a/Project.toml b/Project.toml
index 03f5db5..fb48cec 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Lehmann"
 uuid = "95bf888a-8996-4655-9f35-1c0506bdfefe"
 authors = ["Kun Chen", "Tao Wang", "Xiansheng Cai"]
-version = "0.2.1"
+version = "0.2.2"
 
 [deps]
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
diff --git a/build.jl b/build.jl
index c7e6dd6..d226f1a 100644
--- a/build.jl
+++ b/build.jl
@@ -3,13 +3,14 @@ using Lehmann
 using Printf
 
 # rtol = [-6, -8, -10, -12, -14]
-rtol = [-7, -9, -11, -13]
-Λ = [100, 1000, 10000, 100000, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14]
+# rtol = [-7, -9, -11, -13]
+# Λ = [100, 1000, 10000, 100000, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14]
 # Λ = [1e11, 1e12, 1e13, 1e14]
-# rtol = [-12]
-# Λ = [1000000,]
+rtol = [-12]
+Λ = [1000000,]
 algorithm = :functional
-folder = "./basis/"
+# folder = "./basis/"
+folder = "./"
 
 for lambda in Λ
     for err in rtol
diff --git a/example/SYK.jl b/example/SYK.jl
index f7f8627..e41d18f 100644
--- a/example/SYK.jl
+++ b/example/SYK.jl
@@ -17,7 +17,7 @@ A SYK model solver based on a forward fixed-point iteration method.
 
  The SYK Green's function has particle-hole symmetry when μ=0. 
  You may enforce such symmetry by setting `symmetry = :ph` when initialize the DLR grids.
- A symmetrized solver tends to be more robust than the unsymmetrized counterpart.
+ A symmetrized solver tends to be more robust than a unsymmetrized one.
 """
 
 using Lehmann
@@ -50,7 +50,7 @@ function dyson(d, sigma_q, mu)
     end
 end
 
-function solve_syk_with_fixpoint_iter(d, mu, tol = d.rtol * 10; mix = 0.1, maxiter = 1000, G_x = zeros(ComplexF64, length(d)))
+function solve_syk_with_fixpoint_iter(d, mu, tol = d.rtol * 10; mix = 0.1, maxiter = 5000, G_x = zeros(ComplexF64, length(d)), verbose = true)
 
     for iter in 1:maxiter
 
@@ -61,8 +61,10 @@ function solve_syk_with_fixpoint_iter(d, mu, tol = d.rtol * 10; mix = 0.1, maxit
         G_x_new = matfreq2tau(d, G_q_new)
 
 
-        if iter % (maxiter / 10) == 0
-            println("round $iter: change $(diff(G_x_new, G_x))")
+        if verbose
+            if iter % (maxiter / 10) == 0
+                println("round $iter: change $(diff(G_x_new, G_x))")
+            end
         end
         if maximum(abs.(G_x_new .- G_x)) < tol && iter > 10
             break
@@ -83,26 +85,51 @@ function printG(d, G_x)
     println()
 end
 
-printstyled("=====     Symmetrized DLR solver for SYK model     =======\n", color = :yellow)
-mix = 0.1
-dsym = DLRGrid(Euv = 5.0, β = 1000.0, isFermi = true, rtol = 1e-8, symmetry = :ph) # Initialize DLR object
-G_x_ph = solve_syk_with_fixpoint_iter(dsym, 0.00, mix = mix)
-printG(dsym, G_x_ph)
-
-printstyled("=====     Unsymmetrized DLR solver for SYK model     =======\n", color = :yellow)
-mix = 0.02
-dnone = DLRGrid(Euv = 5.0, β = 1000.0, isFermi = true, rtol = 1e-8, symmetry = :none) # Initialize DLR object
-G_x_none = solve_syk_with_fixpoint_iter(dnone, 0.00, mix = mix)
-printG(dnone, G_x_none)
-
-printstyled("=====     Unsymmetrized versus Symmetrized DLR solver    =======\n", color = :yellow)
-@printf("%15s%40s%40s%40s\n", "τ", "sym DLR (interpolated)", "unsym DLR", "difference")
-G_x_interp = tau2tau(dsym, G_x_ph, dnone.τ)
-for i in 1:dnone.size
-    if dnone.τ[i] <= dnone.β / 2
-        @printf("%15.8f%40.15f%40.15f%40.15f\n", dnone.τ[i], real(G_x_interp[i]), real(G_x_none[i]), abs(real(G_x_interp[i] - G_x_none[i])))
-    end
+verbose = false
+
+printstyled("=====    Prepare the expected Green's function of the SYK model     =======\n", color = :yellow)
+dsym_correct = DLRGrid(Euv = 5.0, β = 10000.0, isFermi = true, rtol = 1e-14, symmetry = :ph) # Initialize DLR object
+G_x_correct = solve_syk_with_fixpoint_iter(dsym_correct, 0.00, mix = 0.1, verbose = false)
+printG(dsym_correct, G_x_correct)
+
+printstyled("=====    Test Symmetrized and Unsymmetrized DLR solver for SYK model     =======\n", color = :yellow)
+
+@printf("%30s%30s%30s%15s\n", "Euv", "symmetrized solver error", "unsymmetrized solver error", "good or bad")
+for Euv in LinRange(5.0, 10.0, 50)
+
+    rtol = 1e-10
+    β = 10000.0
+    # printstyled("=====     Symmetrized DLR solver for SYK model     =======\n", color = :yellow)
+    mix = 0.01
+    dsym = DLRGrid(Euv = Euv, β = β, isFermi = true, rtol = rtol, symmetry = :ph, rebuild = true, verbose = false) # Initialize DLR object
+    G_x_ph = solve_syk_with_fixpoint_iter(dsym, 0.00, mix = mix, verbose = verbose)
+    # printG(dsym, G_x_ph)
+
+    # printstyled("=====     Unsymmetrized DLR solver for SYK model     =======\n", color = :yellow)
+    mix = 0.01
+    dnone = DLRGrid(Euv = Euv, β = β, isFermi = true, rtol = rtol, symmetry = :none, rebuild = true, verbose = false) # Initialize DLR object
+    G_x_none = solve_syk_with_fixpoint_iter(dnone, 0.00, mix = mix, verbose = verbose)
+    # printG(dnone, G_x_none)
+
+    # printstyled("=====     Unsymmetrized versus Symmetrized DLR solver    =======\n", color = :yellow)
+    # @printf("%15s%40s%40s%40s\n", "τ", "sym DLR (interpolated)", "unsym DLR", "difference")
+    # G_x_interp = tau2tau(dsym_correct, G_x_correct, dnone.τ)
+    # for i in 1:dnone.size
+    #     if dnone.τ[i] <= dnone.β / 2
+    #         @printf("%15.8f%40.15f%40.15f%40.15f\n", dnone.τ[i], real(G_x_interp[i]), real(G_x_none[i]), abs(real(G_x_interp[i] - G_x_none[i])))
+    #     end
+    # end
+
+    G_x_interp_ph = tau2tau(dsym_correct, G_x_correct, dsym.τ)
+    G_x_interp_none = tau2tau(dsym_correct, G_x_correct, dnone.τ)
+    d_ph = diff(G_x_interp_ph, G_x_ph)
+    d_none = diff(G_x_interp_none, G_x_none)
+    flag = (d_ph < 100rtol) && (d_none < 100rtol) ? "good" : "bad"
+
+    @printf("%30.15f%30.15e%30.15e%20s\n", Euv, d_ph, d_none, flag)
+    # println("symmetric Euv = $Euv maximumal difference: ", diff(G_x_interp, G_x_ph))
+    # println("non symmetric Euv = $Euv maximumal difference: ", diff(G_x_interp, G_x_none))
+
 end
-println("maximumal difference: ", diff(G_x_interp, G_x_none))
 
 
diff --git a/src/dlr.jl b/src/dlr.jl
index 9464aa3..2bdd8ff 100644
--- a/src/dlr.jl
+++ b/src/dlr.jl
@@ -42,8 +42,8 @@ struct DLRGrid
     τ::Vector{Float64}
 
     """
-    function DLRGrid(Euv, β, rtol, isFermi::Bool; symmetry::Symbol = :none, rebuild = false, folder = nothing, algorithm = :functional, verbose = 0)
-    function DLRGrid(; Euv, β, isFermi::Bool, symmetry::Symbol = :none, rtol = 1e-8, rebuild = false, folder = nothing, algorithm = :functional, verbose = 0)
+    function DLRGrid(Euv, β, rtol, isFermi::Bool; symmetry::Symbol = :none, rebuild = false, folder = nothing, algorithm = :functional, verbose = false)
+    function DLRGrid(; Euv, β, isFermi::Bool, symmetry::Symbol = :none, rtol = 1e-8, rebuild = false, folder = nothing, algorithm = :functional, verbose = false)
 
     Create DLR grids
 
@@ -54,9 +54,10 @@ struct DLRGrid
     - `symmetry`  : particle-hole symmetric :ph, or particle-hole asymmetric :pha, or :none
     - `rtol`      : tolerance absolute error
     - `rebuild`   : set false to load DLR basis from the file, set true to recalculate the DLR basis on the fly
-    - `folder`    : the folder to load the DLR file if rebuild = false, or the folder to save the DLR file if rebuild = true
+    - `folder`    : if rebuild is true and folder is set, then dlrGrid will be rebuilt and saved to the specified folder
+                    if rebuild is false and folder is set, then dlrGrid will be loaded from the specified folder
     - `algorithm` : if rebuild = true, then set :functional to use the functional algorithm to generate the DLR basis, or set :discrete to use the matrix algorithm.
-    - `verbose`   : 0 not to print DLRGrid to terminal, >0 to print
+    - `verbose`   : false not to print DLRGrid to terminal, or true to print
     """
     function DLRGrid(Euv, β, rtol, isFermi::Bool, symmetry::Symbol = :none; rebuild = false, folder = nothing, algorithm = :functional, verbose = false)
         Λ = Euv * β # dlr only depends on this dimensionless scale
@@ -73,39 +74,80 @@ struct DLRGrid
             @warn("Current implementation may cause ~ 3-4 digits loss for rtol ≥ 1e-6!")
         end
 
-        if Λ < 100
-            Λ = Int(100)
-        else
-            Λ = 10^(Int(ceil(log10(Λ)))) # get smallest n so that Λ<10^n
-        end
-
         rtolpower = Int(floor(log10(rtol))) # get the biggest n so that rtol>1e-n
         if abs(rtolpower) < 4
             rtolpower = -4
         end
+        rtol = 10.0^float(rtolpower)
+
+        function finddlr(folder, filename)
+            searchdir(path, key) = filter(x -> occursin(key, x), readdir(path))
+            for dir in folder
+                if length(searchdir(dir, filename)) > 0
+                    #dlr file found
+                    return joinpath(dir, filename)
+                end
+            end
+            @warn("Cann't find the DLR file $filename in the folders $folder. Regenerating DLR...")
+            return nothing
+        end
 
-        if symmetry == :none
-            # if isFermi
-            filename = "universal_$(Λ)_1e$(rtolpower).dlr"
-            # else
-            #     error("Generic bosonic dlr has not yet been implemented!")
-            # end
-        elseif symmetry == :ph
-            filename = "ph_$(Λ)_1e$(rtolpower).dlr"
-        elseif symmetry == :pha
-            filename = "pha_$(Λ)_1e$(rtolpower).dlr"
-        else
-            error("$symmetry is not implemented!")
+        function filename(lambda, errpower)
+            lambda = Int(floor(lambda))
+            errstr = "1e$errpower"
+
+            if symmetry == :none
+                return "universal_$(lambda)_$(errstr).dlr"
+            elseif symmetry == :ph
+                return "ph_$(lambda)_$(errstr).dlr"
+            elseif symmetry == :pha
+                return "pha_$(lambda)_$(errstr).dlr"
+            else
+                error("$symmetry is not implemented!")
+            end
         end
 
-        dlr = new(isFermi, symmetry, Euv, β, Λ, rtol, [], [], [], [])
-        if rebuild
-            _build!(dlr, folder, filename, algorithm, verbose)
-        else
-            _load!(dlr, folder, filename, algorithm, verbose)
+
+        if rebuild == false
+            if isnothing(folder)
+                Λfloor = Λ < 100 ? Int(100) : 10^(Int(ceil(log10(Λ)))) # get smallest n so that Λ<10^n
+
+                folderList = [string(@__DIR__, "/../basis/"),]
+                file = filename(Λfloor, rtolpower)
+
+                dlrfile = finddlr(folderList, file)
+
+                if isnothing(dlrfile) == false
+                    dlr = new(isFermi, symmetry, Euv, β, Λfloor, 10.0^(float(rtolpower)), [], [], [], [])
+                    _load!(dlr, dlrfile, verbose)
+                    return dlr
+                else
+                    @warn("No DLR is found in the folder $folder, try to rebuild instead.")
+                end
+            else
+                file = filename(Euv * β, rtolpower)
+                folderList = [folder,]
+
+                dlrfile = finddlr(folderList, file)
+
+                if isnothing(dlrfile) == false
+                    dlr = new(isFermi, symmetry, Euv, β, Euv * β, rtol, [], [], [], [])
+                    _load!(dlr, dlrfile, verbose)
+                    return dlr
+                else
+                    @warn("No DLR is found in the folder $folder, try to rebuild instead.")
+                end
+            end
+
         end
+
+        # try to rebuild the dlrGrid
+        dlr = new(isFermi, symmetry, Euv, β, Euv * β, rtol, [], [], [], [])
+        file2save = filename(Euv * β, rtolpower)
+        _build!(dlr, folder, file2save, algorithm, verbose)
         return dlr
     end
+
     function DLRGrid(; Euv, β, isFermi::Bool, symmetry::Symbol = :none, rtol = 1e-14, rebuild = false, folder = nothing, algorithm = :functional, verbose = false)
         return DLRGrid(Euv, β, rtol, isFermi, symmetry; rebuild = rebuild, folder = folder, algorithm = algorithm, verbose = verbose)
     end
@@ -133,29 +175,7 @@ Base.size(dlrGrid::DLRGrid) = length(dlrGrid.ω)
 Base.length(dlrGrid::DLRGrid) = length(dlrGrid.ω)
 rank(dlrGrid::DLRGrid) = length(dlrGrid.ω)
 
-function _load!(dlrGrid::DLRGrid, folder, filename, algorithm = :functional, verbose = false)
-    searchdir(path, key) = filter(x -> occursin(key, x), readdir(path))
-
-    function finddlr(folder, filename)
-        for dir in folder
-            if length(searchdir(dir, filename)) > 0
-                #dlr file found
-                return joinpath(dir, filename)
-            end
-        end
-        @warn("Cann't find the DLR file $filename in the folders $folder. Regenerating DLR...")
-        return nothing
-    end
-
-    folder = isnothing(folder) ? [] : collect(folder)
-    push!(folder, string(@__DIR__, "/../basis/"))
-
-    dlrfile = finddlr(folder, filename)
-
-    if isnothing(dlrfile)
-        _build!(dlrGrid, nothing, nothing, algorithm)
-        return
-    end
+function _load!(dlrGrid::DLRGrid, dlrfile, verbose = false)
 
     grid = readdlm(dlrfile, comments = true, comment_char = '#')
     # println("reading $filename")
@@ -205,6 +225,7 @@ function _build!(dlrGrid::DLRGrid, folder, filename, algorithm, verbose = false)
         push!(dlrGrid.n, n)
         push!(dlrGrid.ωn, isFermi ? (2n + 1.0) * π / β : 2n * π / β)
     end
+    # println(rank)
 end
 
 
diff --git a/src/functional/builder.jl b/src/functional/builder.jl
index 9e66a6f..f387cfd 100644
--- a/src/functional/builder.jl
+++ b/src/functional/builder.jl
@@ -107,13 +107,13 @@ function printCandidate(basis, idx)
     @printf("%3i : ω=%24.8f ∈ (%24.8f, %24.8f) -> error=%24.16g\n", basis.N, basis.grid[idx], lower, upper, basis.residual[idx])
 end
 
-function QR(Λ, rtol, proj, g0; N = nothing)
+function QR(Λ, rtol, proj, g0; N = nothing, verbose = false)
     basis = Basis(Λ, rtol)
     # println(g0)
     for g in g0
         idx = addBasis!(basis, proj, Float(g))
         # @printf("%3i : ω=%24.8f ∈ (%24.8f, %24.8f) -> error=%24.16g\n", 1, g, 0, Λ, basis.residual[idx])
-        printCandidate(basis, idx)
+        verbose && printCandidate(basis, idx)
     end
 
     # @code_warntype Residual(basis, proj, Float(1.0))
@@ -125,7 +125,7 @@ function QR(Λ, rtol, proj, g0; N = nothing)
 
         newω = basis.candidate[ωi]
         idx = addBasis!(basis, proj, newω)
-        printCandidate(basis, idx)
+        verbose && printCandidate(basis, idx)
         # println(length(basis.grid))
         # println(idx)
         # lower = (idx == 1) ? 0 : basis.grid[idx - 1]
@@ -136,9 +136,9 @@ function QR(Λ, rtol, proj, g0; N = nothing)
         # plotResidual(basis, proj, Float(0), Float(100), candidate, residual)
         maxResidual, ωi = findmax(basis.candidateResidual)
     end
-    testOrthgonal(basis)
+    testOrthgonal(basis, verbose)
     # @printf("residual = %.10e, Fnorm/F0 = %.10e\n", residual, residualF(freq, Q, Λ))
-    @printf("residual = %.10e\n", maximum(basis.candidateResidual))
+    verbose && @printf("residual = %.10e\n", maximum(basis.candidateResidual))
     # plotResidual(basis, proj, Float(0), Float(100), basis.candidate, basis.candidateResidual)
     return basis
 end
@@ -215,11 +215,11 @@ function Residual(basis, proj, g::Float)
 end
 
 
-function testOrthgonal(basis)
-    println("testing orthognalization...")
+function testOrthgonal(basis, verbose)
+    # println("testing orthognalization...")
     II = basis.Q * basis.proj * basis.Q'
     maxerr = maximum(abs.(II - I))
-    println("Max Orthognalization Error: ", maxerr)
+    verbose && println("Max Orthognalization Error: ", maxerr)
 end
 
 """