diff --git a/test/Manifest.toml b/test/Manifest.toml
index e962a40..ba86075 100644
--- a/test/Manifest.toml
+++ b/test/Manifest.toml
@@ -1,8 +1,8 @@
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.10.1"
+julia_version = "1.10.2"
 manifest_format = "2.0"
-project_hash = "b7d2887a6e0b6afe3c64da83f9f8503f7d6748ea"
+project_hash = "2e8f71a970a5211ff0d3acbb9f0479ce789c8a02"
 
 [[deps.AbstractFFTs]]
 deps = ["LinearAlgebra"]
@@ -458,6 +458,12 @@ version = "1.4.3"
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
+[[deps.ProgressMeter]]
+deps = ["Distributed", "Printf"]
+git-tree-sha1 = "763a8ceb07833dd51bb9e3bbca372de32c0605ad"
+uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
+version = "1.10.0"
+
 [[deps.QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
 git-tree-sha1 = "9b23c31e76e333e6fb4c1595ae6afa74966a729e"
diff --git a/test/Project.toml b/test/Project.toml
index 0dad22e..0f662b9 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,6 +1,7 @@
 [deps]
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 LsqFit = "2fda8390-95c7-5789-9bda-21331edee243"
+ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228"
diff --git a/test/runtests.jl b/test/runtests.jl
index 2274692..f14e7ad 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,8 +1,9 @@
 using Test
 using SpinShuttling
 using UnicodePlots
+using ProgressMeter
 
-include("testquadrature.jl")
+# include("testquadrature.jl")
 include("testfidelity.jl")
-include("teststochastics.jl")
-include("testspectrum.jl")
+# include("teststochastics.jl")
+# include("testspectrum.jl")
diff --git a/test/testfidelity.jl b/test/testfidelity.jl
index 0208195..f979534 100644
--- a/test/testfidelity.jl
+++ b/test/testfidelity.jl
@@ -2,85 +2,87 @@
 visualize=true
 
 ##
-@testset begin "test single spin shuttling fidelity"
-    T=400; L=10; σ = sqrt(2) / 20; M = 20000; N=601; κₜ=1/20;κₓ=1/0.1;
-    v=L/T;
-    t=range(0, T, N)
-    P=hcat(t, v.*t)
-    B=OrnsteinUhlenbeckField(0,[κₜ,κₓ],σ)
+# @testset begin "test single spin shuttling fidelity"
+#     T=400; L=10; σ = sqrt(2) / 20; M = 20000; N=601; κₜ=1/20;κₓ=1/0.1;
+#     v=L/T;
+#     t=range(0, T, N)
+#     P=hcat(t, v.*t)
+#     B=OrnsteinUhlenbeckField(0,[κₜ,κₓ],σ)
 
-    model=OneSpinModel(T,L,N,B)
-    # test customize println
-    println(model)
+#     model=OneSpinModel(T,L,N,B)
+#     # test customize println
+#     println(model)
 
-    f1=averagefidelity(model)
-    f2, f2_err=sampling(model, fidelity, M)
-    f3=1/2*(1+W(T,L,B))
-    @test isapprox(f1, f3,rtol=1e-2)
-    @test isapprox(f2, f3, rtol=1e-2) 
-    println("NI:", f1)
-    println("MC:", f2)
-    println("TH:", f3)
-end
+#     f1=averagefidelity(model)
+#     f2, f2_err=sampling(model, fidelity, M)
+#     f3=1/2*(1+W(T,L,B))
+#     @test isapprox(f1, f3,rtol=1e-2)
+#     @test isapprox(f2, f3, rtol=1e-2) 
+#     println("NI:", f1)
+#     println("MC:", f2)
+#     println("TH:", f3)
+# end
 
-#
-@testset begin "test single spin forth-back shuttling fidelity"
-    T=200; L=10; σ = sqrt(2) / 20; M = 5000; N=501; κₜ=1/20;κₓ=10; 
-    # exponential should be smaller than 100
-    B=OrnsteinUhlenbeckField(0,[κₜ,κₓ],σ)
+# #
+# @testset begin "test single spin forth-back shuttling fidelity"
+#     T=200; L=10; σ = sqrt(2) / 20; M = 5000; N=501; κₜ=1/20;κₓ=10; 
+#     # exponential should be smaller than 100
+#     B=OrnsteinUhlenbeckField(0,[κₜ,κₓ],σ)
 
-    if visualize
-        t=range(1e-2*T,T, 10)
-        f_mc=[sampling(OneSpinForthBackModel(T,L,N,B), fidelity, M)[1] for T in t]
-        f_ni=[averagefidelity(OneSpinForthBackModel(T,L,N,B)) for T in t]
-        f_th=[(1+W(T,L,B,path=:forthback))/2 for T in t]
-        fig=lineplot(t, f_mc,
-            xlabel="t", ylabel="F", name="monte-carlo sampling",
-            # ribbon=@. sqrt(f_mc_err/M)
-            )
-            lineplot!(fig, t, f_ni, name="numerical integration")
-            lineplot!(fig, t, f_th, name="theoretical fidelity")
-        display(fig)
-    end
+#     if visualize
+#         t=range(1e-2*T,T, 10)
+#         f_mc=[sampling(OneSpinForthBackModel(T,L,N,B), fidelity, M)[1] for T in t]
+#         f_ni=[averagefidelity(OneSpinForthBackModel(T,L,N,B)) for T in t]
+#         f_th=[(1+W(T,L,B,path=:forthback))/2 for T in t]
+#         fig=lineplot(t, f_mc,
+#             xlabel="t", ylabel="F", name="monte-carlo sampling",
+#             # ribbon=@. sqrt(f_mc_err/M)
+#             )
+#             lineplot!(fig, t, f_ni, name="numerical integration")
+#             lineplot!(fig, t, f_th, name="theoretical fidelity")
+#         display(fig)
+#     end
 
-    model=OneSpinForthBackModel(T,L,N,B)
-    # test customize println
-    println(model)
+#     model=OneSpinForthBackModel(T,L,N,B)
+#     # test customize println
+#     println(model)
 
-    f1=averagefidelity(model)
-    f2, f2_err=sampling(model, fidelity, M)
-    f3=1/2*(1+W(T, L, B, path=:forthback))
-    @test isapprox(f1, f3,rtol=1e-2)
-    @test isapprox(f2, f3, rtol=1e-2) 
-    println("NI:", f1)
-    println("MC:", f2)
-    println("TH:", f3)
-end
+#     f1=averagefidelity(model)
+#     f2, f2_err=sampling(model, fidelity, M)
+#     f3=1/2*(1+W(T, L, B, path=:forthback))
+#     @test isapprox(f1, f3,rtol=1e-2)
+#     @test isapprox(f2, f3, rtol=1e-2) 
+#     println("NI:", f1)
+#     println("MC:", f2)
+#     println("TH:", f3)
+# end
 
-##
-@testset begin "test two spin sequenced shuttling fidelity"
-    L=10; σ =sqrt(2)/20; M=20000; N=501; T1=200; T0=25*0.05; κₜ=1/20; κₓ=1/0.1;
-    B=OrnsteinUhlenbeckField(0,[κₜ,κₓ],σ)
-    model=TwoSpinModel(T0, T1, L, N, B)
-    if visualize
-        display(heatmap(collect(model.R.Σ), title="cross covariance matrix, test fig 4"))
-    end
-    f1=averagefidelity(model)
-    f2, f2_err=sampling(model, fidelity, M)
-    f3=1/2*(1+W(T0, T1, L,B))
-    @test isapprox(f1, f3,rtol=1e-2)
-    @test isapprox(f2, f3, rtol=1e-2) 
-    println("NI:", f1)
-    println("MC:", f2)
-    println("TH:", f3)
-end
+# ##
+# @testset begin "test two spin sequenced shuttling fidelity"
+#     L=10; σ =sqrt(2)/20; M=20000; N=501; T1=200; T0=25*0.05; κₜ=1/20; κₓ=1/0.1;
+#     B=OrnsteinUhlenbeckField(0,[κₜ,κₓ],σ)
+#     model=TwoSpinModel(T0, T1, L, N, B)
+#     if visualize
+#         display(heatmap(collect(model.R.Σ), title="cross covariance matrix, test fig 4"))
+#     end
+#     f1=averagefidelity(model)
+#     f2, f2_err=sampling(model, fidelity, M)
+#     f3=1/2*(1+W(T0, T1, L,B))
+#     @test isapprox(f1, f3,rtol=1e-2)
+#     @test isapprox(f2, f3, rtol=1e-2) 
+#     println("NI:", f1)
+#     println("MC:", f2)
+#     println("TH:", f3)
+# end
 
 #
 @testset "1/f noise chacacteristics" begin
-    σ = sqrt(2)/20; M = 4000; N=501; L=10; γ=(1e-3,1e3); # MHz
+    σ = sqrt(2)/20; M = 400; N=501; L=10; γ=(1e-2,1e2); # MHz
     # 0.01 ~ 100 μs
     # v = 0.1 ~ 1000 m/s
-    v=0.1; T=L/v; κₓ=0.01;
+    v=1; T=L/v; κₓ=10;
+    # T=10 
+    # 1/T=0.1 N/T=20 
     B=PinkBrownianField(0,[κₓ],σ, γ)
     model=OneSpinModel(T,L,N,B)
 
@@ -93,20 +95,24 @@ end
     println("MC:", f2)
     println("TH:", f3)
 
-    t=range(0,T,N)
-    f_mc, f_mc_err=sampling(model, fidelity, M, vector=true)
-    t_ni, chi_ni=characteristicfunction(model.R)
-    f_ni= @. (1+real(chi_ni))/2
+    k=10
+    t=range(0,T,k)
+    f_mc=zeros(k);  f_mc_err=zeros(k); f_ni=zeros(k);
+    @showprogress for i in eachindex(t)
+        model=OneSpinModel(t[i],L,N,B)
+        f_mc[i], f_mc_err[i]=sampling(model, fidelity, M)
+        f_ni[i]=averagefidelity(model)
+    end
     f_th=map(T->(1+W(T,L,B))/2, t)|>collect
     if visualize
         fig=lineplot(t,f_mc, 
             xlabel="t", ylabel="F", name="monte-carlo sampling",
             # ribbon=sqrt.(f_mc_err/M)
             )
-            lineplot!(fig, t_ni, f_ni, name="numerical integration")
-            lineplot!(fig, t,f_th, name="theoretical fidelity")
+            lineplot!(fig, t, f_ni, name="numerical integration")
+            lineplot!(fig, t, f_th, name="theoretical fidelity")
         display(fig)
     end
 
-    @test all([abs(f_mc[i]-f_th[i]) < sqrt(f_mc_err[i]) for i in 10:N])
+    @test all([abs(f_mc[i]-f_th[i]) < sqrt(f_mc_err[i]) for i in eachindex(t)])
 end
\ No newline at end of file