initialize func without noise input

src/ekp_interface.jl

@@ -214,6 +214,45 @@ initialize(config::ExperimentConfig; kwargs...) = initialize(
     kwargs...,
 )
 
+function initialize(
+    ensemble_size,
+    observations,
+    prior,
+    output_dir;
+    rng_seed = 1234,
+    ekp_kwargs...,
+)
+    Random.seed!(rng_seed)
+    rng_ekp = Random.MersenneTwister(rng_seed)
+
+    initial_ensemble =
+        EKP.construct_initial_ensemble(rng_ekp, prior, ensemble_size)
+    eki = EKP.EnsembleKalmanProcess(
+        initial_ensemble,
+        observations,
+        EKP.Inversion();
+        rng = rng_ekp,
+        failure_handler_method = EKP.SampleSuccGauss(),
+        ekp_kwargs...,
+    )
+
+    param_dict = get_param_dict(prior)
+
+    save_parameter_ensemble(
+        EKP.get_u_final(eki),  # constraints applied when saving
+        prior,
+        param_dict,
+        output_dir,
+        "parameters.toml",
+        0,  # Initial iteration = 0
+    )
+
+    # Save the EKI object in the 'iteration_000' folder
+    eki_path = joinpath(output_dir, "iteration_000", "eki_file.jld2")
+    JLD2.save_object(eki_path, eki)
+    return eki
+end
+
 function initialize(
     ensemble_size,
     observations,