#!/usr/bin/env python3importnumpyasnp# numpy==1.26.4importpysindyasps# pysindy==1.7.5defmain():# 1. Create sample data to mimic your shape conditions.#    Two trajectories: (2, 101) and (2, 100).t_train_1=np.linspace(0,1,101)t_train_2=np.linspace(0,1,100)x_train_1=np.vstack([np.sin(2*np.pi*t_train_1),np.cos(2*np.pi*t_train_1)    ])# shape (2, 101)x_train_2=np.vstack([np.sin(2*np.pi*t_train_2),np.cos(2*np.pi*t_train_2)    ])# shape (2, 100)# Create x_dot data for x_train_1x_dot_1=np.zeros_like(x_train_1)foriinrange(x_train_1.shape[0]):sfd=ps.SmoothedFiniteDifference(smoother_kws={'window_length':25})x_dot_1[i, :]=sfd._differentiate(x_train_1[i, :],t_train_1[1]-t_train_1[0])x_dot_2=np.zeros_like(x_train_2)foriinrange(x_train_2.shape[0]):x_dot_2[i, :]=sfd._differentiate(x_train_2[i, :],t_train_2[1]-t_train_2[0])x_dot= [x_dot_1.T,x_dot_2.T]# Optional: Control input (u_train) for each trajectory#           shape matches time dimensionu_train_1=np.zeros_like(t_train_1)u_train_2=np.zeros_like(t_train_2)# Combine into lists to represent multiple trajectoriesx_train= [x_train_1,x_train_2]u_train= [u_train_1,u_train_2]# Simple time step (dt) taken from the first trajectorydt=t_train_1[1]-t_train_1[0]# Example feature library (you can choose any)feature_library=ps.PolynomialLibrary(degree=2)# For demonstration, define a single optimizer:frompysindy.optimizersimportSTLSQselected_optimizers= {"STLSQ_example": {"class":STLSQ,"params": {"alpha":0.1,"threshold":0.1,"fit_intercept":True            }        }    }# Check if x_train is a list => multiple trajectoriesxu_list=isinstance(x_train,list)defrun_selected_optimizers(selected_opts):ifnotselected_opts:print("Please select at least one optimizer.")returnmodels_scores= {}models_errors= {}# Example function to compute "prediction error" (stub)# pred_state, state_data shapes must match in time dimension.defcompute_prediction_error(pred_state,state_data):# Just a demo for RMS errorstate_data=state_data[:, :pred_state.shape[1]]return [np.sqrt(np.mean((pred-true)**2))for (pred,true)inzip(pred_state,state_data)            ]# 3. Loop over each optimizerforname,opt_datainselected_opts.items():optimizer_class=opt_data["class"]optimizer_params=opt_data["params"]# 4. Initialize and fit the SINDy modelmodel=ps.SINDy(optimizer=optimizer_class(**optimizer_params),feature_library=feature_library            )model.fit(x=x_train,t=dt,x_dot=x_dot,# Not providing pre-computed derivativesu=u_train,# Control inputsmultiple_trajectories=xu_list,            )# 5. Print model to consoleprint(f"\n===== Trained Model:{name} =====")model.print()# 6. Finally, run the optimizersrun_selected_optimizers(selected_optimizers)if__name__=="__main__":main()