# -*- coding: utf-8 -*- # Copyright (c) 2021, PyRETIS Development Team. # Distributed under the LGPLv2.1+ License. See LICENSE for more info. """This is a simple RETIS example. This example will just consider a simple 1D potential where we aim to calculate the crossing probability and the rate constant. Have fun! """ import numpy as np from tqdm import tqdm from pyretis.core import System, create_box, Particles from pyretis.initiation import initiate_path_simulation from pyretis.core.properties import Property from pyretis.inout.setup import (create_force_field, create_engine, create_orderparameter, create_simulation) from pyretis.analysis.path_analysis import _pcross_lambda_cumulative INTERFACES = [-0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, 1.0] # Let us define the simulation: SETTINGS = {} # Basic settings for the simulation: SETTINGS['simulation'] = { 'task': 'retis', 'steps': 150, 'interfaces': INTERFACES } # Basic settings for the system: SETTINGS['system'] = {'units': 'lj', 'temperature': 0.07} # Basic settings for the Langevin integrator: SETTINGS['engine'] = { 'class': 'Langevin', 'gamma': 0.3, 'high_friction': False, 'seed': 0, 'timestep': 0.002 } # Potential parameters: # The potential is: `V_\text{pot} = a x^4 - b (x - c)^2` SETTINGS['potential'] = [ { 'class': 'DoubleWell', 'a': 1.0, 'b': 2.0, 'c': 0.0, } ] # Settings for the order parameter: SETTINGS['orderparameter'] = { 'class': 'PositionVelocity', 'dim': 'x', 'index': 0, 'periodic': False } # TIS specific settings: SETTINGS['tis'] = { 'freq': 0.5, 'maxlength': 20000, 'aimless': True, 'allowmaxlength': False, 'sigma_v': -1, 'seed': 0, 'zero_momentum': False, 'rescale_energy': False } SETTINGS['initial-path'] = {'method': 'kick'} # RETIS specific settings: SETTINGS['retis'] = { 'swapfreq': 0.5, 'relative_shoots': None, 'nullmoves': True, 'swapsimul': True } # For convenience: TIMESTEP = SETTINGS['engine']['timestep'] ANALYSIS = {'ngrid': 100, 'nblock': 5} def set_up_system(settings): """Set up the system. Parameters ---------- settings : dict The settings required to set up the system. Returns ------- sys : object like :py:class:`.System` A system object we can use in a simulation. """ box = create_box(periodic=[False]) sys = System(temperature=settings['system']['temperature'], units=settings['system']['units'], box=box) sys.forcefield = create_force_field(settings) sys.order_function = create_orderparameter(settings) sys.particles = Particles(dim=1) sys.add_particle(np.array([-1.0]), mass=1, name='Ar', ptype=0) return sys def step_txt(ensembles, retis_result, prun): """Return some text information about the RETIS step. Parameters ---------- ensembles : list of objects like :py:class:`.PathEnsemble` The different path ensembles we are simulating. retis_result : list of lists The results from a RETIS simulation step. prun : list of floats The running average for the ensemble crossing probabilities. Returns ------- out : list of strings Each string contains information about the move performed in an ensemble. """ txt = [] force = 0 # counter for force evaluations # The force counter will just count the number of # force evaluations for generating a path, it will not include # the force evaluation that might be performed prior to propagation, # i.e. the initial force evaluation since this can be stored in memory, # along the path -> i.e. we can avoid it. for ensemble in ensembles: name = ensemble.ensemble_name idx = ensemble.ensemble_number name_of_move = retis_result['move-{}'.format(idx)] accepted = retis_result['accept-{}'.format(idx)] line = [] if name_of_move == 'swap': idx2 = retis_result['all-{}'.format(idx)]['swap-with'] name2 = ensembles[idx2].ensemble_name move = '{} {},'.format(name_of_move, name2) if idx == 0 or (idx == 1 and idx2 == 0): # Evaluate forces when swapping [0^-] <-> [0^+]: force += ensemble.paths[-1]['length'] - 2 elif name_of_move == 'tis': trial_path = retis_result['path-{}'.format(idx)] tis_move = trial_path.generated[0] move = '{} ({}),'.format(name_of_move, tis_move) if tis_move == 'sh': force += ensemble.paths[-1]['length'] - 1 else: move = '{},'.format(name_of_move) line.append('{}: {:11s}'.format(name, move)) line.append('{},'.format(accepted)) if idx > 0: line.append('p = {:<8.6g}'.format(prun[idx])) txt.append(' '.join(line)) return txt, force def probability_path_ensemble(ensemble, step, prun, orderp): """Update running estimates of probabilities for an ensemble. Parameters ---------- ensemble : objects like :py:class:`.PathEnsemble` The ensemble to analyse. step : int The current simulation step. prun : float Current running estimate for the crossing probability for this ensemble. orderp : numpy.array The maximum order parameters for all accepted paths. Returns ------- prun : float Updated running average for the crossing probability. ordernew : numpy.array Updated list of all order parameters seen. lamb : numpy.array Coordinates used for obtaining the crossing probability as a function of the order parameter. pcross : numpy.array The crossing probability as a function of the order parameter. """ ordermax = ensemble.last_path.ordermax[0] success = 1 if ordermax > ensemble.detect else 0 if prun is None: prun = success else: npath = step + 1 prun = float(success + prun * (npath - 1)) / float(npath) if orderp is None: ordernew = np.array([ordermax]) else: ordernew = np.append(orderp, ordermax) ordermax = min(max(ordernew), max(ensemble.interfaces)) ordermin = ensemble.interfaces[1] pcross, lamb = _pcross_lambda_cumulative(ordernew, ordermin, ordermax, ANALYSIS['ngrid']) return prun, ordernew, lamb, pcross def simple_block(data, nblock): """Block error analysis for running average.""" length = len(data) if length < nblock: return float('inf') skip, _ = divmod(len(data), nblock) run_avg = [] block_avg = [] for i in range(nblock): idx = (i + 1) * skip - 1 run_avg.append(data[idx]) if i == 0: block_avg.append(run_avg[i]) else: block_avg.append((i + 1)*run_avg[i] - i*run_avg[i-1]) var = sum([(x - data[-1])**2 for x in block_avg]) / (nblock - 1) err = np.sqrt(var / nblock) return err def analyse_path_ensembles(ensembles, step, variables): """Calculate some properties for the path ensembles. Here we obtain the crossing probabilities and the initial flux. Parameters ---------- ensembles : a list of objects like :py:class:`.PathEnsemble` These objects contain information about accepted paths for the different path ensembles. step : integer The current step number. variables : dict of objects This dict contains variables we can use for updating derived data for the different path ensembles. Returns ------- out : dict of floats A dictionary with computed initial flux, crossing probability and errors in these. """ calc = {'flux': 0, 'fluxe': 0, 'pcross': 0, 'pcrosse': float('inf'), 'kab': 0, 'kabe': float('inf')} length0 = variables['length0'] length1 = variables['length1'] length0.add(ensembles[0].last_path.length) length1.add(ensembles[1].last_path.length) flux = 1.0 / ((length0.mean + length1.mean - 4.0) * TIMESTEP) calc['flux'] = flux variables['flux'].append(flux) fluxe = simple_block(variables['flux'], ANALYSIS['nblock']) calc['fluxe'] = fluxe accprob = 1.0 matched_prob = [] matched_lamb = [] for i, ensemble in enumerate(ensembles): if i == 0: continue prun = variables['prun'][i] orderp = variables['orderp'][i] prun, ordernew, lamb, pcross = probability_path_ensemble(ensemble, step, prun, orderp) variables['orderp'][i] = ordernew variables['prun'][i] = prun variables['pcross'][i] = pcross variables['lamb'][i] = lamb idx = np.where(lamb <= ensemble.detect)[0] matched_lamb.extend(lamb[idx]) matched_prob.extend(pcross[idx] * accprob) accprob *= prun if matched_lamb[-1] < INTERFACES[-1]: pcross = 0 pcrosse = float('inf') else: pcross = matched_prob[-1] variables['match'].append(pcross) pcrosse = simple_block(variables['match'], ANALYSIS['nblock']) calc['pcross'] = pcross calc['pcrosse'] = pcrosse calc['kab'] = flux * pcross if pcross == 0 or flux == 0: calc['kabe'] = float('inf') else: calc['kabe'] = calc['kab'] * np.sqrt(pcrosse**2 / pcross**2 + fluxe**2 / flux**2) return calc def main(): """Just run the simulation.""" print('# CREATING SYSTEM...') system = set_up_system(SETTINGS) print('# CREATING SIMULATION...') sim_args = {'system': system, 'engine': create_engine(SETTINGS)} simulation = create_simulation(SETTINGS, sim_args) print(simulation) print('# INITIATING TRAJECTORIES...') print('# GENERATING INITIAL PATHS') for i, _ in enumerate(initiate_path_simulation(simulation, SETTINGS)): ensemble = simulation.path_ensembles[i] name = ensemble.ensemble_name print('Info about ensemble {}:'.format(name)) print(ensemble) print('Info about the initial path:') print(ensemble.last_path) print('') # We make a dictionary of these variable for easier access: # Set up some variables for storing results: variables = {'length0': Property('Path length in [0^-]'), 'length1': Property('Path length in [0^+]'), 'flux': [], 'match': [], 'orderp': [None for _ in INTERFACES], 'prun': [None for _ in INTERFACES], 'lamb': [None for _ in INTERFACES], 'pcross': [None for _ in INTERFACES]} # Let us look at the resulting path ensembles and paths: ensembles = simulation.path_ensembles analyse_path_ensembles(ensembles, 0, variables) for ensemble in ensembles: name = ensemble.ensemble_name print('Info about ensemble {}:'.format(name)) print(ensemble) print('Info about the initial path:') print(ensemble.last_path) print('') # Run the rest of the simulation. ftot = 0 for result in tqdm(simulation.run(), initial=1, total=SETTINGS['simulation']['steps']): step = result['cycle']['step'] print('# Current cycle: {}'.format(step)) anr = analyse_path_ensembles(ensembles, step, variables) retis_txt, force = step_txt(ensembles, result, variables['prun']) ftot += force for line in retis_txt: print('# {}'.format(line)) print('# Flux: {flux:<8.6g} +- {fluxe:<8.6g}'.format(**anr)) print(('# Crossing probability: {pcross:<8.6g} +-' '{pcrosse:<8.6g}').format(**anr)) print('# K_AB: {kab:<8.6g} +- {kabe:<8.6g}'.format(**anr)) print('# No. of force evaluations: {:g}'.format(force)) print('') print('# Total number of force evaluations: {}'.format(ftot)) if __name__ == '__main__': main()