# -*- 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 animating the algorithm. You can play with the interfaces, the potential parameters, the temperature, the ratio of the different RETIS moves etc. Have fun! """ import sys import colorama import numpy as np import matplotlib as mpl from matplotlib import pylab as plt from matplotlib import animation from matplotlib import gridspec 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 from pyretis.inout import print_to_screen INTERFACES = [-0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, 1.0] PCROSS_LOG = False # or: PCROSS_LOG = True # 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': 'reduced', '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'] = [ {'a': 1.0, 'b': 2.0, 'c': 0.0, 'class': 'DoubleWell'} ] # 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} # Set up for plotting: mpl.rc('font', size=14, family='serif') mpl.rc('lines', color='#262626') mpl.rc('savefig', directory=None) NINT = len(INTERFACES) CMAP = plt.get_cmap('Set1') COLORS = [CMAP(float(i)/float(NINT)) for i in range(NINT)] TXTCOLOR = { 'SW': '#006BA4', 'NU': '#FF800E', 'TR': '#ABABAB', 'SH': '#595959', 'IN': '#808080', } FTOT = 0 def set_up_system(settings): """Set up the system. Parameters ---------- settings : dict The settings required to set up the system. Returns ------- syst : object like :py:class:`.System` A system object we can use in a simulation. """ box = create_box(periodic=[False]) syst = System(temperature=settings['system']['temperature'], units=settings['system']['units'], box=box) syst.forcefield = create_force_field(settings) syst.order_function = create_orderparameter(settings) syst.particles = Particles(dim=1) syst.add_particle(np.array([-1.0]), mass=1, name='Ar', ptype=0) return syst def get_path(path): """Get points on a trajectory, useful for plotting. Parameters ---------- path : object like :py:class:`.PathBase` The path/trajectory we are collecting points from. Returns ------- out[0] : numpy.array The order parameter(s) as a function of time. out[1] : numpy.array The positions as a function of time. out[2] : numpy.array The velocities as a function of time. """ order = [] pos = [] vel = [] leng = path.length if leng <= 50: freq = 1 elif 50 < leng <= 600: freq = 6 elif 600 < leng < 2000: freq = 10 else: freq = 20 for i, point in enumerate(path.phasepoints): if i == 0 or i == leng-1 or i % freq == 0: order.append(point.order) pos.append(point.particles.pos[0]) vel.append(point.particles.vel[0]) return np.array(order), np.array(pos), np.array(vel) 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 of 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 : object 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) variables['pcross2'][i] = pcross*accprob accprob *= prun variables['mlamb'] = matched_lamb variables['mpcross'] = matched_prob 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 matplotlib_setup(): """Set up matplotlib & prepare animation.""" new_fig = plt.figure(figsize=(12, 6)) grid = gridspec.GridSpec(3, 4) ax1 = new_fig.add_subplot(grid[:, :2]) ax2 = new_fig.add_subplot(grid[0, 2:]) ax3 = new_fig.add_subplot(grid[1:, 2:]) if not PCROSS_LOG: axp = ax3.twinx() axes = (ax1, ax2, ax3) plot_patches = {'paths': [], 'prob': [], 'prob2': [], 'matched': None, 'fluxline': None, 'txtmove': [], 'txtcycle': None, 'start': [], 'end': []} k = 0 for i, pos in enumerate(INTERFACES): ax1.axvline(x=pos, lw=2, ls=':', color='#262626') ax3.axvline(x=pos, lw=2, ls=':', color='#262626') newline, = ax1.plot([], [], lw=3, ls='-', color=COLORS[i]) plot_patches['paths'].append(newline) if PCROSS_LOG: newlinep2, = ax3.plot([], [], lw=3, ls='-', color=newline.get_color()) plot_patches['prob2'].append(newlinep2) else: newlinep, = ax3.plot([], [], lw=3, ls='-', color=newline.get_color()) plot_patches['prob'].append(newlinep) newscat = ax1.scatter(None, None, s=75, marker='o', color=newline.get_color()) plot_patches['start'].append(newscat) newscat = ax1.scatter(None, None, s=75, marker='s', color=newline.get_color()) plot_patches['end'].append(newscat) # Note, we also add a line for [0^-], this is just to get # the colors right, plines[0] is not used for anything else... if i == 0: txt_x = pos-0.4 txt_y = 1.8 else: txt_x = INTERFACES[i-1] txt_y = 1.8 - (k-1) * 0.2 txtbox = ax1.text(txt_x, txt_y, '', transform=ax1.transData, backgroundcolor='w', fontsize=12) plot_patches['txtmove'].append(txtbox) if k % 3 == 0 and k > 0: k = 0 k += 1 plot_patches['txtcycle'] = ax1.text(-1.4, -1.8, '', transform=ax1.transData, backgroundcolor='w', fontsize=14) ax1.set_xlabel(r'Order parameter ($\lambda$)') ax1.set_ylabel(r'Velocity ($\dot{\lambda}$)') if PCROSS_LOG: ax3.set_yscale('log') plot_patches['matched'] = ax3.plot([], [], lw=6, ls='-', color='#262626', zorder=0, alpha=0.7)[0] ax3.set_xlim(-1, 1.05) ax3.set_ylim(1e-7, 1) else: axp.set_yscale('log') plot_patches['matched'] = axp.plot([], [], lw=6, ls='-', color='#262626', zorder=0, alpha=0.7)[0] ax3.set_xlim(-1, 1.05) axp.set_ylim(1e-7, 1) ax3.set_ylim(0, 1) ax3.set_xlabel(r'$\lambda$') ax3.set_ylabel(r'Probability') ax1.set_ylim(-2, 2) ax1.set_xlim(-1.5, 1.5) plot_patches['fluxline'] = ax2.plot([0], [0], lw=3, ls='-', color='#4C72B0')[0] ax2.set_ylim(0, 1) ax2.set_xlim(0, 1) ax2.set_xticklabels([]) ax2.set_ylabel('Flux') ax2.set_xlabel('Cycles completed') ax2.locator_params(axis='y', nbins=4) if PCROSS_LOG: new_fig.subplots_adjust(left=0.1, bottom=0.15, right=0.95, top=0.95, wspace=0.5, hspace=0.5) else: new_fig.set_tight_layout(True) return new_fig, plot_patches, axes def analyse_prob(ensemble, props, idx, step): """Update running estimates for probability. Parameters ---------- ensemble : object like :py:class:`.PathEnsemble` The ensemble to analyse. props : dict A dictionary for storing properties we calculate. idx : int An index for the path ensemble. step : int The current simulation step. """ orderp = ensemble.last_path.ordermax[0] success = 1 if orderp > ensemble.detect else 0 prun = props['prun'][idx] if not prun: prun.append(success) else: npath = step + 1 prun.append(float(success + prun[-1] * (npath-1)) / float(npath)) props['orderp'][idx].append(orderp) orderparam = np.array(props['orderp'][idx]) ordermax = min(orderparam.max(), max(ensemble.interfaces)) ordermin = ensemble.interfaces[1] pcross, lamb = _pcross_lambda_cumulative(orderparam, ordermin, ordermax, ANALYSIS['ngrid']) props['pcross'][idx] = (lamb, pcross) def update(frame, simulation, plot_patches, variables, axes): """Run the simulation and update plots. Parameters ---------- frame : int The current frame number, supplied by animation.FuncAnimation. simulation : object like :py:class:`.Simulation` The simulation we are running. plot_patches : dict of objects This dict contains the lines, text boxes etc. from matplotlib which we will use to display our data. variables : dict of objects A dict with results from the simulation. axes : tuple This tuple contains the axes used for plotting. Returns ------- out : list list of the patches to be drawn. """ patches = [] if not simulation.is_finished(): result = simulation.step() step = result['cycle']['step'] ensembles = simulation.path_ensembles print_to_screen('# Current cycle: {}'.format(step), level='info') anr = analyse_path_ensembles(ensembles, step, variables) retis_txt, force = step_txt(ensembles, result, variables['prun']) global FTOT FTOT += force for line in retis_txt: print_to_screen('# {}'.format(line)) print_to_screen('# Flux: {flux:<8.6g} +- {fluxe:<8.6g}'.format(**anr)) print_to_screen(('# Crossing probability: {pcross:<8.6g} +-' '{pcrosse:<8.6g}').format(**anr)) print_to_screen('# K_AB: {kab:<8.6g} +- {kabe:<8.6g}'.format(**anr)) print_to_screen('# No. of force evaluations: {:g}'.format(force)) print_to_screen('') for i, ensemble in enumerate(ensembles): _, pos, vel = get_path(ensemble.last_path) plot_patches['paths'][i].set_data(pos, vel) patches.append(plot_patches['paths'][i]) plot_patches['start'][i].set_offsets((pos[0][0], vel[0][0])) plot_patches['start'][i].set_visible(True) patches.append(plot_patches['start'][i]) plot_patches['end'][i].set_offsets((pos[-1][0], vel[-1][0])) plot_patches['end'][i].set_visible(True) patches.append(plot_patches['end'][i]) if i > 0: if not PCROSS_LOG: plot_patches['prob'][i].set_data(variables['lamb'][i], variables['pcross'][i]) patches.append(plot_patches['prob'][i]) fluxx, fluxy = plot_patches['fluxline'].get_data() fluxx = np.append(fluxx, fluxx[-1] + 1) fluxy = np.append(fluxy, anr['flux']) plot_patches['fluxline'].set_data(fluxx, fluxy) axes[1].set_xlim(0, step+1) axes[1].set_ylim(0, 1.1*fluxy.max()) patches.append(plot_patches['fluxline']) for key in result: if key.startswith('move'): i = int(key.split('-')[1]) if result[key] == 'tis': trial = result['path-{}'.format(i)] txtmove = trial.generated[0].upper() else: txtmove = result[key][:2].upper() plot_patches['txtmove'][i].set_text(txtmove) plot_patches['txtmove'][i].set_color(TXTCOLOR[txtmove]) patches.append(plot_patches['txtmove'][i]) plot_patches['txtcycle'].set_text('Cycle: {}'.format(step)) patches.append(plot_patches['txtcycle']) # match probabilities: for i, ensemble in enumerate(simulation.path_ensembles): if i == 0: continue if PCROSS_LOG: prob2 = variables['pcross2'][i] plot_patches['prob2'][i].set_data(variables['lamb'][i], prob2) patches.append(plot_patches['prob2'][i]) plot_patches['matched'].set_data(variables['mlamb'], variables['mpcross']) patches.append(plot_patches['matched']) return patches # Just return without updating: print_to_screen('# Simulation is done (frame = {})'.format(frame)) print_to_screen('# Total number of force evaluations: {}'.format(FTOT)) patches = [] for key in ('paths', 'prob', 'prob2', 'txtmove', 'start', 'end'): patches.extend(plot_patches[key]) for key in ('matched', 'fluxline', 'txtcycle'): patches.append(plot_patches[key]) return patches def main(): """Run the simulation.""" colorama.init(autoreset=True) print_to_screen('# CREATING SYSTEM', level='info') system = set_up_system(SETTINGS) print_to_screen('# CREATING SIMULATION:', level='info') sim_args = {'system': system, 'engine': create_engine(SETTINGS)} simulation = create_simulation(SETTINGS, sim_args) print_to_screen(simulation) print_to_screen('# GENERATING INITIAL PATHS', level='info') for i, _ in enumerate(initiate_path_simulation(simulation, SETTINGS)): ensemble = simulation.path_ensembles[i] name = ensemble.ensemble_name print_to_screen('Info about ensemble {}:'.format(name), level='success') print_to_screen(ensemble) print_to_screen('Info about the initial path:', level='success') print_to_screen(ensemble.last_path) print_to_screen('') fig, plot_patches, axes = matplotlib_setup() 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], 'mlamb': [None for _ in INTERFACES], 'pcross': [None for _ in INTERFACES], 'mpcross': [None for _ in INTERFACES], 'pcross2': [None for _ in INTERFACES]} _ = animation.FuncAnimation(fig, update, frames=SETTINGS['simulation']['steps']+1, fargs=[simulation, plot_patches, variables, axes], repeat=False, interval=10, blit=use_blit()) plt.show() def use_blit(): """Check if we should use blitting.""" return not sys.platform.startswith('darwin') if __name__ == '__main__': main()