#!/work/yifan.wang/ringdown/master-ringdown-env/bin/python3 # -*- coding: utf-8 -*- from __future__ import absolute_import, unicode_literals, print_function, division __doc__ = """ Script that does default visualizations (marginal plots, 1-d and 2-d). Author: Johannes Buchner (C) 2013-2019 Author: Josh Speagle (MIT licensed) """ import numpy from numpy import exp, log import matplotlib.pyplot as plt import sys, os import json import pymultinest # code from dynesty (MIT licensed) from six.moves import range import logging import types import math import numpy as np import matplotlib.pyplot as pl from matplotlib.ticker import MaxNLocator, NullLocator from matplotlib.colors import LinearSegmentedColormap, colorConverter from matplotlib.ticker import ScalarFormatter from scipy import spatial from scipy.ndimage import gaussian_filter as norm_kde from scipy.stats import gaussian_kde import warnings try: str_type = types.StringTypes float_type = types.FloatType int_type = types.IntType except: str_type = str float_type = float int_type = int SQRTEPS = math.sqrt(float(np.finfo(np.float64).eps)) def _quantile(x, q, weights=None): """ Compute (weighted) quantiles from an input set of samples. Parameters ---------- x : `~numpy.ndarray` with shape (nsamps,) Input samples. q : `~numpy.ndarray` with shape (nquantiles,) The list of quantiles to compute from `[0., 1.]`. weights : `~numpy.ndarray` with shape (nsamps,), optional The associated weight from each sample. Returns ------- quantiles : `~numpy.ndarray` with shape (nquantiles,) The weighted sample quantiles computed at `q`. """ # Initial check. x = np.atleast_1d(x) q = np.atleast_1d(q) # Quantile check. if np.any(q < 0.0) or np.any(q > 1.0): raise ValueError("Quantiles must be between 0. and 1.") if weights is None: # If no weights provided, this simply calls `np.percentile`. return np.percentile(x, list(100.0 * q)) else: # If weights are provided, compute the weighted quantiles. weights = np.atleast_1d(weights) if len(x) != len(weights): raise ValueError("Dimension mismatch: len(weights) != len(x).") idx = np.argsort(x) # sort samples sw = weights[idx] # sort weights cdf = np.cumsum(sw)[:-1] # compute CDF cdf /= cdf[-1] # normalize CDF cdf = np.append(0, cdf) # ensure proper span quantiles = np.interp(q, cdf, x[idx]).tolist() return quantiles def resample_equal(samples, weights, rstate=None): """ Resample a new set of points from the weighted set of inputs such that they all have equal weight. Each input sample appears in the output array either `floor(weights[i] * nsamples)` or `ceil(weights[i] * nsamples)` times, with `floor` or `ceil` randomly selected (weighted by proximity). Parameters ---------- samples : `~numpy.ndarray` with shape (nsamples,) Set of unequally weighted samples. weights : `~numpy.ndarray` with shape (nsamples,) Corresponding weight of each sample. rstate : `~numpy.random.RandomState`, optional `~numpy.random.RandomState` instance. Returns ------- equal_weight_samples : `~numpy.ndarray` with shape (nsamples,) New set of samples with equal weights. Examples -------- >>> x = np.array([[1., 1.], [2., 2.], [3., 3.], [4., 4.]]) >>> w = np.array([0.6, 0.2, 0.15, 0.05]) >>> utils.resample_equal(x, w) array([[ 1., 1.], [ 1., 1.], [ 1., 1.], [ 3., 3.]]) Notes ----- Implements the systematic resampling method described in `Hol, Schon, and Gustafsson (2006) `_. """ if rstate is None: rstate = np.random if abs(np.sum(weights) - 1.) > SQRTEPS: # same tol as in np.random.choice. raise ValueError("Weights do not sum to 1.") # Make N subdivisions and choose positions with a consistent random offset. nsamples = len(weights) positions = (rstate.random() + np.arange(nsamples)) / nsamples # Resample the data. idx = np.zeros(nsamples, dtype=np.int) cumulative_sum = np.cumsum(weights) i, j = 0, 0 while i < nsamples: if positions[i] < cumulative_sum[j]: idx[i] = j i += 1 else: j += 1 return samples[idx] def runplot(results, span=None, logplot=False, kde=True, nkde=1000, color='blue', plot_kwargs=None, label_kwargs=None, lnz_error=True, lnz_truth=None, truth_color='red', truth_kwargs=None, max_x_ticks=8, max_y_ticks=3, use_math_text=True, mark_final_live=True, fig=None): """ Plot live points, ln(likelihood), ln(weight), and ln(evidence) as a function of ln(prior volume). Parameters ---------- results : :class:`~dynesty.results.Results` instance A :class:`~dynesty.results.Results` instance from a nested sampling run. span : iterable with shape (4,), optional A list where each element is either a length-2 tuple containing lower and upper bounds *or* a float from `(0., 1.]` giving the fraction below the maximum. If a fraction is provided, the bounds are chosen to be equal-tailed. An example would be:: span = [(0., 10.), 0.001, 0.2, (5., 6.)] Default is `(0., 1.05 * max(data))` for each element. logplot : bool, optional Whether to plot the evidence on a log scale. Default is `False`. kde : bool, optional Whether to use kernel density estimation to estimate and plot the PDF of the importance weights as a function of log-volume (as opposed to the importance weights themselves). Default is `True`. nkde : int, optional The number of grid points used when plotting the kernel density estimate. Default is `1000`. color : str or iterable with shape (4,), optional A `~matplotlib`-style color (either a single color or a different value for each subplot) used when plotting the lines in each subplot. Default is `'blue'`. plot_kwargs : dict, optional Extra keyword arguments that will be passed to `plot`. label_kwargs : dict, optional Extra keyword arguments that will be sent to the `~matplotlib.axes.Axes.set_xlabel` and `~matplotlib.axes.Axes.set_ylabel` methods. lnz_error : bool, optional Whether to plot the 1, 2, and 3-sigma approximate error bars derived from the ln(evidence) error approximation over the course of the run. Default is `True`. lnz_truth : float, optional A reference value for the evidence that will be overplotted on the evidence subplot if provided. truth_color : str or iterable with shape (ndim,), optional A `~matplotlib`-style color used when plotting :data:`lnz_truth`. Default is `'red'`. truth_kwargs : dict, optional Extra keyword arguments that will be used for plotting :data:`lnz_truth`. max_x_ticks : int, optional Maximum number of ticks allowed for the x axis. Default is `8`. max_y_ticks : int, optional Maximum number of ticks allowed for the y axis. Default is `4`. use_math_text : bool, optional Whether the axis tick labels for very large/small exponents should be displayed as powers of 10 rather than using `e`. Default is `False`. mark_final_live : bool, optional Whether to indicate the final addition of recycled live points (if they were added to the resulting samples) using a dashed vertical line. Default is `True`. fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional If provided, overplot the run onto the provided figure. Otherwise, by default an internal figure is generated. Returns ------- runplot : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`) Output summary plot. """ # Initialize values. if label_kwargs is None: label_kwargs = dict() if plot_kwargs is None: plot_kwargs = dict() if truth_kwargs is None: truth_kwargs = dict() # Set defaults. plot_kwargs['linewidth'] = plot_kwargs.get('linewidth', 5) plot_kwargs['alpha'] = plot_kwargs.get('alpha', 0.7) truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid') truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 3) # Extract results. niter = results['niter'] # number of iterations logvol = results['logvol'] # ln(prior volume) logl = results['logl'] - max(results['logl']) # ln(normalized likelihood) logwt = results['logwt'] - results['logz'][-1] # ln(importance weight) logz = results['logz'] # ln(evidence) logzerr = results['logzerr'] # error in ln(evidence) logzerr[~np.isfinite(logzerr)] = 0. nsamps = len(logwt) # number of samples # Check whether the run was "static" or "dynamic". try: nlive = results['samples_n'] mark_final_live = False except: nlive = np.ones(niter) * results['nlive'] if nsamps - niter == results['nlive']: nlive_final = np.arange(1, results['nlive'] + 1)[::-1] nlive = np.append(nlive, nlive_final) # Check if the final set of live points were added to the results. if mark_final_live: if nsamps - niter == results['nlive']: live_idx = niter else: warnings.warn("The number of iterations and samples differ " "by an amount that isn't the number of final " "live points. `mark_final_live` has been disabled.") mark_final_live = False # Determine plotting bounds for each subplot. data = [nlive, np.exp(logl), np.exp(logwt), np.exp(logz)] if kde: # Derive kernel density estimate. wt_kde = gaussian_kde(resample_equal(-logvol, data[2])) # KDE logvol_new = np.linspace(logvol[0], logvol[-1], nkde) # resample data[2] = wt_kde.pdf(-logvol_new) # evaluate KDE PDF if span is None: span = [(0., 1.05 * max(d)) for d in data] no_span = True else: no_span = False span = list(span) if len(span) != 4: raise ValueError("More bounds provided in `span` than subplots!") for i, _ in enumerate(span): try: ymin, ymax = span[i] except: span[i] = (max(data[i]) * span[i], max(data[i])) if lnz_error and no_span: if logplot: zspan = (np.exp(logz[-1] - 1.3 * 3. * logzerr[-1]), np.exp(logz[-1] + 1.3 * 3. * logzerr[-1])) else: zspan = (0., 1.05 * np.exp(logz[-1] + 3. * logzerr[-1])) span[3] = zspan # Setting up default plot layout. if fig is None: fig, axes = pl.subplots(4, 1, figsize=(16, 16)) xspan = [(0., -min(logvol)) for ax in axes] yspan = span else: fig, axes = fig try: axes.reshape(4, 1) except: raise ValueError("Provided axes do not match the required shape " "for plotting samples.") # If figure is provided, keep previous bounds if they were larger. xspan = [ax.get_xlim() for ax in axes] yspan = [ax.get_ylim() for ax in axes] # One exception: if the bounds are the plotting default `(0., 1.)`, # overwrite them. xspan = [t if t != (0., 1.) else (None, None) for t in xspan] yspan = [t if t != (0., 1.) else (None, None) for t in yspan] # Set up bounds for plotting. [axes[i].set_xlim([min(0., xspan[i][0]), max(-min(logvol), xspan[i][1])]) for i in range(4)] [axes[i].set_ylim([min(span[i][0], yspan[i][0]), max(span[i][1], yspan[i][1])]) for i in range(4)] # Plotting. labels = ['Live Points', 'Likelihood\n(normalized)', 'Importance\nWeight', 'Evidence'] if kde: labels[2] += ' PDF' for i, d in enumerate(data): # Establish axes. ax = axes[i] # Set color(s)/colormap(s). if isinstance(color, str_type): c = color else: c = color[i] # Setup axes. if max_x_ticks == 0: ax.xaxis.set_major_locator(NullLocator()) else: ax.xaxis.set_major_locator(MaxNLocator(max_x_ticks)) if max_y_ticks == 0: ax.yaxis.set_major_locator(NullLocator()) else: ax.yaxis.set_major_locator(MaxNLocator(max_y_ticks)) # Label axes. sf = ScalarFormatter(useMathText=use_math_text) ax.yaxis.set_major_formatter(sf) ax.set_xlabel(r"$-\ln X$", **label_kwargs) ax.set_ylabel(labels[i], **label_kwargs) # Plot run. if logplot and i == 3: ax.semilogy(-logvol, d, color=c, **plot_kwargs) yspan = [ax.get_ylim() for ax in axes] elif kde and i == 2: ax.plot(-logvol_new, d, color=c, **plot_kwargs) else: ax.plot(-logvol, d, color=c, **plot_kwargs) if i == 3 and lnz_error: [ax.fill_between(-logvol, np.exp(logz + s*logzerr), np.exp(logz - s*logzerr), color=c, alpha=0.2) for s in range(1, 4)] # Mark addition of final live points. if mark_final_live: ax.axvline(-logvol[live_idx], color=c, ls="dashed", lw=2, **plot_kwargs) if i == 0: ax.axhline(live_idx, color=c, ls="dashed", lw=2, **plot_kwargs) # Add truth value(s). if i == 3 and lnz_truth is not None: ax.axhline(np.exp(lnz_truth), color=truth_color, **truth_kwargs) return fig, axes def traceplot(results, span=None, quantiles=[0.025, 0.5, 0.975], smooth=0.02, post_color='blue', post_kwargs=None, kde=True, nkde=1000, trace_cmap='plasma', trace_color=None, trace_kwargs=None, connect=False, connect_highlight=10, connect_color='red', connect_kwargs=None, max_n_ticks=5, use_math_text=False, labels=None, label_kwargs=None, show_titles=False, title_fmt=".2f", title_kwargs=None, truths=None, truth_color='red', truth_kwargs=None, verbose=False, fig=None): """ Plot traces and marginalized posteriors for each parameter. Parameters ---------- results : :class:`~dynesty.results.Results` instance A :class:`~dynesty.results.Results` instance from a nested sampling run. **Compatible with results derived from** `nestle `_. span : iterable with shape (ndim,), optional A list where each element is either a length-2 tuple containing lower and upper bounds or a float from `(0., 1.]` giving the fraction of (weighted) samples to include. If a fraction is provided, the bounds are chosen to be equal-tailed. An example would be:: span = [(0., 10.), 0.95, (5., 6.)] Default is `0.999999426697` (5-sigma credible interval) for each parameter. quantiles : iterable, optional A list of fractional quantiles to overplot on the 1-D marginalized posteriors as vertical dashed lines. Default is `[0.025, 0.5, 0.975]` (the 95%/2-sigma credible interval). smooth : float or iterable with shape (ndim,), optional The standard deviation (either a single value or a different value for each subplot) for the Gaussian kernel used to smooth the 1-D marginalized posteriors, expressed as a fraction of the span. Default is `0.02` (2% smoothing). If an integer is provided instead, this will instead default to a simple (weighted) histogram with `bins=smooth`. post_color : str or iterable with shape (ndim,), optional A `~matplotlib`-style color (either a single color or a different value for each subplot) used when plotting the histograms. Default is `'blue'`. post_kwargs : dict, optional Extra keyword arguments that will be used for plotting the marginalized 1-D posteriors. kde : bool, optional Whether to use kernel density estimation to estimate and plot the PDF of the importance weights as a function of log-volume (as opposed to the importance weights themselves). Default is `True`. nkde : int, optional The number of grid points used when plotting the kernel density estimate. Default is `1000`. trace_cmap : str or iterable with shape (ndim,), optional A `~matplotlib`-style colormap (either a single colormap or a different colormap for each subplot) used when plotting the traces, where each point is colored according to its weight. Default is `'plasma'`. trace_color : str or iterable with shape (ndim,), optional A `~matplotlib`-style color (either a single color or a different color for each subplot) used when plotting the traces. This overrides the `trace_cmap` option by giving all points the same color. Default is `None` (not used). trace_kwargs : dict, optional Extra keyword arguments that will be used for plotting the traces. connect : bool, optional Whether to draw lines connecting the paths of unique particles. Default is `False`. connect_highlight : int or iterable, optional If `connect=True`, highlights the paths of a specific set of particles. If an integer is passed, :data:`connect_highlight` random particle paths will be highlighted. If an iterable is passed, then the particle paths corresponding to the provided indices will be highlighted. connect_color : str, optional The color of the highlighted particle paths. Default is `'red'`. connect_kwargs : dict, optional Extra keyword arguments used for plotting particle paths. max_n_ticks : int, optional Maximum number of ticks allowed. Default is `5`. use_math_text : bool, optional Whether the axis tick labels for very large/small exponents should be displayed as powers of 10 rather than using `e`. Default is `False`. labels : iterable with shape (ndim,), optional A list of names for each parameter. If not provided, the default name used when plotting will follow :math:`x_i` style. label_kwargs : dict, optional Extra keyword arguments that will be sent to the `~matplotlib.axes.Axes.set_xlabel` and `~matplotlib.axes.Axes.set_ylabel` methods. show_titles : bool, optional Whether to display a title above each 1-D marginalized posterior showing the 0.5 quantile along with the upper/lower bounds associated with the 0.025 and 0.975 (95%/2-sigma credible interval) quantiles. Default is `True`. title_fmt : str, optional The format string for the quantiles provided in the title. Default is `'.2f'`. title_kwargs : dict, optional Extra keyword arguments that will be sent to the `~matplotlib.axes.Axes.set_title` command. truths : iterable with shape (ndim,), optional A list of reference values that will be overplotted on the traces and marginalized 1-D posteriors as solid horizontal/vertical lines. Individual values can be exempt using `None`. Default is `None`. truth_color : str or iterable with shape (ndim,), optional A `~matplotlib`-style color (either a single color or a different value for each subplot) used when plotting `truths`. Default is `'red'`. truth_kwargs : dict, optional Extra keyword arguments that will be used for plotting the vertical and horizontal lines with `truths`. verbose : bool, optional Whether to print the values of the computed quantiles associated with each parameter. Default is `False`. fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional If provided, overplot the traces and marginalized 1-D posteriors onto the provided figure. Otherwise, by default an internal figure is generated. Returns ------- traceplot : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`) Output trace plot. """ # Initialize values. if title_kwargs is None: title_kwargs = dict() if label_kwargs is None: label_kwargs = dict() if trace_kwargs is None: trace_kwargs = dict() if connect_kwargs is None: connect_kwargs = dict() if post_kwargs is None: post_kwargs = dict() if truth_kwargs is None: truth_kwargs = dict() # Set defaults. connect_kwargs['alpha'] = connect_kwargs.get('alpha', 0.7) post_kwargs['alpha'] = post_kwargs.get('alpha', 0.6) trace_kwargs['s'] = trace_kwargs.get('s', 3) truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid') truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 2) # Extract weighted samples. samples = results['samples'] logvol = results['logvol'] try: weights = np.exp(results['logwt'] - results['logz'][-1]) except: weights = results['weights'] if kde: # Derive kernel density estimate. wt_kde = gaussian_kde(resample_equal(-logvol, weights)) # KDE logvol_grid = np.linspace(logvol[0], logvol[-1], nkde) # resample wt_grid = wt_kde.pdf(-logvol_grid) # evaluate KDE PDF wts = np.interp(-logvol, -logvol_grid, wt_grid) # interpolate else: wts = weights # Deal with 1D results. A number of extra catches are also here # in case users are trying to plot other results besides the `Results` # instance generated by `dynesty`. samples = np.atleast_1d(samples) if len(samples.shape) == 1: samples = np.atleast_2d(samples) else: assert len(samples.shape) == 2, "Samples must be 1- or 2-D." samples = samples.T assert samples.shape[0] <= samples.shape[1], "There are more " \ "dimensions than samples!" ndim, nsamps = samples.shape # Check weights. if weights.ndim != 1: raise ValueError("Weights must be 1-D.") if nsamps != weights.shape[0]: raise ValueError("The number of weights and samples disagree!") # Check ln(volume). if logvol.ndim != 1: raise ValueError("Ln(volume)'s must be 1-D.") if nsamps != logvol.shape[0]: raise ValueError("The number of ln(volume)'s and samples disagree!") # Check sample IDs. if connect: try: samples_id = results['samples_id'] uid = np.unique(samples_id) except: raise ValueError("Sample IDs are not defined!") try: ids = connect_highlight[0] ids = connect_highlight except: ids = np.random.choice(uid, size=connect_highlight, replace=False) # Determine plotting bounds for marginalized 1-D posteriors. if span is None: span = [0.999999426697 for i in range(ndim)] span = list(span) if len(span) != ndim: raise ValueError("Dimension mismatch between samples and span.") for i, _ in enumerate(span): try: xmin, xmax = span[i] except: q = [0.5 - 0.5 * span[i], 0.5 + 0.5 * span[i]] span[i] = _quantile(samples[i], q, weights=weights) # Setting up labels. if labels is None: labels = [r"$x_{"+str(i+1)+"}$" for i in range(ndim)] # Setting up smoothing. if (isinstance(smooth, int_type) or isinstance(smooth, float_type)): smooth = [smooth for i in range(ndim)] # Setting up default plot layout. if fig is None: fig, axes = pl.subplots(ndim, 2, figsize=(12, 3*ndim)) else: fig, axes = fig try: axes.reshape(ndim, 2) except: raise ValueError("Provided axes do not match the required shape " "for plotting samples.") # Plotting. for i, x in enumerate(samples): # Plot trace. # Establish axes. if np.shape(samples)[0] == 1: ax = axes[1] else: ax = axes[i, 0] # Set color(s)/colormap(s). if trace_color is not None: if isinstance(trace_color, str_type): color = trace_color else: color = trace_color[i] else: color = wts if isinstance(trace_cmap, str_type): cmap = trace_cmap else: cmap = trace_cmap[i] # Setup axes. ax.set_xlim([0., -min(logvol)]) ax.set_ylim([min(x), max(x)]) if max_n_ticks == 0: ax.xaxis.set_major_locator(NullLocator()) ax.yaxis.set_major_locator(NullLocator()) else: ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks)) ax.yaxis.set_major_locator(MaxNLocator(max_n_ticks)) # Label axes. sf = ScalarFormatter(useMathText=use_math_text) ax.yaxis.set_major_formatter(sf) ax.set_xlabel(r"$-\ln X$", **label_kwargs) ax.set_ylabel(labels[i], **label_kwargs) # Generate scatter plot. ax.scatter(-logvol, x, c=color, cmap=cmap, **trace_kwargs) if connect: # Add lines highlighting specific particle paths. for j in ids: sel = (samples_id == j) ax.plot(-logvol[sel], x[sel], color=connect_color, **connect_kwargs) # Add truth value(s). if truths is not None and truths[i] is not None: try: [ax.axhline(t, color=truth_color, **truth_kwargs) for t in truths[i]] except: ax.axhline(truths[i], color=truth_color, **truth_kwargs) # Plot marginalized 1-D posterior. # Establish axes. if np.shape(samples)[0] == 1: ax = axes[0] else: ax = axes[i, 1] # Set color(s). if isinstance(post_color, str_type): color = post_color else: color = post_color[i] # Setup axes ax.set_xlim(span[i]) if max_n_ticks == 0: ax.xaxis.set_major_locator(NullLocator()) ax.yaxis.set_major_locator(NullLocator()) else: ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks)) ax.yaxis.set_major_locator(NullLocator()) # Label axes. sf = ScalarFormatter(useMathText=use_math_text) ax.xaxis.set_major_formatter(sf) ax.set_xlabel(labels[i], **label_kwargs) # Generate distribution. s = smooth[i] if isinstance(s, int_type): # If `s` is an integer, plot a weighted histogram with # `s` bins within the provided bounds. n, b, _ = ax.hist(x, bins=s, weights=weights, color=color, range=np.sort(span[i]), **post_kwargs) x0 = np.array(list(zip(b[:-1], b[1:]))).flatten() y0 = np.array(list(zip(n, n))).flatten() else: # If `s` is a float, oversample the data relative to the # smoothing filter by a factor of 10, then use a Gaussian # filter to smooth the results. bins = int(round(10. / s)) n, b = np.histogram(x, bins=bins, weights=weights, range=np.sort(span[i])) n = norm_kde(n, 10.) x0 = 0.5 * (b[1:] + b[:-1]) y0 = n ax.fill_between(x0, y0, color=color, **post_kwargs) ax.set_ylim([0., max(y0) * 1.05]) # Plot quantiles. if quantiles is not None and len(quantiles) > 0: qs = _quantile(x, quantiles, weights=weights) for q in qs: ax.axvline(q, lw=1, ls="dashed", color=color) if verbose: print("Quantiles:") print(labels[i], [blob for blob in zip(quantiles, qs)]) # Add truth value(s). if truths is not None and truths[i] is not None: try: [ax.axvline(t, color=truth_color, **truth_kwargs) for t in truths[i]] except: ax.axvline(truths[i], color=truth_color, **truth_kwargs) # Set titles. if show_titles: title = None if title_fmt is not None: ql, qm, qh = _quantile(x, [0.025, 0.5, 0.975], weights=weights) q_minus, q_plus = qm - ql, qh - qm fmt = "{{0:{0}}}".format(title_fmt).format title = r"${{{0}}}_{{-{1}}}^{{+{2}}}$" title = title.format(fmt(qm), fmt(q_minus), fmt(q_plus)) title = "{0} = {1}".format(labels[i], title) ax.set_title(title, **title_kwargs) return fig, axes def cornerpoints(results, thin=1, span=None, cmap='plasma', color=None, kde=True, nkde=1000, plot_kwargs=None, labels=None, label_kwargs=None, truths=None, truth_color='red', truth_kwargs=None, max_n_ticks=5, use_math_text=False, fig=None): """ Generate a (sub-)corner plot of (weighted) samples. Parameters ---------- results : :class:`~dynesty.results.Results` instance A :class:`~dynesty.results.Results` instance from a nested sampling run. **Compatible with results derived from** `nestle `_. thin : int, optional Thin the samples so that only each `thin`-th sample is plotted. Default is `1` (no thinning). span : iterable with shape (ndim,), optional A list where each element is either a length-2 tuple containing lower and upper bounds or a float from `(0., 1.]` giving the fraction of (weighted) samples to include. If a fraction is provided, the bounds are chosen to be equal-tailed. An example would be:: span = [(0., 10.), 0.95, (5., 6.)] Default is `1.` for all parameters (no bound). cmap : str, optional A `~matplotlib`-style colormap used when plotting the points, where each point is colored according to its weight. Default is `'plasma'`. color : str, optional A `~matplotlib`-style color used when plotting the points. This overrides the `cmap` option by giving all points the same color. Default is `None` (not used). kde : bool, optional Whether to use kernel density estimation to estimate and plot the PDF of the importance weights as a function of log-volume (as opposed to the importance weights themselves). Default is `True`. nkde : int, optional The number of grid points used when plotting the kernel density estimate. Default is `1000`. plot_kwargs : dict, optional Extra keyword arguments that will be used for plotting the points. labels : iterable with shape (ndim,), optional A list of names for each parameter. If not provided, the default name used when plotting will follow :math:`x_i` style. label_kwargs : dict, optional Extra keyword arguments that will be sent to the `~matplotlib.axes.Axes.set_xlabel` and `~matplotlib.axes.Axes.set_ylabel` methods. truths : iterable with shape (ndim,), optional A list of reference values that will be overplotted on the traces and marginalized 1-D posteriors as solid horizontal/vertical lines. Individual values can be exempt using `None`. Default is `None`. truth_color : str or iterable with shape (ndim,), optional A `~matplotlib`-style color (either a single color or a different value for each subplot) used when plotting `truths`. Default is `'red'`. truth_kwargs : dict, optional Extra keyword arguments that will be used for plotting the vertical and horizontal lines with `truths`. max_n_ticks : int, optional Maximum number of ticks allowed. Default is `5`. use_math_text : bool, optional Whether the axis tick labels for very large/small exponents should be displayed as powers of 10 rather than using `e`. Default is `False`. fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional If provided, overplot the points onto the provided figure object. Otherwise, by default an internal figure is generated. Returns ------- cornerpoints : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`) Output (sub-)corner plot of (weighted) samples. """ # Initialize values. if truth_kwargs is None: truth_kwargs = dict() if label_kwargs is None: label_kwargs = dict() if plot_kwargs is None: plot_kwargs = dict() # Set defaults. plot_kwargs['s'] = plot_kwargs.get('s', 1) truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid') truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 2) truth_kwargs['alpha'] = truth_kwargs.get('alpha', 0.7) # Extract weighted samples. samples = results['samples'] logvol = results['logvol'] try: weights = np.exp(results['logwt'] - results['logz'][-1]) except: weights = results['weights'] if kde: # Derive kernel density estimate. wt_kde = gaussian_kde(resample_equal(-logvol, weights)) # KDE logvol_grid = np.linspace(logvol[0], logvol[-1], nkde) # resample wt_grid = wt_kde.pdf(-logvol_grid) # evaluate KDE PDF weights = np.interp(-logvol, -logvol_grid, wt_grid) # interpolate # Deal with 1D results. A number of extra catches are also here # in case users are trying to plot other results besides the `Results` # instance generated by `dynesty`. samples = np.atleast_1d(samples) if len(samples.shape) == 1: samples = np.atleast_2d(samples) else: assert len(samples.shape) == 2, "Samples must be 1- or 2-D." samples = samples.T assert samples.shape[0] <= samples.shape[1], "There are more " \ "dimensions than samples!" ndim, nsamps = samples.shape # Check weights. if weights.ndim != 1: raise ValueError("Weights must be 1-D.") if nsamps != weights.shape[0]: raise ValueError("The number of weights and samples disagree!") # Determine plotting bounds. if span is not None: if len(span) != ndim: raise ValueError("Dimension mismatch between samples and span.") for i, _ in enumerate(span): try: xmin, xmax = span[i] except: q = [0.5 - 0.5 * span[i], 0.5 + 0.5 * span[i]] span[i] = _quantile(samples[i], q, weights=weights) # Set labels if labels is None: labels = [r"$x_{"+str(i+1)+"}$" for i in range(ndim)] # Set colormap. if color is None: color = weights # Setup axis layout (from `corner.py`). factor = 2.0 # size of side of one panel lbdim = 0.5 * factor # size of left/bottom margin trdim = 0.2 * factor # size of top/right margin whspace = 0.05 # size of width/height margin plotdim = factor * (ndim - 1.) + factor * (ndim - 2.) * whspace dim = lbdim + plotdim + trdim # total size # Initialize figure. if fig is None: fig, axes = pl.subplots(ndim - 1, ndim - 1, figsize=(dim, dim)) else: try: fig, axes = fig axes = np.array(axes).reshape((ndim - 1, ndim - 1)) except: raise ValueError("Mismatch between axes and dimension.") # Format figure. lb = lbdim / dim tr = (lbdim + plotdim) / dim fig.subplots_adjust(left=lb, bottom=lb, right=tr, top=tr, wspace=whspace, hspace=whspace) # Plot the 2-D projected samples. for i, x in enumerate(samples[1:]): for j, y in enumerate(samples[:-1]): ax = axes[i, j] # Setup axes. if span is not None: ax.set_xlim(span[j]) ax.set_ylim(span[i]) if j > i: ax.set_frame_on(False) ax.set_xticks([]) ax.set_yticks([]) continue if max_n_ticks == 0: ax.xaxis.set_major_locator(NullLocator()) ax.yaxis.set_major_locator(NullLocator()) else: ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks, prune="lower")) ax.yaxis.set_major_locator(MaxNLocator(max_n_ticks, prune="lower")) # Label axes. sf = ScalarFormatter(useMathText=use_math_text) ax.xaxis.set_major_formatter(sf) ax.yaxis.set_major_formatter(sf) if i < ndim - 2: ax.set_xticklabels([]) else: [l.set_rotation(45) for l in ax.get_xticklabels()] ax.set_xlabel(labels[j], **label_kwargs) ax.xaxis.set_label_coords(0.5, -0.3) if j > 0: ax.set_yticklabels([]) else: [l.set_rotation(45) for l in ax.get_yticklabels()] ax.set_ylabel(labels[i+1], **label_kwargs) ax.yaxis.set_label_coords(-0.3, 0.5) # Plot distribution. in_bounds = np.ones_like(y).astype('bool') if span is not None and span[i] is not None: in_bounds *= ((x >= span[i][0]) & (x <= span[i][1])) if span is not None and span[j] is not None: in_bounds *= ((y >= span[j][0]) & (y <= span[j][1])) ax.scatter(y[in_bounds][::thin], x[in_bounds][::thin], c=color, cmap=cmap, **plot_kwargs) # Add truth values if truths is not None: if truths[j] is not None: try: [ax.axvline(t, color=truth_color, **truth_kwargs) for t in truths[j]] except: ax.axvline(truths[j], color=truth_color, **truth_kwargs) if truths[i+1] is not None: try: [ax.axhline(t, color=truth_color, **truth_kwargs) for t in truths[i+1]] except: ax.axhline(truths[i+1], color=truth_color, **truth_kwargs) return (fig, axes) def cornerplot(results, span=None, quantiles=[0.025, 0.5, 0.975], color='black', smooth=0.02, hist_kwargs=None, hist2d_kwargs=None, labels=None, label_kwargs=None, show_titles=False, title_fmt=".2f", title_kwargs=None, truths=None, truth_color='red', truth_kwargs=None, max_n_ticks=5, top_ticks=False, use_math_text=False, verbose=False, fig=None): """ Generate a corner plot of the 1-D and 2-D marginalized posteriors. Parameters ---------- results : :class:`~dynesty.results.Results` instance A :class:`~dynesty.results.Results` instance from a nested sampling run. **Compatible with results derived from** `nestle `_. span : iterable with shape (ndim,), optional A list where each element is either a length-2 tuple containing lower and upper bounds or a float from `(0., 1.]` giving the fraction of (weighted) samples to include. If a fraction is provided, the bounds are chosen to be equal-tailed. An example would be:: span = [(0., 10.), 0.95, (5., 6.)] Default is `0.999999426697` (5-sigma credible interval). quantiles : iterable, optional A list of fractional quantiles to overplot on the 1-D marginalized posteriors as vertical dashed lines. Default is `[0.025, 0.5, 0.975]` (spanning the 95%/2-sigma credible interval). color : str or iterable with shape (ndim,), optional A `~matplotlib`-style color (either a single color or a different value for each subplot) used when plotting the histograms. Default is `'black'`. smooth : float or iterable with shape (ndim,), optional The standard deviation (either a single value or a different value for each subplot) for the Gaussian kernel used to smooth the 1-D and 2-D marginalized posteriors, expressed as a fraction of the span. Default is `0.02` (2% smoothing). If an integer is provided instead, this will instead default to a simple (weighted) histogram with `bins=smooth`. hist_kwargs : dict, optional Extra keyword arguments to send to the 1-D (smoothed) histograms. hist2d_kwargs : dict, optional Extra keyword arguments to send to the 2-D (smoothed) histograms. labels : iterable with shape (ndim,), optional A list of names for each parameter. If not provided, the default name used when plotting will follow :math:`x_i` style. label_kwargs : dict, optional Extra keyword arguments that will be sent to the `~matplotlib.axes.Axes.set_xlabel` and `~matplotlib.axes.Axes.set_ylabel` methods. show_titles : bool, optional Whether to display a title above each 1-D marginalized posterior showing the 0.5 quantile along with the upper/lower bounds associated with the 0.025 and 0.975 (95%/2-sigma credible interval) quantiles. Default is `True`. title_fmt : str, optional The format string for the quantiles provided in the title. Default is `'.2f'`. title_kwargs : dict, optional Extra keyword arguments that will be sent to the `~matplotlib.axes.Axes.set_title` command. truths : iterable with shape (ndim,), optional A list of reference values that will be overplotted on the traces and marginalized 1-D posteriors as solid horizontal/vertical lines. Individual values can be exempt using `None`. Default is `None`. truth_color : str or iterable with shape (ndim,), optional A `~matplotlib`-style color (either a single color or a different value for each subplot) used when plotting `truths`. Default is `'red'`. truth_kwargs : dict, optional Extra keyword arguments that will be used for plotting the vertical and horizontal lines with `truths`. max_n_ticks : int, optional Maximum number of ticks allowed. Default is `5`. top_ticks : bool, optional Whether to label the top (rather than bottom) ticks. Default is `False`. use_math_text : bool, optional Whether the axis tick labels for very large/small exponents should be displayed as powers of 10 rather than using `e`. Default is `False`. verbose : bool, optional Whether to print the values of the computed quantiles associated with each parameter. Default is `False`. fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional If provided, overplot the traces and marginalized 1-D posteriors onto the provided figure. Otherwise, by default an internal figure is generated. Returns ------- cornerplot : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`) Output corner plot. """ # Initialize values. if quantiles is None: quantiles = [] if truth_kwargs is None: truth_kwargs = dict() if label_kwargs is None: label_kwargs = dict() if title_kwargs is None: title_kwargs = dict() if hist_kwargs is None: hist_kwargs = dict() if hist2d_kwargs is None: hist2d_kwargs = dict() # Set defaults. hist_kwargs['alpha'] = hist_kwargs.get('alpha', 0.6) hist2d_kwargs['alpha'] = hist2d_kwargs.get('alpha', 0.6) truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid') truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 2) truth_kwargs['alpha'] = truth_kwargs.get('alpha', 0.7) # Extract weighted samples. samples = results['samples'] try: weights = np.exp(results['logwt'] - results['logz'][-1]) except: weights = results['weights'] # Deal with 1D results. A number of extra catches are also here # in case users are trying to plot other results besides the `Results` # instance generated by `dynesty`. samples = np.atleast_1d(samples) if len(samples.shape) == 1: samples = np.atleast_2d(samples) else: assert len(samples.shape) == 2, "Samples must be 1- or 2-D." samples = samples.T assert samples.shape[0] <= samples.shape[1], "There are more " \ "dimensions than samples!" ndim, nsamps = samples.shape # Check weights. if weights.ndim != 1: raise ValueError("Weights must be 1-D.") if nsamps != weights.shape[0]: raise ValueError("The number of weights and samples disagree!") # Determine plotting bounds. if span is None: span = [0.999999426697 for i in range(ndim)] span = list(span) if len(span) != ndim: raise ValueError("Dimension mismatch between samples and span.") for i, _ in enumerate(span): try: xmin, xmax = span[i] except: q = [0.5 - 0.5 * span[i], 0.5 + 0.5 * span[i]] span[i] = _quantile(samples[i], q, weights=weights) # Set labels if labels is None: labels = [r"$x_{"+str(i+1)+"}$" for i in range(ndim)] # Setting up smoothing. if (isinstance(smooth, int_type) or isinstance(smooth, float_type)): smooth = [smooth for i in range(ndim)] # Setup axis layout (from `corner.py`). factor = 2.0 # size of side of one panel lbdim = 0.5 * factor # size of left/bottom margin trdim = 0.2 * factor # size of top/right margin whspace = 0.05 # size of width/height margin plotdim = factor * ndim + factor * (ndim - 1.) * whspace # plot size dim = lbdim + plotdim + trdim # total size # Initialize figure. if fig is None: fig, axes = pl.subplots(ndim, ndim, figsize=(dim, dim)) else: try: fig, axes = fig axes = np.array(axes).reshape((ndim, ndim)) except: raise ValueError("Mismatch between axes and dimension.") # Format figure. lb = lbdim / dim tr = (lbdim + plotdim) / dim fig.subplots_adjust(left=lb, bottom=lb, right=tr, top=tr, wspace=whspace, hspace=whspace) # Plotting. for i, x in enumerate(samples): if np.shape(samples)[0] == 1: ax = axes else: ax = axes[i, i] # Plot the 1-D marginalized posteriors. # Setup axes ax.set_xlim(span[i]) if max_n_ticks == 0: ax.xaxis.set_major_locator(NullLocator()) ax.yaxis.set_major_locator(NullLocator()) else: ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks, prune="lower")) ax.yaxis.set_major_locator(NullLocator()) # Label axes. sf = ScalarFormatter(useMathText=use_math_text) ax.xaxis.set_major_formatter(sf) if i < ndim - 1: if top_ticks: ax.xaxis.set_ticks_position("top") [l.set_rotation(45) for l in ax.get_xticklabels()] else: ax.set_xticklabels([]) else: [l.set_rotation(45) for l in ax.get_xticklabels()] ax.set_xlabel(labels[i], **label_kwargs) ax.xaxis.set_label_coords(0.5, -0.3) # Generate distribution. sx = smooth[i] if isinstance(sx, int_type): # If `sx` is an integer, plot a weighted histogram with # `sx` bins within the provided bounds. n, b, _ = ax.hist(x, bins=sx, weights=weights, color=color, range=np.sort(span[i]), **hist_kwargs) else: # If `sx` is a float, oversample the data relative to the # smoothing filter by a factor of 10, then use a Gaussian # filter to smooth the results. bins = int(round(10. / sx)) n, b = np.histogram(x, bins=bins, weights=weights, range=np.sort(span[i])) n = norm_kde(n, 10.) b0 = 0.5 * (b[1:] + b[:-1]) n, b, _ = ax.hist(b0, bins=b, weights=n, range=np.sort(span[i]), color=color, **hist_kwargs) ax.set_ylim([0., max(n) * 1.05]) # Plot quantiles. if quantiles is not None and len(quantiles) > 0: qs = _quantile(x, quantiles, weights=weights) for q in qs: ax.axvline(q, lw=1, ls="dashed", color=color) if verbose: print("Quantiles:") print(labels[i], [blob for blob in zip(quantiles, qs)]) # Add truth value(s). if truths is not None and truths[i] is not None: try: [ax.axvline(t, color=truth_color, **truth_kwargs) for t in truths[i]] except: ax.axvline(truths[i], color=truth_color, **truth_kwargs) # Set titles. if show_titles: title = None if title_fmt is not None: ql, qm, qh = _quantile(x, [0.025, 0.5, 0.975], weights=weights) q_minus, q_plus = qm - ql, qh - qm fmt = "{{0:{0}}}".format(title_fmt).format title = r"${{{0}}}_{{-{1}}}^{{+{2}}}$" title = title.format(fmt(qm), fmt(q_minus), fmt(q_plus)) title = "{0} = {1}".format(labels[i], title) ax.set_title(title, **title_kwargs) for j, y in enumerate(samples): if np.shape(samples)[0] == 1: ax = axes else: ax = axes[i, j] # Plot the 2-D marginalized posteriors. # Setup axes. if j > i: ax.set_frame_on(False) ax.set_xticks([]) ax.set_yticks([]) continue elif j == i: continue if max_n_ticks == 0: ax.xaxis.set_major_locator(NullLocator()) ax.yaxis.set_major_locator(NullLocator()) else: ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks, prune="lower")) ax.yaxis.set_major_locator(MaxNLocator(max_n_ticks, prune="lower")) # Label axes. sf = ScalarFormatter(useMathText=use_math_text) ax.xaxis.set_major_formatter(sf) ax.yaxis.set_major_formatter(sf) if i < ndim - 1: ax.set_xticklabels([]) else: [l.set_rotation(45) for l in ax.get_xticklabels()] ax.set_xlabel(labels[j], **label_kwargs) ax.xaxis.set_label_coords(0.5, -0.3) if j > 0: ax.set_yticklabels([]) else: [l.set_rotation(45) for l in ax.get_yticklabels()] ax.set_ylabel(labels[i], **label_kwargs) ax.yaxis.set_label_coords(-0.3, 0.5) # Generate distribution. sy = smooth[j] check_ix = isinstance(sx, int_type) check_iy = isinstance(sy, int_type) if check_ix and check_iy: fill_contours = False plot_contours = False else: fill_contours = True plot_contours = True hist2d_kwargs['fill_contours'] = hist2d_kwargs.get('fill_contours', fill_contours) hist2d_kwargs['plot_contours'] = hist2d_kwargs.get('plot_contours', plot_contours) _hist2d(y, x, ax=ax, span=[span[j], span[i]], weights=weights, color=color, smooth=[sy, sx], **hist2d_kwargs) # Add truth values if truths is not None: if truths[j] is not None: try: [ax.axvline(t, color=truth_color, **truth_kwargs) for t in truths[j]] except: ax.axvline(truths[j], color=truth_color, **truth_kwargs) if truths[i] is not None: try: [ax.axhline(t, color=truth_color, **truth_kwargs) for t in truths[i]] except: ax.axhline(truths[i], color=truth_color, **truth_kwargs) return (fig, axes) def _hist2d(x, y, smooth=0.02, span=None, weights=None, levels=None, ax=None, color='gray', plot_datapoints=False, plot_density=True, plot_contours=True, no_fill_contours=False, fill_contours=True, contour_kwargs=None, contourf_kwargs=None, data_kwargs=None, **kwargs): """ Internal function called by :meth:`cornerplot` used to generate a a 2-D histogram/contour of samples. Parameters ---------- x : interable with shape (nsamps,) Sample positions in the first dimension. y : iterable with shape (nsamps,) Sample positions in the second dimension. span : iterable with shape (ndim,), optional A list where each element is either a length-2 tuple containing lower and upper bounds or a float from `(0., 1.]` giving the fraction of (weighted) samples to include. If a fraction is provided, the bounds are chosen to be equal-tailed. An example would be:: span = [(0., 10.), 0.95, (5., 6.)] Default is `0.999999426697` (5-sigma credible interval). weights : iterable with shape (nsamps,) Weights associated with the samples. Default is `None` (no weights). levels : iterable, optional The contour levels to draw. Default are `[0.5, 1, 1.5, 2]`-sigma. ax : `~matplotlib.axes.Axes`, optional An `~matplotlib.axes.axes` instance on which to add the 2-D histogram. If not provided, a figure will be generated. color : str, optional The `~matplotlib`-style color used to draw lines and color cells and contours. Default is `'gray'`. plot_datapoints : bool, optional Whether to plot the individual data points. Default is `False`. plot_density : bool, optional Whether to draw the density colormap. Default is `True`. plot_contours : bool, optional Whether to draw the contours. Default is `True`. no_fill_contours : bool, optional Whether to add absolutely no filling to the contours. This differs from `fill_contours=False`, which still adds a white fill at the densest points. Default is `False`. fill_contours : bool, optional Whether to fill the contours. Default is `True`. contour_kwargs : dict Any additional keyword arguments to pass to the `contour` method. contourf_kwargs : dict Any additional keyword arguments to pass to the `contourf` method. data_kwargs : dict Any additional keyword arguments to pass to the `plot` method when adding the individual data points. """ if ax is None: ax = pl.gca() # Determine plotting bounds. data = [x, y] if span is None: span = [0.999999426697 for i in range(2)] span = list(span) if len(span) != 2: raise ValueError("Dimension mismatch between samples and span.") for i, _ in enumerate(span): try: xmin, xmax = span[i] except: q = [0.5 - 0.5 * span[i], 0.5 + 0.5 * span[i]] span[i] = _quantile(data[i], q, weights=weights) # The default "sigma" contour levels. if levels is None: levels = 1.0 - np.exp(-0.5 * np.arange(0.5, 2.1, 0.5) ** 2) # Color map for the density plot, over-plotted to indicate the # density of the points near the center. density_cmap = LinearSegmentedColormap.from_list( "density_cmap", [color, (1, 1, 1, 0)]) # Color map used to hide the points at the high density areas. white_cmap = LinearSegmentedColormap.from_list( "white_cmap", [(1, 1, 1), (1, 1, 1)], N=2) # This "color map" is the list of colors for the contour levels if the # contours are filled. rgba_color = colorConverter.to_rgba(color) contour_cmap = [list(rgba_color) for l in levels] + [rgba_color] for i, l in enumerate(levels): contour_cmap[i][-1] *= float(i) / (len(levels)+1) # Initialize smoothing. if (isinstance(smooth, int_type) or isinstance(smooth, float_type)): smooth = [smooth, smooth] bins = [] svalues = [] for s in smooth: if isinstance(s, int_type): # If `s` is an integer, the weighted histogram has # `s` bins within the provided bounds. bins.append(s) svalues.append(0.) else: # If `s` is a float, oversample the data relative to the # smoothing filter by a factor of 2, then use a Gaussian # filter to smooth the results. bins.append(int(round(2. / s))) svalues.append(2.) # We'll make the 2D histogram to directly estimate the density. try: H, X, Y = np.histogram2d(x.flatten(), y.flatten(), bins=bins, range=list(map(np.sort, span)), weights=weights) except ValueError: raise ValueError("It looks like at least one of your sample columns " "have no dynamic range.") # Smooth the results. if not np.all(svalues == 0.): H = norm_kde(H, svalues) # Compute the density levels. Hflat = H.flatten() inds = np.argsort(Hflat)[::-1] Hflat = Hflat[inds] sm = np.cumsum(Hflat) sm /= sm[-1] V = np.empty(len(levels)) for i, v0 in enumerate(levels): try: V[i] = Hflat[sm <= v0][-1] except: V[i] = Hflat[0] V.sort() m = (np.diff(V) == 0) if np.any(m) and plot_contours: logging.warning("Too few points to create valid contours.") while np.any(m): V[np.where(m)[0][0]] *= 1.0 - 1e-4 m = (np.diff(V) == 0) V.sort() # Compute the bin centers. X1, Y1 = 0.5 * (X[1:] + X[:-1]), 0.5 * (Y[1:] + Y[:-1]) # Extend the array for the sake of the contours at the plot edges. H2 = H.min() + np.zeros((H.shape[0] + 4, H.shape[1] + 4)) H2[2:-2, 2:-2] = H H2[2:-2, 1] = H[:, 0] H2[2:-2, -2] = H[:, -1] H2[1, 2:-2] = H[0] H2[-2, 2:-2] = H[-1] H2[1, 1] = H[0, 0] H2[1, -2] = H[0, -1] H2[-2, 1] = H[-1, 0] H2[-2, -2] = H[-1, -1] X2 = np.concatenate([X1[0] + np.array([-2, -1]) * np.diff(X1[:2]), X1, X1[-1] + np.array([1, 2]) * np.diff(X1[-2:])]) Y2 = np.concatenate([Y1[0] + np.array([-2, -1]) * np.diff(Y1[:2]), Y1, Y1[-1] + np.array([1, 2]) * np.diff(Y1[-2:])]) # Plot the data points. if plot_datapoints: if data_kwargs is None: data_kwargs = dict() data_kwargs["color"] = data_kwargs.get("color", color) data_kwargs["ms"] = data_kwargs.get("ms", 2.0) data_kwargs["mec"] = data_kwargs.get("mec", "none") data_kwargs["alpha"] = data_kwargs.get("alpha", 0.1) ax.plot(x, y, "o", zorder=-1, rasterized=True, **data_kwargs) # Plot the base fill to hide the densest data points. if (plot_contours or plot_density) and not no_fill_contours: ax.contourf(X2, Y2, H2.T, [V.min(), H.max()], cmap=white_cmap, antialiased=False) if plot_contours and fill_contours: if contourf_kwargs is None: contourf_kwargs = dict() contourf_kwargs["colors"] = contourf_kwargs.get("colors", contour_cmap) contourf_kwargs["antialiased"] = contourf_kwargs.get("antialiased", False) ax.contourf(X2, Y2, H2.T, np.concatenate([[0], V, [H.max()*(1+1e-4)]]), **contourf_kwargs) # Plot the density map. This can't be plotted at the same time as the # contour fills. elif plot_density: ax.pcolor(X, Y, H.max() - H.T, cmap=density_cmap) # Plot the contour edge colors. if plot_contours: if contour_kwargs is None: contour_kwargs = dict() contour_kwargs["colors"] = contour_kwargs.get("colors", color) ax.contour(X2, Y2, H2.T, V, **contour_kwargs) ax.set_xlim(span[0]) ax.set_ylim(span[1]) if len(sys.argv) != 2: sys.stderr.write("""SYNOPSIS: %s output-root: Where the output of a MultiNest run has been written to. Example: chains/1- %s""" % (sys.argv[0], __doc__)) sys.exit(1) prefix = sys.argv[1] print('model "%s"' % prefix) if not os.path.exists(prefix + 'params.json'): sys.stderr.write("""Expected the file %sparams.json with the parameter names. For example, for a three-dimensional problem: ["Redshift $z$", "my parameter 2", "A"] %s""" % (sys.argv[1], __doc__)) sys.exit(2) parameters = json.load(open(prefix + 'params.json')) n_params = len(parameters) a = pymultinest.Analyzer(n_params = n_params, outputfiles_basename = prefix) s = a.get_stats() json.dump(s, open(prefix + 'stats.json', 'w'), indent=4) print(' marginal likelihood:') print(' ln Z = %.1f +- %.1f' % (s['global evidence'], s['global evidence error'])) print(' parameters:') for p, m in zip(parameters, s['marginals']): lo, hi = m['1sigma'] med = m['median'] sigma = (hi - lo) / 2 if sigma == 0: i = 3 else: i = max(0, int(-numpy.floor(numpy.log10(sigma))) + 1) fmt = '%%.%df' % i fmts = '\t'.join([' %-15s' + fmt + " +- " + fmt]) print(fmts % (p, med, sigma)) print('creating marginal plot ...') data = a.get_data() i = data[:,1].argsort()[::-1] samples = data[i,2:] weights = data[i,0] loglike = data[i,1] Z = s['global evidence'] logvol = log(weights) + 0.5 * loglike + Z logvol = logvol - logvol.max() #plt.plot(-0.5 * loglike, logvol, 'x ') #plt.savefig('weights.pdf', bbox_inches='tight') #plt.close() results = dict(samples=samples, weights=weights, logvol=logvol) traceplot(results, labels=parameters, show_titles=True) plt.savefig(prefix + 'trace.pdf', bbox_inches='tight') plt.savefig(prefix + 'trace.png', bbox_inches='tight') plt.close() cornerplot(results, labels=parameters, show_titles=True) plt.savefig(prefix + 'corner.pdf', bbox_inches='tight') plt.savefig(prefix + 'corner.png', bbox_inches='tight') plt.close() cornerpoints(results, labels=parameters) plt.savefig(prefix + 'cornerp.pdf', bbox_inches='tight') plt.savefig(prefix + 'cornerp.png', bbox_inches='tight') plt.close()