# Copyright (c) 2012, GPy authors (see AUTHORS.txt). # Licensed under the BSD 3-clause license (see LICENSE.txt) import pylab as pb import numpy as np import Tango from base_plots import gpplot, x_frame1D, x_frame2D from ...util.misc import param_to_array def plot_fit(model, plot_limits=None, which_data_rows='all', which_data_ycols='all', fixed_inputs=[], levels=20, samples=0, fignum=None, ax=None, resolution=None, plot_raw=False, linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']): """ Plot the posterior of the GP. - In one dimension, the function is plotted with a shaded region identifying two standard deviations. - In two dimsensions, a contour-plot shows the mean predicted function - In higher dimensions, use fixed_inputs to plot the GP with some of the inputs fixed. Can plot only part of the data and part of the posterior functions using which_data_rowsm which_data_ycols. :param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits :type plot_limits: np.array :param which_data_rows: which of the training data to plot (default all) :type which_data_rows: 'all' or a slice object to slice model.X, model.Y :param which_data_ycols: when the data has several columns (independant outputs), only plot these :type which_data_rows: 'all' or a list of integers :param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v. :type fixed_inputs: a list of tuples :param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D :type resolution: int :param levels: number of levels to plot in a contour plot. :type levels: int :param samples: the number of a posteriori samples to plot :type samples: int :param fignum: figure to plot on. :type fignum: figure number :param ax: axes to plot on. :type ax: axes handle :type output: integer (first output is 0) :param linecol: color of line to plot. :type linecol: :param fillcol: color of fill :param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure """ #deal with optional arguments if which_data_rows == 'all': which_data_rows = slice(None) if which_data_ycols == 'all': which_data_ycols = np.arange(model.output_dim) if len(which_data_ycols)==0: raise ValueError('No data selected for plotting') if ax is None: fig = pb.figure(num=fignum) ax = fig.add_subplot(111) if hasattr(model, 'has_uncertain_inputs') and model.has_uncertain_inputs(): X = model.X.mean X_variance = param_to_array(model.X.variance) else: X = model.X X, Y = param_to_array(X, model.Y) if hasattr(model, 'Z'): Z = param_to_array(model.Z) #work out what the inputs are for plotting (1D or 2D) fixed_dims = np.array([i for i,v in fixed_inputs]) free_dims = np.setdiff1d(np.arange(model.input_dim),fixed_dims) plots = {} #one dimensional plotting if len(free_dims) == 1: #define the frame on which to plot Xnew, xmin, xmax = x_frame1D(X[:,free_dims], plot_limits=plot_limits, resolution=resolution or 200) Xgrid = np.empty((Xnew.shape[0],model.input_dim)) Xgrid[:,free_dims] = Xnew for i,v in fixed_inputs: Xgrid[:,i] = v #make a prediction on the frame and plot it if plot_raw: m, v = model._raw_predict(Xgrid) lower = m - 2*np.sqrt(v) upper = m + 2*np.sqrt(v) Y = Y else: m, v, lower, upper = model.predict(Xgrid) Y = Y for d in which_data_ycols: plots['gpplot'] = gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], ax=ax, edgecol=linecol, fillcol=fillcol) plots['dataplot'] = ax.plot(X[which_data_rows,free_dims], Y[which_data_rows, d], 'kx', mew=1.5) #optionally plot some samples if samples: #NOTE not tested with fixed_inputs Ysim = model.posterior_samples(Xgrid, samples) for yi in Ysim.T: plots['posterior_samples'] = ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25) #ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs. #add error bars for uncertain (if input uncertainty is being modelled) if hasattr(model,"has_uncertain_inputs") and model.has_uncertain_inputs(): plots['xerrorbar'] = ax.errorbar(X[which_data_rows, free_dims].flatten(), Y[which_data_rows, which_data_ycols].flatten(), xerr=2 * np.sqrt(X_variance[which_data_rows, free_dims].flatten()), ecolor='k', fmt=None, elinewidth=.5, alpha=.5) #set the limits of the plot to some sensible values ymin, ymax = min(np.append(Y[which_data_rows, which_data_ycols].flatten(), lower)), max(np.append(Y[which_data_rows, which_data_ycols].flatten(), upper)) ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin) ax.set_xlim(xmin, xmax) ax.set_ylim(ymin, ymax) #add inducing inputs (if a sparse model is used) if hasattr(model,"Z"): #Zu = model.Z[:,free_dims] * model._Xscale[:,free_dims] + model._Xoffset[:,free_dims] Zu = Z[:,free_dims] z_height = ax.get_ylim()[0] plots['inducing_inputs'] = ax.plot(Zu, np.zeros_like(Zu) + z_height, 'r|', mew=1.5, markersize=12) #2D plotting elif len(free_dims) == 2: #define the frame for plotting on resolution = resolution or 50 Xnew, _, _, xmin, xmax = x_frame2D(X[:,free_dims], plot_limits, resolution) Xgrid = np.empty((Xnew.shape[0],model.input_dim)) Xgrid[:,free_dims] = Xnew for i,v in fixed_inputs: Xgrid[:,i] = v x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution) #predict on the frame and plot if plot_raw: m, _ = model._raw_predict(Xgrid) Y = Y else: m, _, _, _ = model.predict(Xgrid) Y = Y for d in which_data_ycols: m_d = m[:,d].reshape(resolution, resolution).T plots['contour'] = ax.contour(x, y, m_d, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) plots['dataplot'] = ax.scatter(X[which_data_rows, free_dims[0]], X[which_data_rows, free_dims[1]], 40, Y[which_data_rows, d], cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.) #set the limits of the plot to some sensible values ax.set_xlim(xmin[0], xmax[0]) ax.set_ylim(xmin[1], xmax[1]) if samples: warnings.warn("Samples are rather difficult to plot for 2D inputs...") #add inducing inputs (if a sparse model is used) if hasattr(model,"Z"): #Zu = model.Z[:,free_dims] * model._Xscale[:,free_dims] + model._Xoffset[:,free_dims] Zu = Z[:,free_dims] plots['inducing_inputs'] = ax.plot(Zu[:,free_dims[0]], Zu[:,free_dims[1]], 'wo') else: raise NotImplementedError, "Cannot define a frame with more than two input dimensions" return plots def plot_fit_f(model, *args, **kwargs): """ Plot the GP's view of the world, where the data is normalized and before applying a likelihood. All args and kwargs are passed on to models_plots.plot. """ kwargs['plot_raw'] = True plot_fit(model,*args, **kwargs)