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277 lines
14 KiB
Python
277 lines
14 KiB
Python
import numpy as np
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from .. import kern
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from ..util.plot import gpplot, Tango, x_frame1D, x_frame2D
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import pylab as pb
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from GPy.core.model import Model
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class GPBase(Model):
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"""
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Gaussian process base model for holding shared behaviour between
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sparse_GP and GP models.
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"""
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def __init__(self, X, likelihood, kernel, normalize_X=False):
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self.X = X
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assert len(self.X.shape) == 2
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self.num_data, self.input_dim = self.X.shape
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assert isinstance(kernel, kern.kern)
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self.kern = kernel
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self.likelihood = likelihood
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assert self.X.shape[0] == self.likelihood.data.shape[0]
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self.num_data, self.output_dim = self.likelihood.data.shape
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if normalize_X:
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self._Xoffset = X.mean(0)[None, :]
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self._Xscale = X.std(0)[None, :]
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self.X = (X.copy() - self._Xoffset) / self._Xscale
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else:
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self._Xoffset = np.zeros((1, self.input_dim))
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self._Xscale = np.ones((1, self.input_dim))
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super(GPBase, self).__init__()
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# Model.__init__(self)
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# All leaf nodes should call self._set_params(self._get_params()) at
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# the end
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def getstate(self):
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"""
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Get the current state of the class, here we return everything that is needed to recompute the model.
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"""
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return Model.getstate(self) + [self.X,
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self.num_data,
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self.input_dim,
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self.kern,
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self.likelihood,
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self.output_dim,
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self._Xoffset,
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self._Xscale]
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def setstate(self, state):
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self._Xscale = state.pop()
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self._Xoffset = state.pop()
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self.output_dim = state.pop()
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self.likelihood = state.pop()
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self.kern = state.pop()
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self.input_dim = state.pop()
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self.num_data = state.pop()
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self.X = state.pop()
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Model.setstate(self, state)
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def plot_f(self, samples=0, plot_limits=None, which_data='all', which_parts='all', resolution=None, full_cov=False, fignum=None, ax=None,output=None):
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"""
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Plot the GP's view of the world, where the data is normalized and the
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- In one dimension, the function is plotted with a shaded region identifying two standard deviations.
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- In two dimsensions, a contour-plot shows the mean predicted function
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- Not implemented in higher dimensions
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:param samples: the number of a posteriori samples to plot
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:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
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:param which_data: which if the training data to plot (default all)
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:type which_data: 'all' or a slice object to slice self.X, self.Y
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:param which_parts: which of the kernel functions to plot (additively)
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:type which_parts: 'all', or list of bools
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:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
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:type resolution: int
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:param full_cov:
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:type full_cov: bool
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:param fignum: figure to plot on.
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:type fignum: figure number
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:param ax: axes to plot on.
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:type ax: axes handle
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:param output: which output to plot (for multiple output models only)
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:type output: integer (first output is 0)
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"""
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if which_data == 'all':
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which_data = slice(None)
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if ax is None:
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fig = pb.figure(num=fignum)
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ax = fig.add_subplot(111)
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if self.X.shape[1] == 1 and not hasattr(self,'multioutput'):
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Xnew, xmin, xmax = x_frame1D(self.X, plot_limits=plot_limits)
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if samples == 0:
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m, v = self._raw_predict(Xnew, which_parts=which_parts)
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gpplot(Xnew, m, m - 2 * np.sqrt(v), m + 2 * np.sqrt(v), axes=ax)
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ax.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
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else:
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m, v = self._raw_predict(Xnew, which_parts=which_parts, full_cov=True)
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Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
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gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None, ], axes=ax)
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for i in range(samples):
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ax.plot(Xnew, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
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ax.plot(self.X[which_data], self.likelihood.Y[which_data], 'kx', mew=1.5)
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ax.set_xlim(xmin, xmax)
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ymin, ymax = min(np.append(self.likelihood.Y, m - 2 * np.sqrt(np.diag(v)[:, None]))), max(np.append(self.likelihood.Y, m + 2 * np.sqrt(np.diag(v)[:, None])))
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ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
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ax.set_ylim(ymin, ymax)
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elif self.X.shape[1] == 2 and not hasattr(self,'multioutput'):
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resolution = resolution or 50
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Xnew, xmin, xmax, xx, yy = x_frame2D(self.X, plot_limits, resolution)
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m, v = self._raw_predict(Xnew, which_parts=which_parts)
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m = m.reshape(resolution, resolution).T
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ax.contour(xx, yy, m, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
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ax.scatter(self.X[:, 0], self.X[:, 1], 40, self.likelihood.Y, linewidth=0, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max()) # @UndefinedVariable
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ax.set_xlim(xmin[0], xmax[0])
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ax.set_ylim(xmin[1], xmax[1])
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elif self.X.shape[1] == 2 and hasattr(self,'multioutput'):
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output -= 1
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assert self.num_outputs >= output, 'The model has only %s outputs.' %self.num_outputs
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Xu = self.X[self.X[:,-1]==output ,0:1]
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Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
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if samples == 0:
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m, v = self._raw_predict_single_output(Xnew, output=output, which_parts=which_parts)
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gpplot(Xnew, m, m - 2 * np.sqrt(v), m + 2 * np.sqrt(v), axes=ax)
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ax.plot(Xu[which_data], self.likelihood.Y[self.likelihood.index==output][:,None], 'kx', mew=1.5)
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else:
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m, v = self._raw_predict_single_output(Xnew, output=output, which_parts=which_parts, full_cov=True)
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Ysim = np.random.multivariate_normal(m.flatten(), v, samples)
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gpplot(Xnew, m, m - 2 * np.sqrt(np.diag(v)[:, None]), m + 2 * np.sqrt(np.diag(v))[:, None, ], axes=ax)
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for i in range(samples):
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ax.plot(Xnew, Ysim[i, :], Tango.colorsHex['darkBlue'], linewidth=0.25)
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ax.set_xlim(xmin, xmax)
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ymin, ymax = min(np.append(self.likelihood.Y, m - 2 * np.sqrt(np.diag(v)[:, None]))), max(np.append(self.likelihood.Y, m + 2 * np.sqrt(np.diag(v)[:, None])))
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ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
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ax.set_ylim(ymin, ymax)
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if hasattr(self,'Z'):
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Zu = self.Z[self.Z[:,-1]==output,:]
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Zu = self.Z * self._Xscale + self._Xoffset
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Zu = self.Z[self.Z[:,-1]==output ,0:1] #??
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ax.plot(Zu, np.zeros_like(Zu) + ax.get_ylim()[0], 'r|', mew=1.5, markersize=12)
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elif self.X.shape[1] == 3 and hasattr(self,'multioutput'):
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raise NotImplementedError, "Plots not implemented for multioutput models with 2D inputs...yet"
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output -= 1
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assert self.num_outputs >= output, 'The model has only %s outputs.' %self.num_outputs
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else:
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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def plot(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None, output=None, fixed_inputs=[], linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']):
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"""
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Plot the GP with noise where the likelihood is Gaussian.
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Plot the posterior of the GP.
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- In one dimension, the function is plotted with a shaded region identifying two standard deviations.
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- In two dimsensions, a contour-plot shows the mean predicted function
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- Not implemented in higher dimensions
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Can plot only part of the data and part of the posterior functions
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using which_data and which_functions
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:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
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:type plot_limits: np.array
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:param which_data: which if the training data to plot (default all)
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:type which_data: 'all' or a slice object to slice self.X, self.Y
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:param which_parts: which of the kernel functions to plot (additively)
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:type which_parts: 'all', or list of bools
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:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
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:type resolution: int
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:param levels: number of levels to plot in a contour plot.
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:type levels: int
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:param samples: the number of a posteriori samples to plot
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:type samples: int
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:param fignum: figure to plot on.
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:type fignum: figure number
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:param ax: axes to plot on.
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:type ax: axes handle
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:type output: integer (first output is 0)
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:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
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:type fixed_inputs: a list of tuples
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:param linecol: color of line to plot.
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:type linecol:
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:param fillcol: color of fill
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:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
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"""
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# TODO include samples
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if which_data == 'all':
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which_data = slice(None)
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if ax is None:
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fig = pb.figure(num=fignum)
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ax = fig.add_subplot(111)
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if not hasattr(self,'multioutput'):
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plotdims = self.input_dim - len(fixed_inputs)
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if plotdims == 1:
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resolution = resolution or 200
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Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
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fixed_dims = np.array([i for i,v in fixed_inputs])
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freedim = np.setdiff1d(np.arange(self.input_dim),fixed_dims)
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Xnew, xmin, xmax = x_frame1D(Xu[:,freedim], plot_limits=plot_limits)
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Xgrid = np.empty((Xnew.shape[0],self.input_dim))
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Xgrid[:,freedim] = Xnew
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for i,v in fixed_inputs:
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Xgrid[:,i] = v
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m, _, lower, upper = self.predict(Xgrid, which_parts=which_parts)
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for d in range(m.shape[1]):
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gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax, edgecol=linecol, fillcol=fillcol)
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ax.plot(Xu[which_data,freedim], self.likelihood.data[which_data, d], 'kx', mew=1.5)
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ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
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ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
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ax.set_xlim(xmin, xmax)
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ax.set_ylim(ymin, ymax)
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Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits,resolution=resolution)
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m, _, lower, upper = self.predict(Xnew, which_parts=which_parts)
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for d in range(m.shape[1]):
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gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax)
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ax.plot(Xu[which_data], self.likelihood.data[which_data, d], 'kx', mew=1.5)
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ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
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ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
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ax.set_xlim(xmin, xmax)
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ax.set_ylim(ymin, ymax)
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elif self.X.shape[1] == 2:
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resolution = resolution or 50
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Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
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x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
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m, _, lower, upper = self.predict(Xnew, which_parts=which_parts)
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m = m.reshape(resolution, resolution).T
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ax.contour(x, y, m, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
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Yf = self.likelihood.Y.flatten()
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ax.scatter(self.X[:, 0], self.X[:, 1], 40, Yf, cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.) # @UndefinedVariable
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ax.set_xlim(xmin[0], xmax[0])
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ax.set_ylim(xmin[1], xmax[1])
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else:
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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else:
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assert self.num_outputs > output, 'The model has only %s outputs.' %self.num_outputs
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if self.X.shape[1] == 2:
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resolution = resolution or 200
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Xu = self.X[self.X[:,-1]==output,:] #keep the output of interest
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Xu = self.X * self._Xscale + self._Xoffset
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Xu = self.X[self.X[:,-1]==output ,0:1] #get rid of the index column
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Xnew, xmin, xmax = x_frame1D(Xu, plot_limits=plot_limits)
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m, _, lower, upper = self.predict_single_output(Xnew, which_parts=which_parts,output=output)
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for d in range(m.shape[1]):
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gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax)
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ax.plot(Xu[which_data], self.likelihood.noise_model_list[output].data, 'kx', mew=1.5)
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ymin, ymax = min(np.append(self.likelihood.data, lower)), max(np.append(self.likelihood.data, upper))
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ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
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ax.set_xlim(xmin, xmax)
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ax.set_ylim(ymin, ymax)
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elif self.X.shape[1] == 3:
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raise NotImplementedError, "Plots not yet implemented for multioutput models with 2D inputs"
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resolution = resolution or 50
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else:
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raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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