def plot_mapping(self,
plot_limits=None,
which_data='all',
which_parts='all',
resolution=None,
levels=20,
samples=0,
fignum=None,
ax=None,
fixed_inputs=[],
linecol=Tango.colorsHex['darkBlue']):
"""
Plots the mapping associated with the model.
- In one dimension, the function is plotted.
- In two dimsensions, a contour-plot shows the function
- In higher dimensions, we've not implemented this yet !TODO!
Can plot only part of the data and part of the posterior functions
using which_data and which_functions
: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: which if the training data to plot (default all)
:type which_data: 'all' or a slice object to slice self.X, self.Y
:param which_parts: which of the kernel functions to plot (additively)
:type which_parts: 'all', or list of bools
: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
: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 linecol: color of line to plot.
:type linecol:
:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
"""
# TODO include samples
if which_data == 'all':
which_data = slice(None)
if ax is None:
fig = pb.figure(num=fignum)
ax = fig.add_subplot(111)
plotdims = self.input_dim - len(fixed_inputs)
if plotdims == 1:
Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
fixed_dims = np.array([i for i, v in fixed_inputs])
freedim = np.setdiff1d(np.arange(self.input_dim), fixed_dims)
Xnew, xmin, xmax = x_frame1D(Xu[:, freedim], plot_limits=plot_limits)
Xgrid = np.empty((Xnew.shape[0], self.input_dim))
Xgrid[:, freedim] = Xnew
for i, v in fixed_inputs:
Xgrid[:, i] = v
f = self.predict(Xgrid, which_parts=which_parts)
for d in range(y.shape[1]):
ax.plot(Xnew, f[:, d], edgecol=linecol)
elif self.X.shape[1] == 2:
resolution = resolution or 50
Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
x, y = np.linspace(xmin[0], xmax[0],
resolution), np.linspace(xmin[1], xmax[1],
resolution)
f = self.predict(Xnew, which_parts=which_parts)
m = m.reshape(resolution, resolution).T
ax.contour(x, y, f, levels, vmin=m.min(), vmax=m.max(),
cmap=pb.cm.jet) # @UndefinedVariable
ax.set_xlim(xmin[0], xmax[0])
ax.set_ylim(xmin[1], xmax[1])
else:
raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
def plot_mapping(self, plot_limits=None, which_data='all', which_parts='all', resolution=None, levels=20, samples=0, fignum=None, ax=None, fixed_inputs=[], linecol=Tango.colorsHex['darkBlue']):
"""
Plots the mapping associated with the model.
- In one dimension, the function is plotted.
- In two dimsensions, a contour-plot shows the function
- In higher dimensions, we've not implemented this yet !TODO!
Can plot only part of the data and part of the posterior functions
using which_data and which_functions
: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: which if the training data to plot (default all)
:type which_data: 'all' or a slice object to slice self.X, self.Y
:param which_parts: which of the kernel functions to plot (additively)
:type which_parts: 'all', or list of bools
: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
: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 linecol: color of line to plot.
:type linecol:
:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
"""
# TODO include samples
if which_data == 'all':
which_data = slice(None)
if ax is None:
fig = pb.figure(num=fignum)
ax = fig.add_subplot(111)
plotdims = self.input_dim - len(fixed_inputs)
if plotdims == 1:
Xu = self.X * self._Xscale + self._Xoffset # NOTE self.X are the normalized values now
fixed_dims = np.array([i for i,v in fixed_inputs])
freedim = np.setdiff1d(np.arange(self.input_dim),fixed_dims)
Xnew, xmin, xmax = x_frame1D(Xu[:,freedim], plot_limits=plot_limits)
Xgrid = np.empty((Xnew.shape[0],self.input_dim))
Xgrid[:,freedim] = Xnew
for i,v in fixed_inputs:
Xgrid[:,i] = v
f = self.predict(Xgrid, which_parts=which_parts)
for d in range(y.shape[1]):
ax.plot(Xnew, f[:, d], edgecol=linecol)
elif self.X.shape[1] == 2:
resolution = resolution or 50
Xnew, _, _, xmin, xmax = x_frame2D(self.X, plot_limits, resolution)
x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
f = self.predict(Xnew, which_parts=which_parts)
m = m.reshape(resolution, resolution).T
ax.contour(x, y, f, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet) # @UndefinedVariable
ax.set_xlim(xmin[0], xmax[0])
ax.set_ylim(xmin[1], xmax[1])
else:
raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
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'], Y_metadata=None, data_symbol='kx'):
"""
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 = model.X.variance
else:
X = model.X
Y = model.Y
if sparse.issparse(Y): Y = Y.todense().view(np.ndarray)
if hasattr(model, 'Z'): Z = 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)
else:
if isinstance(model,GPCoregionalizedRegression) or isinstance(model,SparseGPCoregionalizedRegression):
meta = {'output_index': Xgrid[:,-1:].astype(np.int)}
else:
meta = None
m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta)
lower, upper = model.predict_quantiles(Xgrid, Y_metadata=meta)
for d in which_data_ycols:
plots['gpplot'] = gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], ax=ax, edgecol=linecol, fillcol=fillcol)
if not plot_raw: plots['dataplot'] = ax.plot(X[which_data_rows,free_dims], Y[which_data_rows, d], data_symbol, 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]
if isinstance(model,SparseGPCoregionalizedRegression):
Z = Z[Z[:,-1] == Y_metadata['output_index'],:]
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)
else:
if isinstance(model,GPCoregionalizedRegression) or isinstance(model,SparseGPCoregionalizedRegression):
meta = {'output_index': Xgrid[:,-1:].astype(np.int)}
else:
meta = None
m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta)
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)
if not plot_raw: 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(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'],
Y_metadata=None,
data_symbol='kx'):
"""
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 = model.X.variance
else:
X = model.X
Y = model.Y
if sparse.issparse(Y): Y = Y.todense().view(np.ndarray)
if hasattr(model, 'Z'): Z = 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)
else:
if isinstance(model, GPCoregionalizedRegression) or isinstance(
model, SparseGPCoregionalizedRegression):
meta = {'output_index': Xgrid[:, -1:].astype(np.int)}
else:
meta = None
m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta)
lower, upper = model.predict_quantiles(Xgrid, Y_metadata=meta)
for d in which_data_ycols:
plots['gpplot'] = gpplot(Xnew,
m[:, d],
lower[:, d],
upper[:, d],
ax=ax,
edgecol=linecol,
fillcol=fillcol)
if not plot_raw:
plots['dataplot'] = ax.plot(X[which_data_rows, free_dims],
Y[which_data_rows, d],
data_symbol,
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]
if isinstance(model, SparseGPCoregionalizedRegression):
Z = Z[Z[:, -1] == Y_metadata['output_index'], :]
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)
else:
if isinstance(model, GPCoregionalizedRegression) or isinstance(
model, SparseGPCoregionalizedRegression):
meta = {'output_index': Xgrid[:, -1:].astype(np.int)}
else:
meta = None
m, v = model.predict(Xgrid, full_cov=False, Y_metadata=meta)
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)
if not plot_raw:
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