def standard_plot(fit):
"""
Replicate some of the GPy plotting functionality to produce time-series plot by cluster
but adding other features such as colouring etc.
Arguments
=========
fit - a Mixture of Hierarchical Gaussian Process model
Returns
=========
hFig - a handle to the figure
"""
# Init some local vars
organ = fit.name[:-2]
strain = fit.name[-2:]
xTest = np.arange(config.XLIM[0], config.XLIM[1], 0.05)[:, None]
# Work out how many subplots we need
#Ntotal = np.sum(fit.phi_hat > 0.99) # no. of clusters
Ntotal = fit.K # TODO: double check difference between above cmd and this
Nx = np.floor(np.sqrt(Ntotal))
Ny = int(np.ceil(Ntotal/Nx))
Nx = int(Nx)
hFig = plt.figure(figsize=(11.69, 8.27))
# Loop through all clusters
for i, mu, var in zip(range(fit.K), *fit.predict_components(xTest)):
bWant = np.argmax(fit.phi, axis=1) == i # the indices that I want
N = np.sum(bWant)
if N > 0:
hAx = hFig.add_subplot(Nx, Ny, i+1)
# Plot observed data points
hAx.plot(fit.X, fit.Y[bWant, :].T, marker='.', c=config.COL[organ],
mec=config.COL[organ], lw=0, alpha=0.1)
# Plot GP: edgecol = mean line col; fillcol = CI col
gpplot(xTest.flatten(), mu.flatten(), mu-2.*np.sqrt(np.diag(var)),
mu+2.*np.sqrt(np.diag(var)), edgecol=config.COL[organ],
fillcol=config.COL['Shade'], ax=hAx, alpha=0.1)
# Label plot, same limits etc.
hAx.axhline(y=0, color=config.COL['Zero'], linestyle='--',
linewidth=config.LWD['M'])
name = "{}_{}_{:02d}".format(organ[:2], strain, (i+1))
hAx.set_title("{} (N={})".format(name, N), fontsize=9)
# Align all subplots
align_subplots(Nx, Ny, xlim=config.XLIM, ylim=config.YLIM)
return hFig
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='darkBlue',fillcol='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 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
m, v = model.predict(Xgrid)
lower = m - 2*np.sqrt(v)
upper = m + 2*np.sqrt(v)
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], 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)
#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.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 sausage_plot(layer, Xnew, ax):
mu, var = layer.predict(Xnew)
gpplot(Xnew, mu, mu + 2 * np.sqrt(var), mu - 2 * np.sqrt(var), ax=ax)
gp_std = np.std(gp_curves, axis=0)
wgp_mean = np.mean(wgp_curves, axis=0)
wgp_std = np.std(wgp_curves, axis=0)
#svm_mean = np.mean(svm_curves, axis=0)
#svm_std = np.std(svm_curves, axis=0)
x_plot = np.array(range(1, data.shape[0] / FOLDS))
gp_random_mean = np.mean(gp_random_curves, axis=0)
gp_random_std = np.std(gp_random_curves, axis=0)
from GPy.plotting.matplot_dep.base_plots import gpplot
fig, axarr = plt.subplots(1,1)
gpplot(x_plot, gp_mean, (gp_mean - (2*gp_std)),
(gp_mean + (2*gp_std)), ax=axarr)
gpplot(x_plot, wgp_mean, (wgp_mean - (2*wgp_std)),
(wgp_mean + (2*wgp_std)), ax=axarr,
edgecol='DarkGreen',
fillcol='LightGreen')
gpplot(x_plot, gp_random_mean, (gp_random_mean - (2*gp_random_std)),
(gp_random_mean + (2*gp_random_std)), ax=axarr,
edgecol='k',
fillcol='LightGray')
#gpplot(x_plot, svm_mean, (svm_mean - (2*svm_std)),
# (svm_mean + (2*svm_std)), ax=axarr,
# edgecol='DarkGreen',
# fillcol='LightGreen')
#print gp_curves
#print wgp_curves
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='darkBlue',
fillcol='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 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
m, v = model.predict(Xgrid)
lower = m - 2 * np.sqrt(v)
upper = m + 2 * np.sqrt(v)
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],
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)
#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.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 sausage_plot(layer, Xnew, ax):
mu, var = layer.predict(Xnew)
gpplot(Xnew, mu, mu + 2*np.sqrt(var), mu - 2*np.sqrt(var), ax=ax)
