# Dimensionality Reduction with Gaussian Processes¶

## 22nd January 2015¶

### written by Max Zwiessele, Neil D. Lawrence¶

In [29]:
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import display
import pods
import GPy
import string


For this lab, we've created a dataset digits.npy containing all handwritten digits from $0 \cdots 9$ handwritten, provided by deCampos et al. [2009]. All digits were cropped and scaled down to an appropriate format. You can retrieve the dataset as follows:

In [1]:
import urllib
#urllib.urlretrieve('http://staffwww.dcs.sheffield.ac.uk/people/J.Hensman/gpsummer/Lab3.zip', 'Lab3.zip')
import zipfile
zip = zipfile.ZipFile('Lab3.zip', 'r')
for name in zip.namelist():
zip.extract(name, '.')
from load_plotting import * # for plotting

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-1-9f66f706e90d> in <module>()
2 #urllib.urlretrieve('http://staffwww.dcs.sheffield.ac.uk/people/J.Hensman/gpsummer/Lab3.zip', 'Lab3.zip')
3 #import zipfile
----> 4 zip = zipfile.ZipFile('Lab3.zip', 'r')
5 for name in zip.namelist():
6     zip.extract(name, '.')

NameError: name 'zipfile' is not defined

We will only use some of the digits for the demonstrations in this lab class, but you can edit the code below to select different subsets of the digit data as you wish.

In [31]:
digits = np.load('digits.npy')
which = [0,1,2,6,7,9] # which digits to work on
digits = digits[which,:,:,:]
num_classes, num_samples, height, width = digits.shape
labels = np.array([[str(l)]*num_samples for l in which])


You can try to plot some sample using plt.matshow.

## Principal Component Analysis¶

Principal component analysis (PCA) finds a rotation of the observed outputs, such that the rotated principal component (PC) space maximizes the variance of the data observed, sorted from most to least important (most to least variable in the corresponding PC).

In order to apply PCA in an easy way, we have included a PCA module in pca.py. You can import the module by import <path.to.pca> (without the ending .py!). To run PCA on the digits we have to reshape (Hint: np.reshape ) digits .

• What is the right shape $n \times d$ to use?

We will call the reshaped observed outputs $\mathbf{Y}$ in the following.

In [32]:
Y = digits.reshape((digits.shape[0]*digits.shape[1],digits.shape[2]*digits.shape[3]))
Yn = Y-Y.mean()


Now let’s run PCA on the reshaped dataset $\mathbf{Y}$:

In [33]:
import pca
p = pca.PCA(Y) # create PCA class with digits dataset


The resulting plot will show the lower dimensional representation of the digits in 2 dimensions.

In [34]:
p.plot_fracs(20) # plot first 20 eigenvalue fractions
p.plot_2d(Y,labels=labels.flatten(), colors=colors)
plt.legend()

Out[34]:
<matplotlib.legend.Legend at 0x11110c990>

## Gaussian Process Latent Variable Model¶

The Gaussian Process Latent Variable Model (GP-LVM) embeds of PCA into a Gaussian process framework, where the latent inputs $\mathbf{X}$ are learnt as hyperparameters and the mapping variables $\mathbf{W}$ are integrated out. The advantage of this interpretation is it allows PCA to be generalized in a non linear way by replacing the resulting linear covariance witha non linear covariance. But first, let's see how GPLVM is equivalent to PCA using an automatic relevance determination (ARD, see e.g. Bishop et al. [2006]) linear kernel:

In [63]:
colors = ["#3FCC94", "#DD4F23", "#C6D63B", "#D44271",
"#E4A42C", "#4F9139", "#6DDA4C", "#85831F",
"#B36A29", "#CF4E4A"]
def plot_model(m, which_dims, labels):
fig = plt.figure(); ax = fig.add_subplot(111)
X = m.X[:,which_dims]
ulabs = []
for lab in labels:
if not lab in ulabs:
ulabs.append(lab)
pass
pass
for i, lab in enumerate(ulabs):
ax.scatter(*X[labels==lab].T,marker='o',color=colors[i],label=lab)
pass
pass

In [65]:
input_dim = 4 # How many latent dimensions to use
kernel = GPy.kern.Linear(input_dim, ARD=True) # ARD kernel
#kernel += GPy.kern.white(input_dim) + GPy.kern.bias(input_dim)
model = GPy.models.GPLVM(Yn, input_dim=input_dim, kernel=kernel)
model.Gaussian_noise.variance = model.Y.var()/20. # start noise is 5% of datanoise

In [64]:
model.optimize(messages=1, max_iters=1000) # optimize for 1000 iterations

KeyboardInterrupt caught, calling on_optimization_end() to round things up

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-64-a23b65fda55b> in <module>()
----> 1 model.optimize(messages=1, max_iters=1000) # optimize for 1000 iterations

/Users/neil/SheffieldML/GPy/GPy/core/gp.pyc in optimize(self, optimizer, start, **kwargs)
439         self.inference_method.on_optimization_start()
440         try:
--> 441             super(GP, self).optimize(optimizer, start, **kwargs)
442         except KeyboardInterrupt:
443             print "KeyboardInterrupt caught, calling on_optimization_end() to round things up"

/Users/neil/SheffieldML/GPy/GPy/core/model.pyc in optimize(self, optimizer, start, **kwargs)
256             opt = optimizer(start, model=self, **kwargs)
257
259
260         self.optimization_runs.append(opt)

/Users/neil/SheffieldML/GPy/GPy/inference/optimization/optimization.pyc in run(self, **kwargs)
49     def run(self, **kwargs):
50         start = dt.datetime.now()
---> 51         self.opt(**kwargs)
52         end = dt.datetime.now()
53         self.time = str(end - start)

/Users/neil/SheffieldML/GPy/GPy/inference/optimization/optimization.pyc in opt(self, f_fp, f, fp)
134
135         opt_result = optimize.fmin_l_bfgs_b(f_fp, self.x_init, iprint=iprint,
--> 136                                             maxfun=self.max_iters, **opt_dict)
137         self.x_opt = opt_result[0]
138         self.f_opt = f_fp(self.x_opt)[0]

/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/lbfgsb.pyc in fmin_l_bfgs_b(func, x0, fprime, args, approx_grad, bounds, m, factr, pgtol, epsilon, iprint, maxfun, maxiter, disp, callback)
184
185     res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds,
--> 186                            **opts)

/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/lbfgsb.pyc in _minimize_lbfgsb(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, **unknown_options)
312                 # minimization routine wants f and g at the current x
313                 # Overwrite f and g:
--> 314                 f, g = func_and_grad(x)
316             # new iteration

263     else:
--> 265             f = fun(x, *args)
266             g = jac(x, *args)
267             return f, g

/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in function_wrapper(*wrapper_args)
279     def function_wrapper(*wrapper_args):
280         ncalls[0] += 1
--> 281         return function(*(wrapper_args + args))
282
283     return ncalls, function_wrapper

/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in __call__(self, x, *args)
57     def __call__(self, x, *args):
58         self.x = numpy.asarray(x).copy()
---> 59         fg = self.fun(x, *args)
60         self.jac = fg[1]
61         return fg[0]

201         try:
--> 202             self.optimizer_array = x
204             self._fail_count = 0

/Users/neil/SheffieldML/GPy/GPy/core/parameterization/parameterized.pyc in __setattr__(self, name, val)
313             except AttributeError:
314                 pass
--> 315         object.__setattr__(self, name, val);
316
317     #===========================================================================

/Users/neil/SheffieldML/GPy/GPy/core/parameterization/parameter_core.pyc in optimizer_array(self, p)
650
651         self._optimizer_copy_transformed = False
--> 652         self.trigger_update()
653
654     def _get_params_transformed(self):

/Users/neil/SheffieldML/GPy/GPy/core/parameterization/updateable.pyc in trigger_update(self, trigger_parent)
53             #print "Warning: updates are off, updating the model will do nothing"
54             return
---> 55         self._trigger_params_changed(trigger_parent)

/Users/neil/SheffieldML/GPy/GPy/core/parameterization/parameter_core.pyc in _trigger_params_changed(self, trigger_parent)
666         """
667         [p._trigger_params_changed(trigger_parent=False) for p in self.parameters if not p.is_fixed]
--> 668         self.notify_observers(None, None if trigger_parent else -np.inf)
669
670     def _size_transformed(self):

/Users/neil/SheffieldML/GPy/GPy/core/parameterization/observable.pyc in notify_observers(self, which, min_priority)
55             which = self
56         if min_priority is None:
---> 57             [callble(self, which=which) for _, _, callble in self.observers]
58         else:
59             for p, _, callble in self.observers:

979         """
980         self._optimizer_copy_transformed = False # tells the optimizer array to update on next request
--> 981         self.parameters_changed()
982     def _pass_through_notify_observers(self, me, which=None):
983         self.notify_observers(which=which)

/Users/neil/SheffieldML/GPy/GPy/models/gplvm.pyc in parameters_changed(self)
41
42     def parameters_changed(self):
---> 43         super(GPLVM, self).parameters_changed()
45

/Users/neil/SheffieldML/GPy/GPy/core/gp.pyc in parameters_changed(self)
153             this method yourself, there may be unexpected consequences.
154         """

/Users/neil/SheffieldML/GPy/GPy/inference/latent_function_inference/exact_gaussian_inference.pyc in inference(self, kern, X, likelihood, Y, Y_metadata)
53         log_marginal =  0.5*(-Y.size * log_2_pi - Y.shape[1] * W_logdet - np.sum(alpha * YYT_factor))
54
---> 55         dL_dK = 0.5 * (tdot(alpha) - Y.shape[1] * Wi)
56

/Users/neil/SheffieldML/GPy/GPy/util/linalg.pyc in tdot(*args, **kwargs)
373 def tdot(*args, **kwargs):
374     if _blas_available:
--> 375         return tdot_blas(*args, **kwargs)
376     else:
377         return tdot_numpy(*args, **kwargs)

/Users/neil/SheffieldML/GPy/GPy/util/linalg.pyc in tdot_blas(mat, out)
364     LDC = c_int(np.max(out.strides) / 8)
365     dsyrk(byref(UPLO), byref(TRANS), byref(N), byref(K),
--> 366             byref(ALPHA), A, byref(LDA), byref(BETA), C, byref(LDC))
367
368     symmetrify(out, upper=True)

KeyboardInterrupt: 
In [66]:
model.kern.plot_ARD()
plot_model(model, model.linear.variances.argsort()[-2:], labels.flatten())
plt.legend()

Out[66]:
<matplotlib.legend.Legend at 0x1156bbc50>
In [37]:
model.X.l


Model: GPLVM
Log-likelihood: -33271.1699363
Number of Parameters: 1325

GPLVM. Value Constraint Prior Tied to
latent_mean (330, 4)
linear.variances (4,) +ve
Gaussian_noise.variance0.122065887823 +ve

As you can see the solution with a linear kernel is the same as the PCA solution with the exception of rotational changes and axis flips.

For the sake of time, the solution you see was only running for 1000 iterations, thus it might not be converged fully yet. The GP-LVM proceeds by iterative optimization of the inputs to the covariance. As we saw in the lecture earlier, for the linear covariance, these latent points can be optimized with an eigenvalue problem, but generally, for non-linear covariance functions, we are obliged to use gradient based optimization.

### Exercise 1¶

How do your linear solutions differ between PCA and GPLVM with a linear kernel? Look at the plots and also try and consider how the linear ARD parameters compare to the eigenvalues of the principal components.

### Exercise 2¶

The next step is to use a non-linear mapping between inputs $\mathbf{X}$ and ouputs $\mathbf{Y}$ by selecting the exponentiated quadratic (GPy.kern.RBF) covariance function. How does the nonlinear model differe from the linear model? Are there digits that the GPLVM with an exponentiated quadratic covariance can separate, which PCA is not able to? Try modifying the covariance function and running the model again. For example you could try a combination of the linear and exponentiated quadratic covariance function or the Matern 5/2. If you run into stability problems try initializing the covariance function parameters differently.

In [38]:
kern = GPy.kern.RBF(input_dim)


## Bayesian GPLVM¶

In GP-LVM we use a point estimate of the distribution of the input $\mathbf{X}$. This estimate is derived through maximum likelihood or through a maximum a posteriori (MAP) approach. Ideally, we would like to also estimate a distribution over the input $\mathbf{X}$. In the Bayesian GPLVM we approximate the true distribution $p(\mathbf{X}|\mathbf{Y})$ by a variational approximation $q(\mathbf{X})$ and integrate $\mathbf{X}$ out.

Approximating the posterior in this way allows us to optimize a lower bound on the marginal likelihood. Handling the uncertainty in a principled way allows the model to make an assessment of whether a particular latent dimension is required, or the variation is better explained by noise. This allows the algorithm to switch off latent dimensions. The switching off can take some time though, so below in Section 6 we provide a pre-learnt module, but to complete section 6 you'll need to be working in the IPython console instead of the notebook.

For the moment we'll run a short experiment applying the Bayesian GP-LVM with an exponentiated quadratic covariance function.

In [68]:
# Model optimization
input_dim = 5 # How many latent dimensions to use
kern = GPy.kern.RBF(input_dim,ARD=True) # ARD kernel
model = GPy.models.BayesianGPLVM(Yn, input_dim=input_dim, kernel=kern, num_inducing=25)

# initialize noise as 1% of variance in data
model.Gaussian_noise.variance = model.Y.var()/100.

In [39]:
model.optimize('scg', messages=1, max_iters=1000)

clang: warning: argument unused during compilation: '-fopenmp'
In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1093.cpp:11:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array.h:26:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array-impl.h:37:
/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: warning: '&&' within '||' [-Wlogical-op-parentheses]
return ((first_ < last_) && (stride_ == 1) || (first_ == last_));
~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~ ~~
/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: note: place parentheses around the '&&' expression to silence this warning
return ((first_ < last_) && (stride_ == 1) || (first_ == last_));
^
(                                 )
In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1093.cpp:23:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:4:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1761:
/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: "Using deprecated NumPy API, disable it by "          "#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-W#warnings]
#warning "Using deprecated NumPy API, disable it by " \
^
#include <omp.h>
^
2 warnings and 1 error generated.

Weave compilation failed. Falling back to (slower) numpy implementation

I      F              Scale          |g|
0009   3.436208e+04   1.525879e-05   6.324972e+07
0015   2.942537e+04   3.725290e-09   2.794171e+06
0021   2.881152e+04   9.094947e-13   4.659488e+05
0059   2.830256e+04   4.503600e+00   1.301392e+05
0072   2.698886e+04   2.684355e-07   7.800661e+04
0201   2.409968e+04   1.000000e-15   2.942905e+04
0443   2.263323e+04   1.000000e-15   9.618643e+03
0710   2.248227e+04   1.000000e-15   9.640829e+02
1000   2.239184e+04   1.000000e-15   5.204208e+03
maxiter exceeded

In [69]:
def plot_model(m, which_dims, labels):
fig = plt.figure(); ax = fig.add_subplot(111)
X = m.X[:,which_dims]
ulabs = []
for lab in labels:
if not lab in ulabs:
ulabs.append(lab)
pass
pass
for i, lab in enumerate(ulabs):
ax.scatter(*X.mean[labels==lab].T,marker='o',color=colors[i],label=lab)
pass
pass

In [70]:
# Plotting the model
plot_model(model, model.rbf.lengthscale.argsort()[:2], labels.flatten())
plt.legend()
model.kern.plot_ARD()
# Saving the model:
model.pickle('bgplvm_rbf.pickle')


Because we are now also considering the uncertainty in the model, this optimization can take some time. However, you are free to interrupt the optimization at any point selecting Kernel->Interupt from the notepad menu. This will leave you with the model, m in the current state and you can plot and look into the model parameters.

### Exercise 3¶

How does the Bayesian GP-LVM compare with the standard model?

### Preoptimized Model¶

A good way of working with latent variable models is to interact with the latent dimensions, generating data. This is a little bit tricky in the notebook, so below in section 6 we provide code for setting up an interactive demo in the standard IPython shell. If you are working on your own machine you can try this now. Otherwise continue with section 5.

## Multiview Learning: Manifold Relevance Determination¶

In Manifold Relevance Determination we try to find one latent space, common for $K$ observed output sets (modalities) $\{\mathbf{Y}_{k}\}_{k=1}^{K}$. Each modality is associated with a separate set of ARD parameters so that it switches off different parts of the whole latent space and, therefore, $\mathbf{X}$ is softly segmented into parts that are private to some, or shared for all modalities. Can you explain what happens in the following example?

Again, you can stop the optimizer at any point and explore the result obtained with the so far training:

In [19]:
model = GPy.examples.dimensionality_reduction.mrd_simulation(optimize = False, plot=False)
model.optimize(messages=True, max_iters=3e3, optimizer = 'bfgs')

Running L-BFGS-B (Scipy implementation) Code:
secs      i        f              |g|
0.083  000001   1.934041e+04   1.982470e+08
0.41  000007   6.000690e+03   1.657623e+04
0.79  000013   5.259096e+03   4.557697e+04
2  000038   4.742348e+03   1.456837e+03
3  000062   4.565038e+03   1.066674e+03
5.2  000105   4.480234e+03   1.104947e+02
6.1  000132   4.474337e+03   1.238711e+01
8.5  000190   4.473657e+03   2.018479e-01
15  000339   4.473331e+03   1.432108e-02
15  000347   4.473331e+03   3.241356e-02
Optimization finished in 15.147 Seconds


In [18]:
_ = model.X.plot()
model.plot_scales()

Out[18]:
[<matplotlib.axes._subplots.AxesSubplot at 0x111e186d0>,
<matplotlib.axes._subplots.AxesSubplot at 0x111ea3dd0>,
<matplotlib.axes._subplots.AxesSubplot at 0x111eb0210>]

### Exercise 4¶

The simulated data set is a sinusoid and a double frequency sinusoid function as input signals.

Which signal is shared across the three datasets? Which are private? Are there signals shared only between two of the three datasets?

# Exercise 4

## Interactive Demo: For Use Outside the Notepad¶

The module below loads a pre-optimized Bayesian GPLVM model (like the one you just trained) and allows you to interact with the latent space. Three interactive figures pop up: the latent space, the ARD scales and a sample in the output space (corresponding to the current selected latent point of the other figure). You can sample with the mouse from the latent space and obtain samples in the output space. You can select different latent dimensions to vary by clicking on the corresponding scales with the left and right mouse buttons. This will also cause the latent space to be projected on the selected latent dimensions in the other figure.

In [11]:
import urllib2, os, sys

model_path =  'digit_bgplvm_demo.pickle' # local name for model file
status = ""

re = 0
if len(sys.argv) == 2:
re = 1

url = 'http://staffwww.dcs.sheffield.ac.uk/people/M.Zwiessele/gpss/lab3/digit_bgplvm_demo.pickle'
with open(model_path, 'wb') as f:
u = urllib2.urlopen(url)
meta = u.info()

file_size_dl = 0
block_sz = 8192
while True:
if not buff:
break
file_size_dl += len(buff)
f.write(buff)
sys.stdout.write(" "*(len(status)) + "\r")
status = r"{:7.3f}/{:.3f}MB [{: >7.2%}]".format(file_size_dl/(1.*1e6), file_size/(1.*1e6), float(file_size_dl)/file_size)
sys.stdout.write(status)
sys.stdout.flush()
sys.stdout.write(" "*(len(status)) + "\r")
print status
else:

Downloading: digit_bgplvm_demo.pickle
1.600/1.600MB [100.00%]

In [12]:
import cPickle as pickle
with open('./digit_bgplvm_demo.pickle', 'rb') as f:

clang: warning: argument unused during compilation: '-fopenmp'
In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1094.cpp:11:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array.h:26:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array-impl.h:37:
/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: warning: '&&' within '||' [-Wlogical-op-parentheses]
return ((first_ < last_) && (stride_ == 1) || (first_ == last_));
~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~ ~~
/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: note: place parentheses around the '&&' expression to silence this warning
return ((first_ < last_) && (stride_ == 1) || (first_ == last_));
^
(                                 )
In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1094.cpp:23:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:4:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:
In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1761:
/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: "Using deprecated NumPy API, disable it by "          "#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-W#warnings]
#warning "Using deprecated NumPy API, disable it by " \
^
#include <omp.h>
^
2 warnings and 1 error generated.

Weave compilation failed. Falling back to (slower) numpy implementation



Prepare for plotting of this model. If you run on a webserver the interactive plotting will not work. Thus, you can skip to the next codeblock and run it on your own machine, later.

In [16]:
fig = plt.figure('Latent Space & Scales', figsize=(16,6))

fig_out = plt.figure('Output', figsize=(1,1))

data_show = GPy.plotting.matplot_dep.visualize.image_show(model.Y[0:1, :], dimensions=(16, 16), transpose=0, invert=0, scale=False, axes=ax_image)
lvm_visualizer = GPy.plotting.matplot_dep.visualize.lvm_dimselect(model.X.mean.copy(), model, data_show, ax_latent, ax_scales, labels=labels.flatten())

    Index    |      mean       |  Constraint  |   Prior   |  Tied to
[0 0]    |     -1.2875148  |              |           |    N/A
[0 1]    |    -0.23449731  |              |           |    N/A
[0 2]    |    0.021141743  |              |           |    N/A
[0 3]    |     -1.1064083  |              |           |    N/A
[0 4]    |     -1.0419867  |              |           |    N/A
[1 0]    |     -1.0494874  |              |           |    N/A
[1 1]    |    -0.19597324  |              |           |    N/A
[1 2]    |     0.11431049  |              |           |    N/A
[1 3]    |     -0.7168742  |              |           |    N/A
[1 4]    |     -1.1353298  |              |           |    N/A
[2 0]    |     -1.7831573  |              |           |    N/A
[2 1]    |    -0.39102269  |              |           |    N/A
[2 2]    |      1.4732891  |              |           |    N/A
[2 3]    |    0.088935034  |              |           |    N/A
[2 4]    |    -0.76806973  |              |           |    N/A
[3 0]    |    -0.99378649  |              |           |    N/A
[3 1]    |     0.10770137  |              |           |    N/A
[3 2]    |     0.13317655  |              |           |    N/A
[3 3]    |     0.97261429  |              |           |    N/A
[3 4]    |    -0.98947013  |              |           |    N/A
[4 0]    |     -1.4105533  |              |           |    N/A
[4 1]    |   -0.025334191  |              |           |    N/A
[4 2]    |    -0.17219684  |              |           |    N/A
[4 3]    |      1.0193768  |              |           |    N/A
[4 4]    |     -1.4817101  |              |           |    N/A
[5 0]    |    -0.38133961  |              |           |    N/A
[5 1]    |     0.10082104  |              |           |    N/A
[5 2]    |    -0.74633462  |              |           |    N/A
[5 3]    |    -0.43987256  |              |           |    N/A
[5 4]    |     -1.2530002  |              |           |    N/A
[6 0]    |    -0.29501522  |              |           |    N/A
[6 1]    |    0.079535029  |              |           |    N/A
[6 2]    |    -0.98985724  |              |           |    N/A
[6 3]    |       0.938468  |              |           |    N/A
[6 4]    |     -1.4503978  |              |           |    N/A
[7 0]    |     -1.0881307  |              |           |    N/A
[7 1]    |     0.16567686  |              |           |    N/A
[7 2]    |    0.049003439  |              |           |    N/A
[7 3]    |     0.60245844  |              |           |    N/A
[7 4]    |     -1.2225138  |              |           |    N/A
[8 0]    |     -1.7947299  |              |           |    N/A
[8 1]    |    -0.39587198  |              |           |    N/A
[8 2]    |      1.4642626  |              |           |    N/A
[8 3]    |     0.19817634  |              |           |    N/A
[8 4]    |    -0.82434553  |              |           |    N/A
[9 0]    |    -0.86013063  |              |           |    N/A
[9 1]    |    0.080626498  |              |           |    N/A
[9 2]    |   -0.062338038  |              |           |    N/A
[9 3]    |      0.3047738  |              |           |    N/A
[9 4]    |     -1.3470944  |              |           |    N/A
[10  0]   |    -0.45013494  |              |           |    N/A
[10  1]   |     0.13939767  |              |           |    N/A
[10  2]   |    -0.41494957  |              |           |    N/A
[10  3]   |     0.40539967  |              |           |    N/A
[10  4]   |     -1.2524523  |              |           |    N/A
[11  0]   |     -1.7297853  |              |           |    N/A
[11  1]   |    -0.12058588  |              |           |    N/A
[11  2]   |      1.0075511  |              |           |    N/A
[11  3]   |     0.99835007  |              |           |    N/A
[11  4]   |     -1.0629356  |              |           |    N/A
[12  0]   |    -0.69427579  |              |           |    N/A
[12  1]   |      0.2251535  |              |           |    N/A
[12  2]   |    -0.11988893  |              |           |    N/A
[12  3]   |     0.99866892  |              |           |    N/A
[12  4]   |     -1.3175047  |              |           |    N/A
[13  0]   |     -1.3625222  |              |           |    N/A
[13  1]   |    -0.31724194  |              |           |    N/A
[13  2]   |      1.5702513  |              |           |    N/A
[13  3]   |    -0.84288357  |              |           |    N/A
[13  4]   |    -0.51170594  |              |           |    N/A
[14  0]   |     -1.6274691  |              |           |    N/A
[14  1]   |    -0.13652015  |              |           |    N/A
[14  2]   |     0.50835469  |              |           |    N/A
[14  3]   |      1.1190293  |              |           |    N/A
[14  4]   |     -1.0127023  |              |           |    N/A
[15  0]   |    -0.78131366  |              |           |    N/A
[15  1]   |     0.11813936  |              |           |    N/A
[15  2]   |     0.02529459  |              |           |    N/A
[15  3]   |     0.13395947  |              |           |    N/A
[15  4]   |      -1.323848  |              |           |    N/A
[16  0]   |     -1.5610036  |              |           |    N/A
[16  1]   |    -0.36893836  |              |           |    N/A
[16  2]   |      1.0336005  |              |           |    N/A
[16  3]   |    -0.34261046  |              |           |    N/A
[16  4]   |    -0.83944034  |              |           |    N/A
[17  0]   |     -1.3114442  |              |           |    N/A
[17  1]   |     0.13900899  |              |           |    N/A
[17  2]   |    -0.11087409  |              |           |    N/A
[17  3]   |      1.6914932  |              |           |    N/A
[17  4]   |     -1.1594638  |              |           |    N/A
[18  0]   |     -1.4202316  |              |           |    N/A
[18  1]   |   -0.037367175  |              |           |    N/A
[18  2]   |   -0.078721342  |              |           |    N/A
[18  3]   |     0.56729146  |              |           |    N/A
[18  4]   |     -1.3533693  |              |           |    N/A
[19  0]   |    -0.67668244  |              |           |    N/A
[19  1]   |     0.22949184  |              |           |    N/A
[19  2]   |    -0.43979079  |              |           |    N/A
[19  3]   |     0.94848926  |              |           |    N/A
[19  4]   |     -1.5314685  |              |           |    N/A
[20  0]   |     -1.2607565  |              |           |    N/A
[20  1]   |    0.095709345  |              |           |    N/A
[20  2]   |     0.36248257  |              |           |    N/A
[20  3]   |     0.33347008  |              |           |    N/A
[20  4]   |     -1.1327955  |              |           |    N/A
[21  0]   |    -0.77926076  |              |           |    N/A
[21  1]   |    0.095992814  |              |           |    N/A
[21  2]   |    0.052352407  |              |           |    N/A
[21  3]   |    -0.38729308  |              |           |    N/A
[21  4]   |     -1.2612454  |              |           |    N/A
[22  0]   |     -1.5388033  |              |           |    N/A
[22  1]   |     -0.2602525  |              |           |    N/A
[22  2]   |      1.0848588  |              |           |    N/A
[22  3]   |     0.24956974  |              |           |    N/A
[22  4]   |    -0.79132732  |              |           |    N/A
[23  0]   |      -1.380618  |              |           |    N/A
[23  1]   |  0.00092159901  |              |           |    N/A
[23  2]   |    0.067600903  |              |           |    N/A
[23  3]   |     0.97153395  |              |           |    N/A
[23  4]   |     -1.3665104  |              |           |    N/A
[24  0]   |     -1.6871887  |              |           |    N/A
[24  1]   |    -0.18357747  |              |           |    N/A
[24  2]   |     0.59648334  |              |           |    N/A
[24  3]   |     0.87015877  |              |           |    N/A
[24  4]   |     -1.1813841  |              |           |    N/A
[25  0]   |     -1.4416102  |              |           |    N/A
[25  1]   |    -0.19167098  |              |           |    N/A
[25  2]   |     0.49483012  |              |           |    N/A
[25  3]   |      0.5938973  |              |           |    N/A
[25  4]   |     -1.0284283  |              |           |    N/A
[26  0]   |     -1.3719645  |              |           |    N/A
[26  1]   |   -0.069520929  |              |           |    N/A
[26  2]   |   0.0082202872  |              |           |    N/A
[26  3]   |     0.97835069  |              |           |    N/A
[26  4]   |      -1.125555  |              |           |    N/A
[27  0]   |     -1.1562362  |              |           |    N/A
[27  1]   |   -0.010856099  |              |           |    N/A
[27  2]   |     0.27798262  |              |           |    N/A
[27  3]   |     0.68472056  |              |           |    N/A
[27  4]   |     -1.1103574  |              |           |    N/A
[28  0]   |    -0.80741648  |              |           |    N/A
[28  1]   |    0.043960451  |              |           |    N/A
[28  2]   |   -0.040076777  |              |           |    N/A
[28  3]   |    -0.11056082  |              |           |    N/A
[28  4]   |       -1.42242  |              |           |    N/A
[29  0]   |     -1.2452388  |              |           |    N/A
[29  1]   |    0.070611476  |              |           |    N/A
[29  2]   |     0.62373232  |              |           |    N/A
[29  3]   |     0.89917651  |              |           |    N/A
[29  4]   |    -0.97164992  |              |           |    N/A
[30  0]   |     -1.2044757  |              |           |    N/A
[30  1]   |   0.0027143916  |              |           |    N/A
[30  2]   |      1.1226677  |              |           |    N/A
[30  3]   |    0.030847422  |              |           |    N/A
[30  4]   |     -0.7024259  |              |           |    N/A
[31  0]   |     -1.0785856  |              |           |    N/A
[31  1]   |     0.17494202  |              |           |    N/A
[31  2]   |    -0.44027603  |              |           |    N/A
[31  3]   |      1.8718791  |              |           |    N/A
[31  4]   |     -1.3444748  |              |           |    N/A
[32  0]   |      -1.339818  |              |           |    N/A
[32  1]   |   -0.029276441  |              |           |    N/A
[32  2]   |     0.21862218  |              |           |    N/A
[32  3]   |     0.19186776  |              |           |    N/A
[32  4]   |     -1.1785243  |              |           |    N/A
[33  0]   |    -0.66007498  |              |           |    N/A
[33  1]   |     0.16092675  |              |           |    N/A
[33  2]   |    -0.26940977  |              |           |    N/A
[33  3]   |    0.080664161  |              |           |    N/A
[33  4]   |     -1.4844387  |              |           |    N/A
[34  0]   |     -0.7411235  |              |           |    N/A
[34  1]   |     0.10701081  |              |           |    N/A
[34  2]   |     0.21181226  |              |           |    N/A
[34  3]   |    -0.33401034  |              |           |    N/A
[34  4]   |     -1.2008109  |              |           |    N/A
[35  0]   |     -1.0720687  |              |           |    N/A
[35  1]   |    -0.43894886  |              |           |    N/A
[35  2]   |     0.62101063  |              |           |    N/A
[35  3]   |       -2.08453  |              |           |    N/A
[35  4]   |    -0.61274989  |              |           |    N/A
[36  0]   |      -1.257925  |              |           |    N/A
[36  1]   |    -0.41433484  |              |           |    N/A
[36  2]   |     0.69718163  |              |           |    N/A
[36  3]   |      -1.750593  |              |           |    N/A
[36  4]   |     -0.7589382  |              |           |    N/A
[37  0]   |      -1.691719  |              |           |    N/A
[37  1]   |    -0.38452491  |              |           |    N/A
[37  2]   |      1.0164139  |              |           |    N/A
[37  3]   |    -0.22913552  |              |           |    N/A
[37  4]   |    -0.94314015  |              |           |    N/A
[38  0]   |    -0.48402784  |              |           |    N/A
[38  1]   |     0.20973347  |              |           |    N/A
[38  2]   |    -0.57653038  |              |           |    N/A
[38  3]   |     0.97915344  |              |           |    N/A
[38  4]   |     -1.5523214  |              |           |    N/A
[39  0]   |     -1.1657703  |              |           |    N/A
[39  1]   |     0.01245768  |              |           |    N/A
[39  2]   |     -0.2985338  |              |           |    N/A
[39  3]   |     0.61470735  |              |           |    N/A
[39  4]   |     -1.2926483  |              |           |    N/A
[40  0]   |     -1.7180017  |              |           |    N/A
[40  1]   |    -0.26432964  |              |           |    N/A
[40  2]   |     0.86554006  |              |           |    N/A
[40  3]   |     0.88011877  |              |           |    N/A
[40  4]   |     -1.1076494  |              |           |    N/A
[41  0]   |     -1.4842749  |              |           |    N/A
[41  1]   |   -0.047085545  |              |           |    N/A
[41  2]   |     0.23109379  |              |           |    N/A
[41  3]   |       1.298264  |              |           |    N/A
[41  4]   |     -1.2305949  |              |           |    N/A
[42  0]   |     -1.7702539  |              |           |    N/A
[42  1]   |    -0.30008294  |              |           |    N/A
[42  2]   |       1.208562  |              |           |    N/A
[42  3]   |      1.0288659  |              |           |    N/A
[42  4]   |    -0.92736345  |              |           |    N/A
[43  0]   |     -1.2523001  |              |           |    N/A
[43  1]   |    -0.36012216  |              |           |    N/A
[43  2]   |     0.98669178  |              |           |    N/A
[43  3]   |     -1.5109242  |              |           |    N/A
[43  4]   |    -0.77268998  |              |           |    N/A
[44  0]   |     -1.5567122  |              |           |    N/A
[44  1]   |     -0.3422431  |              |           |    N/A
[44  2]   |     0.47043188  |              |           |    N/A
[44  3]   |    -0.67521062  |              |           |    N/A
[44  4]   |     -1.1061464  |              |           |    N/A
[45  0]   |    -0.82814275  |              |           |    N/A
[45  1]   |      0.1263314  |              |           |    N/A
[45  2]   |    -0.30121029  |              |           |    N/A
[45  3]   |      1.9287828  |              |           |    N/A
[45  4]   |     -1.4377055  |              |           |    N/A
[46  0]   |     -1.3151985  |              |           |    N/A
[46  1]   |     0.04496179  |              |           |    N/A
[46  2]   |    -0.64682224  |              |           |    N/A
[46  3]   |      0.3180119  |              |           |    N/A
[46  4]   |     -1.3864842  |              |           |    N/A
[47  0]   |     -1.1570866  |              |           |    N/A
[47  1]   |    -0.43403609  |              |           |    N/A
[47  2]   |     0.93971194  |              |           |    N/A
[47  3]   |     -1.8019281  |              |           |    N/A
[47  4]   |    -0.63403486  |              |           |    N/A
[48  0]   |    -0.93078968  |              |           |    N/A
[48  1]   |      0.2405842  |              |           |    N/A
[48  2]   |     0.37438759  |              |           |    N/A
[48  3]   |     0.85875249  |              |           |    N/A
[48  4]   |     -1.1511917  |              |           |    N/A
[49  0]   |      -1.091084  |              |           |    N/A
[49  1]   |    -0.07689441  |              |           |    N/A
[49  2]   |     0.83655163  |              |           |    N/A
[49  3]   |    -0.70292959  |              |           |    N/A
[49  4]   |    -0.71648236  |              |           |    N/A
[50  0]   |     -1.2098996  |              |           |    N/A
[50  1]   |   -0.074390407  |              |           |    N/A
[50  2]   |      0.1229143  |              |           |    N/A
[50  3]   |   -0.030406697  |              |           |    N/A
[50  4]   |     -1.0544861  |              |           |    N/A
[51  0]   |     -1.2287694  |              |           |    N/A
[51  1]   |   -0.017926632  |              |           |    N/A
[51  2]   |    -0.13127978  |              |           |    N/A
[51  3]   |      1.3421873  |              |           |    N/A
[51  4]   |      -1.275728  |              |           |    N/A
[52  0]   |     -1.1248658  |              |           |    N/A
[52  1]   |    -0.30373428  |              |           |    N/A
[52  2]   |     0.60357067  |              |           |    N/A
[52  3]   |     -1.8015827  |              |           |    N/A
[52  4]   |    -0.69942565  |              |           |    N/A
[53  0]   |     -1.1406003  |              |           |    N/A
[53  1]   |    -0.10054461  |              |           |    N/A
[53  2]   |     0.55801746  |              |           |    N/A
[53  3]   |     -0.7609749  |              |           |    N/A
[53  4]   |    -0.87073706  |              |           |    N/A
[54  0]   |     -1.2483793  |              |           |    N/A
[54  1]   |    -0.29369503  |              |           |    N/A
[54  2]   |     0.80916549  |              |           |    N/A
[54  3]   |      -1.380307  |              |           |    N/A
[54  4]   |    -0.59901189  |              |           |    N/A
[55  0]   |     0.47127449  |              |           |    N/A
[55  1]   |     0.44097014  |              |           |    N/A
[55  2]   |    -0.71305046  |              |           |    N/A
[55  3]   |    -0.57237539  |              |           |    N/A
[55  4]   |      0.5691448  |              |           |    N/A
[56  0]   |     0.23502688  |              |           |    N/A
[56  1]   |    -0.75161408  |              |           |    N/A
[56  2]   |   -0.024346393  |              |           |    N/A
[56  3]   |     0.29645644  |              |           |    N/A
[56  4]   |       1.501118  |              |           |    N/A
[57  0]   |     0.32391131  |              |           |    N/A
[57  1]   |      2.0866579  |              |           |    N/A
[57  2]   |      0.8888028  |              |           |    N/A
[57  3]   |      1.2641514  |              |           |    N/A
[57  4]   |      1.5443565  |              |           |    N/A
[58  0]   |     0.34926779  |              |           |    N/A
[58  1]   |     0.52400093  |              |           |    N/A
[58  2]   |     -1.0919157  |              |           |    N/A
[58  3]   |      2.0531596  |              |           |    N/A
[58  4]   |    -0.79859985  |              |           |    N/A
[59  0]   |      0.1783122  |              |           |    N/A
[59  1]   |     0.65125809  |              |           |    N/A
[59  2]   |     -1.3427128  |              |           |    N/A
[59  3]   |     0.50745642  |              |           |    N/A
[59  4]   |    -0.74886499  |              |           |    N/A
[60  0]   |     0.30930271  |              |           |    N/A
[60  1]   |     0.33367582  |              |           |    N/A
[60  2]   |     -1.1307539  |              |           |    N/A
[60  3]   |     -1.1770539  |              |           |    N/A
[60  4]   |    -0.21640105  |              |           |    N/A
[61  0]   |     0.35497426  |              |           |    N/A
[61  1]   |      1.7961725  |              |           |    N/A
[61  2]   |     0.96866591  |              |           |    N/A
[61  3]   |      1.8596859  |              |           |    N/A
[61  4]   |      1.0676581  |              |           |    N/A
[62  0]   |     0.69904661  |              |           |    N/A
[62  1]   |     0.89232884  |              |           |    N/A
[62  2]   |     0.55699177  |              |           |    N/A
[62  3]   |     0.84744524  |              |           |    N/A
[62  4]   |      1.4071842  |              |           |    N/A
[63  0]   |     0.64662876  |              |           |    N/A
[63  1]   |     -1.1013111  |              |           |    N/A
[63  2]   |       0.176817  |              |           |    N/A
[63  3]   |    -0.20488164  |              |           |    N/A
[63  4]   |     0.87095259  |              |           |    N/A
[64  0]   |     0.40461498  |              |           |    N/A
[64  1]   |    -0.33138652  |              |           |    N/A
[64  2]   |    -0.59040029  |              |           |    N/A
[64  3]   |      1.4775862  |              |           |    N/A
[64  4]   |    -0.32818954  |              |           |    N/A
[65  0]   |     0.14301783  |              |           |    N/A
[65  1]   |     0.48440558  |              |           |    N/A
[65  2]   |     -1.2795281  |              |           |    N/A
[65  3]   |      1.3089612  |              |           |    N/A
[65  4]   |    -0.95679585  |              |           |    N/A
[66  0]   |     0.28804939  |              |           |    N/A
[66  1]   |    -0.10722456  |              |           |    N/A
[66  2]   |    -0.83717731  |              |           |    N/A
[66  3]   |      2.3903941  |              |           |    N/A
[66  4]   |    -0.48470842  |              |           |    N/A
[67  0]   |     0.66484543  |              |           |    N/A
[67  1]   |     0.61867752  |              |           |    N/A
[67  2]   |     0.78915892  |              |           |    N/A
[67  3]   |       1.009124  |              |           |    N/A
[67  4]   |     0.94101762  |              |           |    N/A
[68  0]   |     0.76546908  |              |           |    N/A
[68  1]   |      0.7348515  |              |           |    N/A
[68  2]   |      1.6230274  |              |           |    N/A
[68  3]   |    -0.35000098  |              |           |    N/A
[68  4]   |      1.5872603  |              |           |    N/A
[69  0]   |     0.39986474  |              |           |    N/A
[69  1]   |    -0.84876137  |              |           |    N/A
[69  2]   |     0.18037433  |              |           |    N/A
[69  3]   |    -0.36866049  |              |           |    N/A
[69  4]   |      1.0524382  |              |           |    N/A
[70  0]   |      0.3193521  |              |           |    N/A
[70  1]   |     0.55492875  |              |           |    N/A
[70  2]   |      -1.121578  |              |           |    N/A
[70  3]   |     -1.4054942  |              |           |    N/A
[70  4]   |    -0.19546472  |              |           |    N/A
[71  0]   |     0.62139897  |              |           |    N/A
[71  1]   |     0.67417929  |              |           |    N/A
[71  2]   |      1.5484394  |              |           |    N/A
[71  3]   |    0.046509942  |              |           |    N/A
[71  4]   |      1.3300257  |              |           |    N/A
[72  0]   |    0.014221708  |              |           |    N/A
[72  1]   |     -0.7191417  |              |           |    N/A
[72  2]   |    -0.56084194  |              |           |    N/A
[72  3]   |     0.15421407  |              |           |    N/A
[72  4]   |      1.6084191  |              |           |    N/A
[73  0]   |     0.22743708  |              |           |    N/A
[73  1]   |     -1.0731867  |              |           |    N/A
[73  2]   |     0.71892311  |              |           |    N/A
[73  3]   |     0.78686692  |              |           |    N/A
[73  4]   |      1.6685559  |              |           |    N/A
[74  0]   |     0.34285046  |              |           |    N/A
[74  1]   |     -0.9479463  |              |           |    N/A
[74  2]   |     0.70244502  |              |           |    N/A
[74  3]   |   -0.017096127  |              |           |    N/A
[74  4]   |       1.574107  |              |           |    N/A
[75  0]   |     0.49115202  |              |           |    N/A
[75  1]   |      1.3836399  |              |           |    N/A
[75  2]   |     0.48924073  |              |           |    N/A
[75  3]   |      1.7686391  |              |           |    N/A
[75  4]   |      1.6638412  |              |           |    N/A
[76  0]   |     0.29418665  |              |           |    N/A
[76  1]   |     0.61977005  |              |           |    N/A
[76  2]   |     -1.0791473  |              |           |    N/A
[76  3]   |      1.8883507  |              |           |    N/A
[76  4]   |    -0.79267216  |              |           |    N/A
[77  0]   |     0.66824688  |              |           |    N/A
[77  1]   |      1.2591661  |              |           |    N/A
[77  2]   |      1.2743335  |              |           |    N/A
[77  3]   |    0.080974739  |              |           |    N/A
[77  4]   |      2.0750742  |              |           |    N/A
[78  0]   |     0.21734525  |              |           |    N/A
[78  1]   |    0.012292683  |              |           |    N/A
[78  2]   |    -0.98162627  |              |           |    N/A
[78  3]   |      1.2680324  |              |           |    N/A
[78  4]   |    -0.57942121  |              |           |    N/A
[79  0]   |     0.54292542  |              |           |    N/A
[79  1]   |      1.4933795  |              |           |    N/A
[79  2]   |      1.6678868  |              |           |    N/A
[79  3]   |      0.3779169  |              |           |    N/A
[79  4]   |      2.2735676  |              |           |    N/A
[80  0]   |     0.34663959  |              |           |    N/A
[80  1]   |    -0.42335997  |              |           |    N/A
[80  2]   |    0.088956747  |              |           |    N/A
[80  3]   |      1.9759399  |              |           |    N/A
[80  4]   |    -0.36239259  |              |           |    N/A
[81  0]   |     0.49328372  |              |           |    N/A
[81  1]   |  -0.0057312456  |              |           |    N/A
[81  2]   |    -0.74534807  |              |           |    N/A
[81  3]   |      2.5564256  |              |           |    N/A
[81  4]   |    -0.60886628  |              |           |    N/A
[82  0]   |     0.12032314  |              |           |    N/A
[82  1]   |     0.20507937  |              |           |    N/A
[82  2]   |     -1.1895574  |              |           |    N/A
[82  3]   |     0.19176388  |              |           |    N/A
[82  4]   |    -0.88913081  |              |           |    N/A
[83  0]   |    0.098795832  |              |           |    N/A
[83  1]   |   -0.031157082  |              |           |    N/A
[83  2]   |     -1.5252481  |              |           |    N/A
[83  3]   |    -0.52934446  |              |           |    N/A
[83  4]   |    0.095282193  |              |           |    N/A
[84  0]   |       0.064567  |              |           |    N/A
[84  1]   |      0.1772639  |              |           |    N/A
[84  2]   |     -1.2566249  |              |           |    N/A
[84  3]   |      1.4085925  |              |           |    N/A
[84  4]   |    -0.98607287  |              |           |    N/A
[85  0]   |     0.14419197  |              |           |    N/A
[85  1]   |    0.023173152  |              |           |    N/A
[85  2]   |      -1.126651  |              |           |    N/A
[85  3]   |      0.8171482  |              |           |    N/A
[85  4]   |    -0.71304219  |              |           |    N/A
[86  0]   |     0.33766916  |              |           |    N/A
[86  1]   |    -0.32637456  |              |           |    N/A
[86  2]   |    -0.34118122  |              |           |    N/A
[86  3]   |      2.1873517  |              |           |    N/A
[86  4]   |    -0.58550279  |              |           |    N/A
[87  0]   |     0.11864693  |              |           |    N/A
[87  1]   |     -1.1308406  |              |           |    N/A
[87  2]   |     0.80490553  |              |           |    N/A
[87  3]   |      1.3065016  |              |           |    N/A
[87  4]   |      1.2415789  |              |           |    N/A
[88  0]   |      0.6206257  |              |           |    N/A
[88  1]   |      1.5260205  |              |           |    N/A
[88  2]   |     -1.3016134  |              |           |    N/A
[88  3]   |      1.8501646  |              |           |    N/A
[88  4]   |      1.7888944  |              |           |    N/A
[89  0]   |    0.088389646  |              |           |    N/A
[89  1]   |     0.41241725  |              |           |    N/A
[89  2]   |     -1.3657001  |              |           |    N/A
[89  3]   |    -0.30036163  |              |           |    N/A
[89  4]   |    -0.73955886  |              |           |    N/A
[90  0]   |     0.31324873  |              |           |    N/A
[90  1]   |     0.54686801  |              |           |    N/A
[90  2]   |    -0.94545476  |              |           |    N/A
[90  3]   |     -1.1691832  |              |           |    N/A
[90  4]   |    -0.18659468  |              |           |    N/A
[91  0]   |    0.089904508  |              |           |    N/A
[91  1]   |     -1.2962176  |              |           |    N/A
[91  2]   |      1.2366114  |              |           |    N/A
[91  3]   |    -0.62887638  |              |           |    N/A
[91  4]   |      1.5020548  |              |           |    N/A
[92  0]   |     0.70239495  |              |           |    N/A
[92  1]   |      1.3296561  |              |           |    N/A
[92  2]   |      1.0020011  |              |           |    N/A
[92  3]   |    -0.22597158  |              |           |    N/A
[92  4]   |      2.4922033  |              |           |    N/A
[93  0]   |     0.25967301  |              |           |    N/A
[93  1]   |      2.0466967  |              |           |    N/A
[93  2]   |     0.35612774  |              |           |    N/A
[93  3]   |      2.1684332  |              |           |    N/A
[93  4]   |      1.3487448  |              |           |    N/A
[94  0]   |     0.14733716  |              |           |    N/A
[94  1]   |     0.49794515  |              |           |    N/A
[94  2]   |     -1.2379763  |              |           |    N/A
[94  3]   |      1.0790159  |              |           |    N/A
[94  4]   |    -0.98291793  |              |           |    N/A
[95  0]   |      0.6436347  |              |           |    N/A
[95  1]   |      1.3365236  |              |           |    N/A
[95  2]   |     0.98410919  |              |           |    N/A
[95  3]   |     0.63195561  |              |           |    N/A
[95  4]   |      2.2911135  |              |           |    N/A
[96  0]   |     0.52464684  |              |           |    N/A
[96  1]   |      1.5616369  |              |           |    N/A
[96  2]   |      1.2039617  |              |           |    N/A
[96  3]   |      1.0681428  |              |           |    N/A
[96  4]   |      2.0038873  |              |           |    N/A
[97  0]   |     0.61876028  |              |           |    N/A
[97  1]   |      1.6776997  |              |           |    N/A
[97  2]   |     0.96884553  |              |           |    N/A
[97  3]   |     0.19170397  |              |           |    N/A
[97  4]   |      2.4967786  |              |           |    N/A
[98  0]   |     0.52814821  |              |           |    N/A
[98  1]   |     0.88416714  |              |           |    N/A
[98  2]   |     -1.2387021  |              |           |    N/A
[98  3]   |     -1.2417761  |              |           |    N/A
[98  4]   |     0.69857482  |              |           |    N/A
[99  0]   |     0.38543761  |              |           |    N/A
[99  1]   |      1.6785971  |              |           |    N/A
[99  2]   |       1.069482  |              |           |    N/A
[99  3]   |      1.7658319  |              |           |    N/A
[99  4]   |      2.0935175  |              |           |    N/A
[100   0]  |     0.12497864  |              |           |    N/A
[100   1]  |     0.40841362  |              |           |    N/A
[100   2]  |     -1.1549148  |              |           |    N/A
[100   3]  |      1.3094959  |              |           |    N/A
[100   4]  |     -1.1042244  |              |           |    N/A
[101   0]  |     0.67971626  |              |           |    N/A
[101   1]  |       1.077259  |              |           |    N/A
[101   2]  |     0.68344155  |              |           |    N/A
[101   3]  |     0.18013594  |              |           |    N/A
[101   4]  |      1.7945321  |              |           |    N/A
[102   0]  |     0.17141074  |              |           |    N/A
[102   1]  |     0.52591166  |              |           |    N/A
[102   2]  |     -1.5102102  |              |           |    N/A
[102   3]  |     0.94640606  |              |           |    N/A
[102   4]  |    -0.67267332  |              |           |    N/A
[103   0]  |    0.076015848  |              |           |    N/A
[103   1]  |     -1.2122749  |              |           |    N/A
[103   2]  |      1.2313817  |              |           |    N/A
[103   3]  |     0.52236159  |              |           |    N/A
[103   4]  |      1.7505918  |              |           |    N/A
[104   0]  |     0.10452085  |              |           |    N/A
[104   1]  |     0.33207113  |              |           |    N/A
[104   2]  |     -1.3062117  |              |           |    N/A
[104   3]  |    0.029957686  |              |           |    N/A
[104   4]  |    -0.83981646  |              |           |    N/A
[105   0]  |     0.21179555  |              |           |    N/A
[105   1]  |     0.61016169  |              |           |    N/A
[105   2]  |      -1.379273  |              |           |    N/A
[105   3]  |    -0.29039232  |              |           |    N/A
[105   4]  |    -0.57968008  |              |           |    N/A
[106   0]  |    -0.16138239  |              |           |    N/A
[106   1]  |     -1.3343625  |              |           |    N/A
[106   2]  |      1.7847193  |              |           |    N/A
[106   3]  |     0.21615843  |              |           |    N/A
[106   4]  |       1.888242  |              |           |    N/A
[107   0]  |     0.85792084  |              |           |    N/A
[107   1]  |    -0.58053443  |              |           |    N/A
[107   2]  |    -0.10522263  |              |           |    N/A
[107   3]  |     -1.0787202  |              |           |    N/A
[107   4]  |     0.74634344  |              |           |    N/A
[108   0]  |     0.51820114  |              |           |    N/A
[108   1]  |    -0.52237723  |              |           |    N/A
[108   2]  |    -0.34572421  |              |           |    N/A
[108   3]  |    -0.48955723  |              |           |    N/A
[108   4]  |     0.73316312  |              |           |    N/A
[109   0]  |     0.41767796  |              |           |    N/A
[109   1]  |      -1.044575  |              |           |    N/A
[109   2]  |     0.67023783  |              |           |    N/A
[109   3]  |    -0.96397171  |              |           |    N/A
[109   4]  |     0.92013923  |              |           |    N/A
[110   0]  |      1.0017676  |              |           |    N/A
[110   1]  |     0.45265443  |              |           |    N/A
[110   2]  |      1.7499172  |              |           |    N/A
[110   3]  |    -0.10991751  |              |           |    N/A
[110   4]  |    -0.38947802  |              |           |    N/A
[111   0]  |      1.2095775  |              |           |    N/A
[111   1]  |     0.64030902  |              |           |    N/A
[111   2]  |       1.459901  |              |           |    N/A
[111   3]  |      1.0612148  |              |           |    N/A
[111   4]  |    -0.31320184  |              |           |    N/A
[112   0]  |      1.6884169  |              |           |    N/A
[112   1]  |     0.06791331  |              |           |    N/A
[112   2]  |      1.3362566  |              |           |    N/A
[112   3]  |     0.91702217  |              |           |    N/A
[112   4]  |     -0.7273492  |              |           |    N/A
[113   0]  |     0.28612118  |              |           |    N/A
[113   1]  |      1.9066151  |              |           |    N/A
[113   2]  |      1.6705801  |              |           |    N/A
[113   3]  |    -0.25179961  |              |           |    N/A
[113   4]  |     0.69585084  |              |           |    N/A
[114   0]  |     0.77512953  |              |           |    N/A
[114   1]  |      1.9225001  |              |           |    N/A
[114   2]  |     -1.6509121  |              |           |    N/A
[114   3]  |       1.044113  |              |           |    N/A
[114   4]  |      1.5846648  |              |           |    N/A
[115   0]  |      1.2077584  |              |           |    N/A
[115   1]  |       1.372759  |              |           |    N/A
[115   2]  |     -1.9943037  |              |           |    N/A
[115   3]  |     0.48188848  |              |           |    N/A
[115   4]  |      1.3635665  |              |           |    N/A
[116   0]  |      0.8557562  |              |           |    N/A
[116   1]  |      1.5967625  |              |           |    N/A
[116   2]  |    -0.63000032  |              |           |    N/A
[116   3]  |       1.085521  |              |           |    N/A
[116   4]  |     0.82934451  |              |           |    N/A
[117   0]  |      0.9283899  |              |           |    N/A
[117   1]  |      1.0338555  |              |           |    N/A
[117   2]  |     0.15734838  |              |           |    N/A
[117   3]  |      1.2040654  |              |           |    N/A
[117   4]  |     0.59988666  |              |           |    N/A
[118   0]  |     0.95776481  |              |           |    N/A
[118   1]  |      1.2797853  |              |           |    N/A
[118   2]  |     0.68571367  |              |           |    N/A
[118   3]  |     -1.8675973  |              |           |    N/A
[118   4]  |    -0.22820872  |              |           |    N/A
[119   0]  |      1.1267425  |              |           |    N/A
[119   1]  |      1.1923096  |              |           |    N/A
[119   2]  |    -0.39363364  |              |           |    N/A
[119   3]  |     0.96913474  |              |           |    N/A
[119   4]  |     0.19080817  |              |           |    N/A
[120   0]  |     0.54176498  |              |           |    N/A
[120   1]  |      1.7534673  |              |           |    N/A
[120   2]  |     -1.4025993  |              |           |    N/A
[120   3]  |      2.3394955  |              |           |    N/A
[120   4]  |      1.4656319  |              |           |    N/A
[121   0]  |     0.83512483  |              |           |    N/A
[121   1]  |      1.4755992  |              |           |    N/A
[121   2]  |      1.4085262  |              |           |    N/A
[121   3]  |    -0.51102436  |              |           |    N/A
[121   4]  |     0.57023728  |              |           |    N/A
[122   0]  |     0.59419584  |              |           |    N/A
[122   1]  |      1.4966417  |              |           |    N/A
[122   2]  |   -0.015384771  |              |           |    N/A
[122   3]  |      1.2550201  |              |           |    N/A
[122   4]  |     0.51207476  |              |           |    N/A
[123   0]  |     0.72923173  |              |           |    N/A
[123   1]  |      1.3084403  |              |           |    N/A
[123   2]  |      1.2702877  |              |           |    N/A
[123   3]  |     -1.4152112  |              |           |    N/A
[123   4]  |     0.12936872  |              |           |    N/A
[124   0]  |     0.99239885  |              |           |    N/A
[124   1]  |     0.48563638  |              |           |    N/A
[124   2]  |      1.9831259  |              |           |    N/A
[124   3]  |     -0.4665909  |              |           |    N/A
[124   4]  |    -0.15064971  |              |           |    N/A
[125   0]  |      1.2798567  |              |           |    N/A
[125   1]  |     0.69674079  |              |           |    N/A
[125   2]  |      1.0953054  |              |           |    N/A
[125   3]  |     0.59036677  |              |           |    N/A
[125   4]  |   -0.051811588  |              |           |    N/A
[126   0]  |     0.62434026  |              |           |    N/A
[126   1]  |    -0.31396425  |              |           |    N/A
[126   2]  |      2.5924076  |              |           |    N/A
[126   3]  |    0.090606303  |              |           |    N/A
[126   4]  |     -0.8375108  |              |           |    N/A
[127   0]  |     0.51182134  |              |           |    N/A
[127   1]  |     0.46694669  |              |           |    N/A
[127   2]  |     0.69422445  |              |           |    N/A
[127   3]  |    -0.96529765  |              |           |    N/A
[127   4]  |     -0.2924822  |              |           |    N/A
[128   0]  |     0.79486008  |              |           |    N/A
[128   1]  |    -0.05266395  |              |           |    N/A
[128   2]  |      2.4086583  |              |           |    N/A
[128   3]  |     -0.6023594  |              |           |    N/A
[128   4]  |     -1.0698543  |              |           |    N/A
[129   0]  |      1.1162028  |              |           |    N/A
[129   1]  |      1.5353853  |              |           |    N/A
[129   2]  |     -0.7398911  |              |           |    N/A
[129   3]  |     0.62964334  |              |           |    N/A
[129   4]  |     0.52597794  |              |           |    N/A
[130   0]  |      1.0599093  |              |           |    N/A
[130   1]  |      1.3716375  |              |           |    N/A
[130   2]  |     -1.7349234  |              |           |    N/A
[130   3]  |     0.61591931  |              |           |    N/A
[130   4]  |      1.0705262  |              |           |    N/A
[131   0]  |     0.78600745  |              |           |    N/A
[131   1]  |      1.6004757  |              |           |    N/A
[131   2]  |     0.35571116  |              |           |    N/A
[131   3]  |    0.090121925  |              |           |    N/A
[131   4]  |     0.95201158  |              |           |    N/A
[132   0]  |      1.0544531  |              |           |    N/A
[132   1]  |      1.1283768  |              |           |    N/A
[132   2]  |      1.1422202  |              |           |    N/A
[132   3]  |   -0.079182012  |              |           |    N/A
[132   4]  |     0.13006769  |              |           |    N/A
[133   0]  |      1.0359744  |              |           |    N/A
[133   1]  |      1.0075035  |              |           |    N/A
[133   2]  |     0.83272876  |              |           |    N/A
[133   3]  |     0.89467701  |              |           |    N/A
[133   4]  |     0.10455973  |              |           |    N/A
[134   0]  |     0.89685375  |              |           |    N/A
[134   1]  |       1.456662  |              |           |    N/A
[134   2]  |      1.2243136  |              |           |    N/A
[134   3]  |    -0.16765253  |              |           |    N/A
[134   4]  |     0.96250713  |              |           |    N/A
[135   0]  |      1.1620116  |              |           |    N/A
[135   1]  |     0.75367613  |              |           |    N/A
[135   2]  |      1.3623528  |              |           |    N/A
[135   3]  |    -0.27605204  |              |           |    N/A
[135   4]  |     0.17973523  |              |           |    N/A
[136   0]  |     0.44028353  |              |           |    N/A
[136   1]  |      0.8779522  |              |           |    N/A
[136   2]  |     0.65793248  |              |           |    N/A
[136   3]  |    0.096514042  |              |           |    N/A
[136   4]  |    -0.90728074  |              |           |    N/A
[137   0]  |      1.1082214  |              |           |    N/A
[137   1]  |     0.90382165  |              |           |    N/A
[137   2]  |      1.5484204  |              |           |    N/A
[137   3]  |     0.29815228  |              |           |    N/A
[137   4]  |     0.14074364  |              |           |    N/A
[138   0]  |     0.73821529  |              |           |    N/A
[138   1]  |    0.047245848  |              |           |    N/A
[138   2]  |      2.2871898  |              |           |    N/A
[138   3]  |     0.10712552  |              |           |    N/A
[138   4]  |     -0.6664158  |              |           |    N/A
[139   0]  |     0.91466481  |              |           |    N/A
[139   1]  |      1.1126219  |              |           |    N/A
[139   2]  |     0.65051561  |              |           |    N/A
[139   3]  |    -0.46453846  |              |           |    N/A
[139   4]  |    0.029498286  |              |           |    N/A
[140   0]  |      1.0915227  |              |           |    N/A
[140   1]  |     0.68332697  |              |           |    N/A
[140   2]  |      1.2040024  |              |           |    N/A
[140   3]  |     0.29925399  |              |           |    N/A
[140   4]  |     0.06274457  |              |           |    N/A
[141   0]  |     0.98379441  |              |           |    N/A
[141   1]  |      1.5458913  |              |           |    N/A
[141   2]  |     -1.2489877  |              |           |    N/A
[141   3]  |      1.5109086  |              |           |    N/A
[141   4]  |     0.70468352  |              |           |    N/A
[142   0]  |      1.0026036  |              |           |    N/A
[142   1]  |    0.033972936  |              |           |    N/A
[142   2]  |       1.937505  |              |           |    N/A
[142   3]  |     0.69818667  |              |           |    N/A
[142   4]  |     -1.5015852  |              |           |    N/A
[143   0]  |     0.87120433  |              |           |    N/A
[143   1]  |      1.8247318  |              |           |    N/A
[143   2]  |     -2.1011924  |              |           |    N/A
[143   3]  |     0.47557477  |              |           |    N/A
[143   4]  |       1.723063  |              |           |    N/A
[144   0]  |     0.69812487  |              |           |    N/A
[144   1]  |      1.5102399  |              |           |    N/A
[144   2]  |    0.031732744  |              |           |    N/A
[144   3]  |    0.020908967  |              |           |    N/A
[144   4]  |     0.50349107  |              |           |    N/A
[145   0]  |      1.2112548  |              |           |    N/A
[145   1]  |      1.5788801  |              |           |    N/A
[145   2]  |     -1.8248288  |              |           |    N/A
[145   3]  |    0.099923896  |              |           |    N/A
[145   4]  |      1.3243544  |              |           |    N/A
[146   0]  |     0.87683168  |              |           |    N/A
[146   1]  |      1.7501846  |              |           |    N/A
[146   2]  |     0.22593671  |              |           |    N/A
[146   3]  |     0.60777909  |              |           |    N/A
[146   4]  |     0.82771182  |              |           |    N/A
[147   0]  |      1.5025387  |              |           |    N/A
[147   1]  |     -0.1162381  |              |           |    N/A
[147   2]  |      2.0034208  |              |           |    N/A
[147   3]  |    0.083791749  |              |           |    N/A
[147   4]  |    -0.96696114  |              |           |    N/A
[148   0]  |      1.1413468  |              |           |    N/A
[148   1]  |      1.1401221  |              |           |    N/A
[148   2]  |     0.20142241  |              |           |    N/A
[148   3]  |  -0.0091745197  |              |           |    N/A
[148   4]  |     0.12477314  |              |           |    N/A
[149   0]  |     0.99649198  |              |           |    N/A
[149   1]  |     0.44024845  |              |           |    N/A
[149   2]  |      1.1838626  |              |           |    N/A
[149   3]  |    -0.23898241  |              |           |    N/A
[149   4]  |    -0.84836939  |              |           |    N/A
[150   0]  |     0.43432519  |              |           |    N/A
[150   1]  |      1.8651496  |              |           |    N/A
[150   2]  |      1.4806006  |              |           |    N/A
[150   3]  |    0.040013937  |              |           |    N/A
[150   4]  |     0.62337045  |              |           |    N/A
[151   0]  |     0.88819047  |              |           |    N/A
[151   1]  |      1.9718677  |              |           |    N/A
[151   2]  |     -1.4050764  |              |           |    N/A
[151   3]  |     0.18727603  |              |           |    N/A
[151   4]  |      1.0322324  |              |           |    N/A
[152   0]  |      1.3256822  |              |           |    N/A
[152   1]  |   -0.067048955  |              |           |    N/A
[152   2]  |      2.0933394  |              |           |    N/A
[152   3]  |    -0.83382787  |              |           |    N/A
[152   4]  |     -1.3234661  |              |           |    N/A
[153   0]  |       1.251931  |              |           |    N/A
[153   1]  |      1.3293365  |              |           |    N/A
[153   2]  |     -2.0469417  |              |           |    N/A
[153   3]  |     0.14953212  |              |           |    N/A
[153   4]  |      1.5343947  |              |           |    N/A
[154   0]  |      1.1653077  |              |           |    N/A
[154   1]  |     0.11390447  |              |           |    N/A
[154   2]  |      2.0779094  |              |           |    N/A
[154   3]  |     0.74818067  |              |           |    N/A
[154   4]  |    -0.97920823  |              |           |    N/A
[155   0]  |     0.49124807  |              |           |    N/A
[155   1]  |     0.37272585  |              |           |    N/A
[155   2]  |     0.40709879  |              |           |    N/A
[155   3]  |     0.33834975  |              |           |    N/A
[155   4]  |     -1.1002439  |              |           |    N/A
[156   0]  |      0.8757905  |              |           |    N/A
[156   1]  |     0.82007053  |              |           |    N/A
[156   2]  |      1.1865308  |              |           |    N/A
[156   3]  |     -1.7636321  |              |           |    N/A
[156   4]  |    -0.12922386  |              |           |    N/A
[157   0]  |     0.68755488  |              |           |    N/A
[157   1]  |      1.7206489  |              |           |    N/A
[157   2]  |     -0.4389582  |              |           |    N/A
[157   3]  |     0.28171988  |              |           |    N/A
[157   4]  |   0.0039244578  |              |           |    N/A
[158   0]  |     0.27456717  |              |           |    N/A
[158   1]  |      1.9530979  |              |           |    N/A
[158   2]  |     0.43073246  |              |           |    N/A
[158   3]  |      1.2169568  |              |           |    N/A
[158   4]  |     0.48812279  |              |           |    N/A
[159   0]  |      1.0335449  |              |           |    N/A
[159   1]  |      0.7220902  |              |           |    N/A
[159   2]  |      1.6111492  |              |           |    N/A
[159   3]  |    -0.40019008  |              |           |    N/A
[159   4]  |    -0.89807148  |              |           |    N/A
[160   0]  |      1.1983891  |              |           |    N/A
[160   1]  |     0.16190674  |              |           |    N/A
[160   2]  |      1.7317941  |              |           |    N/A
[160   3]  |     0.85437403  |              |           |    N/A
[160   4]  |    -0.40386546  |              |           |    N/A
[161   0]  |      0.3895714  |              |           |    N/A
[161   1]  |      1.9174208  |              |           |    N/A
[161   2]  |      1.0590066  |              |           |    N/A
[161   3]  |   -0.032772029  |              |           |    N/A
[161   4]  |     0.43868904  |              |           |    N/A
[162   0]  |      1.2265026  |              |           |    N/A
[162   1]  |     0.48798111  |              |           |    N/A
[162   2]  |      1.2844631  |              |           |    N/A
[162   3]  |     0.88626793  |              |           |    N/A
[162   4]  |    -0.67580484  |              |           |    N/A
[163   0]  |     0.79172301  |              |           |    N/A
[163   1]  |    0.089572933  |              |           |    N/A
[163   2]  |      2.2456629  |              |           |    N/A
[163   3]  |   0.0051178631  |              |           |    N/A
[163   4]  |    -0.80233702  |              |           |    N/A
[164   0]  |     0.73324081  |              |           |    N/A
[164   1]  |   -0.056978695  |              |           |    N/A
[164   2]  |      2.3862018  |              |           |    N/A
[164   3]  |    -0.84758236  |              |           |    N/A
[164   4]  |     -1.0860372  |              |           |    N/A
[165   0]  |   -0.082985712  |              |           |    N/A
[165   1]  |      1.6584744  |              |           |    N/A
[165   2]  |    -0.60135353  |              |           |    N/A
[165   3]  |    -0.85536732  |              |           |    N/A
[165   4]  |     0.45773379  |              |           |    N/A
[166   0]  |     -1.2666288  |              |           |    N/A
[166   1]  |     0.26357605  |              |           |    N/A
[166   2]  |     -1.4675743  |              |           |    N/A
[166   3]  |      0.2463991  |              |           |    N/A
[166   4]  |     0.47851761  |              |           |    N/A
[167   0]  |      -1.337638  |              |           |    N/A
[167   1]  |   -0.050654002  |              |           |    N/A
[167   2]  |     0.19259431  |              |           |    N/A
[167   3]  |   -0.058398637  |              |           |    N/A
[167   4]  |     0.74094685  |              |           |    N/A
[168   0]  |    -0.74246729  |              |           |    N/A
[168   1]  |      1.3625493  |              |           |    N/A
[168   2]  |      1.0473977  |              |           |    N/A
[168   3]  |    -0.29591282  |              |           |    N/A
[168   4]  |     0.14663234  |              |           |    N/A
[169   0]  |     -1.7516546  |              |           |    N/A
[169   1]  |     0.57961565  |              |           |    N/A
[169   2]  |    -0.93722745  |              |           |    N/A
[169   3]  |     -0.3760243  |              |           |    N/A
[169   4]  |    -0.54070601  |              |           |    N/A
[170   0]  |     -1.3401927  |              |           |    N/A
[170   1]  |     0.60244813  |              |           |    N/A
[170   2]  |     -1.8638386  |              |           |    N/A
[170   3]  |    -0.37129122  |              |           |    N/A
[170   4]  |    0.014120987  |              |           |    N/A
[171   0]  |     -1.3595652  |              |           |    N/A
[171   1]  |     0.66617924  |              |           |    N/A
[171   2]  |    -0.88692101  |              |           |    N/A
[171   3]  |    -0.48414518  |              |           |    N/A
[171   4]  |      0.1992099  |              |           |    N/A
[172   0]  |    -0.58734024  |              |           |    N/A
[172   1]  |      1.1530583  |              |           |    N/A
[172   2]  |     -0.8832163  |              |           |    N/A
[172   3]  |    -0.46256039  |              |           |    N/A
[172   4]  |    -0.10716343  |              |           |    N/A
[173   0]  |     -1.5061097  |              |           |    N/A
[173   1]  |     0.34884979  |              |           |    N/A
[173   2]  |     0.89050515  |              |           |    N/A
[173   3]  |    -0.72100058  |              |           |    N/A
[173   4]  |      0.6953196  |              |           |    N/A
[174   0]  |    -0.72064182  |              |           |    N/A
[174   1]  |      1.0731736  |              |           |    N/A
[174   2]  |      1.2160469  |              |           |    N/A
[174   3]  |    -0.16821339  |              |           |    N/A
[174   4]  |   -0.092112161  |              |           |    N/A
[175   0]  |    -0.75710679  |              |           |    N/A
[175   1]  |     0.88144755  |              |           |    N/A
[175   2]  |    -0.95550404  |              |           |    N/A
[175   3]  |    -0.21136646  |              |           |    N/A
[175   4]  |       0.325881  |              |           |    N/A
[176   0]  |     -1.3410145  |              |           |    N/A
[176   1]  |    0.063646567  |              |           |    N/A
[176   2]  |    -0.40040175  |              |           |    N/A
[176   3]  |     0.20100837  |              |           |    N/A
[176   4]  |     0.87497332  |              |           |    N/A
[177   0]  |      -1.350612  |              |           |    N/A
[177   1]  |     0.93468122  |              |           |    N/A
[177   2]  |     0.28857988  |              |           |    N/A
[177   3]  |    -0.82428377  |              |           |    N/A
[177   4]  |    0.059753282  |              |           |    N/A
[178   0]  |      -1.276305  |              |           |    N/A
[178   1]  |     0.40546151  |              |           |    N/A
[178   2]  |      1.0025826  |              |           |    N/A
[178   3]  |    -0.34310448  |              |           |    N/A
[178   4]  |     0.99487965  |              |           |    N/A
[179   0]  |      -1.740922  |              |           |    N/A
[179   1]  |      0.6175522  |              |           |    N/A
[179   2]  |     -1.1234255  |              |           |    N/A
[179   3]  |    -0.48719172  |              |           |    N/A
[179   4]  |     -0.5590587  |              |           |    N/A
[180   0]  |     -1.3019011  |              |           |    N/A
[180   1]  |     0.55287135  |              |           |    N/A
[180   2]  |    -0.24807659  |              |           |    N/A
[180   3]  |    -0.40100993  |              |           |    N/A
[180   4]  |     0.53570663  |              |           |    N/A
[181   0]  |     -1.4596008  |              |           |    N/A
[181   1]  |   -0.018462987  |              |           |    N/A
[181   2]  |    -0.68124837  |              |           |    N/A
[181   3]  |     -2.6988806  |              |           |    N/A
[181   4]  |    -0.39893512  |              |           |    N/A
[182   0]  |     -1.1351624  |              |           |    N/A
[182   1]  |    0.034121654  |              |           |    N/A
[182   2]  |     -1.1304327  |              |           |    N/A
[182   3]  |     0.41417966  |              |           |    N/A
[182   4]  |     0.54251922  |              |           |    N/A
[183   0]  |     -1.0119664  |              |           |    N/A
[183   1]  |     0.23386253  |              |           |    N/A
[183   2]  |     -1.0164281  |              |           |    N/A
[183   3]  |   -0.092703676  |              |           |    N/A
[183   4]  |     0.71905668  |              |           |    N/A
[184   0]  |       -1.40831  |              |           |    N/A
[184   1]  |     0.41922525  |              |           |    N/A
[184   2]  |     0.20785261  |              |           |    N/A
[184   3]  |    -0.27944972  |              |           |    N/A
[184   4]  |      0.6967641  |              |           |    N/A
[185   0]  |     -1.2098677  |              |           |    N/A
[185   1]  |     0.98702122  |              |           |    N/A
[185   2]  |    -0.53419897  |              |           |    N/A
[185   3]  |    -0.28014312  |              |           |    N/A
[185   4]  |    -0.21769902  |              |           |    N/A
[186   0]  |    0.010482025  |              |           |    N/A
[186   1]  |      1.8169175  |              |           |    N/A
[186   2]  |    -0.58713654  |              |           |    N/A
[186   3]  |     -2.3243591  |              |           |    N/A
[186   4]  |     0.55647094  |              |           |    N/A
[187   0]  |      -1.429068  |              |           |    N/A
[187   1]  |     0.82206337  |              |           |    N/A
[187   2]  |     0.94413987  |              |           |    N/A
[187   3]  |    -0.96417858  |              |           |    N/A
[187   4]  |     0.17971537  |              |           |    N/A
[188   0]  |     -1.4415627  |              |           |    N/A
[188   1]  |      0.1784502  |              |           |    N/A
[188   2]  |    -0.94521054  |              |           |    N/A
[188   3]  |     -0.1767501  |              |           |    N/A
[188   4]  |      0.6963196  |              |           |    N/A
[189   0]  |     -1.2007477  |              |           |    N/A
[189   1]  |     0.83457411  |              |           |    N/A
[189   2]  |      1.2652726  |              |           |    N/A
[189   3]  |     -1.2351702  |              |           |    N/A
[189   4]  |     0.47630601  |              |           |    N/A
[190   0]  |     -1.2519314  |              |           |    N/A
[190   1]  |     0.84722462  |              |           |    N/A
[190   2]  |    -0.29051904  |              |           |    N/A
[190   3]  |    -0.58638343  |              |           |    N/A
[190   4]  |     0.24761131  |              |           |    N/A
[191   0]  |     -1.4722828  |              |           |    N/A
[191   1]  |   -0.041753384  |              |           |    N/A
[191   2]  |      -1.119129  |              |           |    N/A
[191   3]  |     0.26502064  |              |           |    N/A
[191   4]  |     0.66859317  |              |           |    N/A
[192   0]  |     -1.2827502  |              |           |    N/A
[192   1]  |    0.086436505  |              |           |    N/A
[192   2]  |      -0.171497  |              |           |    N/A
[192   3]  |    0.054768068  |              |           |    N/A
[192   4]  |      1.1000862  |              |           |    N/A
[193   0]  |     -1.6738883  |              |           |    N/A
[193   1]  |     0.72049078  |              |           |    N/A
[193   2]  |    -0.83088059  |              |           |    N/A
[193   3]  |     -0.7352363  |              |           |    N/A
[193   4]  |     -1.1884218  |              |           |    N/A
[194   0]  |     -1.1174016  |              |           |    N/A
[194   1]  |     0.92625011  |              |           |    N/A
[194   2]  |       1.168318  |              |           |    N/A
[194   3]  |    -0.51104157  |              |           |    N/A
[194   4]  |     0.65308614  |              |           |    N/A
[195   0]  |     -1.2412397  |              |           |    N/A
[195   1]  |     0.93442541  |              |           |    N/A
[195   2]  |    -0.77182615  |              |           |    N/A
[195   3]  |      -0.579282  |              |           |    N/A
[195   4]  |   -0.032537294  |              |           |    N/A
[196   0]  |     -1.2453605  |              |           |    N/A
[196   1]  |     0.62458832  |              |           |    N/A
[196   2]  |    -0.42640618  |              |           |    N/A
[196   3]  |   -0.011987663  |              |           |    N/A
[196   4]  |     0.45165863  |              |           |    N/A
[197   0]  |     -1.5602864  |              |           |    N/A
[197   1]  |     0.82548622  |              |           |    N/A
[197   2]  |     0.37571692  |              |           |    N/A
[197   3]  |    -0.82044502  |              |           |    N/A
[197   4]  |    -0.13047866  |              |           |    N/A
[198   0]  |    -0.63961672  |              |           |    N/A
[198   1]  |      1.1074693  |              |           |    N/A
[198   2]  |     -1.3047197  |              |           |    N/A
[198   3]  |     -1.3582298  |              |           |    N/A
[198   4]  |     0.16814523  |              |           |    N/A
[199   0]  |   -0.060358772  |              |           |    N/A
[199   1]  |      1.6410294  |              |           |    N/A
[199   2]  |     -1.2748522  |              |           |    N/A
[199   3]  |     -2.0158021  |              |           |    N/A
[199   4]  |     0.32527392  |              |           |    N/A
[200   0]  |    -0.31386589  |              |           |    N/A
[200   1]  |      1.8857685  |              |           |    N/A
[200   2]  |    -0.38241732  |              |           |    N/A
[200   3]  |     -1.9814314  |              |           |    N/A
[200   4]  |      0.3644265  |              |           |    N/A
[201   0]  |     -1.2119914  |              |           |    N/A
[201   1]  |     0.13523947  |              |           |    N/A
[201   2]  |    -0.81420564  |              |           |    N/A
[201   3]  |    -0.58653783  |              |           |    N/A
[201   4]  |      0.5047257  |              |           |    N/A
[202   0]  |     -1.4541073  |              |           |    N/A
[202   1]  |    -0.17706895  |              |           |    N/A
[202   2]  |    -0.63598362  |              |           |    N/A
[202   3]  |   -0.037948641  |              |           |    N/A
[202   4]  |     0.85934261  |              |           |    N/A
[203   0]  |     -1.6270759  |              |           |    N/A
[203   1]  |      0.3157894  |              |           |    N/A
[203   2]  |     -1.1112573  |              |           |    N/A
[203   3]  |     0.27128595  |              |           |    N/A
[203   4]  |     0.10336247  |              |           |    N/A
[204   0]  |     -1.1807524  |              |           |    N/A
[204   1]  |     0.96500297  |              |           |    N/A
[204   2]  |    -0.35731819  |              |           |    N/A
[204   3]  |    -0.67369006  |              |           |    N/A
[204   4]  |     0.24033014  |              |           |    N/A
[205   0]  |      -1.554744  |              |           |    N/A
[205   1]  |   0.0089364793  |              |           |    N/A
[205   2]  |    -0.66371466  |              |           |    N/A
[205   3]  |    -0.01708671  |              |           |    N/A
[205   4]  |     0.54637007  |              |           |    N/A
[206   0]  |      -1.228704  |              |           |    N/A
[206   1]  |      1.0270921  |              |           |    N/A
[206   2]  |      1.0701756  |              |           |    N/A
[206   3]  |    -0.91143096  |              |           |    N/A
[206   4]  |     0.15601036  |              |           |    N/A
[207   0]  |     -1.6996015  |              |           |    N/A
[207   1]  |  -0.0089222125  |              |           |    N/A
[207   2]  |    -0.26440311  |              |           |    N/A
[207   3]  |    -0.26963687  |              |           |    N/A
[207   4]  |     0.41376067  |              |           |    N/A
[208   0]  |    -0.45104525  |              |           |    N/A
[208   1]  |      1.4660365  |              |           |    N/A
[208   2]  |  -0.0027497551  |              |           |    N/A
[208   3]  |     -1.9421575  |              |           |    N/A
[208   4]  |     0.25840182  |              |           |    N/A
[209   0]  |     -1.1367244  |              |           |    N/A
[209   1]  |     0.61567764  |              |           |    N/A
[209   2]  |     0.41349453  |              |           |    N/A
[209   3]  |    -0.38805667  |              |           |    N/A
[209   4]  |     0.62350718  |              |           |    N/A
[210   0]  |    -0.69528978  |              |           |    N/A
[210   1]  |      1.1199851  |              |           |    N/A
[210   2]  |      -0.829981  |              |           |    N/A
[210   3]  |    -0.82366618  |              |           |    N/A
[210   4]  |     0.17284962  |              |           |    N/A
[211   0]  |     -1.3938026  |              |           |    N/A
[211   1]  |      0.5312083  |              |           |    N/A
[211   2]  |     -0.2073715  |              |           |    N/A
[211   3]  |    -0.53290763  |              |           |    N/A
[211   4]  |     0.48254503  |              |           |    N/A
[212   0]  |    -0.89367413  |              |           |    N/A
[212   1]  |      1.0371383  |              |           |    N/A
[212   2]  |     0.11961214  |              |           |    N/A
[212   3]  |    -0.66645906  |              |           |    N/A
[212   4]  |     0.50789707  |              |           |    N/A
[213   0]  |     -1.0997454  |              |           |    N/A
[213   1]  |      1.2560698  |              |           |    N/A
[213   2]  |     0.61002414  |              |           |    N/A
[213   3]  |    -0.96455809  |              |           |    N/A
[213   4]  |    0.069657131  |              |           |    N/A
[214   0]  |     -1.2724259  |              |           |    N/A
[214   1]  |     0.41124815  |              |           |    N/A
[214   2]  |     0.16602347  |              |           |    N/A
[214   3]  |    -0.58894863  |              |           |    N/A
[214   4]  |     0.76924472  |              |           |    N/A
[215   0]  |     -1.3551126  |              |           |    N/A
[215   1]  |    -0.10211504  |              |           |    N/A
[215   2]  |     -1.0388801  |              |           |    N/A
[215   3]  |     0.15381488  |              |           |    N/A
[215   4]  |     0.67487445  |              |           |    N/A
[216   0]  |     -1.4514609  |              |           |    N/A
[216   1]  |      0.4696875  |              |           |    N/A
[216   2]  |    -0.41961801  |              |           |    N/A
[216   3]  |   -0.079553051  |              |           |    N/A
[216   4]  |     0.52087665  |              |           |    N/A
[217   0]  |    -0.65055904  |              |           |    N/A
[217   1]  |      1.4565894  |              |           |    N/A
[217   2]  |    -0.63528141  |              |           |    N/A
[217   3]  |     -1.3737066  |              |           |    N/A
[217   4]  |     0.10077001  |              |           |    N/A
[218   0]  |     -1.0613208  |              |           |    N/A
[218   1]  |     0.59834954  |              |           |    N/A
[218   2]  |     -1.5408635  |              |           |    N/A
[218   3]  |    -0.10557701  |              |           |    N/A
[218   4]  |     0.16134768  |              |           |    N/A
[219   0]  |     -1.3916723  |              |           |    N/A
[219   1]  |     0.75002979  |              |           |    N/A
[219   2]  |    -0.95766443  |              |           |    N/A
[219   3]  |     -0.2998695  |              |           |    N/A
[219   4]  |    -0.24368228  |              |           |    N/A
[220   0]  |      1.5023417  |              |           |    N/A
[220   1]  |     0.12950851  |              |           |    N/A
[220   2]  |     -1.0523144  |              |           |    N/A
[220   3]  |     -1.1838966  |              |           |    N/A
[220   4]  |     -1.1179983  |              |           |    N/A
[221   0]  |      1.2649706  |              |           |    N/A
[221   1]  |    -0.24118173  |              |           |    N/A
[221   2]  |    -0.91721225  |              |           |    N/A
[221   3]  |    -0.55747904  |              |           |    N/A
[221   4]  |    -0.59693955  |              |           |    N/A
[222   0]  |      1.3856108  |              |           |    N/A
[222   1]  |    -0.26651613  |              |           |    N/A
[222   2]  |     0.83041977  |              |           |    N/A
[222   3]  |    -0.24433045  |              |           |    N/A
[222   4]  |      -1.527922  |              |           |    N/A
[223   0]  |      2.0637229  |              |           |    N/A
[223   1]  |    -0.51142703  |              |           |    N/A
[223   2]  |     0.47274556  |              |           |    N/A
[223   3]  |     0.65945141  |              |           |    N/A
[223   4]  |      -2.134762  |              |           |    N/A
[224   0]  |      1.0586174  |              |           |    N/A
[224   1]  |     -1.1578725  |              |           |    N/A
[224   2]  |    -0.47528785  |              |           |    N/A
[224   3]  |       0.532792  |              |           |    N/A
[224   4]  |    -0.63529848  |              |           |    N/A
[225   0]  |     0.77097646  |              |           |    N/A
[225   1]  |     -1.0515724  |              |           |    N/A
[225   2]  |    -0.53314562  |              |           |    N/A
[225   3]  |    -0.73795145  |              |           |    N/A
[225   4]  |     0.51307998  |              |           |    N/A
[226   0]  |      1.5819052  |              |           |    N/A
[226   1]  |    -0.12176156  |              |           |    N/A
[226   2]  |    -0.91360773  |              |           |    N/A
[226   3]  |      1.4907873  |              |           |    N/A
[226   4]  |     -2.1142421  |              |           |    N/A
[227   0]  |     0.76596465  |              |           |    N/A
[227   1]  |    -0.66328887  |              |           |    N/A
[227   2]  |     -1.0560966  |              |           |    N/A
[227   3]  |     0.27936266  |              |           |    N/A
[227   4]  |      -0.862081  |              |           |    N/A
[228   0]  |       1.040484  |              |           |    N/A
[228   1]  |     -1.2198849  |              |           |    N/A
[228   2]  |     0.82591666  |              |           |    N/A
[228   3]  |    -0.64339115  |              |           |    N/A
[228   4]  |    -0.68049385  |              |           |    N/A
[229   0]  |      1.5909729  |              |           |    N/A
[229   1]  |  -0.0055724629  |              |           |    N/A
[229   2]  |    -0.88187676  |              |           |    N/A
[229   3]  |    -0.86988441  |              |           |    N/A
[229   4]  |     -0.8398575  |              |           |    N/A
[230   0]  |      1.2053244  |              |           |    N/A
[230   1]  |     0.55251803  |              |           |    N/A
[230   2]  |    -0.91117447  |              |           |    N/A
[230   3]  |      -1.655982  |              |           |    N/A
[230   4]  |    -0.89845764  |              |           |    N/A
[231   0]  |      1.5727181  |              |           |    N/A
[231   1]  |    -0.65274475  |              |           |    N/A
[231   2]  |    -0.75729346  |              |           |    N/A
[231   3]  |      1.5140621  |              |           |    N/A
[231   4]  |     -1.4758103  |              |           |    N/A
[232   0]  |      1.3931795  |              |           |    N/A
[232   1]  |    0.064019575  |              |           |    N/A
[232   2]  |    -0.63397844  |              |           |    N/A
[232   3]  |     -1.3049945  |              |           |    N/A
[232   4]  |    -0.80313882  |              |           |    N/A
[233   0]  |      1.3393722  |              |           |    N/A
[233   1]  |     0.56118496  |              |           |    N/A
[233   2]  |     0.25158656  |              |           |    N/A
[233   3]  |     -2.1435407  |              |           |    N/A
[233   4]  |    -0.77716583  |              |           |    N/A
[234   0]  |       1.232094  |              |           |    N/A
[234   1]  |    -0.54390645  |              |           |    N/A
[234   2]  |     -1.3967378  |              |           |    N/A
[234   3]  |      0.4134416  |              |           |    N/A
[234   4]  |    -0.71761981  |              |           |    N/A
[235   0]  |      1.4859327  |              |           |    N/A
[235   1]  |    0.072824188  |              |           |    N/A
[235   2]  |    -0.96111873  |              |           |    N/A
[235   3]  |    -0.83123963  |              |           |    N/A
[235   4]  |     -1.4144059  |              |           |    N/A
[236   0]  |       1.269026  |              |           |    N/A
[236   1]  |     0.14148959  |              |           |    N/A
[236   2]  |     -1.1397432  |              |           |    N/A
[236   3]  |    -0.85229771  |              |           |    N/A
[236   4]  |     -1.1169994  |              |           |    N/A
[237   0]  |      1.4817643  |              |           |    N/A
[237   1]  |     0.40238886  |              |           |    N/A
[237   2]  |     -1.2392186  |              |           |    N/A
[237   3]  |    -0.81508993  |              |           |    N/A
[237   4]  |    -0.71908596  |              |           |    N/A
[238   0]  |     0.39675881  |              |           |    N/A
[238   1]  |     -1.6078641  |              |           |    N/A
[238   2]  |     0.86908821  |              |           |    N/A
[238   3]  |    -0.28013181  |              |           |    N/A
[238   4]  |     0.34911504  |              |           |    N/A
[239   0]  |      1.8188381  |              |           |    N/A
[239   1]  |    -0.44933859  |              |           |    N/A
[239   2]  |    -0.10914852  |              |           |    N/A
[239   3]  |    -0.33063076  |              |           |    N/A
[239   4]  |     -1.3851574  |              |           |    N/A
[240   0]  |      1.0416998  |              |           |    N/A
[240   1]  |    -0.99296771  |              |           |    N/A
[240   2]  |    -0.32709209  |              |           |    N/A
[240   3]  |    -0.68000969  |              |           |    N/A
[240   4]  |    -0.28009393  |              |           |    N/A
[241   0]  |      1.3705898  |              |           |    N/A
[241   1]  |    -0.54535927  |              |           |    N/A
[241   2]  |     0.62377543  |              |           |    N/A
[241   3]  |     -1.3554417  |              |           |    N/A
[241   4]  |     -1.1477312  |              |           |    N/A
[242   0]  |      1.3303371  |              |           |    N/A
[242   1]  |     0.27384554  |              |           |    N/A
[242   2]  |    -0.56334299  |              |           |    N/A
[242   3]  |     -1.3979519  |              |           |    N/A
[242   4]  |     -1.3651679  |              |           |    N/A
[243   0]  |       1.647826  |              |           |    N/A
[243   1]  |    0.013556256  |              |           |    N/A
[243   2]  |      0.2771632  |              |           |    N/A
[243   3]  |     -1.6916383  |              |           |    N/A
[243   4]  |    -0.88514924  |              |           |    N/A
[244   0]  |      1.0571562  |              |           |    N/A
[244   1]  |     -1.3967925  |              |           |    N/A
[244   2]  |     0.62172998  |              |           |    N/A
[244   3]  |    -0.79163436  |              |           |    N/A
[244   4]  |    -0.68278386  |              |           |    N/A
[245   0]  |       1.373024  |              |           |    N/A
[245   1]  |    -0.68769988  |              |           |    N/A
[245   2]  |    0.075176586  |              |           |    N/A
[245   3]  |     -1.0923433  |              |           |    N/A
[245   4]  |    -0.74313848  |              |           |    N/A
[246   0]  |      1.1709326  |              |           |    N/A
[246   1]  |      -1.089189  |              |           |    N/A
[246   2]  |    -0.19443726  |              |           |    N/A
[246   3]  |     0.75590109  |              |           |    N/A
[246   4]  |    -0.61519866  |              |           |    N/A
[247   0]  |      1.5775461  |              |           |    N/A
[247   1]  |    0.035453657  |              |           |    N/A
[247   2]  |    0.035037833  |              |           |    N/A
[247   3]  |     -1.5241338  |              |           |    N/A
[247   4]  |    -0.89657553  |              |           |    N/A
[248   0]  |      1.0842779  |              |           |    N/A
[248   1]  |     0.85855915  |              |           |    N/A
[248   2]  |     -1.0285048  |              |           |    N/A
[248   3]  |     -2.0987039  |              |           |    N/A
[248   4]  |  0.00083361523  |              |           |    N/A
[249   0]  |     0.71420199  |              |           |    N/A
[249   1]  |     -1.0663256  |              |           |    N/A
[249   2]  |    -0.17906179  |              |           |    N/A
[249   3]  |    -0.12233165  |              |           |    N/A
[249   4]  |    -0.33266356  |              |           |    N/A
[250   0]  |      1.8654544  |              |           |    N/A
[250   1]  |    -0.21416926  |              |           |    N/A
[250   2]  |    -0.57360857  |              |           |    N/A
[250   3]  |      1.0205986  |              |           |    N/A
[250   4]  |     -1.9642817  |              |           |    N/A
[251   0]  |     0.75207263  |              |           |    N/A
[251   1]  |     -1.3669656  |              |           |    N/A
[251   2]  |     0.35969276  |              |           |    N/A
[251   3]  |    -0.51289449  |              |           |    N/A
[251   4]  |     0.26155547  |              |           |    N/A
[252   0]  |     0.63568323  |              |           |    N/A
[252   1]  |     -1.4425356  |              |           |    N/A
[252   2]  |     0.51507947  |              |           |    N/A
[252   3]  |    -0.68763494  |              |           |    N/A
[252   4]  |    -0.49110247  |              |           |    N/A
[253   0]  |       1.227607  |              |           |    N/A
[253   1]  |    -0.59262216  |              |           |    N/A
[253   2]  |    -0.61383237  |              |           |    N/A
[253   3]  |      1.9131739  |              |           |    N/A
[253   4]  |     -1.4069083  |              |           |    N/A
[254   0]  |      1.3719153  |              |           |    N/A
[254   1]  |     0.65361095  |              |           |    N/A
[254   2]  |    -0.67946659  |              |           |    N/A
[254   3]  |     -1.5258112  |              |           |    N/A
[254   4]  |    -0.44877015  |              |           |    N/A
[255   0]  |       1.550834  |              |           |    N/A
[255   1]  |     0.32731979  |              |           |    N/A
[255   2]  |    0.040307214  |              |           |    N/A
[255   3]  |     -1.9807104  |              |           |    N/A
[255   4]  |    -0.85928956  |              |           |    N/A
[256   0]  |      1.6334315  |              |           |    N/A
[256   1]  |   -0.021295483  |              |           |    N/A
[256   2]  |    -0.22861344  |              |           |    N/A
[256   3]  |     -1.4713121  |              |           |    N/A
[256   4]  |    -0.93345297  |              |           |    N/A
[257   0]  |      1.0938254  |              |           |    N/A
[257   1]  |     -1.1407344  |              |           |    N/A
[257   2]  |     0.38605243  |              |           |    N/A
[257   3]  |    -0.92615743  |              |           |    N/A
[257   4]  |      -0.775072  |              |           |    N/A
[258   0]  |      1.1783376  |              |           |    N/A
[258   1]  |    -0.84733479  |              |           |    N/A
[258   2]  |     -1.3293688  |              |           |    N/A
[258   3]  |     0.64618434  |              |           |    N/A
[258   4]  |    -0.76651108  |              |           |    N/A
[259   0]  |      1.5492019  |              |           |    N/A
[259   1]  |     0.16645435  |              |           |    N/A
[259   2]  |     -1.0509702  |              |           |    N/A
[259   3]  |    -0.88782752  |              |           |    N/A
[259   4]  |    -0.83104944  |              |           |    N/A
[260   0]  |      1.2660285  |              |           |    N/A
[260   1]  |     -1.1945697  |              |           |    N/A
[260   2]  |    0.062204729  |              |           |    N/A
[260   3]  |    -0.24174016  |              |           |    N/A
[260   4]  |    -0.16405757  |              |           |    N/A
[261   0]  |      1.2375273  |              |           |    N/A
[261   1]  |     -1.1224077  |              |           |    N/A
[261   2]  |      0.2411175  |              |           |    N/A
[261   3]  |    -0.98922245  |              |           |    N/A
[261   4]  |    -0.40187428  |              |           |    N/A
[262   0]  |      1.4385191  |              |           |    N/A
[262   1]  |    -0.56381352  |              |           |    N/A
[262   2]  |    -0.60924523  |              |           |    N/A
[262   3]  |    -0.11530107  |              |           |    N/A
[262   4]  |    -0.81486656  |              |           |    N/A
[263   0]  |      1.2663611  |              |           |    N/A
[263   1]  |    -0.91563984  |              |           |    N/A
[263   2]  |     0.10542889  |              |           |    N/A
[263   3]  |     -1.0992649  |              |           |    N/A
[263   4]  |     -0.6182895  |              |           |    N/A
[264   0]  |     0.53129395  |              |           |    N/A
[264   1]  |     -1.5933585  |              |           |    N/A
[264   2]  |    0.059953505  |              |           |    N/A
[264   3]  |    -0.20749319  |              |           |    N/A
[264   4]  |    0.054848835  |              |           |    N/A
[265   0]  |     0.20809783  |              |           |    N/A
[265   1]  |     -1.8109445  |              |           |    N/A
[265   2]  |      1.4088404  |              |           |    N/A
[265   3]  |    -0.38937848  |              |           |    N/A
[265   4]  |     0.65005321  |              |           |    N/A
[266   0]  |      1.4564482  |              |           |    N/A
[266   1]  |    -0.34429458  |              |           |    N/A
[266   2]  |     -1.3538463  |              |           |    N/A
[266   3]  |     0.22657071  |              |           |    N/A
[266   4]  |      -1.218924  |              |           |    N/A
[267   0]  |      1.3853012  |              |           |    N/A
[267   1]  |    -0.49791129  |              |           |    N/A
[267   2]  |    -0.20417967  |              |           |    N/A
[267   3]  |     -1.0088839  |              |           |    N/A
[267   4]  |    -0.67923687  |              |           |    N/A
[268   0]  |     0.93850157  |              |           |    N/A
[268   1]  |     -1.2487162  |              |           |    N/A
[268   2]  |    -0.11264797  |              |           |    N/A
[268   3]  |    -0.14857672  |              |           |    N/A
[268   4]  |     0.23053145  |              |           |    N/A
[269   0]  |      1.6263163  |              |           |    N/A
[269   1]  |     0.19756024  |              |           |    N/A
[269   2]  |    -0.16354099  |              |           |    N/A
[269   3]  |     -1.6079968  |              |           |    N/A
[269   4]  |    -0.86395977  |              |           |    N/A
[270   0]  |      1.4336207  |              |           |    N/A
[270   1]  |     -1.1306745  |              |           |    N/A
[270   2]  |    -0.17677898  |              |           |    N/A
[270   3]  |    0.026346393  |              |           |    N/A
[270   4]  |   -0.067318025  |              |           |    N/A
[271   0]  |     0.96891888  |              |           |    N/A
[271   1]  |     -1.5117588  |              |           |    N/A
[271   2]  |     0.38292393  |              |           |    N/A
[271   3]  |     0.21699701  |              |           |    N/A
[271   4]  |     0.40027433  |              |           |    N/A
[272   0]  |     0.60718555  |              |           |    N/A
[272   1]  |     -1.3350276  |              |           |    N/A
[272   2]  |     0.67365229  |              |           |    N/A
[272   3]  |    -0.45982293  |              |           |    N/A
[272   4]  |     -0.3741388  |              |           |    N/A
[273   0]  |      1.2272048  |              |           |    N/A
[273   1]  |    -0.45772637  |              |           |    N/A
[273   2]  |     -1.4118475  |              |           |    N/A
[273   3]  |      2.0157324  |              |           |    N/A
[273   4]  |     -1.6251771  |              |           |    N/A
[274   0]  |     0.95477729  |              |           |    N/A
[274   1]  |    -0.84624004  |              |           |    N/A
[274   2]  |    -0.57474795  |              |           |    N/A
[274   3]  |      0.3874594  |              |           |    N/A
[274   4]  |     -1.0430853  |              |           |    N/A
[275   0]  |    -0.28956109  |              |           |    N/A
[275   1]  |    -0.98717866  |              |           |    N/A
[275   2]  |     0.58412528  |              |           |    N/A
[275   3]  |      1.7117273  |              |           |    N/A
[275   4]  |    0.060382711  |              |           |    N/A
[276   0]  |    -0.18864417  |              |           |    N/A
[276   1]  |     -1.3186609  |              |           |    N/A
[276   2]  |     -1.6740805  |              |           |    N/A
[276   3]  |     -0.5625592  |              |           |    N/A
[276   4]  |     0.49585909  |              |           |    N/A
[277   0]  |    -0.62496871  |              |           |    N/A
[277   1]  |     -1.8241972  |              |           |    N/A
[277   2]  |     0.69166033  |              |           |    N/A
[277   3]  |     -1.3350519  |              |           |    N/A
[277   4]  |      1.7673069  |              |           |    N/A
[278   0]  |     0.79159152  |              |           |    N/A
[278   1]  |     -1.3153642  |              |           |    N/A
[278   2]  |    -0.17819017  |              |           |    N/A
[278   3]  |       0.370884  |              |           |    N/A
[278   4]  |     0.70754472  |              |           |    N/A
[279   0]  |    -0.44203619  |              |           |    N/A
[279   1]  |     -1.5239753  |              |           |    N/A
[279   2]  |   -0.007817131  |              |           |    N/A
[279   3]  |      1.8031073  |              |           |    N/A
[279   4]  |      1.5853709  |              |           |    N/A
[280   0]  |     0.20283178  |              |           |    N/A
[280   1]  |     -1.4576344  |              |           |    N/A
[280   2]  |     -1.2368305  |              |           |    N/A
[280   3]  |    0.065385473  |              |           |    N/A
[280   4]  |      1.0625415  |              |           |    N/A
[281   0]  |    -0.43176794  |              |           |    N/A
[281   1]  |     -1.7283052  |              |           |    N/A
[281   2]  |    -0.19339227  |              |           |    N/A
[281   3]  |      1.3549092  |              |           |    N/A
[281   4]  |      1.5874792  |              |           |    N/A
[282   0]  |    0.016325446  |              |           |    N/A
[282   1]  |     -1.2445521  |              |           |    N/A
[282   2]  |     0.32250311  |              |           |    N/A
[282   3]  |      1.0698983  |              |           |    N/A
[282   4]  |      1.6912002  |              |           |    N/A
[283   0]  |    -0.57293485  |              |           |    N/A
[283   1]  |     -1.6858442  |              |           |    N/A
[283   2]  |    0.087553732  |              |           |    N/A
[283   3]  |     -1.0192876  |              |           |    N/A
[283   4]  |      1.5660044  |              |           |    N/A
[284   0]  |     0.14720112  |              |           |    N/A
[284   1]  |       -1.68052  |              |           |    N/A
[284   2]  |     0.38785294  |              |           |    N/A
[284   3]  |     0.61199678  |              |           |    N/A
[284   4]  |     0.70235422  |              |           |    N/A
[285   0]  |    -0.25291024  |              |           |    N/A
[285   1]  |     -1.5529302  |              |           |    N/A
[285   2]  |    -0.84212099  |              |           |    N/A
[285   3]  |      1.1283542  |              |           |    N/A
[285   4]  |      1.6894099  |              |           |    N/A
[286   0]  |     0.10680774  |              |           |    N/A
[286   1]  |     -1.8296834  |              |           |    N/A
[286   2]  |     0.22024607  |              |           |    N/A
[286   3]  |     0.52281929  |              |           |    N/A
[286   4]  |     0.57377973  |              |           |    N/A
[287   0]  |    -0.25071324  |              |           |    N/A
[287   1]  |    -0.83304841  |              |           |    N/A
[287   2]  |     0.69641969  |              |           |    N/A
[287   3]  |     0.70875901  |              |           |    N/A
[287   4]  |    -0.39860598  |              |           |    N/A
[288   0]  |    0.060519585  |              |           |    N/A
[288   1]  |     -1.6687119  |              |           |    N/A
[288   2]  |    -0.76828951  |              |           |    N/A
[288   3]  |     -1.5574972  |              |           |    N/A
[288   4]  |      1.3272527  |              |           |    N/A
[289   0]  |     0.76261463  |              |           |    N/A
[289   1]  |     -1.1055319  |              |           |    N/A
[289   2]  |    -0.86594122  |              |           |    N/A
[289   3]  |     0.44800086  |              |           |    N/A
[289   4]  |     0.27646443  |              |           |    N/A
[290   0]  |     0.21122489  |              |           |    N/A
[290   1]  |     -1.4654719  |              |           |    N/A
[290   2]  |    -0.82783575  |              |           |    N/A
[290   3]  |    0.024943797  |              |           |    N/A
[290   4]  |     0.33651832  |              |           |    N/A
[291   0]  |     0.19296968  |              |           |    N/A
[291   1]  |     -1.5550711  |              |           |    N/A
[291   2]  |     -1.5375729  |              |           |    N/A
[291   3]  |     -1.3015707  |              |           |    N/A
[291   4]  |      1.1171721  |              |           |    N/A
[292   0]  |   -0.075272615  |              |           |    N/A
[292   1]  |     -1.3656201  |              |           |    N/A
[292   2]  |     -1.2435894  |              |           |    N/A
[292   3]  |      -1.201071  |              |           |    N/A
[292   4]  |      1.0866169  |              |           |    N/A
[293   0]  |    -0.63122556  |              |           |    N/A
[293   1]  |     -1.1443705  |              |           |    N/A
[293   2]  |     -1.1690023  |              |           |    N/A
[293   3]  |    0.044897533  |              |           |    N/A
[293   4]  |    0.044429516  |              |           |    N/A
[294   0]  |    -0.71883317  |              |           |    N/A
[294   1]  |    -0.98170064  |              |           |    N/A
[294   2]  |    -0.12979708  |              |           |    N/A
[294   3]  |     -1.2590619  |              |           |    N/A
[294   4]  |     0.49615593  |              |           |    N/A
[295   0]  |     0.02721688  |              |           |    N/A
[295   1]  |     -1.4923147  |              |           |    N/A
[295   2]  |     -1.3935117  |              |           |    N/A
[295   3]  |    0.018380115  |              |           |    N/A
[295   4]  |      1.3372804  |              |           |    N/A
[296   0]  |    -0.63992171  |              |           |    N/A
[296   1]  |     -1.5752549  |              |           |    N/A
[296   2]  |      1.7744251  |              |           |    N/A
[296   3]  |      -1.609849  |              |           |    N/A
[296   4]  |      2.0791899  |              |           |    N/A
[297   0]  |    0.028494928  |              |           |    N/A
[297   1]  |     -1.9563547  |              |           |    N/A
[297   2]  |     0.10546141  |              |           |    N/A
[297   3]  |      0.1663655  |              |           |    N/A
[297   4]  |     0.54935476  |              |           |    N/A
[298   0]  |     -0.4489622  |              |           |    N/A
[298   1]  |     -1.7455185  |              |           |    N/A
[298   2]  |     0.78640827  |              |           |    N/A
[298   3]  |      1.2610935  |              |           |    N/A
[298   4]  |      1.2589962  |              |           |    N/A
[299   0]  |    -0.58262096  |              |           |    N/A
[299   1]  |    -0.84261721  |              |           |    N/A
[299   2]  |      1.6756126  |              |           |    N/A
[299   3]  |     0.31782328  |              |           |    N/A
[299   4]  |     0.80236797  |              |           |    N/A
[300   0]  |    -0.46729376  |              |           |    N/A
[300   1]  |     -1.7119039  |              |           |    N/A
[300   2]  |   0.0091058492  |              |           |    N/A
[300   3]  |      1.6778996  |              |           |    N/A
[300   4]  |      1.4842851  |              |           |    N/A
[301   0]  |    -0.16500867  |              |           |    N/A
[301   1]  |     -1.8489952  |              |           |    N/A
[301   2]  |    -0.53979109  |              |           |    N/A
[301   3]  |     0.61455768  |              |           |    N/A
[301   4]  |     0.99717959  |              |           |    N/A
[302   0]  |    -0.21547063  |              |           |    N/A
[302   1]  |     -1.7202098  |              |           |    N/A
[302   2]  |        0.90159  |              |           |    N/A
[302   3]  |      1.0949186  |              |           |    N/A
[302   4]  |     0.78169895  |              |           |    N/A
[303   0]  |    -0.46644639  |              |           |    N/A
[303   1]  |    -0.81378327  |              |           |    N/A
[303   2]  |    -0.57381631  |              |           |    N/A
[303   3]  |    0.032419976  |              |           |    N/A
[303   4]  |   -0.087583827  |              |           |    N/A
[304   0]  |    -0.49289124  |              |           |    N/A
[304   1]  |    -0.80634591  |              |           |    N/A
[304   2]  |     0.45237796  |              |           |    N/A
[304   3]  |    -0.14894555  |              |           |    N/A
[304   4]  |   -0.031550492  |              |           |    N/A
[305   0]  |    -0.37606301  |              |           |    N/A
[305   1]  |     -1.5228454  |              |           |    N/A
[305   2]  |    -0.57339499  |              |           |    N/A
[305   3]  |     0.85769823  |              |           |    N/A
[305   4]  |       1.650645  |              |           |    N/A
[306   0]  |    -0.18975699  |              |           |    N/A
[306   1]  |     -1.3062251  |              |           |    N/A
[306   2]  |     -1.5362748  |              |           |    N/A
[306   3]  |      -1.341293  |              |           |    N/A
[306   4]  |     0.22736117  |              |           |    N/A
[307   0]  |    -0.48980051  |              |           |    N/A
[307   1]  |    -0.91379629  |              |           |    N/A
[307   2]  |    -0.14981381  |              |           |    N/A
[307   3]  |     0.86139654  |              |           |    N/A
[307   4]  |     0.17053329  |              |           |    N/A
[308   0]  |    -0.46040917  |              |           |    N/A
[308   1]  |    -0.53206359  |              |           |    N/A
[308   2]  |     0.23235583  |              |           |    N/A
[308   3]  |       2.301328  |              |           |    N/A
[308   4]  |     0.11125743  |              |           |    N/A
[309   0]  |     0.40857925  |              |           |    N/A
[309   1]  |     -1.6379197  |              |           |    N/A
[309   2]  |     0.65068613  |              |           |    N/A
[309   3]  |     0.51600147  |              |           |    N/A
[309   4]  |      0.7611934  |              |           |    N/A
[310   0]  |     0.82302009  |              |           |    N/A
[310   1]  |     0.10987953  |              |           |    N/A
[310   2]  |     -1.5562344  |              |           |    N/A
[310   3]  |     -1.4369645  |              |           |    N/A
[310   4]  |      0.2851506  |              |           |    N/A
[311   0]  |   -0.070577454  |              |           |    N/A
[311   1]  |     -1.2382726  |              |           |    N/A
[311   2]  |     0.18697341  |              |           |    N/A
[311   3]  |    -0.48780538  |              |           |    N/A
[311   4]  |   -0.085003363  |              |           |    N/A
[312   0]  |     0.49184604  |              |           |    N/A
[312   1]  |     -1.5769251  |              |           |    N/A
[312   2]  |     0.62645515  |              |           |    N/A
[312   3]  |     0.13261042  |              |           |    N/A
[312   4]  |      0.5457622  |              |           |    N/A
[313   0]  |    -0.46621528  |              |           |    N/A
[313   1]  |     -1.8677992  |              |           |    N/A
[313   2]  |     0.66017943  |              |           |    N/A
[313   3]  |     0.70921663  |              |           |    N/A
[313   4]  |      1.1799784  |              |           |    N/A
[314   0]  |    -0.37400936  |              |           |    N/A
[314   1]  |     -1.6834969  |              |           |    N/A
[314   2]  |    -0.55969844  |              |           |    N/A
[314   3]  |     -1.0333583  |              |           |    N/A
[314   4]  |      1.6937075  |              |           |    N/A
[315   0]  |       -0.72537  |              |           |    N/A
[315   1]  |     -1.8461147  |              |           |    N/A
[315   2]  |      0.4531435  |              |           |    N/A
[315   3]  |     0.68506947  |              |           |    N/A
[315   4]  |      1.3201936  |              |           |    N/A
[316   0]  |    -0.68078834  |              |           |    N/A
[316   1]  |     -1.7669602  |              |           |    N/A
[316   2]  |    -0.16612833  |              |           |    N/A
[316   3]  |     0.13381419  |              |           |    N/A
[316   4]  |       1.652347  |              |           |    N/A
[317   0]  |    -0.42688314  |              |           |    N/A
[317   1]  |     -1.4065926  |              |           |    N/A
[317   2]  |    -0.11150564  |              |           |    N/A
[317   3]  |     -1.1589298  |              |           |    N/A
[317   4]  |     0.26852501  |              |           |    N/A
[318   0]  |    0.021463562  |              |           |    N/A
[318   1]  |     -1.7030605  |              |           |    N/A
[318   2]  |    -0.32636872  |              |           |    N/A
[318   3]  |     0.72989742  |              |           |    N/A
[318   4]  |     0.80571791  |              |           |    N/A
[319   0]  |    -0.54655674  |              |           |    N/A
[319   1]  |     -0.5928447  |              |           |    N/A
[319   2]  |      1.9761612  |              |           |    N/A
[319   3]  |      1.2707787  |              |           |    N/A
[319   4]  |   -0.018046675  |              |           |    N/A
[320   0]  |    -0.22543537  |              |           |    N/A
[320   1]  |     -1.4730983  |              |           |    N/A
[320   2]  |     -1.1713179  |              |           |    N/A
[320   3]  |     0.99582384  |              |           |    N/A
[320   4]  |      1.3408475  |              |           |    N/A
[321   0]  |    -0.33252908  |              |           |    N/A
[321   1]  |     -0.9661308  |              |           |    N/A
[321   2]  |      1.7735912  |              |           |    N/A
[321   3]  |    -0.54017044  |              |           |    N/A
[321   4]  |   -0.055975653  |              |           |    N/A
[322   0]  |   -0.035358089  |              |           |    N/A
[322   1]  |     -1.4837955  |              |           |    N/A
[322   2]  |   -0.086440238  |              |           |    N/A
[322   3]  |     -2.4694696  |              |           |    N/A
[322   4]  |       1.270724  |              |           |    N/A
[323   0]  |     0.23007479  |              |           |    N/A
[323   1]  |     -1.5975994  |              |           |    N/A
[323   2]  |     -1.8607377  |              |           |    N/A
[323   3]  |    -0.82202625  |              |           |    N/A
[323   4]  |      1.0422344  |              |           |    N/A
[324   0]  |     0.56265934  |              |           |    N/A
[324   1]  |     -1.6170419  |              |           |    N/A
[324   2]  |     -1.9162011  |              |           |    N/A
[324   3]  |     -1.3892741  |              |           |    N/A
[324   4]  |     0.20411191  |              |           |    N/A
[325   0]  |     -0.3744509  |              |           |    N/A
[325   1]  |     -1.8383164  |              |           |    N/A
[325   2]  |    -0.59546382  |              |           |    N/A
[325   3]  |    -0.22285848  |              |           |    N/A
[325   4]  |      1.4815139  |              |           |    N/A
[326   0]  |    -0.62366405  |              |           |    N/A
[326   1]  |     -1.7004402  |              |           |    N/A
[326   2]  |    -0.40517124  |              |           |    N/A
[326   3]  |     0.56138406  |              |           |    N/A
[326   4]  |      1.5711392  |              |           |    N/A
[327   0]  |     0.53551683  |              |           |    N/A
[327   1]  |     -1.1793747  |              |           |    N/A
[327   2]  |     -1.5227214  |              |           |    N/A
[327   3]  |     0.15365292  |              |           |    N/A
[327   4]  |    -0.38799009  |              |           |    N/A
[328   0]  |    -0.25634027  |              |           |    N/A
[328   1]  |    -0.77313394  |              |           |    N/A
[328   2]  |     -1.4650413  |              |           |    N/A
[328   3]  |    -0.12647891  |              |           |    N/A
[328   4]  |     0.13726144  |              |           |    N/A
[329   0]  |    -0.63074429  |              |           |    N/A
[329   1]  |    -0.86712769  |              |           |    N/A
[329   2]  |     -1.0220996  |              |           |    N/A
[329   3]  |    0.082290092  |              |           |    N/A
[329   4]  |      0.4475059  |              |           |    N/A
use left and right mouse buttons to select dimensions


Observations

Confirm the following observations by interacting with the demo:

• We tend to obtain more "strange" outputs when sampling from latent space areas away from the training inputs.
• When sampling from the two dominant latent dimensions (the ones corresponding to large scales) we differentiate between all digits. Also note that projecting the latent space into the two dominant dimensions better separates the classes.
• When sampling from less dominant latent dimensions the outputs vary in a more subtle way.

You can also run the dimensionality reduction example

In [ ]:
GPy.examples.dimensionality_reduction.bgplvm_simulation()


Questions

• Can you see a difference in the ARD parameters to the non Bayesian GPLVM?
• How does the Bayesian GPLVM allow the ARD parameters of the RBF kernel magnify the two first dimensions?
• Is Bayesian GPLVM better in differentiating between different kinds of digits?
• Why does the starting noise variance have to be lower then the variance of the observed values?
• How come we use the lowest variance when using a linear kernel, but the highest lengtscale when using an RBF kernel?

## References¶

C. M. Bishop. Pattern recognition and machine learning, volume 1. springer New York, 2006.

T. de Campos, B. R. Babu, and M. Varma. Character recognition in natural images. VISAPP 2009.

N. D. Lawrence. Probabilistic non-linear principal component analysis with Gaussian process latent variable models. In Journal of Machine Learning Research 6, pp 1783--1816, 2005