Dimensionality Reduction with Gaussian Processes

Gaussian Process Winter School, Genova, Italy

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 
--> 258         opt.run(f_fp=self._objective_grads, f=self._objective, fp=self._grads)
    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)
    187     d = {'grad': res['jac'],
    188          'task': res['message'],

/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)
    315         elif task_str.startswith(b'NEW_X'):
    316             # new iteration

/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/lbfgsb.pyc in func_and_grad(x)
    263     else:
    264         def func_and_grad(x):
--> 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]

/Users/neil/SheffieldML/GPy/GPy/core/model.pyc in _objective_grads(self, x)
    200     def _objective_grads(self, x):
    201         try:
--> 202             self.optimizer_array = x
    203             obj_f, obj_grads = self.objective_function(), self._transform_gradients(self.objective_function_gradients())
    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:

/Users/neil/SheffieldML/GPy/GPy/core/parameterization/parameter_core.pyc in _parameters_changed_notification(self, me, which)
    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()
     44         self.X.gradient = self.kern.gradients_X(self.grad_dict['dL_dK'], self.X, None)
     45 

/Users/neil/SheffieldML/GPy/GPy/core/gp.pyc in parameters_changed(self)
    153             this method yourself, there may be unexpected consequences.
    154         """
--> 155         self.posterior, self._log_marginal_likelihood, self.grad_dict = self.inference_method.inference(self.kern, self.X, self.likelihood, self.Y_normalized, self.Y_metadata)
    156         self.likelihood.update_gradients(self.grad_dict['dL_dthetaL'])
    157         self.kern.update_gradients_full(self.grad_dict['dL_dK'], self.X)

/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 
     57         dL_dthetaL = likelihood.exact_inference_gradients(np.diag(dL_dK),Y_metadata)

/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 1 answer

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 " \
 ^
/Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1093.cpp:24:10: fatal error: 'omp.h' file not found
#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?

# Exercise 3 answer

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

if re or not os.path.exists(model_path): # only download the model new, if it was not already
    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 = int(meta.getheaders("Content-Length")[0])
        print "Downloading: %s" % (model_path)

        file_size_dl = 0
        block_sz = 8192
        while True:
            buff = u.read(block_sz)
            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:
    print "Already cached, to reload run with 'reload' as the only argument"
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:
    model = pickle.load(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 " \
 ^
/Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1094.cpp:24:10: fatal error: 'omp.h' file not found
#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))
ax_latent = fig.add_subplot(121)
ax_scales = fig.add_subplot(122)

fig_out = plt.figure('Output', figsize=(1,1))
ax_image  = fig_out.add_subplot(111)
fig_out.tight_layout(pad=0)

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