[merge] merge master into devel

This commit is contained in:
Max Zwiessele 2015-09-08 17:25:44 +01:00
commit cf2673632b
12 changed files with 257 additions and 314 deletions

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@ -1,222 +0,0 @@
/home/maxz/Documents/gpy/GPy/__init__.py:docstring of GPy.load:1: WARNING: Inline interpreted text or phrase reference start-string without end-string.
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.optimize:8: ERROR: Unknown interpreted text role "module".
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predict_wishard_embedding:6: WARNING: Field list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:5: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:10: WARNING: Block quote ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/core/model.py:docstring of GPy.core.model.Model.optimize_restarts:29: WARNING: Explicit markup ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/doc/GPy.core.rst:57: WARNING: autodoc: failed to import module u'GPy.core.svigp'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named svigp
/home/maxz/Documents/gpy/doc/GPy.core.rst:65: WARNING: autodoc: failed to import module u'GPy.core.symbolic'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
File "/home/maxz/Documents/gpy/GPy/core/symbolic.py", line 10, in <module>
from sympy.utilities.lambdify import lambdastr, _imp_namespace, _get_namespace
ImportError: No module named lambdify
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Indexable.unset_priors:1: WARNING: Inline emphasis start-string without end-string.
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Nameable.hierarchy_name:4: WARNING: Field list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Parameterizable.traverse:1: WARNING: Inline emphasis start-string without end-string.
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Parameterizable.traverse:1: WARNING: Inline strong start-string without end-string.
/home/maxz/Documents/gpy/GPy/core/parameterization/parameterized.py:docstring of GPy.core.parameterization.parameterized.Parameterized:18: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/GPy/core/parameterization/parameterized.py:docstring of GPy.core.parameterization.parameterized.Parameterized:20: WARNING: Block quote ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/core/parameterization/ties_and_remappings.py:docstring of GPy.core.parameterization.ties_and_remappings.Tie:18: SEVERE: Unexpected section title or transition.
================================
/home/maxz/Documents/gpy/doc/GPy.examples.rst:50: WARNING: autodoc: failed to import module u'GPy.examples.stochastic'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named stochastic
/home/maxz/Documents/gpy/doc/GPy.examples.rst:58: WARNING: autodoc: failed to import module u'GPy.examples.tutorials'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named tutorials
/home/maxz/Documents/gpy/doc/GPy.inference.latent_function_inference.rst:82: WARNING: autodoc: failed to import module u'GPy.inference.latent_function_inference.var_dtc_gpu'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named var_dtc_gpu
/home/maxz/Documents/gpy/doc/GPy.inference.optimization.rst:42: WARNING: autodoc: failed to import module u'GPy.inference.optimization.sgd'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named sgd
/home/maxz/Documents/gpy/GPy/kern/_src/coregionalize.py:docstring of GPy.kern._src.coregionalize.Coregionalize:5: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/doc/GPy.kern._src.rst:73: WARNING: autodoc: failed to import module u'GPy.kern._src.hierarchical'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named hierarchical
/home/maxz/Documents/gpy/GPy/kern/_src/independent_outputs.py:docstring of GPy.kern._src.independent_outputs.IndependentOutputs:9: WARNING: Field list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:24: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:22: WARNING: Inline literal start-string without end-string.
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:25: WARNING: Block quote ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:27: WARNING: Definition list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:27: WARNING: Inline literal start-string without end-string.
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:27: WARNING: Inline interpreted text or phrase reference start-string without end-string.
/home/maxz/Documents/gpy/doc/GPy.kern._src.rst:177: WARNING: autodoc: failed to import module u'GPy.kern._src.symbolic'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
File "/home/maxz/Documents/gpy/GPy/kern/_src/symbolic.py", line 5, in <module>
from ...core.symbolic import Symbolic_core
File "/home/maxz/Documents/gpy/GPy/core/symbolic.py", line 10, in <module>
from sympy.utilities.lambdify import lambdastr, _imp_namespace, _get_namespace
ImportError: No module named lambdify
/home/maxz/Documents/gpy/GPy/models/gp_kronecker_gaussian_regression.py:docstring of GPy.models.gp_kronecker_gaussian_regression.GPKroneckerGaussianRegression:13: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/GPy/models/gp_kronecker_gaussian_regression.py:docstring of GPy.models.gp_kronecker_gaussian_regression.GPKroneckerGaussianRegression:18: WARNING: Block quote ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/doc/GPy.models.rst:66: WARNING: autodoc: failed to import module u'GPy.models.gp_multioutput_regression'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named gp_multioutput_regression
/home/maxz/Documents/gpy/GPy/models/gp_var_gauss.py:docstring of GPy.models.gp_var_gauss.GPVariationalGaussianApproximation:9: WARNING: Definition list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:32: WARNING: Field list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:32: WARNING: Inline interpreted text or phrase reference start-string without end-string.
/home/maxz/Documents/gpy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:34: WARNING: Definition list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/doc/GPy.models.rst:138: WARNING: autodoc: failed to import module u'GPy.models.sparse_gp_multioutput_regression'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named sparse_gp_multioutput_regression
/home/maxz/Documents/gpy/doc/GPy.models.rst:178: WARNING: autodoc: failed to import module u'GPy.models.svigp_regression'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named svigp_regression
/home/maxz/Documents/gpy/GPy/plotting/matplot_dep/netpbmfile.py:docstring of GPy.plotting.matplot_dep.netpbmfile.imread:6: SEVERE: Unexpected section title.
Examples
--------
/home/maxz/Documents/gpy/GPy/plotting/matplot_dep/netpbmfile.py:docstring of GPy.plotting.matplot_dep.netpbmfile.imsave:4: SEVERE: Unexpected section title.
Examples
--------
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_checkgrad:6: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_checkgrad:7: WARNING: Block quote ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_partial:7: WARNING: Definition list ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_partial:9: ERROR: Unexpected indentation.
docstring of GPy.util.datasets.hapmap3:7: WARNING: Block quote ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/doc/GPy.util.rst:74: WARNING: autodoc: failed to import module u'GPy.util.erfcx'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named erfcx
/home/maxz/Documents/gpy/doc/GPy.util.rst:146: WARNING: autodoc: failed to import module u'GPy.util.mpi'; the following exception was raised:
Traceback (most recent call last):
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
__import__(self.modname)
ImportError: No module named mpi
/home/maxz/Documents/gpy/GPy/util/netpbmfile.py:docstring of GPy.util.netpbmfile.imread:6: SEVERE: Unexpected section title.
Examples
--------
/home/maxz/Documents/gpy/GPy/util/netpbmfile.py:docstring of GPy.util.netpbmfile.imsave:4: SEVERE: Unexpected section title.
Examples
--------
/home/maxz/Documents/gpy/doc/GPy.util.rst:2: SEVERE: Duplicate ID: "module-GPy.util.subarray_and_sorting".
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:8: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:11: SEVERE: Unexpected section title.
Examples:
=========
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:19: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:21: WARNING: Block quote ends without a blank line; unexpected unindent.
/home/maxz/Documents/gpy/GPy/util/block_matrices.py:docstring of GPy.util.block_matrices.block_dot:3: ERROR: Undefined substitution referenced: "A11.B11|B12.B12".
/home/maxz/Documents/gpy/GPy/util/block_matrices.py:docstring of GPy.util.block_matrices.block_dot:3: ERROR: Undefined substitution referenced: "A21.B21|A22.B22".
/home/maxz/Documents/gpy/doc/installation.rst:22: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/doc/installation.rst:27: ERROR: Unexpected indentation.
/home/maxz/Documents/gpy/doc/tuto_creating_new_kernels.rst:58: WARNING: Inline literal start-string without end-string.
/home/maxz/Documents/gpy/doc/tuto_creating_new_models.rst:24: ERROR: Unknown target name: "parameterized".
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:83: WARNING: Title underline too short.
Interacting with Parameters:
=======================
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Interacting with Parameters:
=======================
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Regular expressions
----------------
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:164: WARNING: Title underline too short.
Setting and fetching parameters `parameter_array`
------------------------------------------
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Setting and fetching parameters `parameter_array`
------------------------------------------
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Getting the model parameter's gradients
============================
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Getting the model parameter's gradients
============================
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:236: WARNING: Title underline too short.
Adjusting the model's constraints
================================
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Adjusting the model's constraints
================================
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Available Constraints
==============
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Available Constraints
==============
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Tying Parameters
============
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Tying Parameters
============
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*******************
Parameterization handling
*******************
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Parameter handles
==============
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:py:class:`~GPy.core.parameterization.parameterized.Parameterized`
==========
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:py:class:`~GPy.core.parameterization.parameterized.Parameterized`
==========
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:py:class:`~GPy.core.parameterization.param.Param`
===========
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:py:class:`~GPy.core.parameterization.param.Param`
===========
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@ -13,9 +13,9 @@ First we import the libraries we will need ::
For most kernels, the dimension is the only mandatory parameter to define a kernel object. However, it is also possible to specify the values of the parameters. For example, the three following commands are valid for defining a squared exponential kernel (ie rbf or Gaussian) ::
ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(input_dim=1, variance = .75, lengthscale=2.)
ker3 = GPy.kern.rbf(1, .5, .5)
ker1 = GPy.kern.RBF(1) # Equivalent to ker1 = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.RBF(input_dim=1, variance = .75, lengthscale=2.)
ker3 = GPy.kern.RBF(1, .5, .5)
A ``print`` and a ``plot`` functions are implemented to represent kernel objects. The commands ::
@ -52,21 +52,18 @@ Operations to combine kernels
In ``GPy``, kernel objects can be added or multiplied. In both cases, two kinds of operations are possible since one can assume that the kernels to add/multiply are defined on the same space or on different subspaces. In other words, it is possible to use two kernels :math:`k_1,\ k_2` over :math:`\mathbb{R} \times \mathbb{R}` to create
* a kernel over :math:`\mathbb{R} \times \mathbb{R}`: :math:`k(x,y) = k_1(x,y) \times k_2(x,y)`
* a kernel over :math:`\mathbb{R}^2 \times \mathbb{R}^2`: :math:`k(\mathbf{x},\mathbf{y}) = k_1(x_1,y_1) \times k_2(x_2,y_2)`
* a kernel over :math:`\mathbb{R} \times \mathbb{R}`: :math:`k(x,y) = k_1(x,y) \times k_2(x,y)`.
These two options are available in GPy using the flag ``tensor`` in the ``add`` and ``prod`` functions. Here is a quick example ::
This is available in GPy via the ``add`` and ``prod`` functions. Here is a quick example ::
k1 = GPy.kern.rbf(1,1.,2.)
k1 = GPy.kern.RBF(1,1.,2.)
k2 = GPy.kern.Matern32(1, 0.5, 0.2)
# Product of kernels
k_prod = k1.prod(k2) # By default, tensor=False
k_prodtens = k1.prod(k2,tensor=True)
k_prod = k1.prod(k2)
# Sum of kernels
k_add = k1.add(k2) # By default, tensor=False
k_addtens = k1.add(k2,tensor=True)
k_add = k1.add(k2)
.. # plots
pb.figure(figsize=(8,8))
@ -75,23 +72,23 @@ These two options are available in GPy using the flag ``tensor`` in the ``add``
pb.title('prod')
pb.subplot(2,2,2)
k_prodtens.plot()
pb.title('tensor prod')
pb.title('prod')
pb.subplot(2,2,3)
k_add.plot()
pb.title('sum')
pb.subplot(2,2,4)
k_addtens.plot()
pb.title('tensor sum')
pb.title('sum')
pb.subplots_adjust(wspace=0.3, hspace=0.3)
.. figure:: Figures/tuto_kern_overview_multadd.png
:align: center
:height: 500px
A shortcut for ``add`` and ``prod`` (with default flag ``tensor=False``) is provided by the usual ``+`` and ``*`` operators. Here is another example where we create a periodic kernel with some decay ::
A shortcut for ``add`` and ``prod`` is provided by the usual ``+`` and ``*`` operators. Here is another example where we create a periodic kernel with some decay ::
k1 = GPy.kern.rbf(1,1.,2)
k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
k1 = GPy.kern.RBF(1,1.,2)
k2 = GPy.kern.PeriodicMatern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
k = k1 * k2 # equivalent to k = k1.prod(k2)
print k
@ -116,14 +113,14 @@ A shortcut for ``add`` and ``prod`` (with default flag ``tensor=False``) is prov
In general, ``kern`` objects can be seen as a sum of ``kernparts`` objects, where the later are covariance functions defined on the same space. For example, the following code ::
k = (k1+k2)*(k1+k2)
print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[2].name, '\n', k.parts[3].name
print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[1].parts[0].name, '\n', k.parts[1].parts[1].name, '\n'
returns ::
add_1
add_2
rbf
periodic_Matern52
rbf<times>rbf
rbf<times>periodic_Mat52
periodic_Mat52<times>rbf
periodic_Mat52<times>periodic_Mat52
Constraining the parameters
===========================
@ -137,9 +134,9 @@ Various constrains can be applied to the parameters of a kernel
When calling one of these functions, the parameters to constrain can either by specified by a regular expression that matches its name or by a number that corresponds to the rank of the parameter. Here is an example ::
k1 = GPy.kern.rbf(1)
k1 = GPy.kern.RBF(1)
k2 = GPy.kern.Matern32(1)
k3 = GPy.kern.white(1)
k3 = GPy.kern.White(1)
k = k1 + k2 + k3
print k
@ -182,9 +179,9 @@ In two dimensions ANOVA kernels have the following form:
Let us assume that we want to define an ANOVA kernel with a Matern 3/2 kernel for :math:`k_i`. As seen previously, we can define this kernel as follows ::
k_cst = GPy.kern.bias(1,variance=1.)
k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
Kanova = (k_cst + k_mat).prod(k_cst + k_mat,tensor=True)
k_cst = GPy.kern.Bias(1,variance=1.)
k_mat = GPy.kern.Matern52(1,variance=1.,lengthscale=3)
Kanova = (k_cst + k_mat).prod(k_cst + k_mat)
print Kanova
Printing the resulting kernel outputs the following ::
@ -257,17 +254,17 @@ The submodels can be represented with the option ``which_function`` of ``plot``:
import GPy
pb.ion()
ker1 = GPy.kern.rbf(D=1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=3.)
ker3 = GPy.kern.rbf(1, .5, .25)
ker1 = GPy.kern.RBF(D=1) # Equivalent to ker1 = GPy.kern.RBF(D=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.RBF(D=1, variance = .75, lengthscale=3.)
ker3 = GPy.kern.RBF(1, .5, .25)
ker1.plot()
ker2.plot()
ker3.plot()
#pb.savefig("Figures/tuto_kern_overview_basicdef.png")
kernels = [GPy.kern.rbf(1), GPy.kern.exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.bias(1), GPy.kern.linear(1), GPy.kern.spline(1), GPy.kern.periodic_exponential(1), GPy.kern.periodic_Matern32(1), GPy.kern.periodic_Matern52(1), GPy.kern.white(1)]
kernel_names = ["GPy.kern.rbf", "GPy.kern.exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.bias", "GPy.kern.linear", "GPy.kern.spline", "GPy.kern.periodic_exponential", "GPy.kern.periodic_Matern32", "GPy.kern.periodic_Matern52", "GPy.kern.white"]
kernels = [GPy.kern.RBF(1), GPy.kern.Exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.Bias(1), GPy.kern.Linear(1), GPy.kern.PeriodicExponential(1), GPy.kern.PeriodicMatern32(1), GPy.kern.PeriodicMatern52(1), GPy.kern.White(1)]
kernel_names = ["GPy.kern.RBF", "GPy.kern.Exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.Bias", "GPy.kern.Linear", "GPy.kern.PeriodicExponential", "GPy.kern.PeriodicMatern32", "GPy.kern.PeriodicMatern52", "GPy.kern.White"]
pb.figure(figsize=(16,12))
pb.subplots_adjust(wspace=.5, hspace=.5)