Fix lint issues related to comparisons with None

limit upper pytest version in workflows

.github/workflows/test-and-deploy.yml

@@ -39,7 +39,7 @@ jobs:
       - name: Install test dependencies
         run: |
           pip install matplotlib
-          pip install pytest
+          pip install 'pytest<8'
 
       - name: pytest
         run: |
@@ -71,7 +71,7 @@ jobs:
       - name: Install test dependencies
         run: |
           pip install matplotlib
-          pip install pytest
+          pip install 'pytest<8'
 
       - name: pytest
         run: |
@@ -103,7 +103,7 @@ jobs:
       - name: Install test dependencies
         run: |
           pip install matplotlib
-          pip install pytest
+          pip install 'pytest<8'
 
       - name: pytest
         run: |

CHANGELOG.md

@@ -1,6 +1,11 @@
 # Changelog
 
 ## Unreleased
+* fix pickle and deep copy for classification models inheriting from EP #1108 [olamarre]
+
+* update prior `__new__` methods #1098 [MartinBubel]
+
+* fix invalid escape sequence #1011 [janmayer]
 
 ## v1.13.2 (2024-07-21)
 * update string checks in initialization method for latent variable and put `empirical_samples` init-method on a deprecation path

GPy/core/gp.py

@@ -194,7 +194,7 @@ class GP(Model):
     # Make sure to name this variable and the predict functions will "just work"
     # In maths the predictive variable is:
     #         K_{xx} - K_{xp}W_{pp}^{-1}K_{px}
-    #         W_{pp} := \texttt{Woodbury inv}
+    #         W_{pp} := \\texttt{Woodbury inv}
     #         p := _predictive_variable
 
     @property
@@ -283,7 +283,7 @@ class GP(Model):
 
     def log_likelihood(self):
         """
-        The log marginal likelihood of the model, :math:`p(\mathbf{y})`, this is the objective function of the model being optimised
+        The log marginal likelihood of the model, :math:`p(\\mathbf{y})`, this is the objective function of the model being optimised
         """
         return self._log_marginal_likelihood
 
@@ -296,9 +296,9 @@ class GP(Model):
         diagonal of the covariance is returned.
 
         .. math::
-            p(f*|X*, X, Y) = \int^{\inf}_{\inf} p(f*|f,X*)p(f|X,Y) df
-                        = N(f*| K_{x*x}(K_{xx} + \Sigma)^{-1}Y, K_{x*x*} - K_{xx*}(K_{xx} + \Sigma)^{-1}K_{xx*}
-            \Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance}
+            p(f*|X*, X, Y) = \\int^{\\inf}_{\\inf} p(f*|f,X*)p(f|X,Y) df
+                        = N(f*| K_{x*x}(K_{xx} + \\Sigma)^{-1}Y, K_{x*x*} - K_{xx*}(K_{xx} + \\Sigma)^{-1}K_{xx*}
+            \\Sigma := \\texttt{Likelihood.variance / Approximate likelihood covariance}
         """
         mu, var = self.posterior._raw_predict(kern=self.kern if kern is None else kern, Xnew=Xnew, pred_var=self._predictive_variable, full_cov=full_cov)
         if self.mean_function is not None:
@@ -702,7 +702,7 @@ class GP(Model):
         Calculation of the log predictive density
 
         .. math:
-            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
+            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\\mu_{*}\\sigma^{2}_{*})
 
         :param x_test: test locations (x_{*})
         :type x_test: (Nx1) array
@@ -718,7 +718,7 @@ class GP(Model):
         Calculation of the log predictive density by sampling
 
         .. math:
-            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
+            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\\mu_{*}\\sigma^{2}_{*})
 
         :param x_test: test locations (x_{*})
         :type x_test: (Nx1) array
@@ -734,24 +734,24 @@ class GP(Model):
 
     def _raw_posterior_covariance_between_points(self, X1, X2):
         """
-        Computes the posterior covariance between points. Does not account for 
+        Computes the posterior covariance between points. Does not account for
         normalization or likelihood
 
         :param X1: some input observations
         :param X2: other input observations
 
-        :returns: 
+        :returns:
             cov: raw posterior covariance: k(X1,X2) - k(X1,X) G^{-1} K(X,X2)
         """
         return self.posterior.covariance_between_points(self.kern, self.X, X1, X2)
 
 
-    def posterior_covariance_between_points(self, X1, X2, Y_metadata=None, 
-                                            likelihood=None, 
+    def posterior_covariance_between_points(self, X1, X2, Y_metadata=None,
+                                            likelihood=None,
                                             include_likelihood=True):
         """
-        Computes the posterior covariance between points. Includes likelihood 
-        variance as well as normalization so that evaluation at (x,x) is consistent 
+        Computes the posterior covariance between points. Includes likelihood
+        variance as well as normalization so that evaluation at (x,x) is consistent
         with model.predict
 
         :param X1: some input observations
@@ -762,8 +762,8 @@ class GP(Model):
                                    the predicted underlying latent function f.
         :type include_likelihood: bool
 
-        :returns: 
-            cov: posterior covariance, a Numpy array, Nnew x Nnew if 
+        :returns:
+            cov: posterior covariance, a Numpy array, Nnew x Nnew if
             self.output_dim == 1, and Nnew x Nnew x self.output_dim otherwise.
         """
 
@@ -774,7 +774,7 @@ class GP(Model):
             mean, _ = self._raw_predict(X1, full_cov=True)
             if likelihood is None:
                 likelihood = self.likelihood
-            _, cov = likelihood.predictive_values(mean, cov, full_cov=True, 
+            _, cov = likelihood.predictive_values(mean, cov, full_cov=True,
                                                   Y_metadata=Y_metadata)
 
         if self.normalizer is not None:

GPy/core/parameterization/priors.py

@@ -580,7 +580,11 @@ class DGPLVM(Prior):
     domain = _REAL
 
     def __new__(cls, sigma2, lbl, x_shape):
-        return super(Prior, cls).__new__(cls, sigma2, lbl, x_shape)
+        newfunc = super(Prior, cls).__new__
+        if newfunc is object.__new__:
+            return newfunc(cls)
+        else:
+            return newfunc(cls, sigma2, lbl, x_shape)
 
     def __init__(self, sigma2, lbl, x_shape):
         self.sigma2 = sigma2
@@ -1275,7 +1279,12 @@ class HalfT(Prior):
             for instance in cls._instances:
                 if instance().A == A and instance().nu == nu:
                     return instance()
-        o = super(Prior, cls).__new__(cls, A, nu)
+
+        newfunc = super(Prior, cls).__new__
+        if newfunc is object.__new__:
+            o = newfunc(cls)
+        else:
+            o = newfunc(cls, A, nu)
         cls._instances.append(weakref.ref(o))
         return cls._instances[-1]()
 

GPy/core/sparse_gp_mpi.py

@@ -38,7 +38,7 @@ class SparseGP_MPI(SparseGP):
                  mean_function=None, inference_method=None, name='sparse gp',
                  Y_metadata=None, mpi_comm=None, normalizer=False):
         self._IN_OPTIMIZATION_ = False
-        if mpi_comm != None:
+        if mpi_comm is not None:
             if inference_method is None:
                 inference_method = VarDTC_minibatch(mpi_comm=mpi_comm)
             else:
@@ -52,7 +52,7 @@ class SparseGP_MPI(SparseGP):
 
         self.mpi_comm = mpi_comm
         # Manage the data (Y) division
-        if mpi_comm != None:
+        if mpi_comm is not None:
             from ..util.parallel import divide_data
             N_start, N_end, N_list = divide_data(Y.shape[0], mpi_comm.rank, mpi_comm.size)
             self.N_range = (N_start, N_end)
@@ -65,7 +65,7 @@ class SparseGP_MPI(SparseGP):
     def __getstate__(self):
         dc = super(SparseGP_MPI, self).__getstate__()
         dc['mpi_comm'] = None
-        if self.mpi_comm != None:
+        if self.mpi_comm is not None:
             del dc['N_range']
             del dc['N_list']
             del dc['Y_local']
@@ -81,7 +81,7 @@ class SparseGP_MPI(SparseGP):
 
     @SparseGP.optimizer_array.setter
     def optimizer_array(self, p):
-        if self.mpi_comm != None:
+        if self.mpi_comm is not None:
             if self._IN_OPTIMIZATION_ and self.mpi_comm.rank==0:
                 self.mpi_comm.Bcast(np.int32(1),root=0)
             self.mpi_comm.Bcast(p, root=0)

GPy/core/symbolic.py

@@ -44,7 +44,7 @@ class Symbolic_core():
         self._set_derivatives(derivatives)
         self._set_parameters(parameters)
         # Convert the expressions to a list for common sub expression elimination
-        # We should find the following type of expressions: 'function', 'derivative', 'second_derivative', 'third_derivative'. 
+        # We should find the following type of expressions: 'function', 'derivative', 'second_derivative', 'third_derivative'.
         self.update_expression_list()
 
         # Apply any global stabilisation operations to expressions.
@@ -86,7 +86,7 @@ class Symbolic_core():
         # object except as cached. For covariance functions this is X
         # and Z, for likelihoods F and for mapping functions X.
         self.cacheable_vars = [] # list of everything that's cacheable
-        for var in cacheable:            
+        for var in cacheable:
             self.variables[var] = [e for e in vars if e.name.split('_')[0]==var.lower()]
             self.cacheable_vars += self.variables[var]
         for var in cacheable:
@@ -105,7 +105,7 @@ class Symbolic_core():
             for derivative in derivatives:
                 derivative_arguments += self.variables[derivative]
 
-            # Do symbolic work to compute derivatives.        
+            # Do symbolic work to compute derivatives.
             for key, func in self.expressions.items():
                 # if func['function'].is_Matrix:
                 #     rows = func['function'].shape[0]
@@ -126,7 +126,7 @@ class Symbolic_core():
                 if theta.name in parameters:
                     val = parameters[theta.name]
             # Add parameter.
-            
+
             self.link_parameters(Param(theta.name, val, None))
             #self._set_attribute(theta.name, )
 
@@ -174,7 +174,7 @@ class Symbolic_core():
             code = self.code[function]['derivative'][theta.name]
             gradient[theta.name] = (partial*eval(code, self.namespace)).sum()
         return gradient
-        
+
     def eval_gradients_X(self, function, partial, **kwargs):
         if 'X' in kwargs:
             gradients_X = np.zeros_like(kwargs['X'])
@@ -194,7 +194,7 @@ class Symbolic_core():
         for variable, code in self.variable_sort(self.code['parameters_changed']):
             lcode += self._print_code(variable) + ' = ' + self._print_code(code) + '\n'
         return lcode
-    
+
     def code_update_cache(self):
         lcode = ''
         for var in self.cacheable:
@@ -208,7 +208,7 @@ class Symbolic_core():
             for i, theta in enumerate(self.variables[var]):
                 lcode+= "\t" + var + '= np.atleast_2d(' + var + ')\n'
                 lcode+= "\t" + self._print_code(theta.name) + ' = ' + var + '[:, ' + str(i) + "]" + reorder + "\n"
-    
+
         for variable, code in self.variable_sort(self.code['update_cache']):
             lcode+= self._print_code(variable) + ' = ' + self._print_code(code) + "\n"
 
@@ -250,7 +250,7 @@ class Symbolic_core():
         """Make sure namespace gets updated when setting attributes."""
         setattr(self, name, value)
         self.namespace.update({name: getattr(self, name)})
-        
+
 
     def update_expression_list(self):
         """Extract a list of expressions from the dictionary of expressions."""
@@ -260,9 +260,9 @@ class Symbolic_core():
         for fname, fexpressions in self.expressions.items():
             for type, texpressions in fexpressions.items():
                 if type == 'function':
-                    self.expression_list.append(texpressions)            
+                    self.expression_list.append(texpressions)
                     self.expression_keys.append([fname, type])
-                    self.expression_order.append(1) 
+                    self.expression_order.append(1)
                 elif type[-10:] == 'derivative':
                     for dtype, expression in texpressions.items():
                         self.expression_list.append(expression)
@@ -274,9 +274,9 @@ class Symbolic_core():
                         elif type[:-10] == 'third_':
                             self.expression_order.append(5) #sym.count_ops(self.expressions[type][dtype]))
                 else:
-                    self.expression_list.append(fexpressions[type])            
+                    self.expression_list.append(fexpressions[type])
                     self.expression_keys.append([fname, type])
-                    self.expression_order.append(2) 
+                    self.expression_order.append(2)
 
         # This step may be unecessary.
         # Not 100% sure if the sub expression elimination is order sensitive. This step orders the list with the 'function' code first and derivatives after.
@@ -313,7 +313,7 @@ class Symbolic_core():
             sym_var = sym.var(cache_prefix + str(i))
             self.variables[cache_prefix].append(sym_var)
             replace_dict[expr.name] = sym_var
-            
+
         for i, expr in enumerate(params_change_list):
             sym_var = sym.var(sub_prefix + str(i))
             self.variables[sub_prefix].append(sym_var)
@@ -329,7 +329,7 @@ class Symbolic_core():
         for keys in self.expression_keys:
             for replace, void in common_sub_expressions:
                 setInDict(self.expressions, keys, getFromDict(self.expressions, keys).subs(replace, replace_dict[replace.name]))
-        
+
         self.expressions['parameters_changed'] = {}
         self.expressions['update_cache'] = {}
         for var, expr in common_sub_expressions:
@@ -339,7 +339,7 @@ class Symbolic_core():
                 self.expressions['update_cache'][replace_dict[var.name].name] = expr
             else:
                 self.expressions['parameters_changed'][replace_dict[var.name].name] = expr
-            
+
 
     def _gen_code(self):
         """Generate code for the list of expressions provided using the common sub-expression eliminator to separate out portions that are computed multiple times."""
@@ -357,8 +357,8 @@ class Symbolic_core():
             return code
 
         self.code = match_key(self.expressions)
-                            
- 
+
+
     def _expr2code(self, arg_list, expr):
         """Convert the given symbolic expression into code."""
         code = lambdastr(arg_list, expr)
@@ -379,7 +379,7 @@ class Symbolic_core():
     def _display_expression(self, keys, user_substitutes={}):
         """Helper function for human friendly display of the symbolic components."""
         # Create some pretty maths symbols for the display.
-        sigma, alpha, nu, omega, l, variance = sym.var('\sigma, \alpha, \nu, \omega, \ell, \sigma^2')
+        sigma, alpha, nu, omega, l, variance = sym.var(r'\sigma, \alpha, \nu, \omega, \ell, \sigma^2')
         substitutes = {'scale': sigma, 'shape': alpha, 'lengthscale': l, 'variance': variance}
         substitutes.update(user_substitutes)
 
@@ -416,5 +416,5 @@ class Symbolic_core():
                 return int(digits[0])
             else:
                 return x[0]
-            
+
         return sorted(var_dict.items(), key=sort_key, reverse=reverse)

GPy/inference/latent_function_inference/expectation_propagation.py

@@ -134,10 +134,10 @@ class posteriorParams(posteriorParamsBase):
         B = np.eye(num_data) + Sroot_tilde_K * tau_tilde_root[None,:]
         L = jitchol(B)
         V, _ = dtrtrs(L, Sroot_tilde_K, lower=1)
-        Sigma = K - np.dot(V.T,V) #K - KS^(1/2)BS^(1/2)K = (K^(-1) + \Sigma^(-1))^(-1)
+        Sigma = K - np.dot(V.T,V) #K - KS^(1/2)BS^(1/2)K = (K^(-1) + \\Sigma^(-1))^(-1)
 
         aux_alpha , _ = dpotrs(L, tau_tilde_root * (np.dot(K, ga_approx.v) + mean_prior), lower=1)
-        alpha = ga_approx.v - tau_tilde_root * aux_alpha #(K + Sigma^(\tilde))^(-1) (/mu^(/tilde) - /mu_p)
+        alpha = ga_approx.v - tau_tilde_root * aux_alpha #(K + Sigma^(\\tilde))^(-1) (/mu^(/tilde) - /mu_p)
         mu = np.dot(K, alpha) + mean_prior
 
         return posteriorParams(mu=mu, Sigma=Sigma, L=L)
@@ -151,8 +151,8 @@ class posteriorParamsDTC(posteriorParamsBase):
         DSYR(LLT,Kmn[:,i].copy(),delta_tau)
         L = jitchol(LLT)
         V,info = dtrtrs(L,Kmn,lower=1)
-        self.Sigma_diag = np.maximum(np.sum(V*V,-2), np.finfo(float).eps)  #diag(K_nm (L L^\top)^(-1)) K_mn
-        si = np.sum(V.T*V[:,i],-1) #(V V^\top)[:,i]
+        self.Sigma_diag = np.maximum(np.sum(V*V,-2), np.finfo(float).eps)  #diag(K_nm (L L^\\top)^(-1)) K_mn
+        si = np.sum(V.T*V[:,i],-1) #(V V^\\top)[:,i]
         self.mu += (delta_v-delta_tau*self.mu[i])*si
         #mu = np.dot(Sigma, v_tilde)
 
@@ -229,24 +229,17 @@ class EPBase(object):
         v_diff = np.mean(np.square(ga_approx.v-self.ga_approx_old.v))
         return ((tau_diff < self.epsilon) and (v_diff < self.epsilon))
 
-    def __setstate__(self, state):
-        super(EPBase, self).__setstate__(state[0])
-        self.epsilon, self.eta, self.delta = state[1]
-        self.reset()
-
-    def __getstate__(self):
-        return [super(EPBase, self).__getstate__() , [self.epsilon, self.eta, self.delta]]
-
     def _save_to_input_dict(self):
-        input_dict = super(EPBase, self)._save_to_input_dict()
-        input_dict["epsilon"]=self.epsilon
-        input_dict["eta"]=self.eta
-        input_dict["delta"]=self.delta
-        input_dict["always_reset"]=self.always_reset
-        input_dict["max_iters"]=self.max_iters
-        input_dict["ep_mode"]=self.ep_mode
-        input_dict["parallel_updates"]=self.parallel_updates
-        input_dict["loading"]=True
+        input_dict = {
+            "epsilon": self.epsilon,
+            "eta": self.eta,
+            "delta": self.delta,
+            "always_reset": self.always_reset,
+            "max_iters": self.max_iters,
+            "ep_mode": self.ep_mode,
+            "parallel_updates": self.parallel_updates,
+            "loading": True
+        }
         return input_dict
 
 class EP(EPBase, ExactGaussianInference):
@@ -391,11 +384,11 @@ class EP(EPBase, ExactGaussianInference):
 
 
         aux_alpha , _ = dpotrs(post_params.L, tau_tilde_root * (np.dot(K, ga_approx.v) +  mean_prior), lower=1)
-        alpha = (ga_approx.v - tau_tilde_root * aux_alpha)[:,None] #(K + Sigma^(\tilde))^(-1) (/mu^(/tilde) -  /mu_p)
+        alpha = (ga_approx.v - tau_tilde_root * aux_alpha)[:,None] #(K + Sigma^(\\tilde))^(-1) (/mu^(/tilde) -  /mu_p)
 
         LWi, _ = dtrtrs(post_params.L, np.diag(tau_tilde_root), lower=1)
         Wi = np.dot(LWi.T,LWi)
-        symmetrify(Wi) #(K + Sigma^(\tilde))^(-1)
+        symmetrify(Wi) #(K + Sigma^(\\tilde))^(-1)
 
         dL_dK = 0.5 * (tdot(alpha) - Wi)
         dL_dthetaL = likelihood.ep_gradients(Y, cav_params.tau, cav_params.v, np.diag(dL_dK), Y_metadata=Y_metadata, quad_mode='gh')
@@ -530,7 +523,7 @@ class EPDTC(EPBase, VarDTC):
         #initial values - Gaussian factors
         #Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
         LLT0 = Kmm.copy()
-        Lm = jitchol(LLT0) #K_m = L_m L_m^\top
+        Lm = jitchol(LLT0) #K_m = L_m L_m^\\top
         Vm,info = dtrtrs(Lm, Kmn,lower=1)
         # Lmi = dtrtri(Lm)
         # Kmmi = np.dot(Lmi.T,Lmi)

GPy/inference/latent_function_inference/laplace.py

@@ -27,7 +27,7 @@ class Laplace(LatentFunctionInference):
         """
         Laplace Approximation
 
-        Find the moments \hat{f} and the hessian at this point
+        Find the moments \\hat{f} and the hessian at this point
         (using Newton-Raphson) of the unnormalised posterior
 
         """

GPy/inference/latent_function_inference/pep.py

@@ -8,14 +8,14 @@ log_2_pi = np.log(2*np.pi)
 class PEP(LatentFunctionInference):
     '''
     Sparse Gaussian processes using Power-Expectation Propagation
-    for regression: alpha \approx 0 gives VarDTC and alpha = 1 gives FITC
-    
-    Reference: A Unifying Framework for Sparse Gaussian Process Approximation using 
+    for regression: alpha \\approx 0 gives VarDTC and alpha = 1 gives FITC
+
+    Reference: A Unifying Framework for Sparse Gaussian Process Approximation using
     Power Expectation Propagation, https://arxiv.org/abs/1605.07066
-    
+
     '''
     const_jitter = 1e-6
-    
+
     def __init__(self, alpha):
         super(PEP, self).__init__()
         self.alpha = alpha
@@ -69,7 +69,7 @@ class PEP(LatentFunctionInference):
         #compute dL_dR
         Uv = np.dot(U, v)
         dL_dR = 0.5*(np.sum(U*np.dot(U,P), 1) - (1.0+alpha_const_term)/beta_star + np.sum(np.square(Y), 1) - 2.*np.sum(Uv*Y, 1) \
-            + np.sum(np.square(Uv), 1))*beta_star**2 
+            + np.sum(np.square(Uv), 1))*beta_star**2
 
         # Compute dL_dKmm
         vvT_P = tdot(v.reshape(-1,1)) + P

GPy/inference/latent_function_inference/posterior.py

@@ -82,7 +82,7 @@ class Posterior(object):
         Posterior mean
         $$
         K_{xx}v
-        v := \texttt{Woodbury vector}
+        v := \\texttt{Woodbury vector}
         $$
         """
         if self._mean is None:
@@ -95,7 +95,7 @@ class Posterior(object):
         Posterior covariance
         $$
         K_{xx} - K_{xx}W_{xx}^{-1}K_{xx}
-        W_{xx} := \texttt{Woodbury inv}
+        W_{xx} := \\texttt{Woodbury inv}
         $$
         """
         if self._covariance is None:
@@ -146,8 +146,8 @@ class Posterior(object):
         """
         return $L_{W}$ where L is the lower triangular Cholesky decomposition of the Woodbury matrix
         $$
-        L_{W}L_{W}^{\top} = W^{-1}
-        W^{-1} := \texttt{Woodbury inv}
+        L_{W}L_{W}^{\\top} = W^{-1}
+        W^{-1} := \\texttt{Woodbury inv}
         $$
         """
         if self._woodbury_chol is None:
@@ -178,8 +178,8 @@ class Posterior(object):
         """
         The inverse of the woodbury matrix, in the gaussian likelihood case it is defined as
         $$
-        (K_{xx} + \Sigma_{xx})^{-1}
-        \Sigma_{xx} := \texttt{Likelihood.variance / Approximate likelihood covariance}
+        (K_{xx} + \\Sigma_{xx})^{-1}
+        \\Sigma_{xx} := \\texttt{Likelihood.variance / Approximate likelihood covariance}
         $$
         """
         if self._woodbury_inv is None:
@@ -200,8 +200,8 @@ class Posterior(object):
         """
         Woodbury vector in the gaussian likelihood case only is defined as
         $$
-        (K_{xx} + \Sigma)^{-1}Y
-        \Sigma := \texttt{Likelihood.variance / Approximate likelihood covariance}
+        (K_{xx} + \\Sigma)^{-1}Y
+        \\Sigma := \\texttt{Likelihood.variance / Approximate likelihood covariance}
         $$
         """
         if self._woodbury_vector is None:

GPy/inference/latent_function_inference/var_dtc_parallel.py

@@ -118,7 +118,7 @@ class VarDTC_minibatch(LatentFunctionInference):
         if not het_noise:
             YRY_full = trYYT*beta
 
-        if self.mpi_comm != None:
+        if self.mpi_comm is not None:
             from mpi4py import MPI
             psi0_all = np.array(psi0_full)
             psi1Y_all = psi1Y_full.copy()
@@ -142,7 +142,7 @@ class VarDTC_minibatch(LatentFunctionInference):
 
         num_data, output_dim = Y.shape
         input_dim = Z.shape[0]
-        if self.mpi_comm != None:
+        if self.mpi_comm is not None:
             from mpi4py import MPI
             num_data_all = np.array(num_data,dtype=np.int32)
             self.mpi_comm.Allreduce([np.int32(num_data), MPI.INT], [num_data_all, MPI.INT])
@@ -384,7 +384,7 @@ def update_gradients(model, mpi_comm=None):
                 dL_dthetaL += grad_dict['dL_dthetaL']
 
     # Gather the gradients from multiple MPI nodes
-    if mpi_comm != None:
+    if mpi_comm is not None:
         from mpi4py import MPI
         if het_noise:
             raise "het_noise not implemented!"
@@ -407,7 +407,7 @@ def update_gradients(model, mpi_comm=None):
     # update for the KL divergence
     model.variational_prior.update_gradients_KL(X)
 
-    if mpi_comm != None:
+    if mpi_comm is not None:
         from mpi4py import MPI
         KL_div_all = np.array(KL_div)
         mpi_comm.Allreduce([np.float64(KL_div), MPI.DOUBLE], [KL_div_all, MPI.DOUBLE])
@@ -467,7 +467,7 @@ def update_gradients_sparsegp(model, mpi_comm=None):
             dL_dthetaL += grad_dict['dL_dthetaL']
     
     # Gather the gradients from multiple MPI nodes
-    if mpi_comm != None:
+    if mpi_comm is not None:
         from mpi4py import MPI
         if het_noise:
             raise "het_noise not implemented!"

GPy/kern/src/coregionalize.py

@@ -25,12 +25,12 @@ class Coregionalize(Kern):
     This covariance has the form:
 
     .. math::
-       \mathbf{B} = \mathbf{W}\mathbf{W}^\intercal + \mathrm{diag}(kappa)
+       \\mathbf{B} = \\mathbf{W}\\mathbf{W}^\\intercal + \\mathrm{diag}(kappa)
 
     An intrinsic/linear coregionalization covariance function of the form:
 
     .. math::
-       k_2(x, y)=\mathbf{B} k(x, y)
+       k_2(x, y)=\\mathbf{B} k(x, y)
 
     it is obtained as the tensor product between a covariance function
     k(x, y) and B.

GPy/kern/src/eq_ode1.py

@@ -15,7 +15,7 @@ class EQ_ODE1(Kern):
 
     This outputs of this kernel have the form
     .. math::
-       \frac{\text{d}y_j}{\text{d}t} = \sum_{i=1}^R w_{j,i} u_i(t-\delta_j) - d_jy_j(t)
+       \\frac{\\text{d}y_j}{\\text{d}t} = \\sum_{i=1}^R w_{j,i} u_i(t-\\delta_j) - d_jy_j(t)
 
     where :math:`R` is the rank of the system, :math:`w_{j,i}` is the sensitivity of the :math:`j`th output to the :math:`i`th latent function, :math:`d_j` is the decay rate of the :math:`j`th output and :math:`u_i(t)` are independent latent Gaussian processes goverened by an exponentiated quadratic covariance.
 

GPy/kern/src/eq_ode2.py

@@ -15,7 +15,7 @@ class EQ_ODE2(Kern):
 
     This outputs of this kernel have the form
     .. math::
-       \frac{\text{d}^2y_j(t)}{\text{d}^2t} + C_j\frac{\text{d}y_j(t)}{\text{d}t} + B_jy_j(t) = \sum_{i=1}^R w_{j,i} u_i(t)
+       \\frac{\\text{d}^2y_j(t)}{\\text{d}^2t} + C_j\\frac{\\text{d}y_j(t)}{\\text{d}t} + B_jy_j(t) = \\sum_{i=1}^R w_{j,i} u_i(t)
 
     where :math:`R` is the rank of the system, :math:`w_{j,i}` is the sensitivity of the :math:`j`th output to the :math:`i`th latent function, :math:`d_j` is the decay rate of the :math:`j`th output and :math:`f_i(t)` and :math:`g_i(t)` are independent latent Gaussian processes goverened by an exponentiated quadratic covariance.
 

GPy/kern/src/grid_kerns.py

@@ -45,7 +45,7 @@ class GridRBF(GridKern):
 
     .. math::
 
-       k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg)
+       k(r) = \\sigma^2 \\exp \\bigg(- \\frac{1}{2} r^2 \\bigg)
 
     """
     _support_GPU = True

GPy/kern/src/kern.py

@@ -146,25 +146,25 @@ class Kern(Parameterized):
     def psi0(self, Z, variational_posterior):
         """
         .. math::
-            \psi_0 = \sum_{i=0}^{n}E_{q(X)}[k(X_i, X_i)]
+            \\psi_0 = \\sum_{i=0}^{n}E_{q(X)}[k(X_i, X_i)]
         """
         return self.psicomp.psicomputations(self, Z, variational_posterior)[0]
     def psi1(self, Z, variational_posterior):
         """
         .. math::
-            \psi_1^{n,m} = E_{q(X)}[k(X_n, Z_m)]
+            \\psi_1^{n,m} = E_{q(X)}[k(X_n, Z_m)]
         """
         return self.psicomp.psicomputations(self, Z, variational_posterior)[1]
     def psi2(self, Z, variational_posterior):
         """
         .. math::
-            \psi_2^{m,m'} = \sum_{i=0}^{n}E_{q(X)}[ k(Z_m, X_i) k(X_i, Z_{m'})]
+            \\psi_2^{m,m'} = \\sum_{i=0}^{n}E_{q(X)}[ k(Z_m, X_i) k(X_i, Z_{m'})]
         """
         return self.psicomp.psicomputations(self, Z, variational_posterior, return_psi2_n=False)[2]
     def psi2n(self, Z, variational_posterior):
         """
         .. math::
-            \psi_2^{n,m,m'} = E_{q(X)}[ k(Z_m, X_n) k(X_n, Z_{m'})]
+            \\psi_2^{n,m,m'} = E_{q(X)}[ k(Z_m, X_n) k(X_n, Z_{m'})]
 
         Thus, we do not sum out n, compared to psi2
         """
@@ -173,7 +173,7 @@ class Kern(Parameterized):
         """
         .. math::
 
-            \\frac{\partial L}{\partial X} = \\frac{\partial L}{\partial K}\\frac{\partial K}{\partial X}
+            \\frac{\\partial L}{\\partial X} = \\frac{\\partial L}{\\partial K}\\frac{\\partial K}{\\partial X}
         """
         raise NotImplementedError
     def gradients_X_X2(self, dL_dK, X, X2):
@@ -182,7 +182,7 @@ class Kern(Parameterized):
         """
         .. math::
 
-            \\frac{\partial^2 L}{\partial X\partial X_2} = \\frac{\partial L}{\partial K}\\frac{\partial^2 K}{\partial X\partial X_2}
+            \\frac{\\partial^2 L}{\\partial X\\partial X_2} = \\frac{\\partial L}{\\partial K}\\frac{\\partial^2 K}{\\partial X\\partial X_2}
         """
         raise NotImplementedError("This is the second derivative of K wrt X and X2, and not implemented for this kernel")
     def gradients_XX_diag(self, dL_dKdiag, X, cov=True):
@@ -203,7 +203,7 @@ class Kern(Parameterized):
     def update_gradients_full(self, dL_dK, X, X2):
         """Set the gradients of all parameters when doing full (N) inference."""
         raise NotImplementedError
-    
+
     def reset_gradients(self):
         raise NotImplementedError
 
@@ -216,9 +216,9 @@ class Kern(Parameterized):
 
         .. math::
 
-            \\frac{\partial L}{\partial \\theta_i} & = \\frac{\partial L}{\partial \psi_0}\\frac{\partial \psi_0}{\partial \\theta_i}\\
-                & \quad + \\frac{\partial L}{\partial \psi_1}\\frac{\partial \psi_1}{\partial \\theta_i}\\
-                & \quad + \\frac{\partial L}{\partial \psi_2}\\frac{\partial \psi_2}{\partial \\theta_i}
+            \\frac{\\partial L}{\\partial \\theta_i} & = \\frac{\\partial L}{\\partial \\psi_0}\\frac{\\partial \\psi_0}{\\partial \\theta_i}\\
+                & \\quad + \\frac{\\partial L}{\\partial \\psi_1}\\frac{\\partial \\psi_1}{\\partial \\theta_i}\\
+                & \\quad + \\frac{\\partial L}{\\partial \\psi_2}\\frac{\\partial \\psi_2}{\\partial \\theta_i}
 
         Thus, we push the different derivatives through the gradients of the psi
         statistics. Be sure to set the gradients for all kernel

GPy/kern/src/linear.py

@@ -16,15 +16,15 @@ class Linear(Kern):
 
     .. math::
 
-       k(x,y) = \sum_{i=1}^{\\text{input_dim}} \sigma^2_i x_iy_i
+       k(x,y) = \\sum_{i=1}^{\\text{input_dim}} \\sigma^2_i x_iy_i
 
     :param input_dim: the number of input dimensions
     :type input_dim: int
-    :param variances: the vector of variances :math:`\sigma^2_i`
+    :param variances: the vector of variances :math:`\\sigma^2_i`
     :type variances: array or list of the appropriate size (or float if there
                      is only one variance parameter)
     :param ARD: Auto Relevance Determination. If False, the kernel has only one
-                variance parameter \sigma^2, otherwise there is one variance
+                variance parameter \\sigma^2, otherwise there is one variance
                 parameter per dimension.
     :type ARD: Boolean
     :rtype: kernel object
@@ -121,7 +121,7 @@ class Linear(Kern):
         the returned array is of shape [NxNxQxQ].
 
         ..math:
-            \frac{\partial^2 K}{\partial X2 ^2} = - \frac{\partial^2 K}{\partial X\partial X2}
+            \\frac{\\partial^2 K}{\\partial X2 ^2} = - \\frac{\\partial^2 K}{\\partial X\\partial X2}
 
         ..returns:
             dL2_dXdX2:  [NxMxQxQ] for X [NxQ] and X2[MxQ] (X2 is X if, X2 is None)

GPy/kern/src/mlp.py

@@ -20,12 +20,12 @@ class MLP(Kern):
 
     :param input_dim: the number of input dimensions
     :type input_dim: int
-    :param variance: the variance :math:`\sigma^2`
+    :param variance: the variance :math:`\\sigma^2`
     :type variance: float
-    :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\sigma^2_w`
+    :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\\sigma^2_w`
     :type weight_variance: array or list of the appropriate size (or float if there is only one weight variance parameter)
-    :param bias_variance: the variance of the prior over bias parameters :math:`\sigma^2_b`
-    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \sigma^2_w), otherwise there is one weight variance parameter per dimension.
+    :param bias_variance: the variance of the prior over bias parameters :math:`\\sigma^2_b`
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \\sigma^2_w), otherwise there is one weight variance parameter per dimension.
     :type ARD: Boolean
     :rtype: Kernpart object
 

GPy/kern/src/rbf.py

@@ -16,7 +16,7 @@ class RBF(Stationary):
 
     .. math::
 
-       k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg)
+       k(r) = \\sigma^2 \\exp \\bigg(- \\frac{1}{2} r^2 \\bigg)
 
     """
     _support_GPU = True

GPy/kern/src/sde_brownian.py

@@ -12,48 +12,48 @@ import numpy as np
 
 class sde_Brownian(Brownian):
     """
-    
+
     Class provide extra functionality to transfer this covariance function into
     SDE form.
-    
+
     Linear kernel:
 
     .. math::
 
-       k(x,y) = \sigma^2 min(x,y)
+       k(x,y) = \\sigma^2 min(x,y)
 
     """
-    
+
     def sde_update_gradient_full(self, gradients):
         """
         Update gradient in the order in which parameters are represented in the
         kernel
         """
-    
+
         self.variance.gradient = gradients[0]
-        
-    def sde(self): 
-        """ 
-        Return the state space representation of the covariance. 
-        """ 
-        
+
+    def sde(self):
+        """
+        Return the state space representation of the covariance.
+        """
+
         variance = float(self.variance.values) # this is initial variancve in Bayesian linear regression
-        
+
         F = np.array( ((0,1.0),(0,0) ))
         L = np.array( ((1.0,),(0,)) )
         Qc = np.array( ((variance,),) )
         H = np.array( ((1.0,0),) )
-        
+
         Pinf   = np.array( ( (0, -0.5*variance ), (-0.5*variance, 0) ) )
-        #P0 = Pinf.copy() 
-        P0 = np.zeros((2,2))   
+        #P0 = Pinf.copy()
+        P0 = np.zeros((2,2))
         #Pinf   = np.array( ( (t0, 1.0), (1.0, 1.0/t0) ) ) * variance
         dF = np.zeros((2,2,1))
         dQc    = np.ones( (1,1,1) )
-        
+
         dPinf = np.zeros((2,2,1))
         dPinf[:,:,0] = np.array( ( (0, -0.5), (-0.5, 0) ) )
-        #dP0 = dPinf.copy() 
+        #dP0 = dPinf.copy()
         dP0 = np.zeros((2,2,1))
-  
+
         return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)

GPy/kern/src/sde_linear.py

@@ -11,15 +11,15 @@ import numpy as np
 
 class sde_Linear(Linear):
     """
-    
+
     Class provide extra functionality to transfer this covariance function into
     SDE form.
-    
+
     Linear kernel:
 
     .. math::
 
-       k(x,y) = \sum_{i=1}^{input dim} \sigma^2_i x_iy_i
+       k(x,y) = \\sum_{i=1}^{input dim} \\sigma^2_i x_iy_i
 
     """
     def __init__(self, input_dim, X, variances=None, ARD=False, active_dims=None, name='linear'):
@@ -27,40 +27,40 @@ class sde_Linear(Linear):
         Modify the init method, because one extra parameter is required. X - points
         on the X axis.
         """
-        
+
         super(sde_Linear, self).__init__(input_dim, variances, ARD, active_dims, name)
-        
+
         self.t0 = np.min(X)
-        
-    
+
+
     def sde_update_gradient_full(self, gradients):
         """
         Update gradient in the order in which parameters are represented in the
         kernel
         """
-    
+
         self.variances.gradient = gradients[0]
-        
-    def sde(self): 
-        """ 
-        Return the state space representation of the covariance. 
-        """ 
-        
+
+    def sde(self):
+        """
+        Return the state space representation of the covariance.
+        """
+
         variance = float(self.variances.values) # this is initial variancve in Bayesian linear regression
         t0 = float(self.t0)
-        
+
         F = np.array( ((0,1.0),(0,0) ))
         L = np.array( ((0,),(1.0,)) )
         Qc = np.zeros((1,1))
         H = np.array( ((1.0,0),) )
-        
+
         Pinf   = np.zeros((2,2))
-        P0 = np.array( ( (t0**2, t0), (t0, 1) ) ) * variance        
+        P0 = np.array( ( (t0**2, t0), (t0, 1) ) ) * variance
         dF = np.zeros((2,2,1))
         dQc    = np.zeros( (1,1,1) )
-        
+
         dPinf = np.zeros((2,2,1))
         dP0 = np.zeros((2,2,1))
         dP0[:,:,0]  = P0 / variance
-  
+
         return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)

GPy/kern/src/sde_matern.py

@@ -11,15 +11,15 @@ import numpy as np
 
 class sde_Matern32(Matern32):
     """
-    
+
     Class provide extra functionality to transfer this covariance function into
     SDE forrm.
-    
+
     Matern 3/2 kernel:
 
     .. math::
 
-       k(r) = \sigma^2 (1 + \sqrt{3} r) \exp(- \sqrt{3} r) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+       k(r) = \\sigma^2 (1 + \\sqrt{3} r) \\exp(- \\sqrt{3} r) \\ \\ \\ \\  \\text{ where  } r = \\sqrt{\\sum_{i=1}^{input dim} \\frac{(x_i-y_i)^2}{\\ell_i^2} }
 
     """
     def sde_update_gradient_full(self, gradients):
@@ -27,59 +27,59 @@ class sde_Matern32(Matern32):
         Update gradient in the order in which parameters are represented in the
         kernel
         """
-    
+
         self.variance.gradient = gradients[0]
         self.lengthscale.gradient = gradients[1]
-        
-    def sde(self): 
-        """ 
-        Return the state space representation of the covariance. 
-        """ 
-        
+
+    def sde(self):
+        """
+        Return the state space representation of the covariance.
+        """
+
         variance = float(self.variance.values)
         lengthscale = float(self.lengthscale.values)
-        
-        foo  = np.sqrt(3.)/lengthscale 
-        F    = np.array(((0, 1.0), (-foo**2, -2*foo))) 
+
+        foo  = np.sqrt(3.)/lengthscale
+        F    = np.array(((0, 1.0), (-foo**2, -2*foo)))
         L    = np.array(( (0,), (1.0,) ))
-        Qc   = np.array(((12.*np.sqrt(3) / lengthscale**3 * variance,),)) 
-        H    = np.array(((1.0, 0),)) 
+        Qc   = np.array(((12.*np.sqrt(3) / lengthscale**3 * variance,),))
+        H    = np.array(((1.0, 0),))
         Pinf = np.array(((variance, 0.0), (0.0, 3.*variance/(lengthscale**2))))
         P0 = Pinf.copy()
-        
-        # Allocate space for the derivatives 
+
+        # Allocate space for the derivatives
         dF    = np.empty([F.shape[0],F.shape[1],2])
-        dQc   = np.empty([Qc.shape[0],Qc.shape[1],2]) 
-        dPinf = np.empty([Pinf.shape[0],Pinf.shape[1],2]) 
-        # The partial derivatives 
-        dFvariance       = np.zeros((2,2)) 
-        dFlengthscale    = np.array(((0,0), (6./lengthscale**3,2*np.sqrt(3)/lengthscale**2))) 
-        dQcvariance      = np.array((12.*np.sqrt(3)/lengthscale**3)) 
-        dQclengthscale   = np.array((-3*12*np.sqrt(3)/lengthscale**4*variance)) 
-        dPinfvariance    = np.array(((1,0),(0,3./lengthscale**2))) 
-        dPinflengthscale = np.array(((0,0), (0,-6*variance/lengthscale**3))) 
-        # Combine the derivatives 
-        dF[:,:,0]    = dFvariance 
-        dF[:,:,1]    = dFlengthscale 
-        dQc[:,:,0]   = dQcvariance 
-        dQc[:,:,1]   = dQclengthscale 
-        dPinf[:,:,0] = dPinfvariance 
-        dPinf[:,:,1] = dPinflengthscale 
+        dQc   = np.empty([Qc.shape[0],Qc.shape[1],2])
+        dPinf = np.empty([Pinf.shape[0],Pinf.shape[1],2])
+        # The partial derivatives
+        dFvariance       = np.zeros((2,2))
+        dFlengthscale    = np.array(((0,0), (6./lengthscale**3,2*np.sqrt(3)/lengthscale**2)))
+        dQcvariance      = np.array((12.*np.sqrt(3)/lengthscale**3))
+        dQclengthscale   = np.array((-3*12*np.sqrt(3)/lengthscale**4*variance))
+        dPinfvariance    = np.array(((1,0),(0,3./lengthscale**2)))
+        dPinflengthscale = np.array(((0,0), (0,-6*variance/lengthscale**3)))
+        # Combine the derivatives
+        dF[:,:,0]    = dFvariance
+        dF[:,:,1]    = dFlengthscale
+        dQc[:,:,0]   = dQcvariance
+        dQc[:,:,1]   = dQclengthscale
+        dPinf[:,:,0] = dPinfvariance
+        dPinf[:,:,1] = dPinflengthscale
         dP0 = dPinf.copy()
-        
+
         return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)
 
 class sde_Matern52(Matern52):
     """
-    
+
     Class provide extra functionality to transfer this covariance function into
     SDE forrm.
-    
+
     Matern 5/2 kernel:
 
     .. math::
 
-       k(r) = \sigma^2 (1 + \sqrt{5} r + \frac{5}{3}r^2) \exp(- \sqrt{5} r) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+       k(r) = \\sigma^2 (1 + \\sqrt{5} r + \\frac{5}{3}r^2) \\exp(- \\sqrt{5} r) \\ \\ \\ \\  \\text{ where  } r = \\sqrt{\\sum_{i=1}^{input dim} \\frac{(x_i-y_i)^2}{\\ell_i^2} }
 
     """
     def sde_update_gradient_full(self, gradients):
@@ -87,51 +87,51 @@ class sde_Matern52(Matern52):
         Update gradient in the order in which parameters are represented in the
         kernel
         """
-    
+
         self.variance.gradient = gradients[0]
         self.lengthscale.gradient = gradients[1]
-        
-    def sde(self): 
-        """ 
-        Return the state space representation of the covariance. 
-        """ 
-        
+
+    def sde(self):
+        """
+        Return the state space representation of the covariance.
+        """
+
         variance = float(self.variance.values)
         lengthscale = float(self.lengthscale.values)
 
         lamda = np.sqrt(5.0)/lengthscale
-        kappa = 5.0/3.0*variance/lengthscale**2        
-        
+        kappa = 5.0/3.0*variance/lengthscale**2
+
         F = np.array(((0, 1,0), (0, 0, 1), (-lamda**3, -3.0*lamda**2, -3*lamda)))
         L = np.array(((0,),(0,),(1,)))
         Qc = np.array((((variance*400.0*np.sqrt(5.0)/3.0/lengthscale**5),),))
-        H = np.array(((1,0,0),))        
-        
+        H = np.array(((1,0,0),))
+
         Pinf = np.array(((variance,0,-kappa), (0, kappa, 0), (-kappa, 0, 25.0*variance/lengthscale**4)))
         P0 = Pinf.copy()
-        # Allocate space for the derivatives         
-        dF = np.empty((3,3,2))        
-        dQc = np.empty((1,1,2))        
+        # Allocate space for the derivatives
+        dF = np.empty((3,3,2))
+        dQc = np.empty((1,1,2))
         dPinf = np.empty((3,3,2))
-        
-         # The partial derivatives 
+
+         # The partial derivatives
         dFvariance = np.zeros((3,3))
-        dFlengthscale = np.array(((0,0,0),(0,0,0),(15.0*np.sqrt(5.0)/lengthscale**4, 
+        dFlengthscale = np.array(((0,0,0),(0,0,0),(15.0*np.sqrt(5.0)/lengthscale**4,
                                    30.0/lengthscale**3, 3*np.sqrt(5.0)/lengthscale**2)))
         dQcvariance = np.array((((400*np.sqrt(5)/3/lengthscale**5,),)))
-        dQclengthscale = np.array((((-variance*2000*np.sqrt(5)/3/lengthscale**6,),)))        
-        
+        dQclengthscale = np.array((((-variance*2000*np.sqrt(5)/3/lengthscale**6,),)))
+
         dPinf_variance = Pinf/variance
         kappa2 = -2.0*kappa/lengthscale
-        dPinf_lengthscale = np.array(((0,0,-kappa2),(0,kappa2,0),(-kappa2, 
-                                    0,-100*variance/lengthscale**5)))        
-        # Combine the derivatives 
+        dPinf_lengthscale = np.array(((0,0,-kappa2),(0,kappa2,0),(-kappa2,
+                                    0,-100*variance/lengthscale**5)))
+        # Combine the derivatives
         dF[:,:,0] = dFvariance
-        dF[:,:,1] = dFlengthscale        
-        dQc[:,:,0] = dQcvariance         
-        dQc[:,:,1] = dQclengthscale        
+        dF[:,:,1] = dFlengthscale
+        dQc[:,:,0] = dQcvariance
+        dQc[:,:,1] = dQclengthscale
         dPinf[:,:,0] = dPinf_variance
         dPinf[:,:,1] = dPinf_lengthscale
         dP0 = dPinf.copy()
-        
-        return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)  
+
+        return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)

GPy/kern/src/sde_standard_periodic.py

@@ -24,8 +24,8 @@ class sde_StdPeriodic(StdPeriodic):
 
     .. math::
 
-       k(x,y) = \theta_1 \exp \left[  - \frac{1}{2} {}\sum_{i=1}^{input\_dim}
-       \left( \frac{\sin(\frac{\pi}{\lambda_i} (x_i - y_i) )}{l_i} \right)^2 \right] }
+       k(x,y) = \\theta_1 \\exp \\left[  - \\frac{1}{2} {}\\sum_{i=1}^{input\\_dim}
+       \\left( \\frac{\\sin(\\frac{\\pi}{\\lambda_i} (x_i - y_i) )}{l_i} \\right)^2 \\right] }
 
     """
 
@@ -177,7 +177,7 @@ def seriescoeff(m=6, lengthScale=1.0, magnSigma2=1.0, true_covariance=False):
     Calculate the coefficients q_j^2 for the covariance function
     approximation:
 
-        k(\tau) =  \sum_{j=0}^{+\infty} q_j^2 \cos(j\omega_0 \tau)
+        k(\\tau) =  \\sum_{j=0}^{+\\infty} q_j^2 \\cos(j\\omega_0 \\tau)
 
     Reference is:
 

GPy/kern/src/sde_static.py

@@ -12,63 +12,63 @@ import numpy as np
 
 class sde_White(White):
     """
-    
+
     Class provide extra functionality to transfer this covariance function into
     SDE forrm.
-    
+
     White kernel:
 
     .. math::
 
-       k(x,y) = \alpha*\delta(x-y)
+       k(x,y) = \\alpha*\\delta(x-y)
 
     """
-    
+
     def sde_update_gradient_full(self, gradients):
         """
         Update gradient in the order in which parameters are represented in the
         kernel
         """
-    
+
         self.variance.gradient = gradients[0]
-        
-    def sde(self): 
-        """ 
-        Return the state space representation of the covariance. 
-        """ 
-        
-        variance = float(self.variance.values) 
-        
+
+    def sde(self):
+        """
+        Return the state space representation of the covariance.
+        """
+
+        variance = float(self.variance.values)
+
         F = np.array( ((-np.inf,),) )
         L = np.array( ((1.0,),)  )
         Qc = np.array( ((variance,),)  )
         H = np.array( ((1.0,),) )
-        
+
         Pinf   = np.array( ((variance,),)  )
-        P0 = Pinf.copy()     
-        
+        P0 = Pinf.copy()
+
         dF = np.zeros((1,1,1))
         dQc = np.zeros((1,1,1))
         dQc[:,:,0]    = np.array( ((1.0,),) )
-        
+
         dPinf = np.zeros((1,1,1))
         dPinf[:,:,0] = np.array( ((1.0,),) )
         dP0 = dPinf.copy()
-        
+
         return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)
 
 
 class sde_Bias(Bias):
     """
-    
+
     Class provide extra functionality to transfer this covariance function into
     SDE forrm.
-    
+
     Bias kernel:
 
     .. math::
 
-       k(x,y) = \alpha
+       k(x,y) = \\alpha
 
     """
     def sde_update_gradient_full(self, gradients):
@@ -76,28 +76,28 @@ class sde_Bias(Bias):
         Update gradient in the order in which parameters are represented in the
         kernel
         """
-    
+
         self.variance.gradient = gradients[0]
-        
-    def sde(self): 
-        """ 
-        Return the state space representation of the covariance. 
-        """ 
-        variance = float(self.variance.values) 
-        
+
+    def sde(self):
+        """
+        Return the state space representation of the covariance.
+        """
+        variance = float(self.variance.values)
+
         F = np.array( ((0.0,),))
         L = np.array( ((1.0,),))
         Qc = np.zeros((1,1))
         H = np.array( ((1.0,),))
-        
+
         Pinf   = np.zeros((1,1))
-        P0 = np.array( ((variance,),) )      
-        
+        P0 = np.array( ((variance,),) )
+
         dF = np.zeros((1,1,1))
         dQc    = np.zeros((1,1,1))
-        
+
         dPinf = np.zeros((1,1,1))
         dP0 = np.zeros((1,1,1))
         dP0[:,:,0] = np.array( ((1.0,),) )
-        
+
         return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)

GPy/kern/src/sde_stationary.py

@@ -29,7 +29,7 @@ class sde_RBF(RBF):
 
     .. math::
 
-        k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+        k(r) = \\sigma^2 \\exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \\ \\ \\ \\  \\text{ where  } r = \\sqrt{\\sum_{i=1}^{input dim} \\frac{(x_i-y_i)^2}{\\ell_i^2} }
 
     """
 
@@ -102,7 +102,7 @@ class sde_RBF(RBF):
         eps = 1e-12
         if (float(Qc) > 1.0 / eps) or (float(Qc) < eps):
             warnings.warn(
-                """sde_RBF kernel: the noise variance Qc is either very large or very small. 
+                """sde_RBF kernel: the noise variance Qc is either very large or very small.
                                 It influece conditioning of P_inf: {0:e}""".format(
                     float(Qc)
                 )
@@ -204,7 +204,7 @@ class sde_Exponential(Exponential):
 
     .. math::
 
-       k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r \\bigg) \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+       k(r) = \\sigma^2 \\exp \\bigg(- \\frac{1}{2} r \\bigg) \\ \\ \\ \\  \\text{ where  } r = \\sqrt{\\sum_{i=1}^{input dim} \\frac{(x_i-y_i)^2}{\\ell_i^2} }
 
     """
 
@@ -259,7 +259,7 @@ class sde_RatQuad(RatQuad):
 
     .. math::
 
-       k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2} \\bigg)^{- \alpha} \\ \\ \\ \\  \text{ where  } r = \sqrt{\sum_{i=1}^{input dim} \frac{(x_i-y_i)^2}{\ell_i^2} }
+       k(r) = \\sigma^2 \\bigg( 1 + \\frac{r^2}{2} \\bigg)^{- \\alpha} \\ \\ \\ \\  \\text{ where  } r = \\sqrt{\\sum_{i=1}^{input dim} \\frac{(x_i-y_i)^2}{\\ell_i^2} }
 
     """
 

GPy/kern/src/standard_periodic.py

@@ -24,19 +24,19 @@ class StdPeriodic(Kern):
 
     .. math::
 
-       k(x,y) = \theta_1 \exp \left[  - \frac{1}{2} \sum_{i=1}^{input\_dim}
-       \left( \frac{\sin(\frac{\pi}{T_i} (x_i - y_i) )}{l_i} \right)^2 \right] }
+       k(x,y) = \\theta_1 \\exp \\left[  - \\frac{1}{2} \\sum_{i=1}^{input\\_dim}
+       \\left( \\frac{\\sin(\\frac{\\pi}{T_i} (x_i - y_i) )}{l_i} \\right)^2 \\right] }
 
     :param input_dim: the number of input dimensions
     :type input_dim: int
-    :param variance: the variance :math:`\theta_1` in the formula above
+    :param variance: the variance :math:`\\theta_1` in the formula above
     :type variance: float
-    :param period: the vector of periods :math:`\T_i`. If None then 1.0 is assumed.
+    :param period: the vector of periods :math:`\\T_i`. If None then 1.0 is assumed.
     :type period: array or list of the appropriate size (or float if there is only one period parameter)
-    :param lengthscale: the vector of lengthscale :math:`\l_i`. If None then 1.0 is assumed.
+    :param lengthscale: the vector of lengthscale :math:`\\l_i`. If None then 1.0 is assumed.
     :type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter)
     :param ARD1: Auto Relevance Determination with respect to period.
-        If equal to "False" one single period parameter :math:`\T_i` for
+        If equal to "False" one single period parameter :math:`\\T_i` for
         each dimension is assumed, otherwise there is one lengthscale
         parameter per dimension.
     :type ARD1: Boolean
@@ -177,7 +177,7 @@ class StdPeriodic(Kern):
         Returns only diagonal elements.
         """
         return np.zeros(X.shape[0])
-    
+
     def dK2_dXdX2(self, X, X2, dimX, dimX2):
         """
         Compute the second derivative of K with respect to:
@@ -578,9 +578,9 @@ class StdPeriodic(Kern):
             X2 = X
         dX = -np.pi*((dL_dK*K)[:,:,None]*np.sin(2*np.pi/self.period*(X[:,None,:] - X2[None,:,:]))/(2.*np.square(self.lengthscale)*self.period)).sum(1)
         return dX
-    
+
     def gradients_X_diag(self, dL_dKdiag, X):
         return np.zeros(X.shape)
-    
+
     def input_sensitivity(self, summarize=True):
         return self.variance*np.ones(self.input_dim)/self.lengthscale**2

GPy/kern/src/stationary.py

@@ -35,7 +35,7 @@ class Stationary(Kern):
 
     .. math::
 
-        r(x, x') = \\sqrt{ \\sum_{q=1}^Q \\frac{(x_q - x'_q)^2}{\ell_q^2} }.
+        r(x, x') = \\sqrt{ \\sum_{q=1}^Q \\frac{(x_q - x'_q)^2}{\\ell_q^2} }.
 
     By default, there's only one lengthscale: seaprate lengthscales for each
     dimension can be enables by setting ARD=True.
@@ -153,7 +153,7 @@ class Stationary(Kern):
         Efficiently compute the scaled distance, r.
 
         ..math::
-            r = \sqrt( \sum_{q=1}^Q (x_q - x'q)^2/l_q^2 )
+            r = \\sqrt( \\sum_{q=1}^Q (x_q - x'q)^2/l_q^2 )
 
         Note that if thre is only one lengthscale, l comes outside the sum. In
         this case we compute the unscaled distance first (in a separate
@@ -259,7 +259,7 @@ class Stationary(Kern):
         the returned array is of shape [NxNxQxQ].
 
         ..math:
-            \frac{\partial^2 K}{\partial X2 ^2} = - \frac{\partial^2 K}{\partial X\partial X2}
+            \\frac{\\partial^2 K}{\\partial X2 ^2} = - \\frac{\\partial^2 K}{\\partial X\\partial X2}
 
         ..returns:
             dL2_dXdX2:  [NxMxQxQ] in the cov=True case, or [NxMxQ] in the cov=False case,
@@ -295,7 +295,7 @@ class Stationary(Kern):
         Given the derivative of the objective dL_dK, compute the second derivative of K wrt X:
 
         ..math:
-          \frac{\partial^2 K}{\partial X\partial X}
+          \\frac{\\partial^2 K}{\\partial X\\partial X}
 
         ..returns:
             dL2_dXdX: [NxQxQ]
@@ -423,7 +423,7 @@ class OU(Stationary):
 
     .. math::
 
-       k(r) = \\sigma^2 \exp(- r) \\ \\ \\ \\  \\text{ where  } r = \sqrt{\sum_{i=1}^{\text{input_dim}} \\frac{(x_i-y_i)^2}{\ell_i^2} }
+       k(r) = \\sigma^2 \\exp(- r) \\ \\ \\ \\  \\text{ where  } r = \\sqrt{\\sum_{i=1}^{\\text{input_dim}} \\frac{(x_i-y_i)^2}{\\ell_i^2} }
 
     """
 
@@ -460,7 +460,7 @@ class Matern32(Stationary):
 
     .. math::
 
-       k(r) = \\sigma^2 (1 + \\sqrt{3} r) \exp(- \sqrt{3} r) \\ \\ \\ \\  \\text{ where  } r = \sqrt{\sum_{i=1}^{\\text{input_dim}} \\frac{(x_i-y_i)^2}{\ell_i^2} }
+       k(r) = \\sigma^2 (1 + \\sqrt{3} r) \\exp(- \\sqrt{3} r) \\ \\ \\ \\  \\text{ where  } r = \\sqrt{\\sum_{i=1}^{\\text{input_dim}} \\frac{(x_i-y_i)^2}{\\ell_i^2} }
 
     """
 
@@ -559,7 +559,7 @@ class Matern52(Stationary):
 
     .. math::
 
-       k(r) = \sigma^2 (1 + \sqrt{5} r + \\frac53 r^2) \exp(- \sqrt{5} r)
+       k(r) = \\sigma^2 (1 + \\sqrt{5} r + \\frac53 r^2) \\exp(- \\sqrt{5} r)
     """
     def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='Mat52'):
         super(Matern52, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name)
@@ -626,7 +626,7 @@ class ExpQuad(Stationary):
 
     .. math::
 
-       k(r) = \sigma^2 \exp(- 0.5 r^2)
+       k(r) = \\sigma^2 \\exp(- 0.5 r^2)
 
     notes::
      - This is exactly the same as the RBF covariance function, but the
@@ -664,10 +664,10 @@ class ExpQuad(Stationary):
 class Cosine(Stationary):
     """
     Cosine Covariance function
-    
+
     .. math::
 
-        k(r) = \sigma^2 \cos(r)
+        k(r) = \\sigma^2 \\cos(r)
 
     """
     def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='Cosine'):
@@ -682,18 +682,18 @@ class Cosine(Stationary):
 class ExpQuadCosine(Stationary):
     """
     Exponentiated quadratic multiplied by cosine covariance function (spectral mixture kernel).
-    
+
     .. math::
 
-        k(r) = \sigma^2 \exp(-2\pi^2r^2)\cos(2\pi r/T)
+        k(r) = \\sigma^2 \\exp(-2\\pi^2r^2)\\cos(2\\pi r/T)
 
     """
-    
+
     def __init__(self, input_dim, variance=1., lengthscale=None, period=1., ARD=False, active_dims=None, name='ExpQuadCosine'):
         super(ExpQuadCosine, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name)
         self.period = Param('period', period, Logexp())
         self.link_parameters(self.period)
-        
+
     def K_of_r(self, r):
         return self.variance * np.exp(-2*np.pi**2*r**2)*np.cos(2*np.pi*r/self.period)
 
@@ -712,18 +712,18 @@ class ExpQuadCosine(Stationary):
         super(ExpQuadCosine, self).update_gradients_diag(dL_dKdiag, X)
         self.period.gradient = 0.
 
-    
-    
+
+
 class Sinc(Stationary):
     """
     Sinc Covariance function
-    
+
     .. math::
 
-        k(r) = \sigma^2 \sinc(\pi r)
+        k(r) = \\sigma^2 \\sinc(\\pi r)
 
     """
-    
+
     def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='Sinc'):
         super(Sinc, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name)
 
@@ -734,7 +734,7 @@ class Sinc(Stationary):
         # small angle approximation to avoid divide by zero errors.
         return np.where(r<1e-5, -self.variance*4/3*np.pi*np.pi*r, self.variance/r * (np.cos(2*np.pi*r)-np.sinc(2*r)))
 
-    
+
 
 class RatQuad(Stationary):
     """
@@ -742,7 +742,7 @@ class RatQuad(Stationary):
 
     .. math::
 
-       k(r) = \sigma^2 \\bigg( 1 + \\frac{r^2}{2} \\bigg)^{- \\alpha}
+       k(r) = \\sigma^2 \\bigg( 1 + \\frac{r^2}{2} \\bigg)^{- \\alpha}
 
     """
 

GPy/kern/src/todo/eq_ode1.py

@@ -14,23 +14,23 @@ class Eq_ode1(Kernpart):
 
     This outputs of this kernel have the form
     .. math::
-       \frac{\text{d}y_j}{\text{d}t} = \sum_{i=1}^R w_{j,i} f_i(t-\delta_j) +\sqrt{\kappa_j}g_j(t) - d_jy_j(t)
+       \\frac{\\text{d}y_j}{\\text{d}t} = \\sum_{i=1}^R w_{j,i} f_i(t-\\delta_j) +\\sqrt{\\kappa_j}g_j(t) - d_jy_j(t)
 
     where :math:`R` is the rank of the system, :math:`w_{j,i}` is the sensitivity of the :math:`j`th output to the :math:`i`th latent function, :math:`d_j` is the decay rate of the :math:`j`th output and :math:`f_i(t)` and :math:`g_i(t)` are independent latent Gaussian processes goverened by an exponentiated quadratic covariance.
-    
+
     :param output_dim: number of outputs driven by latent function.
     :type output_dim: int
-    :param W: sensitivities of each output to the latent driving function. 
+    :param W: sensitivities of each output to the latent driving function.
     :type W: ndarray (output_dim x rank).
     :param rank: If rank is greater than 1 then there are assumed to be a total of rank latent forces independently driving the system, each with identical covariance.
     :type rank: int
-    :param decay: decay rates for the first order system. 
+    :param decay: decay rates for the first order system.
     :type decay: array of length output_dim.
     :param delay: delay between latent force and output response.
     :type delay: array of length output_dim.
     :param kappa: diagonal term that allows each latent output to have an independent component to the response.
     :type kappa: array of length output_dim.
-    
+
     .. Note: see first order differential equation examples in GPy.examples.regression for some usage.
     """
     def __init__(self,output_dim, W=None, rank=1, kappa=None, lengthscale=1.0,  decay=None, delay=None):
@@ -62,7 +62,7 @@ class Eq_ode1(Kernpart):
         self.is_stationary = False
         self.gaussian_initial = False
         self._set_params(self._get_params())
-        
+
     def _get_params(self):
         param_list = [self.W.flatten()]
         if self.kappa is not None:
@@ -103,11 +103,11 @@ class Eq_ode1(Kernpart):
         param_names += ['decay_%i'%i for i in range(1,self.output_dim)]
         if self.delay is not None:
             param_names += ['delay_%i'%i for i in 1+range(1,self.output_dim)]
-        param_names+= ['lengthscale'] 
+        param_names+= ['lengthscale']
         return param_names
 
     def K(self,X,X2,target):
-        
+
         if X.shape[1] > 2:
             raise ValueError('Input matrix for ode1 covariance should have at most two columns, one containing times, the other output indices')
 
@@ -123,13 +123,13 @@ class Eq_ode1(Kernpart):
     def Kdiag(self,index,target):
         #target += np.diag(self.B)[np.asarray(index,dtype=int).flatten()]
         pass
-    
+
     def _param_grad_helper(self,dL_dK,X,X2,target):
-        
+
         # First extract times and indices.
         self._extract_t_indices(X, X2, dL_dK=dL_dK)
         self._dK_ode_dtheta(target)
-        
+
 
     def _dK_ode_dtheta(self, target):
         """Do all the computations for the ode parts of the covariance function."""
@@ -138,7 +138,7 @@ class Eq_ode1(Kernpart):
         index_ode = self._index[self._index>0]-1
         if self._t2 is None:
             if t_ode.size==0:
-                return        
+                return
             t2_ode = t_ode
             dL_dK_ode = dL_dK_ode[:, self._index>0]
             index2_ode = index_ode
@@ -210,7 +210,7 @@ class Eq_ode1(Kernpart):
         self._index = self._index[self._order]
         self._t = self._t[self._order]
         self._rorder = self._order.argsort() # rorder is for reversing the order
-        
+
         if X2 is None:
             self._t2 = None
             self._index2 = None
@@ -229,7 +229,7 @@ class Eq_ode1(Kernpart):
         if dL_dK is not None:
             self._dL_dK = dL_dK[self._order, :]
             self._dL_dK = self._dL_dK[:, self._order2]
-            
+
     def _K_computations(self, X, X2):
         """Perform main body of computations for the ode1 covariance function."""
         # First extract times and indices.
@@ -253,8 +253,8 @@ class Eq_ode1(Kernpart):
                                                    np.hstack((self._K_ode_eq, self._K_ode))))
         self._K_dvar = self._K_dvar[self._rorder, :]
         self._K_dvar = self._K_dvar[:, self._rorder2]
-        
-        
+
+
         if X2 is None:
             # Matrix giving scales of each output
             self._scale = np.zeros((self._t.size, self._t.size))
@@ -303,7 +303,7 @@ class Eq_ode1(Kernpart):
                 self._K_eq = np.zeros((t_eq.size, t2_eq.size))
                 return
             self._dist2 = np.square(t_eq[:, None] - t2_eq[None, :])
-        
+
         self._K_eq = np.exp(-self._dist2/(2*self.lengthscale*self.lengthscale))
         if self.is_normalized:
             self._K_eq/=(np.sqrt(2*np.pi)*self.lengthscale)
@@ -361,7 +361,7 @@ class Eq_ode1(Kernpart):
             self._K_eq_ode = sK.T
         else:
             self._K_ode_eq = sK
-        
+
     def _K_compute_ode(self):
         # Compute covariances between outputs of the ODE models.
 
@@ -370,7 +370,7 @@ class Eq_ode1(Kernpart):
         if self._t2 is None:
             if t_ode.size==0:
                 self._K_ode = np.zeros((0, 0))
-                return        
+                return
             t2_ode = t_ode
             index2_ode = index_ode
         else:
@@ -379,14 +379,14 @@ class Eq_ode1(Kernpart):
                 self._K_ode = np.zeros((t_ode.size, t2_ode.size))
                 return
             index2_ode = self._index2[self._index2>0]-1
-        
+
         # When index is identical
         h = self._compute_H(t_ode, index_ode, t2_ode, index2_ode, stationary=self.is_stationary)
 
         if self._t2 is None:
             self._K_ode = 0.5 * (h + h.T)
         else:
-            h2 = self._compute_H(t2_ode, index2_ode, t_ode, index_ode, stationary=self.is_stationary)                
+            h2 = self._compute_H(t2_ode, index2_ode, t_ode, index_ode, stationary=self.is_stationary)
             self._K_ode = 0.5 * (h + h2.T)
 
         if not self.is_normalized:
@@ -410,28 +410,28 @@ class Eq_ode1(Kernpart):
             Decay = self.decay[index]
             if self.delay is not None:
                 t = t - self.delay[index]
-            
+
             t_squared = t*t
             half_sigma_decay = 0.5*self.sigma*Decay
             [ln_part_1, sign1] = ln_diff_erfs(half_sigma_decay + t/self.sigma,
                                               half_sigma_decay)
-    
+
             [ln_part_2, sign2] = ln_diff_erfs(half_sigma_decay,
                                               half_sigma_decay - t/self.sigma)
-            
+
             h = (sign1*np.exp(half_sigma_decay*half_sigma_decay
                              + ln_part_1
-                             - log(Decay + D_j)) 
+                             - log(Decay + D_j))
                  - sign2*np.exp(half_sigma_decay*half_sigma_decay
                                 - (Decay + D_j)*t
-                                + ln_part_2 
+                                + ln_part_2
                                 - log(Decay + D_j)))
-    
+
             sigma2 = self.sigma*self.sigma
 
         if update_derivatives:
-        
-            dh_dD_i = ((0.5*Decay*sigma2*(Decay + D_j)-1)*h 
+
+            dh_dD_i = ((0.5*Decay*sigma2*(Decay + D_j)-1)*h
                        + t*sign2*np.exp(
                 half_sigma_decay*half_sigma_decay-(Decay+D_j)*t + ln_part_2
                 )
@@ -439,11 +439,11 @@ class Eq_ode1(Kernpart):
                        (-1 + np.exp(-t_squared/sigma2-Decay*t)
                         + np.exp(-t_squared/sigma2-D_j*t)
                         - np.exp(-(Decay + D_j)*t)))
-        
+
             dh_dD_i = (dh_dD_i/(Decay+D_j)).real
-        
-        
-        
+
+
+
             dh_dD_j = (t*sign2*np.exp(
                 half_sigma_decay*half_sigma_decay-(Decay + D_j)*t+ln_part_2
                 )
@@ -457,7 +457,7 @@ class Eq_ode1(Kernpart):
                           - (-t/sigma2-Decay/2)*np.exp(-t_squared/sigma2 - D_j*t) \
                           - Decay/2*np.exp(-(Decay+D_j)*t))"""
         pass
-    
+
     def _compute_H(self, t, index, t2, index2, update_derivatives=False, stationary=False):
         """Helper function for computing part of the ode1 covariance function.
 
@@ -491,7 +491,7 @@ class Eq_ode1(Kernpart):
         inv_sigma_diff_t = 1./self.sigma*diff_t
         half_sigma_decay_i = 0.5*self.sigma*Decay[:, None]
 
-        ln_part_1, sign1 = ln_diff_erfs(half_sigma_decay_i + t2_mat/self.sigma, 
+        ln_part_1, sign1 = ln_diff_erfs(half_sigma_decay_i + t2_mat/self.sigma,
                                         half_sigma_decay_i - inv_sigma_diff_t,
                                         return_sign=True)
         ln_part_2, sign2 = ln_diff_erfs(half_sigma_decay_i,
@@ -529,7 +529,7 @@ class Eq_ode1(Kernpart):
                 )
                 ))
             self._dh_ddecay = (dh_ddecay/(Decay[:, None]+Decay2[None, :])).real
-            
+
             # Update jth decay gradient
             dh_ddecay2 = (t2_mat*sign2
                          *np.exp(
@@ -539,7 +539,7 @@ class Eq_ode1(Kernpart):
                 )
                          -h)
             self._dh_ddecay2 = (dh_ddecay/(Decay[:, None] + Decay2[None, :])).real
-            
+
             # Update sigma gradient
             self._dh_dsigma = (half_sigma_decay_i*Decay[:, None]*h
                                + 2/(np.sqrt(np.pi)
@@ -547,10 +547,10 @@ class Eq_ode1(Kernpart):
                                *((-diff_t/sigma2-Decay[:, None]/2)
                                  *np.exp(-diff_t*diff_t/sigma2)
                                  + (-t2_mat/sigma2+Decay[:, None]/2)
-                                 *np.exp(-t2_mat*t2_mat/sigma2-Decay[:, None]*t_mat) 
-                                 - (-t_mat/sigma2-Decay[:, None]/2) 
-                                 *np.exp(-t_mat*t_mat/sigma2-Decay2[None, :]*t2_mat) 
+                                 *np.exp(-t2_mat*t2_mat/sigma2-Decay[:, None]*t_mat)
+                                 - (-t_mat/sigma2-Decay[:, None]/2)
+                                 *np.exp(-t_mat*t_mat/sigma2-Decay2[None, :]*t2_mat)
                                  - Decay[:, None]/2
                                  *np.exp(-(Decay[:, None]*t_mat+Decay2[None, :]*t2_mat))))
-                
+
         return h

GPy/kern/src/todo/gibbs.py

@@ -9,13 +9,13 @@ import GPy
 
 class Gibbs(Kernpart):
     """
-    Gibbs non-stationary covariance function. 
+    Gibbs non-stationary covariance function.
 
     .. math::
-       
+
        r = sqrt((x_i - x_j)'*(x_i - x_j))
-       
-       k(x_i, x_j) = \sigma^2*Z*exp(-r^2/(l(x)*l(x) + l(x')*l(x')))
+
+       k(x_i, x_j) = \\sigma^2*Z*exp(-r^2/(l(x)*l(x) + l(x')*l(x')))
 
        Z = (2*l(x)*l(x')/(l(x)*l(x) + l(x')*l(x')^{q/2}
 
@@ -25,18 +25,18 @@ class Gibbs(Kernpart):
         with input location. This leads to an additional term in front of
         the kernel.
 
-        The parameters are :math:`\sigma^2`, the process variance, and
+        The parameters are :math:`\\sigma^2`, the process variance, and
         the parameters of l(x) which is a function that can be
         specified by the user, by default an multi-layer peceptron is
         used.
 
         :param input_dim: the number of input dimensions
-        :type input_dim: int 
-        :param variance: the variance :math:`\sigma^2`
+        :type input_dim: int
+        :param variance: the variance :math:`\\sigma^2`
         :type variance: float
         :param mapping: the mapping that gives the lengthscale across the input space (by default GPy.mappings.MLP is used with 20 hidden nodes).
         :type mapping: GPy.core.Mapping
-        :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \sigma^2_w), otherwise there is one weight variance parameter per dimension.
+        :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \\sigma^2_w), otherwise there is one weight variance parameter per dimension.
         :type ARD: Boolean
         :rtype: Kernpart object
 
@@ -113,7 +113,7 @@ class Gibbs(Kernpart):
             target += 2.*self.mapping.df_dX(self._dL_dl[:, None], X)
         else:
             target += self.mapping.df_dX(self._dL_dl[:, None], X)
-    
+
     def dKdiag_dX(self, dL_dKdiag, X, target):
         """Gradient of diagonal of covariance with respect to X."""
         pass
@@ -123,7 +123,7 @@ class Gibbs(Kernpart):
         target[0] += np.sum(dL_dKdiag)
 
 
-    
+
     def _K_computations(self, X, X2=None):
         """Pre-computations for the covariance function (used both when computing the covariance and its gradients). Here self._dK_dvar and self._K_dist2 are updated."""
         self._lengthscales=self.mapping.f(X)
@@ -146,7 +146,7 @@ class Gibbs(Kernpart):
         """Pre-computations for the gradients of the covaraince function. Here the gradient of the covariance with respect to all the individual lengthscales is computed.
         :param dL_dK: the gradient of the objective with respect to the covariance function.
         :type dL_dK: ndarray"""
-        
+
         self._dL_dl = (dL_dK*self.variance*self._K_dvar*(self.input_dim/2.*(self._lengthscales_two.T**4 - self._lengthscales**4) + 2*self._lengthscales2*self._K_dist2)/(self._w2*self._w2*self._lengthscales)).sum(1)
         if self._lengthscales_two is self._lengthscales:
             self._dL_dl_two = None

GPy/kern/src/todo/hetero.py

@@ -19,11 +19,11 @@ class Hetero(Kernpart):
 
     .. math::
 
-       k(x_i, x_j) = \delta_{i,j} \sigma^2(x_i)
+       k(x_i, x_j) = \\delta_{i,j} \\sigma^2(x_i)
 
-       where :math:`\sigma^2(x)` is a function giving the variance  as a function of input space and :math:`\delta_{i,j}` is the Kronecker delta function.
+       where :math:`\\sigma^2(x)` is a function giving the variance  as a function of input space and :math:`\\delta_{i,j}` is the Kronecker delta function.
 
-    The parameters are the parameters of \sigma^2(x) which is a
+    The parameters are the parameters of \\sigma^2(x) which is a
     function that can be specified by the user, by default an
     multi-layer peceptron is used.
 

GPy/kern/src/todo/poly.py

@@ -11,28 +11,28 @@ class POLY(Kernpart):
     Polynomial kernel parameter initialisation.  Included for completeness, but generally not recommended, is the polynomial kernel:
 
     .. math::
-        k(x, y) = \sigma^2\*(\sigma_w^2 x'y+\sigma_b^b)^d
+        k(x, y) = \\sigma^2\\*(\\sigma_w^2 x'y+\\sigma_b^b)^d
 
-    The kernel parameters are :math:`\sigma^2` (variance), :math:`\sigma^2_w`
-    (weight_variance), :math:`\sigma^2_b` (bias_variance) and d
+    The kernel parameters are :math:`\\sigma^2` (variance), :math:`\\sigma^2_w`
+    (weight_variance), :math:`\\sigma^2_b` (bias_variance) and d
     (degree). Only gradients of the first three are provided for
     kernel optimisation, it is assumed that polynomial degree would
     be set by hand.
 
     The kernel is not recommended as it is badly behaved when the
-    :math:`\sigma^2_w\*x'\*y + \sigma^2_b` has a magnitude greater than one. For completeness
+    :math:`\\sigma^2_w\\*x'\\*y + \\sigma^2_b` has a magnitude greater than one. For completeness
     there is an automatic relevance determination version of this
     kernel provided (NOTE YET IMPLEMENTED!).
     :param input_dim: the number of input dimensions
-    :type input_dim: int 
-    :param variance: the variance :math:`\sigma^2`
+    :type input_dim: int
+    :param variance: the variance :math:`\\sigma^2`
     :type variance: float
-    :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\sigma^2_w`
+    :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\\sigma^2_w`
     :type weight_variance: array or list of the appropriate size (or float if there is only one weight variance parameter)
-    :param bias_variance: the variance of the prior over bias parameters :math:`\sigma^2_b`
+    :param bias_variance: the variance of the prior over bias parameters :math:`\\sigma^2_b`
     :param degree: the degree of the polynomial.
     :type degree: int
-    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter :math:`\sigma^2_w`), otherwise there is one weight variance parameter per dimension.
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter :math:`\\sigma^2_w`), otherwise there is one weight variance parameter per dimension.
     :type ARD: Boolean
     :rtype: Kernpart object
 
@@ -93,7 +93,7 @@ class POLY(Kernpart):
         base_cov_grad = base*dL_dK
 
 
-            
+
         target[0] += np.sum(self._K_dvar*dL_dK)
         target[1] += (self._K_inner_prod*base_cov_grad).sum()
         target[2] += base_cov_grad.sum()
@@ -107,14 +107,14 @@ class POLY(Kernpart):
             target += 2*self.weight_variance*self.degree*self.variance*(((X[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1)
         else:
             target += self.weight_variance*self.degree*self.variance*(((X2[None,:, :])) *(arg**(self.degree-1))[:, :, None]*dL_dK[:, :, None]).sum(1)
-            
+
     def dKdiag_dX(self, dL_dKdiag, X, target):
         """Gradient of diagonal of covariance with respect to X"""
         self._K_diag_computations(X)
         arg = self._K_diag_poly_arg
         target += 2.*self.weight_variance*self.degree*self.variance*X*dL_dKdiag[:, None]*(arg**(self.degree-1))[:, None]
-    
-    
+
+
     def _K_computations(self, X, X2):
         if self.ARD:
             pass
@@ -133,6 +133,6 @@ class POLY(Kernpart):
             self._K_diag_poly_arg = (X*X).sum(1)*self.weight_variance + self.bias_variance
         self._K_diag_dvar = self._K_diag_poly_arg**self.degree
 
-  
+
 
 

GPy/kern/src/todo/rbf_inv.py

@@ -15,9 +15,9 @@ class RBFInv(RBF):
 
     .. math::
 
-       k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \ \ \ \ \  \\text{ where  } r^2 = \sum_{i=1}^d \\frac{ (x_i-x^\prime_i)^2}{\ell_i^2}
+       k(r) = \\sigma^2 \\exp \\bigg(- \\frac{1}{2} r^2 \\bigg) \\ \\ \\ \\ \\  \\text{ where  } r^2 = \\sum_{i=1}^d \\frac{ (x_i-x^\\prime_i)^2}{\\ell_i^2}
 
-    where \ell_i is the lengthscale, \sigma^2 the variance and d the dimensionality of the input.
+    where \\ell_i is the lengthscale, \\sigma^2 the variance and d the dimensionality of the input.
 
     :param input_dim: the number of input dimensions
     :type input_dim: int
@@ -25,7 +25,7 @@ class RBFInv(RBF):
     :type variance: float
     :param lengthscale: the vector of lengthscale of the kernel
     :type lengthscale: array or list of the appropriate size (or float if there is only one lengthscale parameter)
-    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \ell), otherwise there is one lengthscale parameter per dimension.
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \\ell), otherwise there is one lengthscale parameter per dimension.
     :type ARD: Boolean
     :rtype: kernel object
 

GPy/kern/src/trunclinear.py

@@ -14,15 +14,15 @@ class TruncLinear(Kern):
 
     .. math::
 
-       k(x,y) = \sum_{i=1}^input_dim \sigma^2_i \max(0, x_iy_i - \sigma_q)
+       k(x,y) = \\sum_{i=1}^input_dim \\sigma^2_i \\max(0, x_iy_i - \\sigma_q)
 
     :param input_dim: the number of input dimensions
     :type input_dim: int
-    :param variances: the vector of variances :math:`\sigma^2_i`
+    :param variances: the vector of variances :math:`\\sigma^2_i`
     :type variances: array or list of the appropriate size (or float if there
                      is only one variance parameter)
     :param ARD: Auto Relevance Determination. If False, the kernel has only one
-                variance parameter \sigma^2, otherwise there is one variance
+                variance parameter \\sigma^2, otherwise there is one variance
                 parameter per dimension.
     :type ARD: Boolean
     :rtype: kernel object
@@ -113,15 +113,15 @@ class TruncLinear_inf(Kern):
 
     .. math::
 
-       k(x,y) = \sum_{i=1}^input_dim \sigma^2_i \max(0, x_iy_i - \sigma_q)
+       k(x,y) = \\sum_{i=1}^input_dim \\sigma^2_i \\max(0, x_iy_i - \\sigma_q)
 
     :param input_dim: the number of input dimensions
     :type input_dim: int
-    :param variances: the vector of variances :math:`\sigma^2_i`
+    :param variances: the vector of variances :math:`\\sigma^2_i`
     :type variances: array or list of the appropriate size (or float if there
                      is only one variance parameter)
     :param ARD: Auto Relevance Determination. If False, the kernel has only one
-                variance parameter \sigma^2, otherwise there is one variance
+                variance parameter \\sigma^2, otherwise there is one variance
                 parameter per dimension.
     :type ARD: Boolean
     :rtype: kernel object

GPy/likelihoods/bernoulli.py

@@ -243,7 +243,7 @@ class Bernoulli(Likelihood):
         assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape
         #d3logpdf_dlink3 = 2*(y/(inv_link_f**3) - (1-y)/((1-inv_link_f)**3))
         state = np.seterr(divide='ignore')
-        # TODO check y \in {0, 1} or {-1, 1}
+        # TODO check y \\in {0, 1} or {-1, 1}
         d3logpdf_dlink3 = np.where(y==1, 2./(inv_link_f**3), -2./((1.-inv_link_f)**3))
         np.seterr(**state)
         return d3logpdf_dlink3

GPy/likelihoods/exponential.py

@@ -14,7 +14,7 @@ class Exponential(Likelihood):
     Y is expected to take values in {0,1,2,...}
     -----
     $$
-    L(x) = \exp(\lambda) * \lambda**Y_i / Y_i!
+    L(x) = \\exp(\\lambda) * \\lambda**Y_i / Y_i!
     $$
     """
     def __init__(self,gp_link=None):
@@ -46,7 +46,7 @@ class Exponential(Likelihood):
         Log Likelihood Function given link(f)
 
         .. math::
-            \\ln p(y_{i}|\lambda(f_{i})) = \\ln \\lambda(f_{i}) - y_{i}\\lambda(f_{i})
+            \\ln p(y_{i}|\\lambda(f_{i})) = \\ln \\lambda(f_{i}) - y_{i}\\lambda(f_{i})
 
         :param link_f: latent variables (link(f))
         :type link_f: Nx1 array
@@ -65,7 +65,7 @@ class Exponential(Likelihood):
         Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{1}{\\lambda(f)} - y_{i}
+            \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\frac{1}{\\lambda(f)} - y_{i}
 
         :param link_f: latent variables (f)
         :type link_f: Nx1 array
@@ -87,7 +87,7 @@ class Exponential(Likelihood):
         The hessian will be 0 unless i == j
 
         .. math::
-            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\frac{1}{\\lambda(f_{i})^{2}}
+            \\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\frac{1}{\\lambda(f_{i})^{2}}
 
         :param link_f: latent variables link(f)
         :type link_f: Nx1 array
@@ -110,7 +110,7 @@ class Exponential(Likelihood):
         Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{2}{\\lambda(f_{i})^{3}}
+            \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{2}{\\lambda(f_{i})^{3}}
 
         :param link_f: latent variables link(f)
         :type link_f: Nx1 array

GPy/likelihoods/gamma.py

@@ -54,7 +54,7 @@ class Gamma(Likelihood):
         Log Likelihood Function given link(f)
 
         .. math::
-            \\ln p(y_{i}|\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\beta y_{i}\\\\
+            \\ln p(y_{i}|\\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\beta y_{i}\\\\
             \\alpha_{i} = \\beta y_{i}
 
         :param link_f: latent variables (link(f))
@@ -101,7 +101,7 @@ class Gamma(Likelihood):
         The hessian will be 0 unless i == j
 
         .. math::
-            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\beta^{2}\\frac{d\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
+            \\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\beta^{2}\\frac{d\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
             \\alpha_{i} = \\beta y_{i}
 
         :param link_f: latent variables link(f)
@@ -126,7 +126,7 @@ class Gamma(Likelihood):
         Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = -\\beta^{3}\\frac{d^{2}\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
+            \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = -\\beta^{3}\\frac{d^{2}\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
             \\alpha_{i} = \\beta y_{i}
 
         :param link_f: latent variables link(f)

GPy/likelihoods/likelihood.py

@@ -130,7 +130,7 @@ class Likelihood(Parameterized):
         Calculation of the log predictive density
 
         .. math:
-            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
+            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\\mu_{*}\\sigma^{2}_{*})
 
         :param y_test: test observations (y_{*})
         :type y_test: (Nx1) array
@@ -199,7 +199,7 @@ class Likelihood(Parameterized):
 
         .. math:
             log p(y_{*}|D) = log 1/num_samples prod^{S}_{s=1} p(y_{*}|f_{*s})
-            f_{*s} ~ p(f_{*}|\mu_{*}\\sigma^{2}_{*})
+            f_{*s} ~ p(f_{*}|\\mu_{*}\\sigma^{2}_{*})
 
         :param y_test: test observations (y_{*})
         :type y_test: (Nx1) array

GPy/likelihoods/link_functions.py

@@ -145,7 +145,7 @@ class ScaledProbit(Probit):
     """
     def __init__(self, nu=1.):
         self.nu = float(nu)
-        
+
     def transf(self,f):
         return std_norm_cdf(f*self.nu)
 
@@ -157,7 +157,7 @@ class ScaledProbit(Probit):
 
     def d3transf_df3(self,f):
         return (safe_square(f*self.nu)-1.)*std_norm_pdf(f*self.nu)*(self.nu**3)
-    
+
     def to_dict(self):
         """
         Convert the object into a json serializable dictionary.
@@ -180,7 +180,7 @@ class Cloglog(GPTransformation):
 
         or
 
-        f = \log (-\log(1-p))
+        f = \\log (-\\log(1-p))
 
     """
     def transf(self,f):

GPy/likelihoods/poisson.py

@@ -54,7 +54,7 @@ class Poisson(Likelihood):
         Log Likelihood Function given link(f)
 
         .. math::
-            \\ln p(y_{i}|\lambda(f_{i})) = -\\lambda(f_{i}) + y_{i}\\log \\lambda(f_{i}) - \\log y_{i}!
+            \\ln p(y_{i}|\\lambda(f_{i})) = -\\lambda(f_{i}) + y_{i}\\log \\lambda(f_{i}) - \\log y_{i}!
 
         :param link_f: latent variables (link(f))
         :type link_f: Nx1 array
@@ -72,7 +72,7 @@ class Poisson(Likelihood):
         Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{y_{i}}{\\lambda(f_{i})} - 1
+            \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\frac{y_{i}}{\\lambda(f_{i})} - 1
 
         :param link_f: latent variables (f)
         :type link_f: Nx1 array
@@ -92,7 +92,7 @@ class Poisson(Likelihood):
         The hessian will be 0 unless i == j
 
         .. math::
-            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{-y_{i}}{\\lambda(f_{i})^{2}}
+            \\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{-y_{i}}{\\lambda(f_{i})^{2}}
 
         :param link_f: latent variables link(f)
         :type link_f: Nx1 array
@@ -113,7 +113,7 @@ class Poisson(Likelihood):
         Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{2y_{i}}{\\lambda(f_{i})^{3}}
+            \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{2y_{i}}{\\lambda(f_{i})^{3}}
 
         :param link_f: latent variables link(f)
         :type link_f: Nx1 array

GPy/likelihoods/student_t.py

@@ -78,7 +78,7 @@ class StudentT(Likelihood):
         Log Likelihood Function given link(f)
 
         .. math::
-            \\ln p(y_{i}|\lambda(f_{i})) = \\ln \\Gamma\\left(\\frac{v+1}{2}\\right) - \\ln \\Gamma\\left(\\frac{v}{2}\\right) - \\ln \\sqrt{v \\pi\\sigma^{2}} - \\frac{v+1}{2}\\ln \\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right)
+            \\ln p(y_{i}|\\lambda(f_{i})) = \\ln \\Gamma\\left(\\frac{v+1}{2}\\right) - \\ln \\Gamma\\left(\\frac{v}{2}\\right) - \\ln \\sqrt{v \\pi\\sigma^{2}} - \\frac{v+1}{2}\\ln \\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \\lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right)
 
         :param inv_link_f: latent variables (link(f))
         :type inv_link_f: Nx1 array
@@ -107,7 +107,7 @@ class StudentT(Likelihood):
         Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{(v+1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v}
+            \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\frac{(v+1)(y_{i}-\\lambda(f_{i}))}{(y_{i}-\\lambda(f_{i}))^{2} + \\sigma^{2}v}
 
         :param inv_link_f: latent variables (f)
         :type inv_link_f: Nx1 array
@@ -129,7 +129,7 @@ class StudentT(Likelihood):
         The hessian will be 0 unless i == j
 
         .. math::
-            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{(v+1)((y_{i}-\lambda(f_{i}))^{2} - \\sigma^{2}v)}{((y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v)^{2}}
+            \\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{(v+1)((y_{i}-\\lambda(f_{i}))^{2} - \\sigma^{2}v)}{((y_{i}-\\lambda(f_{i}))^{2} + \\sigma^{2}v)^{2}}
 
         :param inv_link_f: latent variables inv_link(f)
         :type inv_link_f: Nx1 array
@@ -154,7 +154,7 @@ class StudentT(Likelihood):
         Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{-2(v+1)((y_{i} - \lambda(f_{i}))^3 - 3(y_{i} - \lambda(f_{i})) \\sigma^{2} v))}{((y_{i} - \lambda(f_{i})) + \\sigma^{2} v)^3}
+            \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{-2(v+1)((y_{i} - \\lambda(f_{i}))^3 - 3(y_{i} - \\lambda(f_{i})) \\sigma^{2} v))}{((y_{i} - \\lambda(f_{i})) + \\sigma^{2} v)^3}
 
         :param inv_link_f: latent variables link(f)
         :type inv_link_f: Nx1 array
@@ -175,7 +175,7 @@ class StudentT(Likelihood):
         Gradient of the log-likelihood function at y given f, w.r.t variance parameter (t_noise)
 
         .. math::
-            \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\sigma^{2}} = \\frac{v((y_{i} - \lambda(f_{i}))^{2} - \\sigma^{2})}{2\\sigma^{2}(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})}
+            \\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\sigma^{2}} = \\frac{v((y_{i} - \\lambda(f_{i}))^{2} - \\sigma^{2})}{2\\sigma^{2}(\\sigma^{2}v + (y_{i} - \\lambda(f_{i}))^{2})}
 
         :param inv_link_f: latent variables link(f)
         :type inv_link_f: Nx1 array
@@ -199,7 +199,7 @@ class StudentT(Likelihood):
         Derivative of the dlogpdf_dlink w.r.t variance parameter (t_noise)
 
         .. math::
-            \\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{df}) = \\frac{-2\\sigma v(v + 1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^2 + \\sigma^2 v)^2}
+            \\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{df}) = \\frac{-2\\sigma v(v + 1)(y_{i}-\\lambda(f_{i}))}{(y_{i}-\\lambda(f_{i}))^2 + \\sigma^2 v)^2}
 
         :param inv_link_f: latent variables inv_link_f
         :type inv_link_f: Nx1 array
@@ -220,7 +220,7 @@ class StudentT(Likelihood):
         Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (t_noise)
 
         .. math::
-            \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}f}) = \\frac{v(v+1)(\\sigma^{2}v - 3(y_{i} - \lambda(f_{i}))^{2})}{(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})^{3}}
+            \\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}f}) = \\frac{v(v+1)(\\sigma^{2}v - 3(y_{i} - \\lambda(f_{i}))^{2})}{(\\sigma^{2}v + (y_{i} - \\lambda(f_{i}))^{2})^{3}}
 
         :param inv_link_f: latent variables link(f)
         :type inv_link_f: Nx1 array

GPy/likelihoods/weibull.py

@@ -54,7 +54,7 @@ class Weibull(Likelihood):
         Log Likelihood Function given link(f)
 
         .. math::
-            \\ln p(y_{i}|\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\beta y_{i}\\\\
+            \\ln p(y_{i}|\\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\beta y_{i}\\\\
             \\alpha_{i} = \\beta y_{i}
 
         :param link_f: latent variables (link(f))
@@ -117,7 +117,7 @@ class Weibull(Likelihood):
         The hessian will be 0 unless i == j
 
         .. math::
-            \\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\beta^{2}\\frac{d\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
+            \\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\beta^{2}\\frac{d\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
             \\alpha_{i} = \\beta y_{i}
 
         :param link_f: latent variables link(f)
@@ -150,7 +150,7 @@ class Weibull(Likelihood):
         Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
 
         .. math::
-            \\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = -\\beta^{3}\\frac{d^{2}\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
+            \\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = -\\beta^{3}\\frac{d^{2}\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
             \\alpha_{i} = \\beta y_{i}
 
         :param link_f: latent variables link(f)

GPy/mappings/additive.py

@@ -10,7 +10,7 @@ class Additive(Mapping):
 
     .. math::
 
-       f(\mathbf{x}*) = f_1(\mathbf{x}*) + f_2(\mathbf(x)*)
+       f(\\mathbf{x}*) = f_1(\\mathbf{x}*) + f_2(\\mathbf(x)*)
 
     :param mapping1: first mapping to add together.
     :type mapping1: GPy.mappings.Mapping

GPy/mappings/compound.py

@@ -9,7 +9,7 @@ class Compound(Mapping):
 
     .. math::
 
-       f(\mathbf{x}) = f_2(f_1(\mathbf{x}))
+       f(\\mathbf{x}) = f_2(f_1(\\mathbf{x}))
 
     :param mapping1: first mapping
     :type mapping1: GPy.mappings.Mapping

GPy/mappings/constant.py

@@ -9,7 +9,7 @@ class Constant(Mapping):
 
     .. math::
 
-       F(\mathbf{x}) = c
+       F(\\mathbf{x}) = c
 
 
     :param input_dim: dimension of input.

GPy/mappings/kernel.py

@@ -12,20 +12,20 @@ class Kernel(Mapping):
 
     .. math::
 
-       f(\mathbf{x}) = \sum_i \alpha_i k(\mathbf{z}_i, \mathbf{x})
+       f(\\mathbf{x}) = \\sum_i \\alpha_i k(\\mathbf{z}_i, \\mathbf{x})
 
     or for multple outputs
 
     .. math::
 
-       f_i(\mathbf{x}) = \sum_j \alpha_{i,j} k(\mathbf{z}_i, \mathbf{x})
+       f_i(\\mathbf{x}) = \\sum_j \\alpha_{i,j} k(\\mathbf{z}_i, \\mathbf{x})
 
 
     :param input_dim: dimension of input.
     :type input_dim: int
     :param output_dim: dimension of output.
     :type output_dim: int
-    :param Z: input observations containing :math:`\mathbf{Z}`
+    :param Z: input observations containing :math:`\\mathbf{Z}`
     :type Z: ndarray
     :param kernel: a GPy kernel, defaults to GPy.kern.RBF
     :type kernel: GPy.kern.kern

GPy/mappings/linear.py

@@ -12,7 +12,7 @@ class Linear(Mapping):
 
     .. math::
 
-       F(\mathbf{x}) = \mathbf{A} \mathbf{x})
+       F(\\mathbf{x}) = \\mathbf{A} \\mathbf{x})
 
 
     :param input_dim: dimension of input.

GPy/models/gp_kronecker_gaussian_regression.py

@@ -22,7 +22,7 @@ class GPKroneckerGaussianRegression(Model):
 
     .. rubric:: References
 
-    .. [stegle_et_al_2011] Stegle, O.; Lippert, C.; Mooij, J.M.; Lawrence, N.D.; Borgwardt, K.:Efficient inference in matrix-variate Gaussian models with \iid observation noise. In: Advances in Neural Information Processing Systems, 2011, Pages 630-638
+    .. [stegle_et_al_2011] Stegle, O.; Lippert, C.; Mooij, J.M.; Lawrence, N.D.; Borgwardt, K.:Efficient inference in matrix-variate Gaussian models with \\iid observation noise. In: Advances in Neural Information Processing Systems, 2011, Pages 630-638
 
     """
     def __init__(self, X1, X2, Y, kern1, kern2, noise_var=1., name='KGPR'):

GPy/models/ss_mrd.py

@@ -183,7 +183,7 @@ class SSMRD(Model):
 
     @Model.optimizer_array.setter
     def optimizer_array(self, p):
-        if self.mpi_comm != None:
+        if self.mpi_comm is not None:
             if self._IN_OPTIMIZATION_ and self.mpi_comm.rank == 0:
                 self.mpi_comm.Bcast(np.int32(1), root=0)
             self.mpi_comm.Bcast(p, root=0)

GPy/models/state_space_main.py

@@ -4002,10 +4002,10 @@ class ContDescrStateSpace(DescreteStateSpace):
         """
         Linear Time-Invariant Stochastic Differential Equation (LTI SDE):
 
-            dx(t) = F x(t) dt + L d \beta  ,where
+            dx(t) = F x(t) dt + L d \\beta  ,where
 
                 x(t): (vector) stochastic process
-                \beta: (vector) Brownian motion process
+                \\beta: (vector) Brownian motion process
                 F, L: (time invariant) matrices of corresponding dimensions
                 Qc: covariance of noise.
 
@@ -4022,7 +4022,7 @@ class ContDescrStateSpace(DescreteStateSpace):
         F,L: LTI SDE matrices of corresponding dimensions
 
         Qc: matrix (n,n)
-            Covarince between different dimensions of noise \beta.
+            Covarince between different dimensions of noise \\beta.
             n is the dimensionality of the noise.
 
         dt: double or iterable

GPy/models/tp_regression.py

@@ -171,7 +171,7 @@ class TPRegression(Model):
 
     def log_likelihood(self):
         """
-        The log marginal likelihood of the model, :math:`p(\mathbf{y})`, this is the objective function of the model being optimised
+        The log marginal likelihood of the model, :math:`p(\\mathbf{y})`, this is the objective function of the model being optimised
         """
         return self._log_marginal_likelihood or self.inference()[1]
 
@@ -184,10 +184,10 @@ class TPRegression(Model):
         diagonal of the covariance is returned.
 
         .. math::
-            p(f*|X*, X, Y) = \int^{\inf}_{\inf} p(f*|f,X*)p(f|X,Y) df
-                        = MVN\left(\nu + N,f*| K_{x*x}(K_{xx})^{-1}Y,
-                        \frac{\nu + \beta - 2}{\nu + N - 2}K_{x*x*} - K_{xx*}(K_{xx})^{-1}K_{xx*}\right)
-            \nu := \texttt{Degrees of freedom}
+            p(f*|X*, X, Y) = \\int^{\\inf}_{\\inf} p(f*|f,X*)p(f|X,Y) df
+                        = MVN\\left(\\nu + N,f*| K_{x*x}(K_{xx})^{-1}Y,
+                        \\frac{\\nu + \\beta - 2}{\\nu + N - 2}K_{x*x*} - K_{xx*}(K_{xx})^{-1}K_{xx*}\\right)
+            \\nu := \\texttt{Degrees of freedom}
         """
         mu, var = self.posterior._raw_predict(kern=self.kern if kern is None else kern, Xnew=Xnew,
                                               pred_var=self._predictive_variable, full_cov=full_cov)

GPy/models/warped_gp.py

@@ -146,7 +146,7 @@ class WarpedGP(GP):
         the jacobian of the warping function here.
 
         .. math:
-            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
+            p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\\mu_{*}\\sigma^{2}_{*})
 
         :param x_test: test locations (x_{*})
         :type x_test: (Nx1) array

GPy/plotting/matplot_dep/visualize.py

@@ -167,7 +167,7 @@ class lvm(matplotlib_show):
 
     def show_sensitivities(self):
         # A click in the bar chart axis for selection a dimension.
-        if self.sense_axes != None:
+        if self.sense_axes is not None:
             self.sense_axes.cla()
             self.sense_axes.bar(np.arange(self.model.input_dim), self.model.input_sensitivity(), color='b')
 

GPy/testing/state_space_main_tests.py

@@ -159,7 +159,7 @@ def generate_brownian_data(
 ):
     """
     Generate brownian data - data from Brownian motion.
-    First point is always 0, and \Beta(0) = 0  - standard conditions for Brownian motion.
+    First point is always 0, and \\Beta(0) = 0  - standard conditions for Brownian motion.
 
     Input:
     --------------------------------

GPy/testing/test_inference.py

@@ -5,6 +5,8 @@
 The test cases for various inference algorithms
 """
 
+import copy
+import pickle
 import numpy as np
 import GPy
 
@@ -146,6 +148,32 @@ class TestInferenceGPEP:
             < 1e6
         )
 
+    def test_pickle_copy_EP(self):
+        """Pickling and deep-copying a classification model employing EP"""
+
+        # Dummy binary classification dataset
+        X = np.array([0, 1, 2, 3]).reshape(-1, 1)
+        Y = np.array([0, 0, 1, 1]).reshape(-1, 1)
+
+        # Some classification model
+        inf = GPy.inference.latent_function_inference.expectation_propagation.EP(
+            max_iters=30, delta=0.5
+        )
+        m = GPy.core.GP(
+            X=X,
+            Y=Y,
+            kernel=GPy.kern.RBF(input_dim=1, variance=1.0, lengthscale=1.0),
+            inference_method = inf,
+            likelihood=GPy.likelihoods.Bernoulli(),
+            mean_function=None
+        )
+        m.optimize()
+
+        m_pickled = pickle.dumps(m)
+        assert pickle.loads(m_pickled) is not None
+
+        assert copy.deepcopy(m) is not None
+
     # NOTE: adding a test like above for parameterized likelihood- the above test is
     # only for probit likelihood which does not have any tunable hyperparameter which is why
     # the term in dictionary of gradients: dL_dthetaL will always be zero. So here we repeat tests for

GPy/testing/test_model.py

@@ -269,8 +269,8 @@ class TestMisc:
         from GPy.core.parameterization.variational import NormalPosterior
 
         X_pred = NormalPosterior(X_pred_mu, X_pred_var)
-        # mu = \int f(x)q(x|mu,S) dx = \int 2x.q(x|mu,S) dx = 2.mu
-        # S = \int (f(x) - m)^2q(x|mu,S) dx = \int f(x)^2 q(x) dx - mu**2 = 4(mu^2 + S) - (2.mu)^2 = 4S
+        # mu = \\int f(x)q(x|mu,S) dx = \\int 2x.q(x|mu,S) dx = 2.mu
+        # S = \\int (f(x) - m)^2q(x|mu,S) dx = \\int f(x)^2 q(x) dx - mu**2 = 4(mu^2 + S) - (2.mu)^2 = 4S
         Y_mu_true = 2 * X_pred_mu
         Y_var_true = 4 * X_pred_var
         Y_mu_pred, Y_var_pred = m.predict_noiseless(X_pred)
@@ -684,7 +684,7 @@ class TestMisc:
         warp_m = GPy.models.WarpedGP(
             X, Y
         )  # , kernel=warp_k)#, warping_function=warp_f)
-        warp_m[".*\.d"].constrain_fixed(1.0)
+        warp_m[r".*\.d"].constrain_fixed(1.0)
         warp_m.optimize_restarts(
             parallel=False, robust=False, num_restarts=5, max_iters=max_iters
         )

GPy/testing/test_prior.py

@@ -3,6 +3,21 @@
 import pytest
 import numpy as np
 import GPy
+from GPy.core.parameterization.priors import (
+    Gaussian,
+    Uniform,
+    LogGaussian,
+    MultivariateGaussian,
+    Gamma,
+    InverseGamma,
+    DGPLVM,
+    DGPLVM_KFDA,
+    DGPLVM_Lamda,
+    DGPLVM_T,
+    HalfT,
+    Exponential,
+    StudentT,
+)
 
 
 class TestPrior:
@@ -178,3 +193,90 @@ class TestPrior:
         # should raise an assertionerror.
         with pytest.raises(AssertionError):
             m.rbf.set_prior(gaussian)
+
+
+def initialize_gaussian_prior() -> None:
+    return Gaussian(0, 1)
+
+
+def initialize_uniform_prior() -> None:
+    return Uniform(0, 1)
+
+
+def initialize_log_gaussian_prior() -> None:
+    return LogGaussian(0, 1)
+
+
+def initialize_multivariate_gaussian_prior() -> None:
+    return MultivariateGaussian(np.zeros(2), np.eye(2))
+
+
+def initialize_gamma_prior() -> None:
+    return Gamma(1, 1)
+
+
+def initialize_inverse_gamma_prior() -> None:
+    return InverseGamma(1, 1)
+
+
+def initialize_dgplvm_prior() -> None:
+    # return DGPLVM(...)
+    raise NotImplementedError("No idea how to initialize this prior")
+
+
+def initialize_dgplvm_kfda_prior() -> None:
+    # return DGPLVM_KFDA(...)
+    raise NotImplementedError("No idea how to initialize this prior")
+
+
+def initialize_dgplvm_lamda_prior() -> None:
+    # return DGPLVM_Lamda(...)
+    raise NotImplementedError("No idea how to initialize this prior")
+
+
+def initialize_dgplvm_t_prior() -> None:
+    # return DGPLVM_T(1, 1, (1, 1))
+    raise NotImplementedError("No idea how to initialize this prior")
+
+
+def initialize_half_t_prior() -> None:
+    return HalfT(1, 1)
+
+
+def initialize_exponential_prior() -> None:
+    return Exponential(1)
+
+
+def initialize_student_t_prior() -> None:
+    return StudentT(1, 1, 1)
+
+
+PRIORS = {
+    "Gaussian": initialize_gaussian_prior,
+    "Uniform": initialize_uniform_prior,
+    "LogGaussian": initialize_log_gaussian_prior,
+    "MultivariateGaussian": initialize_multivariate_gaussian_prior,
+    "Gamma": initialize_gamma_prior,
+    "InverseGamma": initialize_inverse_gamma_prior,
+    # "DGPLVM": initialize_dgplvm_prior,
+    # "DGPLVM_KFDA": initialize_dgplvm_kfda_prior,
+    # "DGPLVM_Lamda": initialize_dgplvm_lamda_prior,
+    # "DGPLVM_T": initialize_dgplvm_t_prior,
+    "HalfT": initialize_half_t_prior,
+    "Exponential": initialize_exponential_prior,
+    "StudentT": initialize_student_t_prior,
+}
+
+
+def check_prior(prior_getter: str) -> None:
+    prior_getter()
+
+
+def test_priors() -> None:
+    for prior_name, prior_getter in PRIORS.items():
+        try:
+            check_prior(prior_getter)
+        except Exception as e:
+            raise RuntimeError(
+                f"Failed to initialize {prior_name} prior"
+            ) from e  # noqa E501

GPy/testing/test_rv_transformation.py

@@ -47,7 +47,7 @@ class TestRVTransformation:
         # ax.hist(phi_s, normed=True, bins=100, alpha=0.25, label='Histogram')
         # ax.plot(phi, kde(phi), '--', linewidth=2, label='Kernel Density Estimation')
         # ax.plot(phi, pdf_phi, ':', linewidth=2, label='Transformed PDF')
-        # ax.set_xlabel(r'transformed $\theta$', fontsize=16)
+        # ax.set_xlabel(r'transformed $\\theta$', fontsize=16)
         # ax.set_ylabel('PDF', fontsize=16)
         # plt.legend(loc='best')
         # plt.show(block=True)

GPy/util/datasets.py

@@ -537,7 +537,7 @@ http://nbviewer.ipython.org/github/sahuguet/notebooks/blob/master/GoogleTrends%2
         # In the notebook they did some data cleaning: remove Javascript header+footer, and translate new Date(....,..,..) into YYYY-MM-DD.
         header = """// Data table response\ngoogle.visualization.Query.setResponse("""
         data = data[len(header):-2]
-        data = re.sub('new Date\((\d+),(\d+),(\d+)\)', (lambda m: '"%s-%02d-%02d"' % (m.group(1).strip(), 1+int(m.group(2)), int(m.group(3)))), data)
+        data = re.sub(r'new Date\((\d+),(\d+),(\d+)\)', (lambda m: '"%s-%02d-%02d"' % (m.group(1).strip(), 1+int(m.group(2)), int(m.group(3)))), data)
         timeseries = json.loads(data)
         columns = [k['label'] for k in timeseries['table']['cols']]
         rows = map(lambda x: [k['v'] for k in x['c']], timeseries['table']['rows'])
@@ -782,7 +782,7 @@ def hapmap3(data_set='hapmap3'):
 
           /  1, iff SNPij==(B1,B1)
     Aij = |  0, iff SNPij==(B1,B2)
-          \ -1, iff SNPij==(B2,B2)
+          \\ -1, iff SNPij==(B2,B2)
 
     The SNP data and the meta information (such as iid, sex and phenotype) are
     stored in the dataframe datadf, index is the Individual ID,
@@ -1011,7 +1011,7 @@ def singlecell_rna_seq_deng(dataset='singlecell_deng'):
     sample_info.columns = c
 
     # get the labels right:
-    rep = re.compile('\(.*\)')
+    rep = re.compile(r'\(.*\)')
     def filter_dev_stage(row):
         if isnull(row):
             row = "2-cell stage embryo"
@@ -1050,7 +1050,7 @@ def singlecell_rna_seq_deng(dataset='singlecell_deng'):
                 #gene_info[file_info.name[:-18]] = inner.Refseq_IDs
 
     # Strip GSM number off data index
-    rep = re.compile('GSM\d+_')
+    rep = re.compile(r'GSM\d+_')
 
     from pandas import MultiIndex
     columns = MultiIndex.from_tuples([row.split('_', 1) for row in data.columns])

GPy/util/netpbmfile.py

@@ -180,24 +180,24 @@ class NetpbmFile(object):
         """Read PAM header and initialize instance."""
         regroups = re.search(
             b"(^P7[\n\r]+(?:(?:[\n\r]+)|(?:#.*)|"
-            b"(HEIGHT\s+\d+)|(WIDTH\s+\d+)|(DEPTH\s+\d+)|(MAXVAL\s+\d+)|"
-            b"(?:TUPLTYPE\s+\w+))*ENDHDR\n)", data).groups()
+            rb"(HEIGHT\s+\d+)|(WIDTH\s+\d+)|(DEPTH\s+\d+)|(MAXVAL\s+\d+)|"
+            rb"(?:TUPLTYPE\s+\w+))*ENDHDR\n)", data).groups()
         self.header = regroups[0]
         self.magicnum = b'P7'
         for group in regroups[1:]:
             key, value = group.split()
             setattr(self, unicode(key).lower(), int(value))
-        matches = re.findall(b"(TUPLTYPE\s+\w+)", self.header)
+        matches = re.findall(rb"(TUPLTYPE\s+\w+)", self.header)
         self.tupltypes = [s.split(None, 1)[1] for s in matches]
 
     def _read_pnm_header(self, data):
         """Read PNM header and initialize instance."""
         bpm = data[1:2] in b"14"
         regroups = re.search(b"".join((
-            b"(^(P[123456]|P7 332)\s+(?:#.*[\r\n])*",
-            b"\s*(\d+)\s+(?:#.*[\r\n])*",
-            b"\s*(\d+)\s+(?:#.*[\r\n])*" * (not bpm),
-            b"\s*(\d+)\s(?:\s*#.*[\r\n]\s)*)")), data).groups() + (1, ) * bpm
+            rb"(^(P[123456]|P7 332)\s+(?:#.*[\r\n])*",
+            rb"\s*(\d+)\s+(?:#.*[\r\n])*",
+            rb"\s*(\d+)\s+(?:#.*[\r\n])*" * (not bpm),
+            rb"\s*(\d+)\s(?:\s*#.*[\r\n]\s)*)")), data).groups() + (1, ) * bpm
         self.header = regroups[0]
         self.magicnum = regroups[1]
         self.width = int(regroups[2])

doc/source/conf.py

@@ -150,7 +150,7 @@ with open('../../GPy/__version__.py', 'r') as f:
     version = f.read()
     release = version
 
-print version
+print(version)
 
 # version = '0.8.8'
 # The full version, including alpha/beta/rc tags.