Handpicked James Hensman's code that ensures that fixes the PDF of transformed variables. Fixed minor plotting bug.

GPy/core/parameterization/parameter_core.py

@@ -13,11 +13,12 @@ Observable Pattern for patameterization
 
 """
 
-from transformations import Transformation,Logexp, NegativeLogexp, Logistic, __fixed__, FIXED, UNFIXED
+from .transformations import Transformation,Logexp, NegativeLogexp, Logistic, __fixed__, FIXED, UNFIXED
 import numpy as np
 import re
 import logging
-from updateable import Updateable
+from .updateable import Updateable
+from functools import reduce
 
 class HierarchyError(Exception):
     """
@@ -36,7 +37,7 @@ def adjust_name_for_printing(name):
         name = name.replace("/", "_l_").replace("@", '_at_')
         name = name.replace("(", "_of_").replace(")", "")
         if re.match(r'^[a-zA-Z_][a-zA-Z0-9-_]*$', name) is None:
-            raise NameError, "name {} converted to {} cannot be further converted to valid python variable name!".format(name2, name)
+            raise NameError("name {} converted to {} cannot be further converted to valid python variable name!".format(name2, name))
         return name
     return ''
 
@@ -65,13 +66,13 @@ class Parentable(object):
         Gets called, when the parent changed, so we can adjust our
         inner attributes according to the new parent.
         """
-        raise NotImplementedError, "shouldnt happen, Parentable objects need to be able to change their parent"
+        raise NotImplementedError("shouldnt happen, Parentable objects need to be able to change their parent")
 
     def _disconnect_parent(self, *args, **kw):
         """
         Disconnect this object from its parent
         """
-        raise NotImplementedError, "Abstract superclass"
+        raise NotImplementedError("Abstract superclass")
 
     @property
     def _highest_parent_(self):
@@ -109,7 +110,10 @@ class Pickleable(object):
                   it properly.
         :param protocol: pickling protocol to use, python-pickle for details.
         """
-        import cPickle as pickle
+        try: #Py2
+            import cPickle as pickle
+        except ImportError: #Py3
+            import pickle
         if isinstance(f, str):
             with open(f, 'wb') as f:
                 pickle.dump(self, f, protocol)
@@ -138,9 +142,9 @@ class Pickleable(object):
             which = self
         which.traverse_parents(parents.append) # collect parents
         for p in parents:
-            if not memo.has_key(id(p)):memo[id(p)] = None # set all parents to be None, so they will not be copied
-        if not memo.has_key(id(self.gradient)):memo[id(self.gradient)] = None # reset the gradient
-        if not memo.has_key(id(self._fixes_)):memo[id(self._fixes_)] = None # fixes have to be reset, as this is now highest parent
+            if not id(p) in memo :memo[id(p)] = None # set all parents to be None, so they will not be copied
+        if not id(self.gradient) in memo:memo[id(self.gradient)] = None # reset the gradient
+        if not id(self._fixes_) in memo :memo[id(self._fixes_)] = None # fixes have to be reset, as this is now highest parent
         copy = copy.deepcopy(self, memo) # and start the copy
         copy._parent_index_ = None
         copy._trigger_params_changed()
@@ -163,14 +167,16 @@ class Pickleable(object):
                        '_Cacher_wrap__cachers', # never pickle cachers
                        ]
         dc = dict()
-        for k,v in self.__dict__.iteritems():
+        #py3 fix
+        #for k,v in self.__dict__.iteritems():
+        for k,v in self.__dict__.items():
             if k not in ignore_list:
                 dc[k] = v
         return dc
 
     def __setstate__(self, state):
         self.__dict__.update(state)
-        from lists_and_dicts import ObserverList
+        from .lists_and_dicts import ObserverList
         self.observers = ObserverList()
         self._setup_observers()
         self._optimizer_copy_transformed = False
@@ -214,7 +220,7 @@ class Gradcheckable(Pickleable, Parentable):
         Perform the checkgrad on the model.
         TODO: this can be done more efficiently, when doing it inside here
         """
-        raise HierarchyError, "This parameter is not in a model with a likelihood, and, therefore, cannot be gradient checked!"
+        raise HierarchyError("This parameter is not in a model with a likelihood, and, therefore, cannot be gradient checked!")
 
 class Nameable(Gradcheckable):
     """
@@ -268,7 +274,7 @@ class Indexable(Nameable, Updateable):
     def __init__(self, name, default_constraint=None, *a, **kw):
         super(Indexable, self).__init__(name=name, *a, **kw)
         self._default_constraint_ = default_constraint
-        from index_operations import ParameterIndexOperations
+        from .index_operations import ParameterIndexOperations
         self.constraints = ParameterIndexOperations()
         self.priors = ParameterIndexOperations()
         if self._default_constraint_ is not None:
@@ -310,7 +316,7 @@ class Indexable(Nameable, Updateable):
         that is an int array, containing the indexes for the flattened
         param inside this parameterized logic.
         """
-        from param import ParamConcatenation
+        from .param import ParamConcatenation
         if isinstance(param, ParamConcatenation):
             return np.hstack((self._raveled_index_for(p) for p in param.params))
         return param._raveled_index() + self._offset_for(param)
@@ -407,7 +413,7 @@ class Indexable(Nameable, Updateable):
         repriorized = self.unset_priors()
         self._add_to_index_operations(self.priors, repriorized, prior, warning)
 
-        from domains import _REAL, _POSITIVE, _NEGATIVE
+        from .domains import _REAL, _POSITIVE, _NEGATIVE
         if prior.domain is _POSITIVE:
             self.constrain_positive(warning)
         elif prior.domain is _NEGATIVE:
@@ -424,19 +430,38 @@ class Indexable(Nameable, Updateable):
 
     def log_prior(self):
         """evaluate the prior"""
-        if self.priors.size > 0:
-            x = self.param_array
-            return reduce(lambda a, b: a + b, (p.lnpdf(x[ind]).sum() for p, ind in self.priors.iteritems()), 0)
-        return 0.
+        if self.priors.size == 0:
+            return 0.
+        x = self.param_array
+        #evaluate the prior log densities
+        log_p = reduce(lambda a, b: a + b, (p.lnpdf(x[ind]).sum() for p, ind in self.priors.items()), 0)
+
+        #account for the transformation by evaluating the log Jacobian (where things are transformed)
+        log_j = 0.
+        priored_indexes = np.hstack([i for p, i in self.priors.items()])
+        for c,j in self.constraints.items():
+            if not isinstance(c, Transformation):continue
+            for jj in j:
+                if jj in priored_indexes:
+                    log_j += c.log_jacobian(x[jj])
+        return log_p + log_j
 
     def _log_prior_gradients(self):
         """evaluate the gradients of the priors"""
-        if self.priors.size > 0:
-            x = self.param_array
-            ret = np.zeros(x.size)
-            [np.put(ret, ind, p.lnpdf_grad(x[ind])) for p, ind in self.priors.iteritems()]
-            return ret
-        return 0.
+        if self.priors.size == 0:
+            return 0.
+        x = self.param_array
+        ret = np.zeros(x.size)
+        #compute derivate of prior density
+        [np.put(ret, ind, p.lnpdf_grad(x[ind])) for p, ind in self.priors.items()]
+        #add in jacobian derivatives if transformed
+        priored_indexes = np.hstack([i for p, i in self.priors.items()])
+        for c,j in self.constraints.items():
+            if not isinstance(c, Transformation):continue
+            for jj in j:
+                if jj in priored_indexes:
+                    ret[jj] += c.log_jacobian_grad(x[jj])
+        return ret
 
     #===========================================================================
     # Tie parameters together
@@ -471,7 +496,7 @@ class Indexable(Nameable, Updateable):
             self.param_array[...] = transform.initialize(self.param_array)
         reconstrained = self.unconstrain()
         added = self._add_to_index_operations(self.constraints, reconstrained, transform, warning)
-        self.notify_observers(self, None if trigger_parent else -np.inf)
+        self.trigger_update(trigger_parent)
         return added
 
     def unconstrain(self, *transforms):
@@ -536,7 +561,7 @@ class Indexable(Nameable, Updateable):
         update the constraints and priors view, so that
         constraining is automized for the parent.
         """
-        from index_operations import ParameterIndexOperationsView
+        from .index_operations import ParameterIndexOperationsView
         #if getattr(self, "_in_init_"):
             #import ipdb;ipdb.set_trace()
             #self.constraints.update(param.constraints, start)
@@ -558,7 +583,7 @@ class Indexable(Nameable, Updateable):
         """
         if warning and reconstrained.size > 0:
             # TODO: figure out which parameters have changed and only print those
-            print "WARNING: reconstraining parameters {}".format(self.hierarchy_name() or self.name)
+            print("WARNING: reconstraining parameters {}".format(self.hierarchy_name() or self.name))
         index = self._raveled_index()
         which.add(what, index)
         return index
@@ -571,7 +596,7 @@ class Indexable(Nameable, Updateable):
         if len(transforms) == 0:
             transforms = which.properties()
         removed = np.empty((0,), dtype=int)
-        for t in transforms:
+        for t in list(transforms):
             unconstrained = which.remove(t, self._raveled_index())
             removed = np.union1d(removed, unconstrained)
             if t is __fixed__:
@@ -612,7 +637,9 @@ class OptimizationHandlable(Indexable):
 
         if not self._optimizer_copy_transformed:
             self._optimizer_copy_.flat = self.param_array.flat
-            [np.put(self._optimizer_copy_, ind, c.finv(self.param_array[ind])) for c, ind in self.constraints.iteritems() if c != __fixed__]
+            #py3 fix
+            #[np.put(self._optimizer_copy_, ind, c.finv(self.param_array[ind])) for c, ind in self.constraints.iteritems() if c != __fixed__]
+            [np.put(self._optimizer_copy_, ind, c.finv(self.param_array[ind])) for c, ind in self.constraints.items() if c != __fixed__]
             if self.has_parent() and (self.constraints[__fixed__].size != 0 or self._has_ties()):
                 fixes = np.ones(self.size).astype(bool)
                 fixes[self.constraints[__fixed__]] = FIXED
@@ -641,21 +668,25 @@ class OptimizationHandlable(Indexable):
         if f is None:
             self.param_array.flat = p
             [np.put(self.param_array, ind, c.f(self.param_array.flat[ind]))
-             for c, ind in self.constraints.iteritems() if c != __fixed__]
+             #py3 fix
+             #for c, ind in self.constraints.iteritems() if c != __fixed__]
+             for c, ind in self.constraints.items() if c != __fixed__]
         else:
             self.param_array.flat[f] = p
             [np.put(self.param_array, ind[f[ind]], c.f(self.param_array.flat[ind[f[ind]]]))
-             for c, ind in self.constraints.iteritems() if c != __fixed__]
+             #py3 fix
+             #for c, ind in self.constraints.iteritems() if c != __fixed__]
+             for c, ind in self.constraints.items() if c != __fixed__]
         #self._highest_parent_.tie.propagate_val()
 
         self._optimizer_copy_transformed = False
         self.trigger_update()
 
     def _get_params_transformed(self):
-        raise DeprecationWarning, "_get|set_params{_optimizer_copy_transformed} is deprecated, use self.optimizer array insetad!"
+        raise DeprecationWarning("_get|set_params{_optimizer_copy_transformed} is deprecated, use self.optimizer array insetad!")
 #
     def _set_params_transformed(self, p):
-        raise DeprecationWarning, "_get|set_params{_optimizer_copy_transformed} is deprecated, use self.optimizer array insetad!"
+        raise DeprecationWarning("_get|set_params{_optimizer_copy_transformed} is deprecated, use self.optimizer array insetad!")
 
     def _trigger_params_changed(self, trigger_parent=True):
         """
@@ -680,19 +711,24 @@ class OptimizationHandlable(Indexable):
         constraint to it.
         """
         self._highest_parent_.tie.collate_gradient()
-        [np.put(g, i, c.gradfactor(self.param_array[i], g[i])) for c, i in self.constraints.iteritems() if c != __fixed__]
+        #py3 fix
+        #[np.put(g, i, c.gradfactor(self.param_array[i], g[i])) for c, i in self.constraints.iteritems() if c != __fixed__]
+        [np.put(g, i, c.gradfactor(self.param_array[i], g[i])) for c, i in self.constraints.items() if c != __fixed__]
         if self._has_fixes(): return g[self._fixes_]
         return g
 
-    def _log_det_jacobian(self):
+    def _transform_gradients_non_natural(self, g):
         """
-        Return the logarithm of the Jacobian needed for a proper change of
-        variables.
+        Transform the gradients by multiplying the gradient factor for each
+        constraint to it.
         """
-        J = np.ones(self.param_array.shape)
-        [np.put(J, i, c.jacobianfactor(self.param_array[i]))
-         for c, i in self.constraints.iteritems() if c != __fixed__]
-        return np.log(J).sum()
+        self._highest_parent_.tie.collate_gradient()
+        #py3 fix
+        #[np.put(g, i, c.gradfactor_non_natural(self.param_array[i], g[i])) for c, i in self.constraints.iteritems() if c != __fixed__]
+        [np.put(g, i, c.gradfactor_non_natural(self.param_array[i], g[i])) for c, i in self.constraints.items() if c != __fixed__]
+        if self._has_fixes(): return g[self._fixes_]
+        return g
+
 
     @property
     def num_params(self):
@@ -700,7 +736,7 @@ class OptimizationHandlable(Indexable):
         Return the number of parameters of this parameter_handle.
         Param objects will always return 0.
         """
-        raise NotImplemented, "Abstract, please implement in respective classes"
+        raise NotImplemented("Abstract, please implement in respective classes")
 
     def parameter_names(self, add_self=False, adjust_for_printing=False, recursive=True):
         """
@@ -749,7 +785,9 @@ class OptimizationHandlable(Indexable):
         self.optimizer_array = x  # makes sure all of the tied parameters get the same init (since there's only one prior object...)
         # now draw from prior where possible
         x = self.param_array.copy()
-        [np.put(x, ind, p.rvs(ind.size)) for p, ind in self.priors.iteritems() if not p is None]
+        #Py3 fix
+        #[np.put(x, ind, p.rvs(ind.size)) for p, ind in self.priors.iteritems() if not p is None]
+        [np.put(x, ind, p.rvs(ind.size)) for p, ind in self.priors.items() if not p is None]
         unfixlist = np.ones((self.size,),dtype=np.bool)
         unfixlist[self.constraints[__fixed__]] = False
         self.param_array.flat[unfixlist] = x.view(np.ndarray).ravel()[unfixlist]
@@ -808,7 +846,7 @@ class Parameterizable(OptimizationHandlable):
     A parameterisable class.
 
     This class provides the parameters list (ArrayList) and standard parameter handling,
-    such as {add|remove}_parameter(), traverse hierarchy and param_array, gradient_array
+    such as {link|unlink}_parameter(), traverse hierarchy and param_array, gradient_array
     and the empty parameters_changed().
 
     This class is abstract and should not be instantiated.
@@ -946,7 +984,7 @@ class Parameterizable(OptimizationHandlable):
             self._add_parameter_name(param, ignore_added_names)
         # and makes sure to not delete programmatically added parameters
         for other in self.parameters[::-1]:
-            if other is not param and other.name.startswith(param.name):
+            if other is not param and other.name == param.name:
                 warn_and_retry(param, _name_digit.match(other.name))
                 return
         if pname not in dir(self):
@@ -1041,6 +1079,9 @@ class Parameterizable(OptimizationHandlable):
                     p = param_to_array(p)
                     d = f.create_dataset(n,p.shape,dtype=p.dtype)
                     d[:] = p
+                if hasattr(self, 'param_array'):
+                    d = f.create_dataset('param_array',self.param_array.shape, dtype=self.param_array.dtype)
+                    d[:] = self.param_array
                 f.close()
             except:
                 raise 'Fails to write the parameters into a HDF5 file!'

GPy/core/parameterization/transformations.py

@@ -3,7 +3,7 @@
 
 
 import numpy as np
-from domains import _POSITIVE,_NEGATIVE, _BOUNDED
+from .domains import _POSITIVE,_NEGATIVE, _BOUNDED
 import weakref
 
 import sys
@@ -31,13 +31,16 @@ class Transformation(object):
         raise NotImplementedError
     def finv(self, model_param):
         raise NotImplementedError
-    def jacobianfactor(self, model_param):
+    def log_jacobian(self, model_param):
         """
-        Return log|det J| where J is the Jacobian of the inverse of the
-        transformation.
+        compute the log of the jacobian of f, evaluated at f(x)= model_param
         """
-        return np.abs([self.gradfactor(np.array([theta]), np.ones((1,)))[0]
-                       for theta in model_param])
+        raise NotImplementedError
+    def log_jacobian_grad(self, model_param):
+        """
+        compute the drivative of the log of the jacobian of f, evaluated at f(x)= model_param
+        """
+        raise NotImplementedError
     def gradfactor(self, model_param, dL_dmodel_param):
         """ df(opt_param)_dopt_param evaluated at self.f(opt_param)=model_param, times the gradient dL_dmodel_param,
 
@@ -49,6 +52,8 @@ class Transformation(object):
             \frac{\frac{\partial L}{\partial f}\left(\left.\partial f(x)}{\partial x}\right|_{x=f^{-1}(f)\right)}
         """
         raise NotImplementedError
+    def gradfactor_non_natural(self, model_param, dL_dmodel_param):
+        return self.gradfactor(model_param, dL_dmodel_param)
     def initialize(self, f):
         """ produce a sensible initial value for f(x)"""
         raise NotImplementedError
@@ -57,12 +62,10 @@ class Transformation(object):
         import matplotlib.pyplot as plt
         from ...plotting.matplot_dep import base_plots
         x = np.linspace(-8,8)
-        base_plots.meanplot(x, self.f(x), ax=axes, *args, **kw)
+        base_plots.meanplot(x, self.f(x),axes=axes*args,**kw)
         axes = plt.gca()
         axes.set_xlabel(xlabel)
         axes.set_ylabel(ylabel)
-        return axes
-
     def __str__(self):
         raise NotImplementedError
     def __repr__(self):
@@ -74,20 +77,46 @@ class Logexp(Transformation):
         return np.where(x>_lim_val, x, np.log1p(np.exp(np.clip(x, -_lim_val, _lim_val)))) + epsilon
         #raises overflow warning: return np.where(x>_lim_val, x, np.log(1. + np.exp(x)))
     def finv(self, f):
-        return np.where(f>_lim_val, f, np.log(np.exp(f+epsilon) - 1.))
+        return np.where(f>_lim_val, f, np.log(np.exp(f+1e-20) - 1.))
     def gradfactor(self, f, df):
         return np.einsum('i,i->i', df, np.where(f>_lim_val, 1., 1. - np.exp(-f)))
     def initialize(self, f):
         if np.any(f < 0.):
-            print "Warning: changing parameters to satisfy constraints"
+            print("Warning: changing parameters to satisfy constraints")
         return np.abs(f)
+    def log_jacobian(self, model_param):
+        return np.where(model_param>_lim_val, model_param, np.log(np.exp(model_param+1e-20) - 1.)) - model_param
+    def log_jacobian_grad(self, model_param):
+        return 1./(np.exp(model_param)-1.)
+    def __str__(self):
+        return '+ve'
+
+class Exponent(Transformation):
+    domain = _POSITIVE
+    def f(self, x):
+        return np.where(x<_lim_val, np.where(x>-_lim_val, np.exp(x), np.exp(-_lim_val)), np.exp(_lim_val))
+    def finv(self, x):
+        return np.log(x)
+    def gradfactor(self, f, df):
+        return np.einsum('i,i->i', df, f)
+    def initialize(self, f):
+        if np.any(f < 0.):
+            print("Warning: changing parameters to satisfy constraints")
+        return np.abs(f)
+    def log_jacobian(self, model_param):
+        return np.log(model_param)
+    def log_jacobian_grad(self, model_param):
+        return 1./model_param
     def __str__(self):
         return '+ve'
 
 
+
 class NormalTheta(Transformation):
+    "Do not use, not officially supported!"
     _instances = []
-    def __new__(cls, mu_indices, var_indices):
+    def __new__(cls, mu_indices=None, var_indices=None):
+        "Do not use, not officially supported!"
         if cls._instances:
             cls._instances[:] = [instance for instance in cls._instances if instance()]
             for instance in cls._instances:
@@ -107,6 +136,7 @@ class NormalTheta(Transformation):
         # that the values are ok
         # Before:
         theta[self.var_indices] = np.abs(-.5/theta[self.var_indices])
+        #theta[self.var_indices] = np.exp(-.5/theta[self.var_indices])
         theta[self.mu_indices] *= theta[self.var_indices]
         return theta # which is now {mu, var}
 
@@ -115,6 +145,7 @@ class NormalTheta(Transformation):
         varp = muvar[self.var_indices]
         muvar[self.mu_indices] /= varp
         muvar[self.var_indices] = -.5/varp
+        #muvar[self.var_indices] = -.5/np.log(varp)
 
         return muvar # which is now {theta1, theta2}
 
@@ -133,7 +164,7 @@ class NormalTheta(Transformation):
 
     def initialize(self, f):
         if np.any(f[self.var_indices] < 0.):
-            print "Warning: changing parameters to satisfy constraints"
+            print("Warning: changing parameters to satisfy constraints")
             f[self.var_indices] = np.abs(f[self.var_indices])
         return f
 
@@ -148,9 +179,10 @@ class NormalTheta(Transformation):
         self.var_indices = state[1]
 
 class NormalNaturalAntti(NormalTheta):
+    "Do not use, not officially supported!"
     _instances = []
-    _logexp = Logexp()
-    def __new__(cls, mu_indices, var_indices):
+    def __new__(cls, mu_indices=None, var_indices=None):
+        "Do not use, not officially supported!"
         if cls._instances:
             cls._instances[:] = [instance for instance in cls._instances if instance()]
             for instance in cls._instances:
@@ -179,7 +211,7 @@ class NormalNaturalAntti(NormalTheta):
 
     def initialize(self, f):
         if np.any(f[self.var_indices] < 0.):
-            print "Warning: changing parameters to satisfy constraints"
+            print("Warning: changing parameters to satisfy constraints")
             f[self.var_indices] = np.abs(f[self.var_indices])
         return f
 
@@ -187,8 +219,10 @@ class NormalNaturalAntti(NormalTheta):
         return "natantti"
 
 class NormalEta(Transformation):
+    "Do not use, not officially supported!"
     _instances = []
-    def __new__(cls, mu_indices, var_indices):
+    def __new__(cls, mu_indices=None, var_indices=None):
+        "Do not use, not officially supported!"
         if cls._instances:
             cls._instances[:] = [instance for instance in cls._instances if instance()]
             for instance in cls._instances:
@@ -220,7 +254,7 @@ class NormalEta(Transformation):
 
     def initialize(self, f):
         if np.any(f[self.var_indices] < 0.):
-            print "Warning: changing parameters to satisfy constraints"
+            print("Warning: changing parameters to satisfy constraints")
             f[self.var_indices] = np.abs(f[self.var_indices])
         return f
 
@@ -228,8 +262,10 @@ class NormalEta(Transformation):
         return "eta"
 
 class NormalNaturalThroughTheta(NormalTheta):
+    "Do not use, not officially supported!"
     _instances = []
-    def __new__(cls, mu_indices, var_indices):
+    def __new__(cls, mu_indices=None, var_indices=None):
+        "Do not use, not officially supported!"
         if cls._instances:
             cls._instances[:] = [instance for instance in cls._instances if instance()]
             for instance in cls._instances:
@@ -259,13 +295,28 @@ class NormalNaturalThroughTheta(NormalTheta):
         #=======================================================================
         return dmuvar # which is now the gradient multiplicator
 
+    def gradfactor_non_natural(self, muvar, dmuvar):
+        mu = muvar[self.mu_indices]
+        var = muvar[self.var_indices]
+        #=======================================================================
+        # theta gradients
+        # This works and the gradient checks!
+        dmuvar[self.mu_indices] *= var
+        dmuvar[self.var_indices] *= 2*(var)**2
+        dmuvar[self.var_indices] += 2*dmuvar[self.mu_indices]*mu
+        #=======================================================================
+
+        return dmuvar # which is now the gradient multiplicator for {theta1, theta2}
+
     def __str__(self):
         return "natgrad"
 
 
 class NormalNaturalWhooot(NormalTheta):
+    "Do not use, not officially supported!"
     _instances = []
-    def __new__(cls, mu_indices, var_indices):
+    def __new__(cls, mu_indices=None, var_indices=None):
+        "Do not use, not officially supported!"
         if cls._instances:
             cls._instances[:] = [instance for instance in cls._instances if instance()]
             for instance in cls._instances:
@@ -299,8 +350,10 @@ class NormalNaturalWhooot(NormalTheta):
         return "natgrad"
 
 class NormalNaturalThroughEta(NormalEta):
+    "Do not use, not officially supported!"
     _instances = []
-    def __new__(cls, mu_indices, var_indices):
+    def __new__(cls, mu_indices=None, var_indices=None):
+        "Do not use, not officially supported!"
         if cls._instances:
             cls._instances[:] = [instance for instance in cls._instances if instance()]
             for instance in cls._instances:
@@ -341,7 +394,7 @@ class LogexpNeg(Transformation):
         return np.einsum('i,i->i', df, np.where(f>_lim_val, -1, -1 + np.exp(-f)))
     def initialize(self, f):
         if np.any(f < 0.):
-            print "Warning: changing parameters to satisfy constraints"
+            print("Warning: changing parameters to satisfy constraints")
         return np.abs(f)
     def __str__(self):
         return '+ve'
@@ -393,27 +446,11 @@ class LogexpClipped(Logexp):
         return np.einsum('i,i->i', df, gf) # np.where(f < self.lower, 0, gf)
     def initialize(self, f):
         if np.any(f < 0.):
-            print "Warning: changing parameters to satisfy constraints"
+            print("Warning: changing parameters to satisfy constraints")
         return np.abs(f)
     def __str__(self):
         return '+ve_c'
 
-class Exponent(Transformation):
-    # TODO: can't allow this to go to zero, need to set a lower bound. Similar with negative Exponent below. See old MATLAB code.
-    domain = _POSITIVE
-    def f(self, x):
-        return np.where(x<_lim_val, np.where(x>-_lim_val, np.exp(x), np.exp(-_lim_val)), np.exp(_lim_val))
-    def finv(self, x):
-        return np.log(x)
-    def gradfactor(self, f, df):
-        return np.einsum('i,i->i', df, f)
-    def initialize(self, f):
-        if np.any(f < 0.):
-            print "Warning: changing parameters to satisfy constraints"
-        return np.abs(f)
-    def __str__(self):
-        return '+ve'
-
 class NegativeExponent(Exponent):
     domain = _NEGATIVE
     def f(self, x):
@@ -449,7 +486,11 @@ class Logistic(Transformation):
             for instance in cls._instances:
                 if instance().lower == lower and instance().upper == upper:
                     return instance()
-        o = super(Transformation, cls).__new__(cls, lower, upper, *args, **kwargs)
+        newfunc = super(Transformation, cls).__new__
+        if newfunc is object.__new__:
+            o = newfunc(cls)  
+        else:
+            o = newfunc(cls, lower, upper, *args, **kwargs)
         cls._instances.append(weakref.ref(o))
         return cls._instances[-1]()
     def __init__(self, lower, upper):
@@ -467,7 +508,7 @@ class Logistic(Transformation):
         return np.einsum('i,i->i', df, (f - self.lower) * (self.upper - f) / self.difference)
     def initialize(self, f):
         if np.any(np.logical_or(f < self.lower, f > self.upper)):
-            print "Warning: changing parameters to satisfy constraints"
+            print("Warning: changing parameters to satisfy constraints")
         #return np.where(np.logical_or(f < self.lower, f > self.upper), self.f(f * 0.), f)
         #FIXME: Max, zeros_like right?
         return np.where(np.logical_or(f < self.lower, f > self.upper), self.f(np.zeros_like(f)), f)