all parameterization stuff now in seperate module -> GPy.core.parameterization

GPy/core/parameterization/param.py

@@ -0,0 +1,593 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import itertools
+import numpy
+from parameter_core import Constrainable, adjust_name_for_printing
+from array_core import ObservableArray
+
+###### printing
+__constraints_name__ = "Constraint"
+__index_name__ = "Index"
+__tie_name__ = "Tied to"
+__precision__ = numpy.get_printoptions()['precision'] # numpy printing precision used, sublassing numpy ndarray after all
+__print_threshold__ = 5
+######      
+
+class Float(numpy.float64, Constrainable):
+    def __init__(self, f, base):
+        super(Float,self).__init__(f)
+        self._base = base
+        
+        
+class Param(ObservableArray, Constrainable):
+    """
+    Parameter object for GPy models.
+
+    :param name:        name of the parameter to be printed
+    :param input_array: array which this parameter handles
+    :param gradient:    callable with one argument, which is the model of this parameter
+    :param args:        additional arguments to gradient
+    :param kwargs:      additional keyword arguments to gradient
+    
+    You can add/remove constraints by calling constrain on the parameter itself, e.g:
+    
+        - self[:,1].constrain_positive()
+        - self[0].tie_to(other)
+        - self.untie()
+        - self[:3,:].unconstrain()
+        - self[1].fix()
+        
+    Fixing parameters will fix them to the value they are right now. If you change
+    the fixed value, it will be fixed to the new value!
+    
+    See :py:class:`GPy.core.parameterized.Parameterized` for more details on constraining etc.
+
+    This ndarray can be stored in lists and checked if it is in.
+
+    >>> import numpy as np
+    >>> x = np.random.normal(size=(10,3))
+    >>> x in [[1], x, [3]]
+    True
+    
+    WARNING: This overrides the functionality of x==y!!!
+    Use numpy.equal(x,y) for element-wise equality testing.
+    """
+    __array_priority__ = 0 # Never give back Param
+    _fixes_ = None
+    def __new__(cls, name, input_array, *args, **kwargs):
+        obj = numpy.atleast_1d(super(Param, cls).__new__(cls, input_array=input_array))
+        obj._current_slice_ = (slice(obj.shape[0]),)
+        obj._realshape_ = obj.shape
+        obj._realsize_ = obj.size
+        obj._realndim_ = obj.ndim
+        obj._updated_ = False
+        from index_operations import SetDict
+        obj._tied_to_me_ = SetDict()
+        obj._tied_to_ = []
+        obj._original_ = True
+        return obj
+
+    def __init__(self, name, input_array):
+        super(Param, self).__init__(name=name)
+        
+    def __array_finalize__(self, obj):
+        # see InfoArray.__array_finalize__ for comments
+        if obj is None: return
+        super(Param, self).__array_finalize__(obj)
+        self._direct_parent_ = getattr(obj, '_direct_parent_', None)
+        self._parent_index_ = getattr(obj, '_parent_index_', None)
+        self._highest_parent_ = getattr(obj, '_highest_parent_', None)
+        self._current_slice_ = getattr(obj, '_current_slice_', None)
+        self._tied_to_me_ = getattr(obj, '_tied_to_me_', None)
+        self._tied_to_ = getattr(obj, '_tied_to_', None)
+        self._realshape_ = getattr(obj, '_realshape_', None)
+        self._realsize_ = getattr(obj, '_realsize_', None)
+        self._realndim_ = getattr(obj, '_realndim_', None)
+        self._updated_ = getattr(obj, '_updated_', None)
+        self._original_ = getattr(obj, '_original_', None)
+        self._name = getattr(obj, 'name', None)
+        
+    def __array_wrap__(self, out_arr, context=None):
+        return out_arr.view(numpy.ndarray)
+    #===========================================================================
+    # Pickling operations
+    #===========================================================================
+    def __reduce_ex__(self):
+        func, args, state = super(Param, self).__reduce__()
+        return func, args, (state, 
+                            (self.name,
+                             self._direct_parent_,
+                             self._parent_index_,
+                             self._highest_parent_,
+                             self._current_slice_,
+                             self._realshape_,
+                             self._realsize_,
+                             self._realndim_,
+                             self._tied_to_me_,
+                             self._tied_to_,
+                             self._updated_,
+                            )
+                            )
+
+    def __setstate__(self, state):
+        super(Param, self).__setstate__(state[0])
+        state = list(state[1])
+        self._updated_ = state.pop()
+        self._tied_to_ = state.pop()
+        self._tied_to_me_ = state.pop()
+        self._realndim_ = state.pop()
+        self._realsize_ = state.pop()
+        self._realshape_ = state.pop()
+        self._current_slice_ = state.pop()
+        self._highest_parent_ = state.pop()
+        self._parent_index_ = state.pop()
+        self._direct_parent_ = state.pop()
+        self.name = state.pop()
+
+    #===========================================================================
+    # get/set parameters
+    #===========================================================================
+
+    def _set_params(self, param, update=True):
+        self.flat = param
+        self._notify_tied_parameters()
+        self._notify_observers()
+        
+    def _get_params(self):
+        return self.flat
+#     @property
+#     def name(self):
+#         """
+#         Name of this parameter. 
+#         This can be a callable without parameters. The callable will be called
+#         every time the name property is accessed.
+#         """
+#         if callable(self.name):
+#             return self.name()
+#         return self.name
+#     @name.setter
+#     def name(self, new_name):
+#         from_name = self.name
+#         self.name = new_name
+#         self._direct_parent_._name_changed(self, from_name)
+    @property
+    def _parameters_(self):
+        return []
+    #===========================================================================
+    # Fixing Parameters:
+    #===========================================================================
+    def constrain_fixed(self, warning=True):
+        """
+        Constrain this paramter to be fixed to the current value it carries.
+        
+        :param warning: print a warning for overwriting constraints.
+        """
+        self._highest_parent_._fix(self,warning)
+    fix = constrain_fixed
+    def unconstrain_fixed(self):
+        """
+        This parameter will no longer be fixed.
+        """
+        self._highest_parent_._unfix(self)
+    unfix = unconstrain_fixed
+    #===========================================================================
+    # Tying operations -> bugged, TODO
+    #===========================================================================
+    def tie_to(self, param):
+        """
+        :param param: the parameter object to tie this parameter to. 
+                      Can be ParamConcatenation (retrieved by regexp search)
+        
+        Tie this parameter to the given parameter.
+        Broadcasting is not allowed, but you can tie a whole dimension to
+        one parameter:  self[:,0].tie_to(other), where other is a one-value
+        parameter.
+        
+        Note: For now only one parameter can have ties, so all of a parameter
+              will be removed, when re-tieing!
+        """
+        #Note: this method will tie to the parameter which is the last in 
+        #      the chain of ties. Thus, if you tie to a tied parameter,
+        #      this tie will be created to the parameter the param is tied
+        #      to.
+
+        assert isinstance(param, Param), "Argument {1} not of type {0}".format(Param,param.__class__)
+        param = numpy.atleast_1d(param)
+        if param.size != 1:
+            raise NotImplementedError, "Broadcast tying is not implemented yet"
+        try:
+            if self._original_: 
+                self[:] = param
+            else: # this happens when indexing created a copy of the array
+                self._direct_parent_._get_original(self)[self._current_slice_] = param
+        except ValueError:
+            raise ValueError("Trying to tie {} with shape {} to {} with shape {}".format(self.name, self.shape, param.name, param.shape))            
+        if param is self:
+            raise RuntimeError, 'Cyclic tieing is not allowed'
+#         if len(param._tied_to_) > 0:
+#             if (self._direct_parent_._get_original(self) is param._direct_parent_._get_original(param)
+#                 and len(set(self._raveled_index())&set(param._tied_to_[0]._raveled_index()))!=0):
+#                 raise RuntimeError, 'Cyclic tieing is not allowed'
+#             self.tie_to(param._tied_to_[0])
+#             return
+        if not param in self._direct_parent_._get_original(self)._tied_to_:
+            self._direct_parent_._get_original(self)._tied_to_ += [param]
+        param._add_tie_listener(self)
+        self._highest_parent_._set_fixed(self)
+        cs = self._highest_parent_._constraints_for(param, param._raveled_index())
+        for cs in self._highest_parent_._constraints_for(param, param._raveled_index()):
+            [self.constrain(c, warning=False) for c in cs]
+#         for t in self._tied_to_me_.keys():
+#             if t is not self:
+#                 t.untie(self)
+#                 t.tie_to(param)
+
+    def untie(self, *ties):
+        """
+        remove all ties.
+        """
+        [t._direct_parent_._get_original(t)._remove_tie_listener(self) for t in self._tied_to_]
+        new_ties = []
+        for t in self._direct_parent_._get_original(self)._tied_to_:
+            for tied in t._tied_to_me_.keys():
+                if t._parent_index_ is tied._parent_index_:
+                    new_ties.append(tied)
+        self._direct_parent_._get_original(self)._tied_to_ = new_ties
+        self._direct_parent_._get_original(self)._highest_parent_._set_unfixed(self)
+#         self._direct_parent_._remove_tie(self, *params)
+    def _notify_tied_parameters(self):
+        for tied, ind in self._tied_to_me_.iteritems():
+            tied._on_tied_parameter_changed(self.base, list(ind))
+    def _add_tie_listener(self, tied_to_me):
+        for t in self._tied_to_me_.keys():
+            if tied_to_me._parent_index_ is t._parent_index_:
+                t_rav_i = t._raveled_index()
+                tr_rav_i = tied_to_me._raveled_index()
+                new_index = list(set(t_rav_i) | set(tr_rav_i))
+                tmp = t._direct_parent_._get_original(t)[numpy.unravel_index(new_index,t._realshape_)]
+                self._tied_to_me_[tmp] = self._tied_to_me_[t] | set(self._raveled_index())
+                del self._tied_to_me_[t]
+                return
+        self._tied_to_me_[tied_to_me] = set(self._raveled_index())
+    def _remove_tie_listener(self, to_remove):
+        for t in self._tied_to_me_.keys():
+            if t._parent_index_ == to_remove._parent_index_:
+                t_rav_i = t._raveled_index()
+                tr_rav_i = to_remove._raveled_index()
+                import ipdb;ipdb.set_trace()
+                new_index = list(set(t_rav_i) - set(tr_rav_i))
+                if new_index:
+                    tmp = t._direct_parent_._get_original(t)[numpy.unravel_index(new_index,t._realshape_)]
+                    self._tied_to_me_[tmp] = self._tied_to_me_[t]
+                    del self._tied_to_me_[t]
+                    if len(self._tied_to_me_[tmp]) == 0:
+                        del self._tied_to_me_[tmp]
+                else:
+                    del self._tied_to_me_[t]
+    def _on_tied_parameter_changed(self, val, ind):
+        if not self._updated_: #not fast_array_equal(self, val[ind]):
+            val = numpy.atleast_1d(val)
+            self._updated_ = True
+            if self._original_:
+                self.__setitem__(slice(None), val[ind], update=False)
+            else: # this happens when indexing created a copy of the array
+                self._direct_parent_._get_original(self).__setitem__(self._current_slice_, val[ind], update=False)
+            self._notify_tied_parameters()
+            self._updated_ = False
+    #===========================================================================
+    # Prior Operations
+    #===========================================================================
+    def set_prior(self, prior):
+        """
+        :param prior: prior to be set for this parameter
+
+        Set prior for this parameter.
+        """
+        if not hasattr(self._highest_parent_, '_set_prior'):
+            raise AttributeError("Parent of type {} does not support priors".format(self._highest_parent_.__class__))
+        self._highest_parent_._set_prior(self, prior)
+    def unset_prior(self, *priors):
+        """
+        :param priors: priors to remove from this parameter
+        
+        Remove all priors from this parameter
+        """
+        self._highest_parent_._remove_prior(self, *priors)
+    #===========================================================================
+    # Array operations -> done
+    #===========================================================================
+    def __getitem__(self, s, *args, **kwargs):
+        if not isinstance(s, tuple):
+            s = (s,)
+        if not reduce(lambda a,b: a or numpy.any(b is Ellipsis), s, False) and len(s) <= self.ndim:
+            s += (Ellipsis,)
+        new_arr = super(Param, self).__getitem__(s, *args, **kwargs)
+        try: new_arr._current_slice_ = s; new_arr._original_ = self.base is new_arr.base
+        except AttributeError: pass# returning 0d array or float, double etc
+        return new_arr
+    def __setitem__(self, s, val, update=True):
+        super(Param, self).__setitem__(s, val, update=update)
+        self._notify_tied_parameters()
+        if update:
+            self._highest_parent_.parameters_changed()
+    #===========================================================================
+    # Index Operations:
+    #===========================================================================
+    def _internal_offset(self):
+        internal_offset = 0
+        extended_realshape = numpy.cumprod((1,) + self._realshape_[:0:-1])[::-1]
+        for i, si in enumerate(self._current_slice_[:self._realndim_]):
+            if numpy.all(si == Ellipsis):
+                continue
+            if isinstance(si, slice):
+                a = si.indices(self._realshape_[i])[0] 
+            elif isinstance(si, (list,numpy.ndarray,tuple)):
+                a = si[0]
+            else: a = si
+            if a<0:
+                a = self._realshape_[i]+a
+            internal_offset += a * extended_realshape[i]
+        return internal_offset
+    def _raveled_index(self, slice_index=None):
+        # return an index array on the raveled array, which is formed by the current_slice
+        # of this object
+        extended_realshape = numpy.cumprod((1,) + self._realshape_[:0:-1])[::-1]
+        ind = self._indices(slice_index)
+        if ind.ndim < 2: ind=ind[:,None]
+        return numpy.asarray(numpy.apply_along_axis(lambda x: numpy.sum(extended_realshape*x), 1, ind), dtype=int)
+    def _expand_index(self, slice_index=None):
+        # this calculates the full indexing arrays from the slicing objects given by get_item for _real..._ attributes
+        # it basically translates slices to their respective index arrays and turns negative indices around
+        # it tells you in the second return argument if it has only seen arrays as indices
+        if slice_index is None:
+            slice_index = self._current_slice_
+        def f(a):
+            a, b = a
+            if a not in (slice(None), Ellipsis):
+                if isinstance(a, slice):
+                    start, stop, step = a.indices(b)
+                    return numpy.r_[start:stop:step]
+                elif isinstance(a, (list,numpy.ndarray,tuple)):
+                    a = numpy.asarray(a, dtype=int)
+                    a[a<0] = b + a[a<0]
+                elif a<0:
+                    a = b+a
+                return numpy.r_[a]
+            return numpy.r_[:b]
+        return itertools.imap(f, itertools.izip_longest(slice_index[:self._realndim_], self._realshape_, fillvalue=slice(self.size)))
+    #===========================================================================
+    # Convienience
+    #===========================================================================
+    @property
+    def is_fixed(self):
+        return self._highest_parent_._is_fixed(self)
+    def round(self, decimals=0, out=None):
+        view = super(Param, self).round(decimals, out).view(Param)
+        view.__array_finalize__(self)
+        return view
+    def _has_fixes(self):
+        return False
+    round.__doc__ = numpy.round.__doc__
+    def _get_original(self, param):
+        return self
+    #===========================================================================
+    # Printing -> done
+    #===========================================================================
+    @property
+    def _description_str(self):
+        if self.size <= 1: return ["%f"%self]
+        else: return [str(self.shape)]
+    def _parameter_names(self, add_name):
+        return [self.name]
+    @property
+    def flattened_parameters(self):
+        return [self]
+    @property
+    def parameter_shapes(self):
+        return [self.shape]
+    @property
+    def _constraints_str(self):
+        return [' '.join(map(lambda c: str(c[0]) if c[1].size==self._realsize_ else "{"+str(c[0])+"}", self._highest_parent_._constraints_iter_items(self)))]
+    @property
+    def _ties_str(self):
+        return [t._short() for t in self._tied_to_] or ['']
+    @property
+    def name_hirarchical(self):
+        if self.has_parent():
+            return self._direct_parent_.hirarchy_name()+adjust_name_for_printing(self.name)
+        return adjust_name_for_printing(self.name)
+    def __repr__(self, *args, **kwargs):
+        name = "\033[1m{x:s}\033[0;0m:\n".format(
+                            x=self.name_hirarchical)
+        return name + super(Param, self).__repr__(*args,**kwargs)
+    def _ties_for(self, rav_index):
+        size = sum(p.size for p in self._tied_to_)
+        ties = numpy.empty(shape=(len(self._tied_to_), numpy.size(rav_index)), dtype=Param)
+        for i, tied_to in enumerate(self._tied_to_):
+            for t, ind in tied_to._tied_to_me_.iteritems():
+                if t._parent_index_ == self._parent_index_:
+                    matches = numpy.where(rav_index[:,None] == t._raveled_index()[None, :])
+                    tt_rav_index = tied_to._raveled_index()
+                    ind_rav_matches = numpy.where(tt_rav_index == numpy.array(list(ind)))[0]
+                    if len(ind) != 1: ties[i, matches[0][ind_rav_matches]] = numpy.take(tt_rav_index, matches[1], mode='wrap')[ind_rav_matches]
+                    else: ties[i, matches[0]] = numpy.take(tt_rav_index, matches[1], mode='wrap')
+        return map(lambda a: sum(a,[]), zip(*[[[tie.flatten()] if tx!=None else [] for tx in t] for t,tie in zip(ties,self._tied_to_)]))
+    def _constraints_for(self, rav_index):
+        return self._highest_parent_._constraints_for(self, rav_index)
+    def _indices(self, slice_index=None):
+        # get a int-array containing all indices in the first axis.
+        if slice_index is None:
+            slice_index = self._current_slice_
+        if isinstance(slice_index, (tuple, list)):
+            clean_curr_slice = [s for s in slice_index if numpy.any(s != Ellipsis)]
+            if (all(isinstance(n, (numpy.ndarray, list, tuple)) for n in clean_curr_slice) 
+                and len(set(map(len,clean_curr_slice))) <= 1):
+                return numpy.fromiter(itertools.izip(*clean_curr_slice),
+                    dtype=[('',int)]*self._realndim_,count=len(clean_curr_slice[0])).view((int, self._realndim_))
+        expanded_index = list(self._expand_index(slice_index))
+        return numpy.fromiter(itertools.product(*expanded_index),
+                 dtype=[('',int)]*self._realndim_,count=reduce(lambda a,b: a*b.size,expanded_index,1)).view((int, self._realndim_))
+    def _max_len_names(self, gen, header):
+        return reduce(lambda a, b:max(a, len(b)), gen, len(header))
+    def _max_len_values(self):
+        return reduce(lambda a, b:max(a, len("{x:=.{0}g}".format(__precision__, x=b))), self.flat, len(self.name_hirarchical))
+    def _max_len_index(self, ind):
+        return reduce(lambda a, b:max(a, len(str(b))), ind, len(__index_name__))
+    def _short(self):
+        # short string to print
+        name = self._direct_parent_.hirarchy_name() + adjust_name_for_printing(self.name)
+        if self._realsize_ < 2:
+            return name
+        ind = self._indices()
+        if ind.size > 4: indstr = ','.join(map(str,ind[:2])) + "..." + ','.join(map(str,ind[-2:])) 
+        else: indstr = ','.join(map(str,ind))
+        return name+'['+indstr+']'
+    def __str__(self, constr_matrix=None, indices=None, ties=None, lc=None, lx=None, li=None, lt=None):
+        filter_ = self._current_slice_
+        vals = self.flat
+        if indices is None: indices = self._indices(filter_)
+        ravi = self._raveled_index(filter_)
+        if constr_matrix is None: constr_matrix = self._constraints_for(ravi)
+        if ties is None: ties = self._ties_for(ravi)
+        ties = [' '.join(map(lambda x: x._short(), t)) for t in ties]
+        if lc is None: lc = self._max_len_names(constr_matrix, __constraints_name__)
+        if lx is None: lx = self._max_len_values()
+        if li is None: li = self._max_len_index(indices)
+        if lt is None: lt = self._max_len_names(ties, __tie_name__)
+        header = "  {i:^{2}s}  |  \033[1m{x:^{1}s}\033[0;0m  |  {c:^{0}s}  |  {t:^{3}s}".format(lc,lx,li,lt, x=self.name_hirarchical, c=__constraints_name__, i=__index_name__, t=__tie_name__) # nice header for printing
+        if not ties: ties = itertools.cycle([''])
+        return "\n".join([header]+["  {i!s:^{3}s}  |  {x: >{1}.{2}g}  |  {c:^{0}s}  |  {t:^{4}s}  ".format(lc,lx,__precision__,li,lt, x=x, c=" ".join(map(str,c)), t=(t or ''), i=i) for i,x,c,t in itertools.izip(indices,vals,constr_matrix,ties)]) # return all the constraints with right indices
+        #except: return super(Param, self).__str__()
+
+class ParamConcatenation(object):
+    def __init__(self, params):
+        """
+        Parameter concatenation for convienience of printing regular expression matched arrays
+        you can index this concatenation as if it was the flattened concatenation
+        of all the parameters it contains, same for setting parameters (Broadcasting enabled).
+
+        See :py:class:`GPy.core.parameter.Param` for more details on constraining.
+        """
+        #self.params = params
+        self.params = []
+        for p in params:
+            for p in p.flattened_parameters:
+                if p not in self.params:
+                    self.params.append(p)           
+        self._param_sizes = [p.size for p in self.params]
+        startstops = numpy.cumsum([0] + self._param_sizes)
+        self._param_slices_ = [slice(start, stop) for start,stop in zip(startstops, startstops[1:])]
+    #===========================================================================
+    # Get/set items, enable broadcasting
+    #===========================================================================
+    def __getitem__(self, s):
+        ind = numpy.zeros(sum(self._param_sizes), dtype=bool); ind[s] = True; 
+        params = [p._get_params()[ind[ps]] for p,ps in zip(self.params, self._param_slices_) if numpy.any(p._get_params()[ind[ps]])]
+        if len(params)==1: return params[0]
+        return ParamConcatenation(params)
+    def __setitem__(self, s, val, update=True):
+        ind = numpy.zeros(sum(self._param_sizes), dtype=bool); ind[s] = True; 
+        vals = self._vals(); vals[s] = val; del val
+        [numpy.place(p, ind[ps], vals[ps]) and p._notify_tied_parameters() 
+         for p, ps in zip(self.params, self._param_slices_)]
+        if update:
+            self.params[0]._highest_parent_.parameters_changed()
+    def _vals(self):
+        return numpy.hstack([p._get_params() for p in self.params])
+    #===========================================================================
+    # parameter operations:
+    #===========================================================================
+    def constrain(self, constraint, warning=True):
+        [param.constrain(constraint) for param in self.params]
+    constrain.__doc__ = Param.constrain.__doc__
+    def constrain_positive(self, warning=True):
+        [param.constrain_positive(warning) for param in self.params]
+    constrain_positive.__doc__ = Param.constrain_positive.__doc__
+    def constrain_fixed(self, warning=True):
+        [param.constrain_fixed(warning) for param in self.params]
+    constrain_fixed.__doc__ = Param.constrain_fixed.__doc__
+    fix = constrain_fixed
+    def constrain_negative(self, warning=True):
+        [param.constrain_negative(warning) for param in self.params]
+    constrain_negative.__doc__ = Param.constrain_negative.__doc__
+    def constrain_bounded(self, lower, upper, warning=True):
+        [param.constrain_bounded(lower, upper, warning) for param in self.params]
+    constrain_bounded.__doc__ = Param.constrain_bounded.__doc__
+    def unconstrain(self, *constraints):
+        [param.unconstrain(*constraints) for param in self.params]
+    unconstrain.__doc__ = Param.unconstrain.__doc__
+    def unconstrain_negative(self):
+        [param.unconstrain_negative() for param in self.params]
+    unconstrain_negative.__doc__ = Param.unconstrain_negative.__doc__
+    def unconstrain_positive(self):
+        [param.unconstrain_positive() for param in self.params]
+    unconstrain_positive.__doc__ = Param.unconstrain_positive.__doc__
+    def unconstrain_fixed(self):
+        [param.unconstrain_fixed() for param in self.params]
+    unconstrain_fixed.__doc__ = Param.unconstrain_fixed.__doc__
+    unfix = unconstrain_fixed
+    def unconstrain_bounded(self, lower, upper):
+        [param.unconstrain_bounded(lower, upper) for param in self.params]
+    unconstrain_bounded.__doc__ = Param.unconstrain_bounded.__doc__
+    def untie(self, *ties):
+        [param.untie(*ties) for param in self.params]
+    __lt__ = lambda self, val: self._vals()<val
+    __le__ = lambda self, val: self._vals()<=val
+    __eq__ = lambda self, val: self._vals()==val
+    __ne__ = lambda self, val: self._vals()!=val
+    __gt__ = lambda self, val: self._vals()>val
+    __ge__ = lambda self, val: self._vals()>=val
+    def __str__(self, *args, **kwargs):
+        def f(p):
+            ind = p._raveled_index()
+            return p._constraints_for(ind), p._ties_for(ind)
+        params = self.params
+        constr_matrices, ties_matrices = zip(*map(f, params))
+        indices = [p._indices() for p in params]
+        lc = max([p._max_len_names(cm, __constraints_name__) for p, cm in itertools.izip(params, constr_matrices)])
+        lx = max([p._max_len_values() for p in params])
+        li = max([p._max_len_index(i) for p, i in itertools.izip(params, indices)])
+        lt = max([p._max_len_names(tm, __tie_name__) for p, tm in itertools.izip(params, ties_matrices)])
+        strings = [p.__str__(cm, i, tm, lc, lx, li, lt) for p, cm, i, tm in itertools.izip(params,constr_matrices,indices,ties_matrices)]
+        return "\n".join(strings)
+        return "\n{}\n".format(" -"+"- | -".join(['-'*l for l in [li,lx,lc,lt]])).join(strings)
+    def __repr__(self):
+        return "\n".join(map(repr,self.params))
+    
+if __name__ == '__main__':
+    
+
+    from GPy.core.parameterized import Parameterized
+    from GPy.core.parameter import Param
+
+    #X = numpy.random.randn(2,3,1,5,2,4,3)
+    X = numpy.random.randn(3,2)
+    print "random done"
+    p = Param("q_mean", X)
+    p1 = Param("q_variance", numpy.random.rand(*p.shape))
+    p2 = Param("Y", numpy.random.randn(p.shape[0],1))
+    
+    p3 = Param("variance", numpy.random.rand())
+    p4 = Param("lengthscale", numpy.random.rand(2))
+    
+    m = Parameterized()
+    rbf = Parameterized(name='rbf')
+    
+    rbf.add_parameter(p3,p4)
+    m.add_parameter(p,p1,rbf)
+    
+    print "setting params"
+    #print m.q_v[3:5,[1,4,5]]
+    print "constraining variance"
+    #m[".*variance"].constrain_positive()
+    #print "constraining rbf"
+    #m.rbf_l.constrain_positive()
+    #m.q_variance[1,[0,5,11,19,2]].tie_to(m.rbf_v)
+    #m.rbf_v.tie_to(m.rbf_l[0])
+    #m.rbf_l[0].tie_to(m.rbf_l[1])
+    #m.q_v.tie_to(m.rbf_v)
+#     m.rbf_l.tie_to(m.rbf_va)
+    # pt = numpy.array(params._get_params_transformed())
+    # ptr = numpy.random.randn(*pt.shape)
+#     params.X.tie_to(params.rbf_v)