processors.py

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"""
 
"""
This file contains various classes supporting modifications to CellML models.
"""
 
import pycml
from pycml import *
import validator
 
 
class ModelModificationError(ValueError):
    """Error thrown if a model modification is invalid."""
    pass
 
    
class ModelModifier(object):
    """Base class supporting common model modification functionality.
    
    This class contains the logic to deal with adding/deleting variables, components, equations, etc.
    and connecting things up.  It also handles re-analysing the model when modifications have been
    completed to ensure that PyCml's internal data structures are up-to-date.
    
    Instances should be created with the model to modify as a single parameter.  Once all
    modifications have been completed, the finalize method must be called to ensure later
    processing of the model (e.g. code generation) will succeed.
    """
    def __init__(self, model):
        """Constructor."""
        self.model = model
        self._units_converter = None
        self.connections_made = set()
        
    def finalize(self, error_handler, pre_units_check_hook=None, check_units=True):
        """Re-do the model validation steps needed for further processing of the model.
        
        Checks connections, etc. and builds up the dependency graph again, then performs
        a topological sort.
        
        If any errors are found during re-validation, the error_handler will be called with the
        list.  Warnings are ignored.
        
        TODO: figure out how to determine how much of this is actually needed - InterfaceGenerator
        can probably get away with less work.
        """
        self._clear_model_caches()
        # We want to see any errors
        logging_info = validator.CellMLValidator.setup_logging(show_errors=True, show_warnings=False)
        # Re-run validation & analysis
        self.model._check_variable_mappings()
        if not self.model._cml_validation_errors:
            assignment_exprs = self.model.search_for_assignments()
            self.model._check_assigned_vars(assignment_exprs)
        if not self.model._cml_validation_errors:
            self.model._classify_variables(assignment_exprs)
            self.model._order_variables(assignment_exprs)
        if not self.model._cml_validation_errors and check_units:
            if callable(pre_units_check_hook):
                pre_units_check_hook()
            self.model._check_connection_units(check_for_units_conversions=False)
            self.model._check_dimensional_consistency(assignment_exprs,
                                                      xml_context=False,
                                                      warn_on_units_errors=self.model.get_option('warn_on_units_errors'),
                                                      check_for_units_conversions=False)
        if self.model._cml_validation_errors:
            error_handler(self.model._cml_validation_errors)
        # Clear up logging
        validator.CellMLValidator.cleanup_logging(logging_info)
 
    def _clear_model_caches(self):
        """
        Clear cached links in the model, since we'll need to recompute many of them
        once we've finished modifying it.  Also clears dependency information.
        """
        for comp in getattr(self.model, u'component', []):
            for math in getattr(comp, u'math', []):
                math._unset_cached_links()
        for var in self.model.get_all_variables():
            var.clear_dependency_info()
        assignment_exprs = self.model.search_for_assignments()
        for expr in assignment_exprs:
            expr.clear_dependency_info()
    
    def create_new_component(self, cname):
        """Create a new component in the model, ensuring the name is unique.
        
        If a component with name cname already exists,
        underscores will be added to the component name to make it unique.
        """
        while True:
            try:
                self.model.get_component_by_name(cname)
                cname += u'_'
            except KeyError:
                # Component with this name doesn't exist
                break
        # Create the component
        comp = cellml_component.create_new(self.model, cname)
        self.model._add_component(comp)
        return comp
    
    def connect_variables(self, source, target):
        """Create a connection between the given source and target variables.
        
        The variables are both specified either by a pair (cname,vname), or as cellml_variable objects.
        The source variable must exist within the model, whereas the target might not, in
        which case it will be created.
        
        Note that in the case that both source and target exist, it might NOT be the case that
        target obtains its value from source.  They might already be connected, and source obtains
        its value from target.  Or they might both obtain their value from a common source.
        
        If the variable names are not identical, any variables created will have the same name as the
        target, if possible.  If there's an existing variable with that name, not connected to the
        source, then underscores will be appended to the name to avoid conflicts.  Note that we do
        check for variables in intermediate components that have the same name as the source and are
        connected to it, to avoid adding unnecessary variables.
        
        Returns the target variable object.
        """
        if isinstance(source, cellml_variable):
            src_cname, src_vname = source.component.name, source.name
        else:
            src_cname, src_vname = source
        if isinstance(target, cellml_variable):
            target_cname, target_vname = target.component.name, target.name
        else:
            target_cname, target_vname = target
        src_comp = self.model.get_component_by_name(src_cname)
        target_comp = self.model.get_component_by_name(target_cname)
        if src_comp == target_comp:
            return target_comp.get_variable_by_name(target_vname)
        # Determine encapsulation paths from target & source to the root
        src_path = self._parent_path(src_comp)
        target_path = self._parent_path(target_comp)
        # At some point these will share a common path, even if it's just the root itself
        meeting_index = self._find_common_tail(src_path, target_path)
        # Construct path from source to target, leaving out the root (None)
        path = src_path[:meeting_index]
        if src_path[meeting_index]:
            path.append(src_path[meeting_index])
        path.extend(reversed(target_path[:meeting_index]))
        # Traverse this path, adding connections at each step
        next_src_var = src_comp.get_variable_by_name(src_vname)
        for i, src_comp in enumerate(path[:-1]):
            target_comp = path[i+1]
            next_src_var = self._make_connection(next_src_var, target_comp, target_vname)
        return next_src_var
    
    def _make_connection(self, src_var, target_comp, target_vname):
        """Make a connection from a source variable to a given component and suggested local name.
        
        Note that in the case that both variables already exist and are connected, the existing
        connection is allowed to flow in either direction.
        """
        src_comp = src_var.component
        target_var = self._find_or_create_variable(target_comp.name, target_vname, src_var)
        # Sanity check the target variable
        if (target_var.get_type() == VarTypes.Mapped
            and target_var.get_source_variable(recurse=True) is src_var.get_source_variable(recurse=True)):
#            print "Connection exists between", src_var, "and target", target_var
            return target_var
        elif target_var.get_type() == VarTypes.Unknown:
            # We've created this variable, so should be ok, but check for gotchas
            assert not(hasattr(target_var, u'initial_value'))
            if src_comp is target_comp.parent():
                src_if = u'private'
                target_if = u'public'
            elif src_comp.parent() is target_comp:
                src_if = u'public'
                target_if = u'private'
            else:
                assert src_comp.parent() is target_comp.parent()
                src_if = u'public'
                target_if = u'public'
                # One special case: if the src_var is actually obtained from a different
                # component at this level or above, in which case we should use the real
                # source, not that given.
                if getattr(src_var, src_if + u'_interface', u'none') == u'in':
                    src_var = src_var.get_source_variable()
            # Check and set the interface attributes
#            print "Connecting source", src_var, src_if, getattr(src_var, src_if + u'_interface', u'none'),
#            print "to", target_var, target_if, getattr(target_var, target_if + u'_interface', u'none')
            assert getattr(src_var, src_if + u'_interface', u'none') != u'in'
            assert getattr(target_var, target_if + u'_interface', u'none') != u'out'
            src_var.xml_set_attribute((src_if + u'_interface', None), u'out')
            target_var.xml_set_attribute((target_if + u'_interface', None), u'in')
            # Create the connection element
            self._create_connection_element(src_var, target_var)
            self.connections_made.add(frozenset([src_var, target_var]))
            # Ensure we handle a later connection attempt between these variables correctly
            target_var._set_source_variable(src_var)
        else:
            # Naming conflict; try again with a different target name
            return self._make_connection(src_var, target_comp, target_vname + u'_')
        return target_var
    
    def _find_connection_element(self, var1, var2):
        """Find any connection element containing a connection of the given variables.
        
        Returns a pair, the first element of which is either the element or None, and the
        second of which is a boolean indicating whether the variables need to be swapped
        in order to match the order of the components in the connection.
        """
        cn1, cn2 = var1.component.name, var2.component.name
        cnames = set([cn1, cn2])
        for conn in getattr(self.model, u'connection', []):
            mc = conn.map_components
            if set([mc.component_1, mc.component_2]) == cnames:
                break
        else:
            conn = None
        if conn:
            swap = conn.map_components.component_1 == cn2
        else:
            swap = False
        return conn, swap
    
    def _create_connection_element(self, var1, var2):
        """Create a connection element connecting the given variables and add to the model.
        
        If there's already a connection element for the relevant pair of components,
        we just add another map_variables element to that.
        """
        conn, swap = self._find_connection_element(var1, var2)
        if conn:
            if swap:
                var1, var2 = var2, var1
        else:
            conn = var1.xml_create_element(u'connection', NSS[u'cml'])
            mapc = var1.xml_create_element(u'map_components', NSS[u'cml'],
                                           attributes={u'component_1': var1.component.name,
                                                       u'component_2': var2.component.name})
            conn.xml_append(mapc)
            self.model.xml_append(conn)
        mapv = var1.xml_create_element(u'map_variables', NSS[u'cml'],
                                       attributes={u'variable_1': var1.name,
                                                   u'variable_2': var2.name})
        conn.xml_append(mapv)
    
    def remove_connection(self, var1, var2):
        """Remove a connection between two variables.
        
        Removes the relevant map_variables element.
        If this results in an empty connection element, removes that as well.
        """
        conn, swap = self._find_connection_element(var1, var2)
        if not conn:
            raise ModelModificationError("Cannot remove non-existent connection.")
        if swap:
            var1, var2 = var2, var1
        # Find the relevant map_variables element
        mapv = conn.xml_xpath(u'cml:map_variables[@variable_1="%s" and @variable_2="%s"]'
                              % (var1.name, var2.name))
        if not mapv:
            raise ModelModificationError("Cannot remove non-existent connection.")
        conn.xml_remove_child(mapv[0])
        if not hasattr(conn, u'map_variables'):
            conn.xml_parent.xml_remove_child(conn)
    
    def remove_connections(self, var):
        """Remove all connection elements for the given variable.
        
        Removes each relevant map_variables element.
        If this results in an empty connection element, removes that as well.
        """
        cname, vname = var.component.name, var.name
        for conn in list(getattr(self.model, u'connection', [])):
            if cname == conn.map_components.component_1:
                vid = u'variable_1'
            elif cname == conn.map_components.component_2:
                vid = u'variable_2'
            else:
                continue
            for mapv in conn.map_variables:
                if vname == getattr(mapv, vid, ''):
                    # Found a connection
                    conn.xml_remove_child(mapv)
                    if not hasattr(conn, u'map_variables'):
                        conn.xml_parent.xml_remove_child(conn)
                    # There can't be any more matching map_variables in this connection
                    break
    
    def _update_connections(self, oldVar, newVar):
        """Change all variables connected to oldVar to be mapped to newVar instead."""
        vars = [v for v in self.model.get_all_variables() if v.get_source_variable(True) is oldVar]
        # Remove old connections, including interfaces and types so creating the new connection works
        for v in vars:
            self.remove_connections(v)
            self.del_attr(v, u'public_interface')
            self.del_attr(v, u'private_interface')
            v.clear_dependency_info()
        # Create new connections
        for v in vars:
            self.connect_variables(newVar, v)
    
    def _find_common_tail(self, l1, l2):
        """Find the first element at which both lists are identical from then on."""
        i = -1
        try:
            while l1[i] == l2[i]:
                i -= 1
        except IndexError:
            # One list is the tail of the other
            pass
        # i now gives the last differing element
        assert i < -1
        return i+1
        
    def _parent_path(self, comp):
        """Return a path of components from that given to the encapsulation root.
        
        The root is specified by None, since we're really dealing with a forest,
        not a tree.
        """
        path = [comp]
        while comp:
            path.append(comp.parent())
            comp = comp.parent()
        return path
 
    def _process_operator(self, expr, operator, func, *args, **kwargs):
        """Apply func to any application of the given operator within the given tree."""
        for elt in self.model.xml_element_children(expr):
            self._process_operator(elt, operator, func, *args, **kwargs)
        if isinstance(expr, mathml_apply) and expr.operator().localName == operator:
            func(expr, *args, **kwargs)
 
    def _find_or_create_variable(self, cname, vname, source):
        """Find a given variable in the model, creating it if necessary.
        
        We look for a variable in the component named cname with the same name as the source.
        If it doesn't exist, a variable named vname will be created in that component (unless
        it already exists).
        The variable will become a mapped variable with the given source.
        Hence if it is created it will have the same units.
        """
        try:
            var = self.model.get_variable_by_name(cname, source.name)
            raise KeyError()
        except KeyError:
            # Have we created it already?
            try:
                var = self.model.get_variable_by_name(cname, vname)
            except KeyError:
                # Create it and add to model
                units = source.component.get_units_by_name(source.units)
                var = self.add_variable(cname, vname, units)
        return var
    
    def add_variable(self, comp, vname, units, **kwargs):
        """Add a new variable to the given component.
        
        Remaining arguments are as for cellml_variable.create_new.
        Returns the new variable object.
        """
        if not isinstance(comp, cellml_component):
            comp = self.model.get_component_by_name(comp)
        units = self.add_units(units)
        var = cellml_variable.create_new(comp, vname, units.name, **kwargs)
        comp._add_variable(var)
        return var
        
    def _get_units_object(self, units):
        """Helper function to convert a units specification into a cellml_units object.
        
        The input can be a cellml_units object, in which case we just return it.
        However, it can also be a serialised CellML units definition, in which case it
        will be parsed to create the object.
        """
        if isinstance(units, cellml_units):
            # We're done
            pass
        else:
            units = amara_parse_cellml(unicode(units))
        assert isinstance(units, cellml_units)
        return units
 
    def add_units(self, units):
        """Add a units definition to the model, if it doesn't already exist.
        
        If the definition isn't in the model, at whole-model level, it will be added.  If the same
        definition is already available, however, that definition should be used by preference.
        Will return the actual units object to use.
        """
        units = self.model._get_units_obj(units)
        try:
            model_units = self.model.get_units_by_name(units.name)
        except KeyError:
            model_units = None
        if model_units:
            assert units.uniquify_tuple == model_units.uniquify_tuple
            units = model_units
        else:
            units.name = self._uniquify_name(units.name, self.model.get_units_by_name)
            self.model.add_units(units.name, units)
            self.model.xml_append(units)
            # Ensure referenced units exist
            for unit in getattr(units, u'unit', []):
                unit._set_units_element(self.add_units(unit.get_units_element()), override=True)
                unit.units = unit.get_units_element().name
        return units
    
    def add_expr_to_comp(self, comp, expr):
        """Add an expression to the mathematics in the given component.
        
        comp may be a cellml_component instance or a component name.
        """
        if not isinstance(comp, cellml_component):
            comp = self.model.get_component_by_name(comp)
        if not hasattr(comp, u'math'):
            # Create the math element
            math = comp.xml_create_element(u'math', NSS[u'm'])
            comp.xml_append(math)
        # Append this expression
        comp.math.xml_append(expr)
    
    def remove_expr(self, expr):
        """Remove an expression (ODE or assignment) from its parent."""
        assert isinstance(expr, mathml_apply)
        if expr.xml_parent:
            expr.xml_parent.safe_remove_child(expr)
            expr.xml_parent = None # Not done by Amara...
        return expr
    
    def remove_definition(self, var, keep_initial_value=False):
        """Remove any existing definition (as an equation) of the given variable.
        
        If keep_initial_value is False, then also remove any initial_value attribute.
        
        If the variable is Mapped, throw a ModelModificationError.
        """
        if var.get_type() == VarTypes.Mapped:
            raise ModelModificationError("Cannot remove the equation defining a mapped variable - remove the definition of its source instead")
        if not keep_initial_value:
            self.del_attr(var, u'initial_value')
        # Note: if this is a variable added by a protocol, then it shouldn't have
        # any dependencies set up yet, so this is a no-op.
        for dep in var.get_all_expr_dependencies():
            self.remove_expr(dep)
        # We know don't know how it will be defined
        var.clear_dependency_info()
 
    def del_attr(self, elt, localName, ns=None):
        """Delete an XML attribute from an element, if it exists."""
        for (pyname, (qname, ns_)) in elt.xml_attributes.items():
            _, name = SplitQName(qname)
            if ns_ == ns and name == localName:
                delattr(elt, pyname)
 
    def _uniquify_var_name(self, varname, comp):
        """Ensure varname is unique within the given component.
        
        Underscores will be appended to the name until it is unique.  The unique name will be returned.
        """
        return self._uniquify_name(varname, comp.get_variable_by_name)
    
    def _uniquify_name(self, name, callable):
        """Ensure the given name is unique within a particular context.
        
        The context is determined by the given function: it will be passed candidate names to test
        for existence, and is expected to throw iff the name is not already used.  Underscores will
        be appended to the given name until callable throws, and the resulting unique name returned.
        """
        while True:
            try:
                callable(name)
                name += u'_'
            except:
                break
        return name
    
    def set_units_converter(self, converter):
        """Set the object used to units-convert variable initial values."""
        self._units_converter = converter
    
    def get_units_converter(self):
        """Get the units converter object, if any has been set."""
        if not self._units_converter:
            raise ModelModificationError("No units converter has been set.")
        return self._units_converter
 
    def _convert_initial_value(self, var, units, do_conversion=True):
        """Convert any initial value of the given variable into the given units.
        
        If there is no initial value, returns None.
        If there is no units converter, leaves the initial_value unchanged.
        """
        if not hasattr(var, u'initial_value'):
            return None
        value = var.initial_value
        if value and self._units_converter and do_conversion:
            if not var.get_units().equals(units):
                try:
                    value = self._units_converter.convert_constant(value, var.get_units(), units, var.component)
                except EvaluationError, e:
                    raise ModelModificationError("Cannot units-convert initial value as requires run-time information:\n"
                                                 + str(e))
        return unicode(value)
 
 
 
class InterfaceGenerator(ModelModifier):
    """Class for generating an interface between a CellML model and external code.
    
    This contains functionality for users to describe the interface desired by the external code, i.e.
    which variables are inputs and/or outputs, and expected units.  It will then create a new component
    within the CellML model containing these variables, and add units conversions where required.  The
    external code then only needs to interact with this new component.
    """
    def __init__(self, model, name='interface', units_converter=None):
        super(InterfaceGenerator, self).__init__(model)
        self._interface_component = None
        self._interface_component_name = name
        self.set_units_converter(units_converter)
    
    def add_input(self, var, units, annotate=True, convert_initial_value=True):
        """Specify a variable as an input to the model.
        
        var should be a cellml_variable object already existing in the model.
        units should be a suitable input to self._get_units_object.
        
        If adding both State and Free variables as inputs, make sure to add the Free variable first,
        otherwise you will not be able to specify units for it.
        
        Set annotate to False if you do not wish a Constant variable to be annotated as a modifiable
        parameter.
        
        If a units converter has been supplied, we will also try to units-convert initial values.
        This may not be possible if special conversions are used, since they may involve variables
        whose values are not known at this time.  If this is the case, set convert_initial_value to
        False to avoid applying the conversion.  A proper solution requires CellML 1.1 features.
        
        The new variable added to the interface component is returned.
        """
        assert isinstance(var, cellml_variable)
        units = self._get_units_object(units)
        var = var.get_source_variable(recurse=True) # Ensure we work with source variables only
        var_name = var.fullname(cellml=True)
        # Check that the variable has a suitable type to be an input
        t = var.get_type()
        if t == VarTypes.Computed:
            raise ModelModificationError("Cannot specify computed variable " + var.fullname() + " as an input")
        elif t not in [VarTypes.Constant, VarTypes.Free, VarTypes.State]:
            raise ModelModificationError("Variable " + var.fullname() + " has unexpected type " + str(t))
        # Add a new variable with desired units to the interface component
        comp = self.get_interface_component()
        newvar = self.add_variable(comp, var_name, units, id=var.cmeta_id,
                                   initial_value=self._convert_initial_value(var, units, convert_initial_value),
                                   interfaces={u'public': u'out'})
        newvar._set_type(t)
        # Remove initial value and id from the original, if they exist
        self.del_attr(var, u'initial_value')
        self.del_attr(var, u'id', NSS['cmeta'])
        # If the original variable was a state variable, split the defining equation
        if t == VarTypes.State:
            self._split_ode(newvar, var)
        # Annotate the new variable as a parameter if the original was a constant
        if t == VarTypes.Constant and annotate:
            newvar.set_is_modifiable_parameter(True)
 
        self._update_connections(var, newvar)
        return newvar
    
    def add_output(self, var, units, annotate=True):
        """Specify a variable as an output of the model.
        
        var should be a cellml_variable object already existing in the model.
        units should be a suitable input to self._get_units_object.
        The new variable will take the cmeta:id of the original, and hence existing metadata
        annotations will refer to the new variable.
        If annotate is set to True, the new variable will also be annotated as a derived quantity.
        
        The new variable added to the interface component is returned.
        """
        assert isinstance(var, cellml_variable)
        units = self._get_units_object(units)
        var = var.get_source_variable(recurse=True)
        var_name = var.fullname(cellml=True)
        comp = self.get_interface_component()
        newvar = self.add_variable(comp, var_name, units, id=var.cmeta_id)
        self.del_attr(var, u'id', NSS['cmeta'])
        self.connect_variables(var, newvar)
        if annotate:
            newvar.set_is_derived_quantity(True)
        return newvar
    
    def add_output_function(self, resultName, operator, argVars, units):
        """Add an output that's defined as a (MathML) function of existing model variables.
        
        The desired units are those of the function's result.  The function arguments will be
        imported with their units as given by the model, and the function calculated.  This result
        will then be units-converted if necessary.
        
        The new variable added to the interface component is returned.
        """
        # Add the result variable
        comp = self.get_interface_component()
        units = self._get_units_object(units)
        result_var = self.add_variable(comp, resultName, units)
        result_var.set_pe_keep(True)
        # Map the argument variables
        operands = []
        for var in argVars:
            operands.append(self.add_output(var, var.get_units(), annotate=False).name)
        # Create the new function and assign it to result_var
        expr = mathml_apply.create_new(self.model, operator, operands)
        assign = mathml_apply.create_new(self.model, u'eq', [result_var.name, expr])
        self.add_expr_to_comp(comp, assign)
        return result_var
    
    def make_var_constant(self, var, value):
        """Turn a variable into a constant."""
        self.remove_definition(var)
        var.clear_dependency_info()
        var.initial_value = unicode(str(value))
        var._set_type(VarTypes.Constant)
    
    def make_var_computed_constant(self, var, value):
        """Turn a variable into a Computed variable with constant value definition."""
        self.remove_definition(var)
        var.clear_dependency_info()
        defn = mathml_apply.create_new(self.model, u'eq', 
                                       [var.name, (unicode(str(value)), var.get_units().name)])
        self.add_expr_to_comp(var.component, defn)
        var._set_type(VarTypes.Computed)
 
    def finalize(self, *args, **kwargs):
        """Override finalize to also set up standard interface elements not defined individually."""
        self._add_all_odes_to_interface()
        self._transform_derivatives_on_rhs()
        super(InterfaceGenerator, self).finalize(*args, **kwargs)
 
    def _transform_derivatives_on_rhs(self):
        """Transform any equations with derivatives on the RHS to use the variable defining it instead.
        
        self._split_ode must have been used for all derivatives before calling this method.  This means
        that each ODE now has a variable to which the RHS is assigned.  Rather than using the derivative
        directly, which could break the dependency chain if units conversions are used for time, equations
        should refer to this new variable instead.
        """
        for expr in self.model.search_for_assignments():
            self._process_operator(list(expr.operands())[1], u'diff', self._transform_derivative_on_rhs)
 
    def _transform_derivative_on_rhs(self, expr):
        """Transform a derivative on the RHS of an equation to refer to the defining variable.
        
        Helper method used by self._transform_derivatives_on_rhs to do the actual transformation.
        """
        # Find the variable to use
        dep_var = expr.diff.dependent_variable.get_source_variable(recurse=True)
        indep_var = expr.diff.independent_variable.get_source_variable(recurse=True)
        ode = dep_var.get_ode_dependency(indep_var)
        rhs_var = ode.eq.rhs.variable.get_source_variable(recurse=True)
        # Ensure there's something mapped to it in this component
        rhs_var = self.connect_variables(rhs_var, (expr.component.name, rhs_var.name))
        # Update this expression
        parent = expr.xml_parent
        parent.xml_insert_after(expr, mathml_ci.create_new(parent, rhs_var.name))
        parent.safe_remove_child(expr)
    
    def _split_ode(self, newVar, oldVar):
        """Split an ODE definition so the derivative goes into the interface component.
        
        The RHS stays where it is, and is assigned to a new variable, which is connected to the interface
        component and assigned to the new derivative.  newVar is the new state variable in the interface
        component, and oldVar will soon be mapped to it by the caller.
        
        Any other equations in the model which use the derivative are transformed to use the new variable
        instead.
        """
        # Get the free variable in the interface component
        free_var = self.model.find_free_vars()[0]
        if free_var.component is not newVar.component:
            free_var = self.add_input(free_var, free_var.get_units())
        # Add a new variable to assign the RHS to, with units of the original derivative
        deriv_name = self._uniquify_var_name(u'd_%s_d_%s' % (oldVar.name, free_var.name), oldVar.component)
        orig_ode = oldVar.get_all_expr_dependencies()[0]
        orig_rhs_var = self.add_variable(oldVar.component, deriv_name, orig_ode.eq.lhs.get_units().extract())
        # Add an output version of this in the interface, with desired units
        desired_units = newVar.get_units().quotient(free_var.get_units())
        mapped_rhs_var = self.add_output(orig_rhs_var, desired_units, annotate=False)
        # Replace the original ODE with an assignment
        orig_rhs = orig_ode.eq.rhs
        orig_ode.safe_remove_child(orig_rhs)
        self.remove_expr(orig_ode)
        self.add_expr_to_comp(oldVar.component,
                              mathml_apply.create_new(self.model, u'eq',
                                                      [orig_rhs_var.name, orig_rhs]))
        # Create a new ODE in the interface component
        new_ode = mathml_diff.create_new(self.model, free_var.name, newVar.name, mapped_rhs_var.name)
        self.add_expr_to_comp(newVar.component, new_ode)
        new_ode.classify_variables(root=True, dependencies_only=True)
    
    def _add_all_odes_to_interface(self):
        """All the derivatives should be considered as model outputs, and state variables as model inputs.
        
        For any that haven't been done explicitly, this method will add the corresponding state variable
        as an input, with its original units, which has the desired effect.
        """
        comp = self.get_interface_component()
        for var in self.model.find_state_vars():
            if var.component is not comp:
                self.add_input(var, var.get_units())
    
    def get_interface_component(self):
        """Get the new component that will contain the interface.
        
        The name will be self._interface_component_name, unless a component with that name already exists,
        in which case underscores will be added to the component name to make it unique.
        """
        if self._interface_component is None:
            self._interface_component = self.create_new_component(unicode(self._interface_component_name))
            self.model.interface_component_name = unicode(self._interface_component_name)
            assert not self._interface_component.ignore_component_name
        return self._interface_component
 
 
class UnitsConverter(ModelModifier):
    """Top-level interface to the units conversion code in PyCml.
    """
    def __init__(self, model, warn_only=None, show_xml_context_only=False):
        super(UnitsConverter, self).__init__(model)
        if warn_only is None:
            warn_only = model.get_option('warn_on_units_errors')
        self.warn_only = warn_only
        self.show_xml_context_only = show_xml_context_only
        self.special_conversions = {}
        self._setup_logger()
        self._converted_mappings = set()
    
    def __del__(self):
        self._cleanup_logger()
        
    def _setup_logger(self):
        logger = logging.getLogger('units-converter')
        logger.setLevel(logging.WARNING)
        formatter = logging.Formatter(fmt="%(name)s: %(message)s")
        handler = logging.StreamHandler(sys.stderr)
        handler.setFormatter(formatter)
        logger.addHandler(handler)
        self._log_handler = handler
    
    def _cleanup_logger(self):
        """Flush logger & remove handler."""
        logger = logging.getLogger('units-converter')
        self._log_handler.flush()
        logger.removeHandler(self._log_handler)
 
    def try_convert(self, func, *args, **kwargs):
        """Call the given function, and log any units errors produced."""
        try:
            func(*args, **kwargs)
        except UnitsError, e:
            if self.show_xml_context_only:
                e.show_xml_context_only()
            if self.warn_only:
                e.warn = True
                e.level = logging.WARNING
            logging.getLogger('units-converter').log(e.level, unicode(e).encode('UTF-8'))
 
    def _apply_special_conversion_for_nested_expr(self, expr, defn_units, desired_units):
        """Apply a special conversion to the given (sub-)expression.
        
        This will get called by mathml_units_mixin._add_units_conversion if a special conversion is required by a nested sub-expression.
        """
        for from_units, to_units in self.special_conversions.iterkeys():
            if (from_units.dimensionally_equivalent(defn_units)
                and to_units.dimensionally_equivalent(desired_units)):
                # We can apply this conversion
                expr = self.special_conversions[(from_units, to_units)](expr)
                DEBUG('units-converter', "Used nested special conversion from", repr(from_units), "to", repr(to_units))#, "giving", expr.xml())
                break
#         else:
#             print "No on nested conv from", repr(from_units), "to", repr(to_units)
        return expr
 
    def _check_special_conversion(self, expr):
        """Check whether a special conversion applies to the given assignment.
        
        Special conversions allow us to do units conversion between dimensionally non-equivalent
        quantities, by utilising biological knowledge.  Available special conversions are added
        using the add_special_conversion method.
        """
        lhs_units = expr.eq.lhs.get_units()
        rhs_units = expr.eq.rhs.get_units()
        if lhs_units.dimensionally_equivalent(rhs_units):
            return
        for from_units, to_units in self.special_conversions.iterkeys():
            if (from_units.dimensionally_equivalent(rhs_units)
                and to_units.dimensionally_equivalent(lhs_units)):
                # We can apply this conversion
                self.special_conversions[(from_units, to_units)](expr)
                DEBUG('units-converter', "Used special conversion from", repr(from_units), "to", repr(to_units))#, "giving", expr.xml())
                break
#         else:
#             print "No on conv from", repr(from_units), "to", repr(to_units)
 
    def add_special_conversion(self, from_units, to_units, converter):
        """Add a new special conversion to the list available.
        
        Special conversions allow us to do units conversion between dimensionally non-equivalent
        quantities, by utilising biological knowledge.  The function "converter" will be called with
        an assignment (top-level mathml_apply instance) that has RHS units equivalent to from_units,
        and LHS units equivalent to to_units.  It should alter the equation in-place (i.e. the
        object passed to it must contain the final equation) to do an appropriate units conversion,
        at least so that LHS and RHS dimensions match.
        """
        self.special_conversions[(from_units, to_units)] = converter
    
    def modify_rhs(self, expr, operator, var):
        """Helper method of use to special units conversions.
        
        Will modify the given expr in-place, replacing the RHS by an application of the given operator.
        The operands will be the existing RHS and a ci element referencing the supplied variable object.
        Connections and variables will be added to ensure that the given variable is available in the
        component in which expr appears.
        
        Returns expr, for ease of chaining expressions.
        """
        assert isinstance(var, cellml_variable)
        # Ensure var is available in expr's component
        local_var_name = var.name
        source_comp = var.component
        expr_comp = expr.component
        if source_comp != expr_comp:
            local_var = self.connect_variables(var, (expr_comp.name, var.fullname(cellml=True)))
            local_var_name = local_var.name
        # Change expr
        rhs = expr.eq.rhs
        expr.safe_remove_child(rhs)
        new_rhs = mathml_apply.create_new(var.model, operator, [rhs, local_var_name])
        expr.xml_append(new_rhs)
        return expr
    
    def times_rhs_by(self, expr, var):
        """Helper method of use to special units conversions.
        
        Will modify the given expr in-place, post-multiplying the RHS by a reference to the given variable object.
        Connections and variables will be added to ensure that the given variable is available in the
        component in which expr appears.
        
        Returns expr, for ease of chaining expressions.
        """
        return self.modify_rhs(expr, u'times', var)
 
    def divide_rhs_by(self, expr, var):
        """Helper method of use to special units conversions.
        
        Will modify the given expr in-place, post-dividing the RHS by a reference to the given variable
        object.
        Connections and variables will be added to ensure that the given variable is available in the
        component in which expr appears.
        
        Returns expr, for ease of chaining expressions.
        """
        return self.modify_rhs(expr, u'divide', var)
    
    def convert_assignments(self, exprs):
        """Apply conversions to any assignments in the given iterable."""
        boolean = self.model.get_units_by_name('cellml:boolean')
        for expr in exprs:
            if isinstance(expr, mathml_apply):
#                 print 'Converting? assignment', element_xpath(expr)
                if self.special_conversions:
                    self.try_convert(self._check_special_conversion, expr)
                self.try_convert(expr._set_in_units, boolean)
    
    def convert_constant(self, value, from_units, to_units, comp):
        """Convert a constant value into desired units."""
        from_units = self.add_units(from_units)
        to_units = self.add_units(to_units)
        expr = mathml_apply.create_new(self.model, u'eq', [(u'0', to_units.name),
                                                           (unicode(value), from_units.name)])
        self.add_expr_to_comp(comp, expr)
        # Nasty hack to make expr.is_top_level return True
        expr._cml_assigns_to = expr.operands().next()
        if self.special_conversions:
            self.try_convert(self._check_special_conversion, expr)
        self.try_convert(expr.eq.rhs._set_in_units, to_units)
        self.remove_expr(expr)
        return expr.eq.rhs.evaluate()
 
    def convert_mapping(self, mapping, comp1, comp2, var1, var2):
        """Apply conversions to a mapping between two variables."""
        model = self.model
        # Check for being already converted
        var_pair = frozenset([var1, var2])
        if var_pair in self._converted_mappings:
            DEBUG('units-converter', 'Skipping already converted mapping', var1, '<->', var2)
            return
        else:
            self._converted_mappings.add(var_pair)
        # Ensure mapping is var1 := var2; swap vars if needed
        swapped = False
        try:
            if var2.get_source_variable() is var1:
                swapped = True
                var1, var2 = var2, var1
                comp1, comp2 = comp2, comp1
        except TypeError:
            pass
        # Get units
        u1 = var1.get_units()
        u2 = var2.get_units()
        DEBUG('units-converter', "Converting mapping of", var1, ":=", var2,
              "(units:", repr(u1), repr(u2), ")")
        if not u1.equals(u2):
            # We need a conversion
            # Add a copy of var1 to comp1, with units as var2
            if getattr(var1, u'public_interface', '') == u'in':
                in_interface = u'public'
            else:
                in_interface = u'private'
            var1_converter = self.add_variable(comp1, var1.name + u'_converter', u2, interfaces={in_interface: u'in'})
            var1._cml_var_type = VarTypes.Computed
            var1._cml_source_var = None
            delattr(var1, in_interface + u'_interface')
            var1_converter._set_source_variable(var2)
            # Add assignment maths for var1 := var1_converter
            app = mathml_apply.create_new(model, u'eq', [var1.name, var1_converter.name])
            self.add_expr_to_comp(comp1, app)
            var1._cml_depends_on = [app]
            app._cml_assigns_to = var1
            # Update mapping to var1_converter := var2
            if swapped:
                mapping.variable_2 = var1_converter.name
            else:
                mapping.variable_1 = var1_converter.name
            # Fix usage counts - var1_converter is only used by app, and so var2 usage decreases
            var1_converter._used()
            for _ in xrange(var1.get_usage_count()):
                var2._decrement_usage_count()
            # Apply units conversion to the assignment
            self.convert_assignments([app])
            # Add the assignment into the sorted list
            assignments = model.get_assignments()
            idx = assignments.index(var1)
            assignments[idx:idx+1] = [var1_converter, app]
    
    def convert_connections(self, connections):
        """Add units conversions for all connections in the given set.
        
        :param connections: a set of variable pairs representing connections.  For each pair of variables a units conversion
        will be added if needed and not already performed.
        """
        model = self.model
        for conn in getattr(model, u'connection', []):
            comp1 = model.get_component_by_name(conn.map_components.component_1)
            comp2 = model.get_component_by_name(conn.map_components.component_2)
            for mapping in conn.map_variables:
                var1 = model.get_variable_by_name(comp1.name, mapping.variable_1)
                var2 = model.get_variable_by_name(comp2.name, mapping.variable_2)
                if frozenset([var1, var2]) in connections:
                    self.convert_mapping(mapping, comp1, comp2, var1, var2)
    
    def add_conversions_for_component(self, comp):
        """Add all units conversions required by the given component.
        
        This allows us to only apply the conversions required by an interface component created
        by an InterfaceGenerator.
        """
        model = self.model
        if self.special_conversions:
            self.model._cml_special_units_converter = self._apply_special_conversion_for_nested_expr
        assignments = model.search_for_assignments(comp)
        self.convert_assignments(assignments)
        if self.special_conversions:
            del self.model._cml_special_units_converter
        for conn in getattr(model, u'connection', []):
            cname1 = conn.map_components.component_1
            cname2 = conn.map_components.component_2
            if comp.name in [cname1, cname2]:
                comp1 = model.get_component_by_name(cname1)
                comp2 = model.get_component_by_name(cname2)
                for mapping in conn.map_variables:
                    var1 = model.get_variable_by_name(cname1, mapping.variable_1)
                    var2 = model.get_variable_by_name(cname2, mapping.variable_2)
                    self.convert_mapping(mapping, comp1, comp2, var1, var2)
    
    def add_all_conversions(self):
        """Add all units conversions required in the given model."""
        model = self.model
        # Mathematical expressions
        self.convert_assignments(model.get_assignments())
        # Connections
        for conn in getattr(model, u'connection', []):
            comp1 = model.get_component_by_name(conn.map_components.component_1)
            comp2 = model.get_component_by_name(conn.map_components.component_2)
            for mapping in conn.map_variables:
                var1 = model.get_variable_by_name(comp1.name, mapping.variable_1)
                var2 = model.get_variable_by_name(comp2.name, mapping.variable_2)
                self.convert_mapping(mapping, comp1, comp2, var1, var2)
        return