Instruction:
Can you tell what is the following Python 3 function doing
def run(self, root=None, infer_gtr=True, relaxed_clock=None, n_iqd = None,
            resolve_polytomies=True, max_iter=0, Tc=None, fixed_clock_rate=None,
            time_marginal=False, sequence_marginal=False, branch_length_mode='auto',
            vary_rate=False, use_covariation=False, **kwargs):

        """
        Run TreeTime reconstruction. Based on the input parameters, it divides
        the analysis into semi-independent jobs and conquers them one-by-one,
        gradually optimizing the tree given the temporal constarints and leaf
        node sequences.

        Parameters
        ----------
        root : str
           Try to find better root position on a given tree. If string is passed,
           the root will be searched according to the specified method. If none,
           use tree as-is.

           See :py:meth:`treetime.TreeTime.reroot` for available rooting methods.

        infer_gtr : bool
           If True, infer GTR model

        relaxed_clock : dic
           If not None, use autocorrelated molecular clock model. Specify the
           clock parameters as :code:`{slack:<slack>, coupling:<coupling>}` dictionary.

        n_iqd : int
           If not None, filter tree nodes which do not obey the molecular clock
           for the particular tree. The nodes, which deviate more than
           :code:`n_iqd` interquantile intervals from the molecular clock
           regression will be marked as 'BAD' and not used in the TreeTime
           analysis

        resolve_polytomies : bool
           If True, attempt to resolve multiple mergers

        max_iter : int
           Maximum number of iterations to optimize the tree

        Tc : float, str
           If not None, use coalescent model to correct the branch lengths by
           introducing merger costs.

           If Tc is float, it is interpreted as the coalescence time scale

           If Tc is str, it should be one of (:code:`opt`, :code:`const`, :code:`skyline`)

        fixed_clock_rate : float
           Fixed clock rate to be used. If None, infer clock rate from the molecular clock.

        time_marginal : bool
           If True, perform a final round of marginal reconstruction of the node's positions.

        sequence_marginal : bool, optional
            use marginal reconstruction for ancestral sequences

        branch_length_mode : str
           Should be one of: :code:`joint`, :code:`marginal`, :code:`input`.

           If 'input', rely on the branch lengths in the input tree and skip directly
           to the maximum-likelihood ancestral sequence reconstruction.
           Otherwise, perform preliminary sequence reconstruction using parsimony
           algorithm and do branch length optimization

        vary_rate : bool or float, optional
            redo the time tree estimation for rates +/- one standard deviation.
            if a float is passed, it is interpreted as standard deviation,
            otherwise this standard deviation is estimated from the root-to-tip regression

        use_covariation : bool, optional
            default False, if False, rate estimates will be performed using simple
            regression ignoring phylogenetic covaration between nodes.

        **kwargs
           Keyword arguments needed by the downstream functions

        Returns
        -------
        TreeTime error/succces code : str
            return value depending on success or error

        """

        # register the specified covaration mode
        self.use_covariation = use_covariation

        if (self.tree is None) or (self.aln is None and self.seq_len is None):
            self.logger("TreeTime.run: ERROR, alignment or tree are missing", 0)
            return ttconf.ERROR
        if (self.aln is None):
            branch_length_mode='input'

        self._set_branch_length_mode(branch_length_mode)

        # determine how to reconstruct and sample sequences
        seq_kwargs = {"marginal_sequences":sequence_marginal or (self.branch_length_mode=='marginal'),
                      "sample_from_profile":"root"}

        tt_kwargs = {'clock_rate':fixed_clock_rate, 'time_marginal':False}
        tt_kwargs.update(kwargs)

        seq_LH = 0
        if "fixed_pi" in kwargs:
            seq_kwargs["fixed_pi"] = kwargs["fixed_pi"]
        if "do_marginal" in kwargs:
            time_marginal=kwargs["do_marginal"]

        # initially, infer ancestral sequences and infer gtr model if desired
        if self.branch_length_mode=='input':
            if self.aln:
                self.infer_ancestral_sequences(infer_gtr=infer_gtr, **seq_kwargs)
                self.prune_short_branches()
        else:
            self.optimize_sequences_and_branch_length(infer_gtr=infer_gtr,
                                                      max_iter=1, prune_short=True, **seq_kwargs)
        avg_root_to_tip = np.mean([x.dist2root for x in self.tree.get_terminals()])

        # optionally reroot the tree either by oldest, best regression or with a specific leaf
        if n_iqd or root=='clock_filter':
            if "plot_rtt" in kwargs and kwargs["plot_rtt"]:
                plot_rtt=True
            else:
                plot_rtt=False
            reroot_mechanism = 'least-squares' if root=='clock_filter' else root
            if self.clock_filter(reroot=reroot_mechanism, n_iqd=n_iqd, plot=plot_rtt)==ttconf.ERROR:
                return ttconf.ERROR
        elif root is not None:
            if self.reroot(root=root)==ttconf.ERROR:
                return ttconf.ERROR

        if self.branch_length_mode=='input':
            if self.aln:
                self.infer_ancestral_sequences(**seq_kwargs)
        else:
            self.optimize_sequences_and_branch_length(max_iter=1, prune_short=False,
                                                      **seq_kwargs)

        # infer time tree and optionally resolve polytomies
        self.logger("###TreeTime.run: INITIAL ROUND",0)
        self.make_time_tree(**tt_kwargs)

        if self.aln:
            seq_LH = self.tree.sequence_marginal_LH if seq_kwargs['marginal_sequences'] else self.tree.sequence_joint_LH
        self.LH =[[seq_LH, self.tree.positional_joint_LH, 0]]

        if root is not None and max_iter:
            if self.reroot(root='least-squares' if root=='clock_filter' else root)==ttconf.ERROR:
                return ttconf.ERROR

        # iteratively reconstruct ancestral sequences and re-infer
        # time tree to ensure convergence.
        niter = 0
        ndiff = 0
        need_new_time_tree=False
        while niter < max_iter:
            self.logger("###TreeTime.run: ITERATION %d out of %d iterations"%(niter+1,max_iter),0)
            # add coalescent prior
            if Tc:
                if Tc=='skyline' and niter<max_iter-1:
                    tmpTc='const'
                else:
                    tmpTc=Tc
                self.add_coalescent_model(tmpTc, **kwargs)
                need_new_time_tree = True

            # estimate a relaxed molecular clock
            if relaxed_clock:
                print("relaxed_clock", relaxed_clock)
                self.relaxed_clock(**relaxed_clock)
                need_new_time_tree = True

            n_resolved=0
            if resolve_polytomies:
                # if polytomies are found, rerun the entire procedure
                n_resolved = self.resolve_polytomies()
                if n_resolved:
                    self.prepare_tree()
                    if self.branch_length_mode!='input': # otherwise reoptimize branch length while preserving branches without mutations
                        self.optimize_sequences_and_branch_length(prune_short=False,
                                                          max_iter=0, **seq_kwargs)

                    need_new_time_tree = True

            if need_new_time_tree:
                self.make_time_tree(**tt_kwargs)
                if self.aln:
                    ndiff = self.infer_ancestral_sequences('ml',**seq_kwargs)
            else: # no refinements, just iterate
                if self.aln:
                    ndiff = self.infer_ancestral_sequences('ml',**seq_kwargs)
                self.make_time_tree(**tt_kwargs)

            self.tree.coalescent_joint_LH = self.merger_model.total_LH() if Tc else 0.0

            if self.aln:
                seq_LH = self.tree.sequence_marginal_LH if seq_kwargs['marginal_sequences'] else self.tree.sequence_joint_LH
            self.LH.append([seq_LH, self.tree.positional_joint_LH, self.tree.coalescent_joint_LH])
            niter+=1

            if ndiff==0 and n_resolved==0 and Tc!='skyline':
                self.logger("###TreeTime.run: CONVERGED",0)
                break

        # if the rate is too be varied and the rate estimate has a valid confidence interval
        # rerun the estimation for variations of the rate
        if vary_rate:
            if type(vary_rate)==float:
                res = self.calc_rate_susceptibility(rate_std=vary_rate, params=tt_kwargs)
            elif self.clock_model['valid_confidence']:
                res = self.calc_rate_susceptibility(params=tt_kwargs)
            else:
                res = ttconf.ERROR

            if res==ttconf.ERROR:
                self.logger("TreeTime.run: rate variation failed and can't be used for confidence estimation", 1, warn=True)

        # if marginal reconstruction requested, make one more round with marginal=True
        # this will set marginal_pos_LH, which to be used as error bar estimations
        if time_marginal:
            self.logger("###TreeTime.run: FINAL ROUND - confidence estimation via marginal reconstruction", 0)
            tt_kwargs['time_marginal']=time_marginal
            self.make_time_tree(**tt_kwargs)

        # explicitly print out which branches are bad and whose dates don't correspond to the input dates
        bad_branches =[n for n in self.tree.get_terminals()
                       if n.bad_branch and n.raw_date_constraint]
        if bad_branches:
            self.logger("TreeTime: The following tips don't fit the clock model, "
                        "please remove them from the tree. Their dates have been reset:",0,warn=True)
            for n in bad_branches:
                self.logger("%s, input date: %s, apparent date: %1.2f"%(n.name, str(n.raw_date_constraint), n.numdate),0,warn=True)

        return ttconf.SUCCESS

Response: This method is used to run the TreeTime reconstruction on a given tree.


Instruction:
Given the following Python 3 function, write the documentation
def _set_branch_length_mode(self, branch_length_mode):
        '''
        if branch_length mode is not explicitly set, set according to
        empirical branch length distribution in input tree

        Parameters
        ----------

         branch_length_mode : str, 'input', 'joint', 'marginal'
            if the maximal branch length in the tree is longer than 0.05, this will
            default to 'input'. Otherwise set to 'joint'
        '''
        if branch_length_mode in ['joint', 'marginal', 'input']:
            self.branch_length_mode = branch_length_mode
        elif self.aln:
            bl_dis = [n.branch_length for n in self.tree.find_clades() if n.up]
            max_bl = np.max(bl_dis)
            if max_bl>0.1:
                bl_mode = 'input'
            else:
                bl_mode = 'joint'
            self.logger("TreeTime._set_branch_length_mode: maximum branch length is %1.3e, using branch length mode %s"%(max_bl, bl_mode),1)
            self.branch_length_mode = bl_mode
        else:
            self.branch_length_mode = 'input'

Response: Set the branch length mode according to the empirical branch length distribution in input tree.


Instruction:
Given the following Python 3 function, write the documentation
def clock_filter(self, reroot='least-squares', n_iqd=None, plot=False):
        '''
        Labels outlier branches that don't seem to follow a molecular clock
        and excludes them from subsequent molecular clock estimation and
        the timetree propagation.

        Parameters
        ----------
         reroot : str
            Method to find the best root in the tree (see :py:meth:`treetime.TreeTime.reroot` for options)

         n_iqd : int
            Number of iqd intervals. The outlier nodes are those which do not fall
            into :math:`IQD\cdot n_iqd` interval (:math:`IQD` is the interval between
            75\ :sup:`th` and 25\ :sup:`th` percentiles)

            If None, the default (3) assumed

         plot : bool
            If True, plot the results

        '''
        if n_iqd is None:
            n_iqd = ttconf.NIQD
        if type(reroot) is list and len(reroot)==1:
            reroot=str(reroot[0])

        terminals = self.tree.get_terminals()
        if reroot:
            if self.reroot(root='least-squares' if reroot=='best' else reroot, covariation=False)==ttconf.ERROR:
                return ttconf.ERROR
        else:
            self.get_clock_model(covariation=False)

        clock_rate = self.clock_model['slope']
        icpt = self.clock_model['intercept']
        res = {}
        for node in terminals:
            if hasattr(node, 'raw_date_constraint') and  (node.raw_date_constraint is not None):
                res[node] = node.dist2root - clock_rate*np.mean(node.raw_date_constraint) - icpt

        residuals = np.array(list(res.values()))
        iqd = np.percentile(residuals,75) - np.percentile(residuals,25)
        for node,r in res.items():
            if abs(r)>n_iqd*iqd and node.up.up is not None:
                self.logger('TreeTime.ClockFilter: marking %s as outlier, residual %f interquartile distances'%(node.name,r/iqd), 3, warn=True)
                node.bad_branch=True
            else:
                node.bad_branch=False

        # redo root estimation after outlier removal
        if reroot and self.reroot(root=reroot)==ttconf.ERROR:
                return ttconf.ERROR

        if plot:
            self.plot_root_to_tip()

        return ttconf.SUCCESS

Response: This method filters outlier branches that do not follow a molecular clock and excludes them from subsequent molecular clock estimation and the timetree propagation.


Instruction:
Create a Python 3 function for
plotting the root - to - tip regression of the current node.

Response:
def plot_root_to_tip(self, add_internal=False, label=True, ax=None):
        """
        Plot root-to-tip regression

        Parameters
        ----------
        add_internal : bool
           If true, plot inte`rnal node positions

        label : bool
           If true, label the plots

        ax : matplotlib axes
           If not None, use the provided matplotlib axes to plot the results
        """
        Treg = self.setup_TreeRegression()
        if self.clock_model and 'cov' in self.clock_model:
            cf = self.clock_model['valid_confidence']
        else:
            cf = False
        Treg.clock_plot(ax=ax, add_internal=add_internal, confidence=cf, n_sigma=2,
                        regression=self.clock_model)


Instruction:
Implement a Python 3 function for
finding best root and re-root the tree to the new root Parameters ---------- root : str Which method should be used to find the best root. Available methods are: :code:`best`, `least-squares` - minimize squared residual or likelihood of root-to-tip regression :code:`min_dev` - minimize variation of root-to-tip distance :code:`oldest` - reroot on the oldest node :code:`<node_name>` - reroot to the node with name :code:`<node_name>` :code:`[<node_name1>, <node_name2>, ...]` - reroot to the MRCA of these nodes force_positive : bool only consider positive rates when searching for the optimal root covariation : bool account for covariation in root-to-tip regression

Response:
def reroot(self, root='least-squares', force_positive=True, covariation=None):
        """
        Find best root and re-root the tree to the new root

        Parameters
        ----------

         root : str
            Which method should be used to find the best root. Available methods are:

            :code:`best`, `least-squares` - minimize squared residual or likelihood of root-to-tip regression

            :code:`min_dev` - minimize variation of root-to-tip distance

            :code:`oldest` - reroot on the oldest node

            :code:`<node_name>` - reroot to the node with name :code:`<node_name>`

            :code:`[<node_name1>, <node_name2>, ...]` - reroot to the MRCA of these nodes

          force_positive : bool
            only consider positive rates when searching for the optimal root

          covariation : bool
             account for covariation in root-to-tip regression
        """
        if type(root) is list and len(root)==1:
            root=str(root[0])

        if root=='best':
            root='least-squares'

        use_cov = self.use_covariation if covariation is None else covariation

        self.logger("TreeTime.reroot: with method or node: %s"%root,0)
        for n in self.tree.find_clades():
            n.branch_length=n.mutation_length

        if (type(root) is str) and \
           (root in rerooting_mechanisms or root in deprecated_rerooting_mechanisms):
            if root in deprecated_rerooting_mechanisms:
                if "ML" in root:
                    use_cov=True
                self.logger('TreeTime.reroot: rerooting mechanisms %s has been renamed to %s'
                             %(root, deprecated_rerooting_mechanisms[root]), 1, warn=True)
                root = deprecated_rerooting_mechanisms[root]

            self.logger("TreeTime.reroot: rerooting will %s covariance and shared ancestry."%("account for" if use_cov else "ignore"),0)
            new_root = self._find_best_root(covariation=use_cov,
                                            slope = 0.0 if root.startswith('min_dev') else None,
                                            force_positive=force_positive and (not root.startswith('min_dev')))
        else:
            if isinstance(root,Phylo.BaseTree.Clade):
                new_root = root
            elif isinstance(root, list):
                new_root = self.tree.common_ancestor(*root)
            elif root in self._leaves_lookup:
                new_root = self._leaves_lookup[root]
            elif root=='oldest':
                new_root = sorted([n for n in self.tree.get_terminals()
                                   if n.raw_date_constraint is not None],
                                   key=lambda x:np.mean(x.raw_date_constraint))[0]
            else:
                self.logger('TreeTime.reroot -- ERROR: unsupported rooting mechanisms or root not found',0,warn=True)
                return ttconf.ERROR

            #this forces a bifurcating root, as we want. Branch lengths will be reoptimized anyway.
            #(Without outgroup_branch_length, gives a trifurcating root, but this will mean
            #mutations may have to occur multiple times.)
            self.tree.root_with_outgroup(new_root, outgroup_branch_length=new_root.branch_length/2)
            self.get_clock_model(covariation=use_cov)

        if new_root == ttconf.ERROR:
            return ttconf.ERROR

        self.logger("TreeTime.reroot: Tree was re-rooted to node "
                    +('new_node' if new_root.name is None else new_root.name), 2)

        self.tree.root.branch_length = self.one_mutation
        self.tree.root.clock_length = self.one_mutation
        self.tree.root.raw_date_constraint = None
        if hasattr(new_root, 'time_before_present'):
            self.tree.root.time_before_present = new_root.time_before_present
        if hasattr(new_root, 'numdate'):
            self.tree.root.numdate = new_root.numdate
        # set root.gamma bc root doesn't have a branch_length_interpolator but gamma is needed
        if not hasattr(self.tree.root, 'gamma'):
            self.tree.root.gamma = 1.0
        for n in self.tree.find_clades():
            n.mutation_length = n.branch_length
            if not hasattr(n, 'clock_length'):
                n.clock_length = n.branch_length
        self.prepare_tree()

        self.get_clock_model(covariation=self.use_covariation)

        return ttconf.SUCCESS


Instruction:
Explain what the following Python 3 code does
def resolve_polytomies(self, merge_compressed=False):
        self.logger("TreeTime.resolve_polytomies: resolving multiple mergers...",1)
        poly_found=0

        for n in self.tree.find_clades():
            if len(n.clades) > 2:
                prior_n_clades = len(n.clades)
                self._poly(n, merge_compressed)
                poly_found+=prior_n_clades - len(n.clades)

        obsolete_nodes = [n for n in self.tree.find_clades() if len(n.clades)==1 and n.up is not None]
        for node in obsolete_nodes:
            self.logger('TreeTime.resolve_polytomies: remove obsolete node '+node.name,4)
            if node.up is not None:
                self.tree.collapse(node)

        if poly_found:
            self.logger('TreeTime.resolve_polytomies: introduces %d new nodes'%poly_found,3)
        else:
            self.logger('TreeTime.resolve_polytomies: No more polytomies to resolve',3)
        return poly_found

Response: Resolves the polytomies on the tree.


Instruction:
Here you have a function in Python 3, explain what it does
def _poly(self, clade, merge_compressed):

        """
        Function to resolve polytomies for a given parent node. If the
        number of the direct decendants is less than three (not a polytomy), does
        nothing. Otherwise, for each pair of nodes, assess the possible LH increase
        which could be gained by merging the two nodes. The increase in the LH is
        basically the tradeoff between the gain of the LH due to the changing the
        branch lenghts towards the optimal values and the decrease due to the
        introduction of the new branch with zero optimal length.
        """

        from .branch_len_interpolator import BranchLenInterpolator

        zero_branch_slope = self.gtr.mu*self.seq_len

        def _c_gain(t, n1, n2, parent):
            """
            cost gain if nodes n1, n2 are joined and their parent is placed at time t
            cost gain = (LH loss now) - (LH loss when placed at time t)
            """
            cg2 = n2.branch_length_interpolator(parent.time_before_present - n2.time_before_present) - n2.branch_length_interpolator(t - n2.time_before_present)
            cg1 = n1.branch_length_interpolator(parent.time_before_present - n1.time_before_present) - n1.branch_length_interpolator(t - n1.time_before_present)
            cg_new = - zero_branch_slope * (parent.time_before_present - t) # loss in LH due to the new branch
            return -(cg2+cg1+cg_new)

        def cost_gain(n1, n2, parent):
            """
            cost gained if the two nodes would have been connected.
            """
            try:
                cg = sciopt.minimize_scalar(_c_gain,
                    bounds=[max(n1.time_before_present,n2.time_before_present), parent.time_before_present],
                    method='Bounded',args=(n1,n2, parent))
                return cg['x'], - cg['fun']
            except:
                self.logger("TreeTime._poly.cost_gain: optimization of gain failed", 3, warn=True)
                return parent.time_before_present, 0.0

        def merge_nodes(source_arr, isall=False):
            mergers = np.array([[cost_gain(n1,n2, clade) if i1<i2 else (0.0,-1.0)
                                    for i1,n1 in enumerate(source_arr)]
                                for i2, n2 in enumerate(source_arr)])
            LH = 0
            while len(source_arr) > 1 + int(isall):
                # max possible gains of the cost when connecting the nodes:
                # this is only a rough approximation because it assumes the new node positions
                # to be optimal
                new_positions = mergers[:,:,0]
                cost_gains = mergers[:,:,1]
                # set zero to large negative value and find optimal pair
                np.fill_diagonal(cost_gains, -1e11)
                idxs = np.unravel_index(cost_gains.argmax(),cost_gains.shape)
                if (idxs[0] == idxs[1]) or cost_gains.max()<0:
                    self.logger("TreeTime._poly.merge_nodes: node is not fully resolved "+clade.name,4)
                    return LH

                n1, n2 = source_arr[idxs[0]], source_arr[idxs[1]]
                LH += cost_gains[idxs]

                new_node = Phylo.BaseTree.Clade()

                # fix positions and branch lengths
                new_node.time_before_present = new_positions[idxs]
                new_node.branch_length = clade.time_before_present - new_node.time_before_present
                new_node.clades = [n1,n2]
                n1.branch_length = new_node.time_before_present - n1.time_before_present
                n2.branch_length = new_node.time_before_present - n2.time_before_present

                # set parameters for the new node
                new_node.up = clade
                n1.up = new_node
                n2.up = new_node
                if hasattr(clade, "cseq"):
                    new_node.cseq = clade.cseq
                    self._store_compressed_sequence_to_node(new_node)

                new_node.mutations = []
                new_node.mutation_length = 0.0
                new_node.branch_length_interpolator = BranchLenInterpolator(new_node, self.gtr, one_mutation=self.one_mutation,
                                                                            branch_length_mode = self.branch_length_mode)
                clade.clades.remove(n1)
                clade.clades.remove(n2)
                clade.clades.append(new_node)
                self.logger('TreeTime._poly.merge_nodes: creating new node as child of '+clade.name,3)
                self.logger("TreeTime._poly.merge_nodes: Delta-LH = " + str(cost_gains[idxs].round(3)), 3)

                # and modify source_arr array for the next loop
                if len(source_arr)>2: # if more than 3 nodes in polytomy, replace row/column
                    for ii in np.sort(idxs)[::-1]:
                        tmp_ind = np.arange(mergers.shape[0])!=ii
                        mergers = mergers[tmp_ind].swapaxes(0,1)
                        mergers = mergers[tmp_ind].swapaxes(0,1)

                    source_arr.remove(n1)
                    source_arr.remove(n2)
                    new_gains = np.array([[cost_gain(n1,new_node, clade) for n1 in source_arr]])
                    mergers = np.vstack((mergers, new_gains)).swapaxes(0,1)

                    source_arr.append(new_node)
                    new_gains = np.array([[cost_gain(n1,new_node, clade) for n1 in source_arr]])
                    mergers = np.vstack((mergers, new_gains)).swapaxes(0,1)
                else: # otherwise just recalculate matrix
                    source_arr.remove(n1)
                    source_arr.remove(n2)
                    source_arr.append(new_node)
                    mergers = np.array([[cost_gain(n1,n2, clade) for n1 in source_arr]
                                       for n2 in source_arr])

            return LH

        stretched = [c for c  in clade.clades if c.mutation_length < c.clock_length]
        compressed = [c for c in clade.clades if c not in stretched]

        if len(stretched)==1 and merge_compressed is False:
            return 0.0

        LH = merge_nodes(stretched, isall=len(stretched)==len(clade.clades))
        if merge_compressed and len(compressed)>1:
            LH += merge_nodes(compressed, isall=len(compressed)==len(clade.clades))

        return LH

Response: Function to resolve the polytomies for a given parent node.


Instruction:
Can you implement a function in Python 3 that
prints the total likelihood of the tree given the constrained leaves and the constrained leaves.

Response:
def print_lh(self, joint=True):
        """
        Print the total likelihood of the tree given the constrained leaves

        Parameters
        ----------

         joint : bool
            If true, print joint LH, else print marginal LH

        """
        try:
            u_lh = self.tree.unconstrained_sequence_LH
            if joint:
                s_lh = self.tree.sequence_joint_LH
                t_lh = self.tree.positional_joint_LH
                c_lh = self.tree.coalescent_joint_LH
            else:
                s_lh = self.tree.sequence_marginal_LH
                t_lh = self.tree.positional_marginal_LH
                c_lh = 0

            print ("###  Tree Log-Likelihood  ###\n"
                " Sequence log-LH without constraints: \t%1.3f\n"
                " Sequence log-LH with constraints:    \t%1.3f\n"
                " TreeTime sequence log-LH:            \t%1.3f\n"
                " Coalescent log-LH:                   \t%1.3f\n"
               "#########################"%(u_lh, s_lh,t_lh, c_lh))
        except:
            print("ERROR. Did you run the corresponding inference (joint/marginal)?")


Instruction:
Can you write a function in Python 3 where it
adds a coalescent model to the tree and optionally optimze the coalescent model with the specified time scale.

Response:
def add_coalescent_model(self, Tc, **kwargs):
        """Add a coalescent model to the tree and optionally optimze

        Parameters
        ----------
        Tc : float,str
            If this is a float, it will be interpreted as the inverse merger
            rate in molecular clock units, if its is a
        """
        from .merger_models import Coalescent
        self.logger('TreeTime.run: adding coalescent prior with Tc='+str(Tc),1)
        self.merger_model = Coalescent(self.tree,
                                       date2dist=self.date2dist, logger=self.logger)

        if Tc=='skyline': # restrict skyline model optimization to last iteration
            self.merger_model.optimize_skyline(**kwargs)
            self.logger("optimized a skyline ", 2)
        else:
            if Tc in ['opt', 'const']:
                self.merger_model.optimize_Tc()
                self.logger("optimized Tc to %f"%self.merger_model.Tc.y[0], 2)
            else:
                try:
                    self.merger_model.set_Tc(Tc)
                except:
                    self.logger("setting of coalescent time scale failed", 1, warn=True)

        self.merger_model.attach_to_tree()


Instruction:
Create a Python 3 function for
allowing the mutation rate to vary on the tree (relaxed molecular clock). Changes of the mutation rates from one branch to another are penalized. In addition, deviation of the mutation rate from the mean rate is penalized. Parameters ---------- slack : float Maximum change in substitution rate between parent and child nodes coupling : float Maximum difference in substitution rates in sibling nodes

Response:
def relaxed_clock(self, slack=None, coupling=None, **kwargs):
        """
        Allow the mutation rate to vary on the tree (relaxed molecular clock).
        Changes of the mutation rates from one branch to another are penalized.
        In addition, deviation of the mutation rate from the mean rate is
        penalized.

        Parameters
        ----------
         slack : float
            Maximum change in substitution rate between parent and child nodes

         coupling : float
            Maximum difference in substitution rates in sibling nodes

        """
        if slack is None: slack=ttconf.MU_ALPHA
        if coupling is None: coupling=ttconf.MU_BETA
        self.logger("TreeTime.relaxed_clock: slack=%f, coupling=%f"%(slack, coupling),2)

        c=1.0/self.one_mutation
        for node in self.tree.find_clades(order='postorder'):
            opt_len = node.mutation_length
            act_len = node.clock_length if hasattr(node, 'clock_length') else node.branch_length

            # opt_len \approx 1.0*len(node.mutations)/node.profile.shape[0] but calculated via gtr model
            # stiffness is the expectation of the inverse variance of branch length (one_mutation/opt_len)
            # contact term: stiffness*(g*bl - bl_opt)^2 + slack(g-1)^2 =
            #               (slack+bl^2) g^2 - 2 (bl*bl_opt+1) g + C= k2 g^2 + k1 g + C
            node._k2 = slack + c*act_len**2/(opt_len+self.one_mutation)
            node._k1 = -2*(c*act_len*opt_len/(opt_len+self.one_mutation) + slack)
            # coupling term: \sum_c coupling*(g-g_c)^2 + Cost_c(g_c|g)
            # given g, g_c needs to be optimal-> 2*coupling*(g-g_c) = 2*child.k2 g_c  + child.k1
            # hence g_c = (coupling*g - 0.5*child.k1)/(coupling+child.k2)
            # substituting yields
            for child in node.clades:
                denom = coupling+child._k2
                node._k2 += coupling*(1.0-coupling/denom)**2 + child._k2*coupling**2/denom**2
                node._k1 += (coupling*(1.0-coupling/denom)*child._k1/denom \
                            - coupling*child._k1*child._k2/denom**2 \
                            + coupling*child._k1/denom)

        for node in self.tree.find_clades(order='preorder'):
            if node.up is None:
                node.gamma = max(0.1, -0.5*node._k1/node._k2)
            else:
                if node.up.up is None:
                    g_up = node.up.gamma
                else:
                    g_up = node.up.branch_length_interpolator.gamma
                node.branch_length_interpolator.gamma = max(0.1,(coupling*g_up - 0.5*node._k1)/(coupling+node._k2))


Instruction:
Can you generate the documentation for the following Python 3 function
def _find_best_root(self, covariation=True, force_positive=True, slope=0, **kwarks):
        '''
        Determine the node that, when the tree is rooted on this node, results
        in the best regression of temporal constraints and root to tip distances.

        Parameters
        ----------

         infer_gtr : bool
            If True, infer new GTR model after re-root

         covariation : bool
            account for covariation structure when rerooting the tree

         force_positive : bool
            only accept positive evolutionary rate estimates when rerooting the tree

        '''
        for n in self.tree.find_clades():
            n.branch_length=n.mutation_length
        self.logger("TreeTime._find_best_root: searching for the best root position...",2)
        Treg = self.setup_TreeRegression(covariation=covariation)
        return Treg.optimal_reroot(force_positive=force_positive, slope=slope)['node']

Response: Find the best root node in the tree.


Instruction:
How would you code a function in Python 3 to
function that attempts to load a tree and build it from the alignment

Response:
def assure_tree(params, tmp_dir='treetime_tmp'):
    """
    Function that attempts to load a tree and build it from the alignment
    if no tree is provided.
    """
    if params.tree is None:
        params.tree = os.path.basename(params.aln)+'.nwk'
        print("No tree given: inferring tree")
        utils.tree_inference(params.aln, params.tree, tmp_dir = tmp_dir)

    if os.path.isdir(tmp_dir):
        shutil.rmtree(tmp_dir)

    try:
        tt = TreeAnc(params.tree)
    except:
        print("Tree loading/building failed.")
        return 1
    return 0


Instruction:
Create a Python 3 function for
creating a GTR model from the input arguments.

Response:
def create_gtr(params):
    """
    parse the arguments referring to the GTR model and return a GTR structure
    """
    model = params.gtr
    gtr_params = params.gtr_params
    if model == 'infer':
        gtr = GTR.standard('jc', alphabet='aa' if params.aa else 'nuc')
    else:
        try:
            kwargs = {}
            if gtr_params is not None:
                for param in gtr_params:
                    keyval = param.split('=')
                    if len(keyval)!=2: continue
                    if keyval[0] in ['pis', 'pi', 'Pi', 'Pis']:
                        keyval[0] = 'pi'
                        keyval[1] = list(map(float, keyval[1].split(',')))
                    elif keyval[0] not in ['alphabet']:
                        keyval[1] = float(keyval[1])
                    kwargs[keyval[0]] = keyval[1]
            else:
                print ("GTR params are not specified. Creating GTR model with default parameters")

            gtr = GTR.standard(model, **kwargs)
            infer_gtr = False
        except:
            print ("Could not create GTR model from input arguments. Using default (Jukes-Cantor 1969)")
            gtr = GTR.standard('jc', alphabet='aa' if params.aa else 'nuc')
            infer_gtr = False
    return gtr


Instruction:
Make a summary of the following Python 3 code
def read_if_vcf(params):
    ref = None
    aln = params.aln
    fixed_pi = None
    if hasattr(params, 'aln') and params.aln is not None:
        if any([params.aln.lower().endswith(x) for x in ['.vcf', '.vcf.gz']]):
            if not params.vcf_reference:
                print("ERROR: a reference Fasta is required with VCF-format alignments")
                return -1
            compress_seq = read_vcf(params.aln, params.vcf_reference)
            sequences = compress_seq['sequences']
            ref = compress_seq['reference']
            aln = sequences

            if not hasattr(params, 'gtr') or params.gtr=="infer": #if not specified, set it:
                alpha = alphabets['aa'] if params.aa else alphabets['nuc']
                fixed_pi = [ref.count(base)/len(ref) for base in alpha]
                if fixed_pi[-1] == 0:
                    fixed_pi[-1] = 0.05
                    fixed_pi = [v-0.01 for v in fixed_pi]

    return aln, ref, fixed_pi

Response: Checks if input is VCF and reads in appropriately if it is


Instruction:
Make a summary of the following Python 3 code
def scan_homoplasies(params):
    if assure_tree(params, tmp_dir='homoplasy_tmp'):
        return 1

    gtr = create_gtr(params)

    ###########################################################################
    ### READ IN VCF
    ###########################################################################
    #sets ref and fixed_pi to None if not VCF
    aln, ref, fixed_pi = read_if_vcf(params)
    is_vcf = True if ref is not None else False

    ###########################################################################
    ### ANCESTRAL RECONSTRUCTION
    ###########################################################################
    treeanc = TreeAnc(params.tree, aln=aln, ref=ref, gtr=gtr, verbose=1,
                      fill_overhangs=True)
    if treeanc.aln is None: # if alignment didn't load, exit
        return 1

    if is_vcf:
        L = len(ref) + params.const
    else:
        L = treeanc.aln.get_alignment_length() + params.const

    N_seq = len(treeanc.aln)
    N_tree = treeanc.tree.count_terminals()
    if params.rescale!=1.0:
        for n in treeanc.tree.find_clades():
            n.branch_length *= params.rescale
            n.mutation_length = n.branch_length

    print("read alignment from file %s with %d sequences of length %d"%(params.aln,N_seq,L))
    print("read tree from file %s with %d leaves"%(params.tree,N_tree))
    print("\ninferring ancestral sequences...")

    ndiff = treeanc.infer_ancestral_sequences('ml', infer_gtr=params.gtr=='infer',
                                      marginal=False, fixed_pi=fixed_pi)
    print("...done.")
    if ndiff==ttconf.ERROR: # if reconstruction failed, exit
        print("Something went wrong during ancestral reconstruction, please check your input files.", file=sys.stderr)
        return 1
    else:
        print("...done.")

    if is_vcf:
        treeanc.recover_var_ambigs()

    ###########################################################################
    ### analysis of reconstruction
    ###########################################################################
    from collections import defaultdict
    from scipy.stats import poisson
    offset = 0 if params.zero_based else 1

    if params.drms:
        DRM_info = read_in_DRMs(params.drms, offset)
        drms = DRM_info['DRMs']

    # construct dictionaries gathering mutations and positions
    mutations = defaultdict(list)
    positions = defaultdict(list)
    terminal_mutations = defaultdict(list)
    for n in treeanc.tree.find_clades():
        if n.up is None:
            continue

        if len(n.mutations):
            for (a,pos, d) in n.mutations:
                if '-' not in [a,d] and 'N' not in [a,d]:
                    mutations[(a,pos+offset,d)].append(n)
                    positions[pos+offset].append(n)
            if n.is_terminal():
                for (a,pos, d) in n.mutations:
                    if '-' not in [a,d] and 'N' not in [a,d]:
                        terminal_mutations[(a,pos+offset,d)].append(n)

    # gather homoplasic mutations by strain
    mutation_by_strain = defaultdict(list)
    for n in treeanc.tree.get_terminals():
        for a,pos,d in n.mutations:
            if pos+offset in positions and len(positions[pos+offset])>1:
                if '-' not in [a,d] and 'N' not in [a,d]:
                    mutation_by_strain[n.name].append([(a,pos+offset,d), len(positions[pos])])

    # total_branch_length is the expected number of substitutions
    # corrected_branch_length is the expected number of observable substitutions
    # (probability of an odd number of substitutions at a particular site)
    total_branch_length = treeanc.tree.total_branch_length()
    corrected_branch_length = np.sum([np.exp(-x.branch_length)*np.sinh(x.branch_length)
                                      for x in treeanc.tree.find_clades()])
    corrected_terminal_branch_length = np.sum([np.exp(-x.branch_length)*np.sinh(x.branch_length)
                                      for x in treeanc.tree.get_terminals()])
    expected_mutations = L*corrected_branch_length
    expected_terminal_mutations = L*corrected_terminal_branch_length

    # make histograms and sum mutations in different categories
    multiplicities = np.bincount([len(x) for x in mutations.values()])
    total_mutations = np.sum([len(x) for x in mutations.values()])

    multiplicities_terminal = np.bincount([len(x) for x in terminal_mutations.values()])
    terminal_mutation_count = np.sum([len(x) for x in terminal_mutations.values()])

    multiplicities_positions = np.bincount([len(x) for x in positions.values()])
    multiplicities_positions[0] = L - np.sum(multiplicities_positions)

    ###########################################################################
    ### Output the distribution of times particular mutations are observed
    ###########################################################################
    print("\nThe TOTAL tree length is %1.3e and %d mutations were observed."
          %(total_branch_length,total_mutations))
    print("Of these %d mutations,"%total_mutations
            +"".join(['\n\t - %d occur %d times'%(n,mi)
                      for mi,n in enumerate(multiplicities) if n]))
    # additional optional output this for terminal mutations only
    if params.detailed:
        print("\nThe TERMINAL branch length is %1.3e and %d mutations were observed."
              %(corrected_terminal_branch_length,terminal_mutation_count))
        print("Of these %d mutations,"%terminal_mutation_count
                +"".join(['\n\t - %d occur %d times'%(n,mi)
                          for mi,n in enumerate(multiplicities_terminal) if n]))

    ###########################################################################
    ### Output the distribution of times mutations at particular positions are observed
    ###########################################################################
    print("\nOf the %d positions in the genome,"%L
            +"".join(['\n\t - %d were hit %d times (expected %1.2f)'%(n,mi,L*poisson.pmf(mi,1.0*total_mutations/L))
                      for mi,n in enumerate(multiplicities_positions) if n]))

    # compare that distribution to a Poisson distribution with the same mean
    p = poisson.pmf(np.arange(10*multiplicities_positions.max()),1.0*total_mutations/L)
    print("\nlog-likelihood difference to Poisson distribution with same mean: %1.3e"%(
            - L*np.sum(p*np.log(p+1e-100))
            + np.sum(multiplicities_positions*np.log(p[:len(multiplicities_positions)]+1e-100))))

    ###########################################################################
    ### Output the mutations that are observed most often
    ###########################################################################
    if params.drms:
        print("\n\nThe ten most homoplasic mutations are:\n\tmut\tmultiplicity\tDRM details (gene drug AAmut)")
        mutations_sorted = sorted(mutations.items(), key=lambda x:len(x[1])-0.1*x[0][1]/L, reverse=True)
        for mut, val in mutations_sorted[:params.n]:
            if len(val)>1:
                print("\t%s%d%s\t%d\t%s"%(mut[0], mut[1], mut[2], len(val),
                    " ".join([drms[mut[1]]['gene'], drms[mut[1]]['drug'], drms[mut[1]]['alt_base'][mut[2]]]) if mut[1] in drms else ""))
            else:
                break
    else:
        print("\n\nThe ten most homoplasic mutations are:\n\tmut\tmultiplicity")
        mutations_sorted = sorted(mutations.items(), key=lambda x:len(x[1])-0.1*x[0][1]/L, reverse=True)
        for mut, val in mutations_sorted[:params.n]:
            if len(val)>1:
                print("\t%s%d%s\t%d"%(mut[0], mut[1], mut[2], len(val)))
            else:
                break

    # optional output specifically for mutations on terminal branches
    if params.detailed:
        if params.drms:
            print("\n\nThe ten most homoplasic mutation on terminal branches are:\n\tmut\tmultiplicity\tDRM details (gene drug AAmut)")
            terminal_mutations_sorted = sorted(terminal_mutations.items(), key=lambda x:len(x[1])-0.1*x[0][1]/L, reverse=True)
            for mut, val in terminal_mutations_sorted[:params.n]:
                if len(val)>1:
                    print("\t%s%d%s\t%d\t%s"%(mut[0], mut[1], mut[2], len(val),
                        " ".join([drms[mut[1]]['gene'], drms[mut[1]]['drug'], drms[mut[1]]['alt_base'][mut[2]]]) if mut[1] in drms else ""))
                else:
                    break
        else:
            print("\n\nThe ten most homoplasic mutation on terminal branches are:\n\tmut\tmultiplicity")
            terminal_mutations_sorted = sorted(terminal_mutations.items(), key=lambda x:len(x[1])-0.1*x[0][1]/L, reverse=True)
            for mut, val in terminal_mutations_sorted[:params.n]:
                if len(val)>1:
                    print("\t%s%d%s\t%d"%(mut[0], mut[1], mut[2], len(val)))
                else:
                    break

    ###########################################################################
    ### Output strains that have many homoplasic mutations
    ###########################################################################
    # TODO: add statistical criterion
    if params.detailed:
        if params.drms:
            print("\n\nTaxons that carry positions that mutated elsewhere in the tree:\n\ttaxon name\t#of homoplasic mutations\t# DRM")
            mutation_by_strain_sorted = sorted(mutation_by_strain.items(), key=lambda x:len(x[1]), reverse=True)
            for name, val in mutation_by_strain_sorted[:params.n]:
                if len(val):
                    print("\t%s\t%d\t%d"%(name, len(val),
                        len([mut for mut,l in val if mut[1] in drms])))
        else:
            print("\n\nTaxons that carry positions that mutated elsewhere in the tree:\n\ttaxon name\t#of homoplasic mutations")
            mutation_by_strain_sorted = sorted(mutation_by_strain.items(), key=lambda x:len(x[1]), reverse=True)
            for name, val in mutation_by_strain_sorted[:params.n]:
                if len(val):
                    print("\t%s\t%d"%(name, len(val)))

    return 0

Response: function implementing treetime homoplasies


Instruction:
Can you create a Python 3 function that
reconstructs the ancestral tree

Response:
def ancestral_reconstruction(params):
    """
    implementing treetime ancestral
    """

    # set up
    if assure_tree(params, tmp_dir='ancestral_tmp'):
        return 1

    outdir = get_outdir(params, '_ancestral')
    basename = get_basename(params, outdir)

    gtr = create_gtr(params)

    ###########################################################################
    ### READ IN VCF
    ###########################################################################
    #sets ref and fixed_pi to None if not VCF
    aln, ref, fixed_pi = read_if_vcf(params)
    is_vcf = True if ref is not None else False

    treeanc = TreeAnc(params.tree, aln=aln, ref=ref, gtr=gtr, verbose=1,
                      fill_overhangs=not params.keep_overhangs)
    ndiff =treeanc.infer_ancestral_sequences('ml', infer_gtr=params.gtr=='infer',
                                             marginal=params.marginal, fixed_pi=fixed_pi)
    if ndiff==ttconf.ERROR: # if reconstruction failed, exit
        return 1

    ###########################################################################
    ### OUTPUT and saving of results
    ###########################################################################
    if params.gtr=="infer":
        print('\nInferred GTR model:')
        print(treeanc.gtr)

    export_sequences_and_tree(treeanc, basename, is_vcf, params.zero_based,
                              report_ambiguous=params.report_ambiguous)

    return 0


Instruction:
Can you generate a brief explanation for the following Python 3 code
def mugration(params):

    ###########################################################################
    ### Parse states
    ###########################################################################
    if os.path.isfile(params.states):
        states = pd.read_csv(params.states, sep='\t' if params.states[-3:]=='tsv' else ',',
                             skipinitialspace=True)
    else:
        print("file with states does not exist")
        return 1

    outdir = get_outdir(params, '_mugration')

    taxon_name = 'name' if 'name' in states.columns else states.columns[0]
    if params.attribute:
        if params.attribute in states.columns:
            attr = params.attribute
        else:
            print("The specified attribute was not found in the metadata file "+params.states, file=sys.stderr)
            print("Available columns are: "+", ".join(states.columns), file=sys.stderr)
            return 1
    else:
        attr = states.columns[1]
        print("Attribute for mugration inference was not specified. Using "+attr, file=sys.stderr)

    leaf_to_attr = {x[taxon_name]:x[attr] for xi, x in states.iterrows()
                    if x[attr]!=params.missing_data}
    unique_states = sorted(set(leaf_to_attr.values()))
    nc = len(unique_states)
    if nc>180:
        print("mugration: can't have more than 180 states!", file=sys.stderr)
        return 1
    elif nc<2:
        print("mugration: only one or zero states found -- this doesn't make any sense", file=sys.stderr)
        return 1

    ###########################################################################
    ### make a single character alphabet that maps to discrete states
    ###########################################################################
    alphabet = [chr(65+i) for i,state in enumerate(unique_states)]
    missing_char = chr(65+nc)
    letter_to_state = {a:unique_states[i] for i,a in enumerate(alphabet)}
    letter_to_state[missing_char]=params.missing_data
    reverse_alphabet = {v:k for k,v in letter_to_state.items()}

    ###########################################################################
    ### construct gtr model
    ###########################################################################
    if params.weights:
        params.infer_gtr = True
        tmp_weights = pd.read_csv(params.weights, sep='\t' if params.states[-3:]=='tsv' else ',',
                             skipinitialspace=True)
        weights = {row[0]:row[1] for ri,row in tmp_weights.iterrows()}
        mean_weight = np.mean(list(weights.values()))
        weights = np.array([weights[c] if c in weights else mean_weight for c in unique_states], dtype=float)
        weights/=weights.sum()
    else:
        weights = np.ones(nc, dtype=float)/nc

    # set up dummy matrix
    W = np.ones((nc,nc), dtype=float)

    mugration_GTR = GTR.custom(pi = weights, W=W, alphabet = np.array(alphabet))
    mugration_GTR.profile_map[missing_char] = np.ones(nc)
    mugration_GTR.ambiguous=missing_char

    ###########################################################################
    ### set up treeanc
    ###########################################################################
    treeanc = TreeAnc(params.tree, gtr=mugration_GTR, verbose=params.verbose,
                      convert_upper=False, one_mutation=0.001)
    pseudo_seqs = [SeqRecord(id=n.name,name=n.name,
                   seq=Seq(reverse_alphabet[leaf_to_attr[n.name]]
                           if n.name in leaf_to_attr else missing_char))
                   for n in treeanc.tree.get_terminals()]
    treeanc.aln = MultipleSeqAlignment(pseudo_seqs)

    ndiff = treeanc.infer_ancestral_sequences(method='ml', infer_gtr=True,
            store_compressed=False, pc=params.pc, marginal=True, normalized_rate=False,
            fixed_pi=weights if params.weights else None)
    if ndiff==ttconf.ERROR: # if reconstruction failed, exit
        return 1

    ###########################################################################
    ### output
    ###########################################################################
    print("\nCompleted mugration model inference of attribute '%s' for"%attr,params.tree)

    basename = get_basename(params, outdir)
    gtr_name = basename + 'GTR.txt'
    with open(gtr_name, 'w') as ofile:
        ofile.write('Character to attribute mapping:\n')
        for state in unique_states:
            ofile.write('  %s: %s\n'%(reverse_alphabet[state], state))
        ofile.write('\n\n'+str(treeanc.gtr)+'\n')
        print("\nSaved inferred mugration model as:", gtr_name)

    terminal_count = 0
    for n in treeanc.tree.find_clades():
        if n.up is None:
            continue
        n.confidence=None
        # due to a bug in older versions of biopython that truncated filenames in nexus export
        # we truncate them by hand and make them unique.
        if n.is_terminal() and len(n.name)>40 and bioversion<"1.69":
            n.name = n.name[:35]+'_%03d'%terminal_count
            terminal_count+=1
        n.comment= '&%s="'%attr + letter_to_state[n.sequence[0]] +'"'

    if params.confidence:
        conf_name = basename+'confidence.csv'
        with open(conf_name, 'w') as ofile:
            ofile.write('#name, '+', '.join(unique_states)+'\n')
            for n in treeanc.tree.find_clades():
                ofile.write(n.name + ', '+', '.join([str(x) for x in n.marginal_profile[0]])+'\n')
        print("Saved table with ancestral state confidences as:", conf_name)

    # write tree to file
    outtree_name = basename+'annotated_tree.nexus'
    Phylo.write(treeanc.tree, outtree_name, 'nexus')
    print("Saved annotated tree as:",outtree_name)

    return 0

Response: Parse the states file and return the treetime mugration sequence.


Instruction:
Can you generate the documentation for the following Python 3 function
def estimate_clock_model(params):

    if assure_tree(params, tmp_dir='clock_model_tmp'):
        return 1
    dates = utils.parse_dates(params.dates)
    if len(dates)==0:
        return 1

    outdir = get_outdir(params, '_clock')

    ###########################################################################
    ### READ IN VCF
    ###########################################################################
    #sets ref and fixed_pi to None if not VCF
    aln, ref, fixed_pi = read_if_vcf(params)
    is_vcf = True if ref is not None else False

    ###########################################################################
    ### ESTIMATE ROOT (if requested) AND DETERMINE TEMPORAL SIGNAL
    ###########################################################################
    if params.aln is None and params.sequence_length is None:
        print("one of arguments '--aln' and '--sequence-length' is required.", file=sys.stderr)
        return 1

    basename = get_basename(params, outdir)
    myTree = TreeTime(dates=dates, tree=params.tree, aln=aln, gtr='JC69',
                      verbose=params.verbose, seq_len=params.sequence_length,
                      ref=ref)
    myTree.tip_slack=params.tip_slack
    if myTree.tree is None:
        print("ERROR: tree loading failed. exiting...")
        return 1

    if params.clock_filter:
        n_bad = [n.name for n in myTree.tree.get_terminals() if n.bad_branch]
        myTree.clock_filter(n_iqd=params.clock_filter, reroot=params.reroot or 'least-squares')
        n_bad_after = [n.name for n in myTree.tree.get_terminals() if n.bad_branch]
        if len(n_bad_after)>len(n_bad):
            print("The following leaves don't follow a loose clock and "
                  "will be ignored in rate estimation:\n\t"
                  +"\n\t".join(set(n_bad_after).difference(n_bad)))

    if not params.keep_root:
        # reroot to optimal root, this assigns clock_model to myTree
        if params.covariation: # this requires branch length estimates
            myTree.run(root="least-squares", max_iter=0,
                       use_covariation=params.covariation)

        res = myTree.reroot(params.reroot,
                      force_positive=not params.allow_negative_rate)
        myTree.get_clock_model(covariation=params.covariation)

        if res==ttconf.ERROR:
            print("ERROR: unknown root or rooting mechanism!\n"
                  "\tvalid choices are 'least-squares', 'ML', and 'ML-rough'")
            return 1
    else:
        myTree.get_clock_model(covariation=params.covariation)

    d2d = utils.DateConversion.from_regression(myTree.clock_model)
    print('\n',d2d)
    print('The R^2 value indicates the fraction of variation in'
          '\nroot-to-tip distance explained by the sampling times.'
          '\nHigher values corresponds more clock-like behavior (max 1.0).')

    print('\nThe rate is the slope of the best fit of the date to'
          '\nthe root-to-tip distance and provides an estimate of'
          '\nthe substitution rate. The rate needs to be positive!'
          '\nNegative rates suggest an inappropriate root.\n')

    print('\nThe estimated rate and tree correspond to a root date:')
    if params.covariation:
        reg = myTree.clock_model
        dp = np.array([reg['intercept']/reg['slope']**2,-1./reg['slope']])
        droot = np.sqrt(reg['cov'][:2,:2].dot(dp).dot(dp))
        print('\n--- root-date:\t %3.2f +/- %1.2f (one std-dev)\n\n'%(-d2d.intercept/d2d.clock_rate, droot))
    else:
        print('\n--- root-date:\t %3.2f\n\n'%(-d2d.intercept/d2d.clock_rate))

    if not params.keep_root:
        # write rerooted tree to file
        outtree_name = basename+'rerooted.newick'
        Phylo.write(myTree.tree, outtree_name, 'newick')
        print("--- re-rooted tree written to \n\t%s\n"%outtree_name)

    table_fname = basename+'rtt.csv'
    with open(table_fname, 'w') as ofile:
        ofile.write("#name, date, root-to-tip distance\n")
        ofile.write("#Dates of nodes that didn't have a specified date are inferred from the root-to-tip regression.\n")
        for n in myTree.tree.get_terminals():
            if hasattr(n, "raw_date_constraint") and (n.raw_date_constraint is not None):
                if np.isscalar(n.raw_date_constraint):
                    tmp_str = str(n.raw_date_constraint)
                elif len(n.raw_date_constraint):
                    tmp_str = str(n.raw_date_constraint[0])+'-'+str(n.raw_date_constraint[1])
                else:
                    tmp_str = ''
                ofile.write("%s, %s, %f\n"%(n.name, tmp_str, n.dist2root))
            else:
                ofile.write("%s, %f, %f\n"%(n.name, d2d.numdate_from_dist2root(n.dist2root), n.dist2root))
        for n in myTree.tree.get_nonterminals(order='preorder'):
            ofile.write("%s, %f, %f\n"%(n.name, d2d.numdate_from_dist2root(n.dist2root), n.dist2root))
        print("--- wrote dates and root-to-tip distances to \n\t%s\n"%table_fname)

    ###########################################################################
    ### PLOT AND SAVE RESULT
    ###########################################################################
    plot_rtt(myTree, outdir+params.plot_rtt)
    return 0

Response: estimate the clock model for a single tree time


Instruction:
How would you code a function in Python 3 to
create delta function distribution.

Response:
def delta_function(cls, x_pos, weight=1., min_width=MIN_INTEGRATION_PEAK):
        """
        Create delta function distribution.
        """

        distribution = cls(x_pos,0.,is_log=True, min_width=min_width)
        distribution.weight  = weight
        return distribution


Instruction:
Make a summary of the following Python 3 code
def multiply(dists):
        '''
        multiplies a list of Distribution objects
        '''
        if  not all([isinstance(k, Distribution) for k in dists]):
            raise NotImplementedError("Can only multiply Distribution objects")

        n_delta = np.sum([k.is_delta for k in dists])
        min_width = np.max([k.min_width for k in dists])
        if n_delta>1:
            raise ArithmeticError("Cannot multiply more than one delta functions!")
        elif n_delta==1:
            delta_dist_ii = np.where([k.is_delta for k in dists])[0][0]
            delta_dist = dists[delta_dist_ii]
            new_xpos = delta_dist.peak_pos
            new_weight  = np.prod([k.prob(new_xpos) for k in dists if k!=delta_dist_ii]) * delta_dist.weight
            res = Distribution.delta_function(new_xpos, weight = new_weight,min_width=min_width)
        else:
            new_xmin = np.max([k.xmin for k in dists])
            new_xmax = np.min([k.xmax for k in dists])

            x_vals = np.unique(np.concatenate([k.x for k in dists]))
            x_vals = x_vals[(x_vals>new_xmin-TINY_NUMBER)&(x_vals<new_xmax+TINY_NUMBER)]
            y_vals = np.sum([k.__call__(x_vals) for k in dists], axis=0)
            peak = y_vals.min()
            ind = (y_vals-peak)<BIG_NUMBER/1000
            n_points = ind.sum()
            if n_points == 0:
                print ("ERROR in distribution multiplication: Distributions do not overlap")
                x_vals = [0,1]
                y_vals = [BIG_NUMBER,BIG_NUMBER]
                res = Distribution(x_vals, y_vals, is_log=True,
                                   min_width=min_width, kind='linear')
            elif n_points == 1:
                res = Distribution.delta_function(x_vals[0])
            else:
                res = Distribution(x_vals[ind], y_vals[ind], is_log=True,
                                   min_width=min_width, kind='linear', assume_sorted=True)

        return res

Response: multiplies a list of Distribution objects a list of Distribution objects


Instruction:
Implement a function in Python 3 to
assign dates to nodes

Response:
def _assign_dates(self):
        """assign dates to nodes

        Returns
        -------
        str
            success/error code
        """
        if self.tree is None:
            self.logger("ClockTree._assign_dates: tree is not set, can't assign dates", 0)
            return ttconf.ERROR

        bad_branch_counter = 0
        for node in self.tree.find_clades(order='postorder'):
            if node.name in self.date_dict:
                tmp_date = self.date_dict[node.name]
                if np.isscalar(tmp_date) and np.isnan(tmp_date):
                    self.logger("WARNING: ClockTree.init: node %s has a bad date: %s"%(node.name, str(tmp_date)), 2, warn=True)
                    node.raw_date_constraint = None
                    node.bad_branch = True
                else:
                    try:
                        tmp = np.mean(tmp_date)
                        node.raw_date_constraint = tmp_date
                        node.bad_branch = False
                    except:
                        self.logger("WARNING: ClockTree.init: node %s has a bad date: %s"%(node.name, str(tmp_date)), 2, warn=True)
                        node.raw_date_constraint = None
                        node.bad_branch = True
            else: # nodes without date contraints

                node.raw_date_constraint = None

                if node.is_terminal():
                    # Terminal branches without date constraints marked as 'bad'
                    node.bad_branch = True
                else:
                    # If all branches dowstream are 'bad', and there is no date constraint for
                    # this node, the branch is marked as 'bad'
                    node.bad_branch = np.all([x.bad_branch for x in node])

            if node.is_terminal() and node.bad_branch:
                bad_branch_counter += 1

        if bad_branch_counter>self.tree.count_terminals()-3:
            self.logger("ERROR: ALMOST NO VALID DATE CONSTRAINTS, EXITING", 1, warn=True)
            return ttconf.ERROR

        return ttconf.SUCCESS


Instruction:
Implement a Python 3 function for
setting the precision of the current locale

Response:
def _set_precision(self, precision):
        '''
        function that sets precision to an (hopfully) reasonable guess based
        on the length of the sequence if not explicitly set
        '''
        # if precision is explicitly specified, use it.

        if self.one_mutation:
            self.min_width = 10*self.one_mutation
        else:
            self.min_width = 0.001
        if precision in [0,1,2,3]:
            self.precision=precision
            if self.one_mutation and self.one_mutation<1e-4 and precision<2:
                self.logger("ClockTree._set_precision: FOR LONG SEQUENCES (>1e4) precision>=2 IS RECOMMENDED."
                            " \n\t **** precision %d was specified by the user"%precision, level=0)
        else:
            # otherwise adjust it depending on the minimal sensible branch length
            if self.one_mutation:
                if self.one_mutation>1e-4:
                    self.precision=1
                else:
                    self.precision=2
            else:
                self.precision=1
            self.logger("ClockTree: Setting precision to level %s"%self.precision, 2)

        if self.precision==0:
            self.node_grid_points = ttconf.NODE_GRID_SIZE_ROUGH
            self.branch_grid_points = ttconf.BRANCH_GRID_SIZE_ROUGH
            self.n_integral = ttconf.N_INTEGRAL_ROUGH
        elif self.precision==2:
            self.node_grid_points = ttconf.NODE_GRID_SIZE_FINE
            self.branch_grid_points = ttconf.BRANCH_GRID_SIZE_FINE
            self.n_integral = ttconf.N_INTEGRAL_FINE
        elif self.precision==3:
            self.node_grid_points = ttconf.NODE_GRID_SIZE_ULTRA
            self.branch_grid_points = ttconf.BRANCH_GRID_SIZE_ULTRA
            self.n_integral = ttconf.N_INTEGRAL_ULTRA
        else:
            self.node_grid_points = ttconf.NODE_GRID_SIZE
            self.branch_grid_points = ttconf.BRANCH_GRID_SIZE
            self.n_integral = ttconf.N_INTEGRAL


Instruction:
Here you have a function in Python 3, explain what it does
def init_date_constraints(self, ancestral_inference=False, clock_rate=None, **kwarks):
        self.logger("ClockTree.init_date_constraints...",2)
        self.tree.coalescent_joint_LH = 0
        if self.aln and (ancestral_inference or (not hasattr(self.tree.root, 'sequence'))):
            self.infer_ancestral_sequences('probabilistic', marginal=self.branch_length_mode=='marginal',
                                            sample_from_profile='root',**kwarks)

        # set the None  for the date-related attributes in the internal nodes.
        # make interpolation objects for the branches
        self.logger('ClockTree.init_date_constraints: Initializing branch length interpolation objects...',3)
        has_clock_length = []
        for node in self.tree.find_clades(order='postorder'):
            if node.up is None:
                node.branch_length_interpolator = None
            else:
                has_clock_length.append(hasattr(node, 'clock_length'))
                # copy the merger rate and gamma if they are set
                if hasattr(node,'branch_length_interpolator') and node.branch_length_interpolator is not None:
                    gamma = node.branch_length_interpolator.gamma
                    merger_cost = node.branch_length_interpolator.merger_cost
                else:
                    gamma = 1.0
                    merger_cost = None

                if self.branch_length_mode=='marginal':
                    node.profile_pair = self.marginal_branch_profile(node)

                node.branch_length_interpolator = BranchLenInterpolator(node, self.gtr,
                            pattern_multiplicity = self.multiplicity, min_width=self.min_width,
                            one_mutation=self.one_mutation, branch_length_mode=self.branch_length_mode)

                node.branch_length_interpolator.merger_cost = merger_cost
                node.branch_length_interpolator.gamma = gamma

        # use covariance in clock model only after initial timetree estimation is done
        use_cov = (np.sum(has_clock_length) > len(has_clock_length)*0.7) and self.use_covariation
        self.get_clock_model(covariation=use_cov, slope=clock_rate)

        # make node distribution objects
        for node in self.tree.find_clades(order="postorder"):
            # node is constrained
            if hasattr(node, 'raw_date_constraint') and node.raw_date_constraint is not None:
                # set the absolute time before present in branch length units
                if np.isscalar(node.raw_date_constraint):
                    tbp = self.date2dist.get_time_before_present(node.raw_date_constraint)
                    node.date_constraint = Distribution.delta_function(tbp, weight=1.0, min_width=self.min_width)
                else:
                    tbp = self.date2dist.get_time_before_present(np.array(node.raw_date_constraint))
                    node.date_constraint = Distribution(tbp, np.ones_like(tbp), is_log=False, min_width=self.min_width)

                if hasattr(node, 'bad_branch') and node.bad_branch is True:
                    self.logger("ClockTree.init_date_constraints -- WARNING: Branch is marked as bad"
                                ", excluding it from the optimization process.\n"
                                "\t\tDate constraint will be ignored!", 4, warn=True)
            else: # node without sampling date set
                node.raw_date_constraint = None
                node.date_constraint = None

Response: Initializes the internal branch length interpolation objects for the internal nodes.


Instruction:
Here you have a function in Python 3, explain what it does
def make_time_tree(self, time_marginal=False, clock_rate=None, **kwargs):
        '''
        Use the date constraints to calculate the most likely positions of
        unconstrained nodes.

        Parameters
        ----------

         time_marginal : bool
            If true, use marginal reconstruction for node positions

         **kwargs
            Key word arguments to initialize dates constraints

        '''
        self.logger("ClockTree: Maximum likelihood tree optimization with temporal constraints",1)

        self.init_date_constraints(clock_rate=clock_rate, **kwargs)

        if time_marginal:
            self._ml_t_marginal(assign_dates = time_marginal=="assign")
        else:
            self._ml_t_joint()

        self.convert_dates()

Response: This function creates a time tree based on the given parameters.


Instruction:
How would you explain what the following Python 3 function does
def _ml_t_joint(self):

        def _cleanup():
            for node in self.tree.find_clades():
                del node.joint_pos_Lx
                del node.joint_pos_Cx

        self.logger("ClockTree - Joint reconstruction:  Propagating leaves -> root...", 2)
        # go through the nodes from leaves towards the root:
        for node in self.tree.find_clades(order='postorder'):  # children first, msg to parents
            # Lx is the maximal likelihood of a subtree given the parent position
            # Cx is the branch length corresponding to the maximally likely subtree
            if node.bad_branch:
                # no information at the node
                node.joint_pos_Lx = None
                node.joint_pos_Cx = None
            else: # all other nodes
                if node.date_constraint is not None and node.date_constraint.is_delta: # there is a time constraint
                    # subtree probability given the position of the parent node
                    # Lx.x is the position of the parent node
                    # Lx.y is the probablity of the subtree (consisting of one terminal node in this case)
                    # Cx.y is the branch length corresponding the optimal subtree
                    bl = node.branch_length_interpolator.x
                    x = bl + node.date_constraint.peak_pos
                    node.joint_pos_Lx = Distribution(x, node.branch_length_interpolator(bl),
                                                     min_width=self.min_width, is_log=True)
                    node.joint_pos_Cx = Distribution(x, bl, min_width=self.min_width) # map back to the branch length
                else: # all nodes without precise constraint but positional information
                    msgs_to_multiply = [node.date_constraint] if node.date_constraint is not None else []
                    msgs_to_multiply.extend([child.joint_pos_Lx for child in node.clades
                                             if child.joint_pos_Lx is not None])

                    # subtree likelihood given the node's constraint and child messages
                    if len(msgs_to_multiply) == 0: # there are no constraints
                        node.joint_pos_Lx = None
                        node.joint_pos_Cx = None
                        continue
                    elif len(msgs_to_multiply)>1: # combine the different msgs and constraints
                        subtree_distribution = Distribution.multiply(msgs_to_multiply)
                    else: # there is exactly one constraint.
                        subtree_distribution = msgs_to_multiply[0]

                    if node.up is None: # this is the root, set dates
                        subtree_distribution._adjust_grid(rel_tol=self.rel_tol_prune)
                        # set root position and joint likelihood of the tree
                        node.time_before_present = subtree_distribution.peak_pos
                        node.joint_pos_Lx = subtree_distribution
                        node.joint_pos_Cx = None
                        node.clock_length = node.branch_length
                    else: # otherwise propagate to parent
                        res, res_t = NodeInterpolator.convolve(subtree_distribution,
                                        node.branch_length_interpolator,
                                        max_or_integral='max',
                                        inverse_time=True,
                                        n_grid_points = self.node_grid_points,
                                        n_integral=self.n_integral,
                                        rel_tol=self.rel_tol_refine)

                        res._adjust_grid(rel_tol=self.rel_tol_prune)

                        node.joint_pos_Lx = res
                        node.joint_pos_Cx = res_t

        # go through the nodes from root towards the leaves and assign joint ML positions:
        self.logger("ClockTree - Joint reconstruction:  Propagating root -> leaves...", 2)
        for node in self.tree.find_clades(order='preorder'):  # root first, msgs to children

            if node.up is None: # root node
                continue # the position was already set on the previous step

            if node.joint_pos_Cx is None: # no constraints or branch is bad - reconstruct from the branch len interpolator
                node.branch_length = node.branch_length_interpolator.peak_pos

            elif isinstance(node.joint_pos_Cx, Distribution):
                # NOTE the Lx distribution is the likelihood, given the position of the parent
                # (Lx.x = parent position, Lx.y = LH of the node_pos given Lx.x,
                # the length of the branch corresponding to the most likely
                # subtree is node.Cx(node.time_before_present))
                subtree_LH = node.joint_pos_Lx(node.up.time_before_present)
                node.branch_length = node.joint_pos_Cx(max(node.joint_pos_Cx.xmin,
                                            node.up.time_before_present)+ttconf.TINY_NUMBER)

            node.time_before_present = node.up.time_before_present - node.branch_length
            node.clock_length = node.branch_length

            # just sanity check, should never happen:
            if node.branch_length < 0 or node.time_before_present < 0:
                if node.branch_length<0 and node.branch_length>-ttconf.TINY_NUMBER:
                    self.logger("ClockTree - Joint reconstruction: correcting rounding error of %s"%node.name, 4)
                    node.branch_length = 0

        self.tree.positional_joint_LH = self.timetree_likelihood()
        # cleanup, if required
        if not self.debug:
            _cleanup()

Response: Compute the joint maximum likelihood assignment of the internal nodes positions by propagating from the tree leaves towards the root.


Instruction:
Implement a Python 3 function for
returning the likelihood of the data given the current branch length in the tree.

Response:
def timetree_likelihood(self):
        '''
        Return the likelihood of the data given the current branch length in the tree
        '''
        LH = 0
        for node in self.tree.find_clades(order='preorder'):  # sum the likelihood contributions of all branches
            if node.up is None: # root node
                continue
            LH -= node.branch_length_interpolator(node.branch_length)

        # add the root sequence LH and return
        if self.aln:
            LH += self.gtr.sequence_logLH(self.tree.root.cseq, pattern_multiplicity=self.multiplicity)
        return LH


Instruction:
Create a Python 3 function for
computing the marginal probability distribution of the internal nodes positions by propagating from the tree leaves towards the root.

Response:
def _ml_t_marginal(self, assign_dates=False):
        """
        Compute the marginal probability distribution of the internal nodes positions by
        propagating from the tree leaves towards the root. The result of
        this operation are the probability distributions of each internal node,
        conditional on the constraints on all leaves of the tree, which have sampling dates.
        The probability distributions are set as marginal_pos_LH attributes to the nodes.

        Parameters
        ----------

         assign_dates : bool, default False
            If True, the inferred dates will be assigned to the nodes as
            :code:`time_before_present' attributes, and their branch lengths
            will be corrected accordingly.
            .. Note::
                Normally, the dates are assigned by running joint reconstruction.

        Returns
        -------

         None
            Every internal node is assigned the probability distribution in form
            of an interpolation object and sends this distribution further towards the
            root.

        """

        def _cleanup():
            for node in self.tree.find_clades():
                try:
                    del node.marginal_pos_Lx
                    del node.subtree_distribution
                    del node.msg_from_parent
                    #del node.marginal_pos_LH
                except:
                    pass

        self.logger("ClockTree - Marginal reconstruction:  Propagating leaves -> root...", 2)
        # go through the nodes from leaves towards the root:
        for node in self.tree.find_clades(order='postorder'):  # children first, msg to parents
            if node.bad_branch:
                # no information
                node.marginal_pos_Lx = None
            else: # all other nodes
                if node.date_constraint is not None and node.date_constraint.is_delta: # there is a time constraint
                    # initialize the Lx for nodes with precise date constraint:
                    # subtree probability given the position of the parent node
                    # position of the parent node is given by the branch length
                    # distribution attached to the child node position
                    node.subtree_distribution = node.date_constraint
                    bl = node.branch_length_interpolator.x
                    x = bl + node.date_constraint.peak_pos
                    node.marginal_pos_Lx = Distribution(x, node.branch_length_interpolator(bl),
                                                        min_width=self.min_width, is_log=True)

                else: # all nodes without precise constraint but positional information
                      # subtree likelihood given the node's constraint and child msg:
                    msgs_to_multiply = [node.date_constraint] if node.date_constraint is not None else []
                    msgs_to_multiply.extend([child.marginal_pos_Lx for child in node.clades
                                             if child.marginal_pos_Lx is not None])

                    # combine the different msgs and constraints
                    if len(msgs_to_multiply)==0:
                        # no information
                        node.marginal_pos_Lx = None
                        continue
                    elif len(msgs_to_multiply)==1:
                        node.subtree_distribution = msgs_to_multiply[0]
                    else: # combine the different msgs and constraints
                        node.subtree_distribution = Distribution.multiply(msgs_to_multiply)

                    if node.up is None: # this is the root, set dates
                        node.subtree_distribution._adjust_grid(rel_tol=self.rel_tol_prune)
                        node.marginal_pos_Lx = node.subtree_distribution
                        node.marginal_pos_LH = node.subtree_distribution
                        self.tree.positional_marginal_LH = -node.subtree_distribution.peak_val
                    else: # otherwise propagate to parent
                        res, res_t = NodeInterpolator.convolve(node.subtree_distribution,
                                        node.branch_length_interpolator,
                                        max_or_integral='integral',
                                        n_grid_points = self.node_grid_points,
                                        n_integral=self.n_integral,
                                        rel_tol=self.rel_tol_refine)
                        res._adjust_grid(rel_tol=self.rel_tol_prune)
                        node.marginal_pos_Lx = res

        self.logger("ClockTree - Marginal reconstruction:  Propagating root -> leaves...", 2)
        from scipy.interpolate import interp1d
        for node in self.tree.find_clades(order='preorder'):

            ## The root node
            if node.up is None:
                node.msg_from_parent = None # nothing beyond the root
            # all other cases (All internal nodes + unconstrained terminals)
            else:
                parent = node.up
                # messages from the complementary subtree (iterate over all sister nodes)
                complementary_msgs = [sister.marginal_pos_Lx for sister in parent.clades
                                            if (sister != node) and (sister.marginal_pos_Lx is not None)]

                # if parent itself got smth from the root node, include it
                if parent.msg_from_parent is not None:
                    complementary_msgs.append(parent.msg_from_parent)
                elif parent.marginal_pos_Lx is not None:
                    complementary_msgs.append(parent.marginal_pos_LH)

                if len(complementary_msgs):
                    msg_parent_to_node = NodeInterpolator.multiply(complementary_msgs)
                    msg_parent_to_node._adjust_grid(rel_tol=self.rel_tol_prune)
                else:
                    x = [parent.numdate, numeric_date()]
                    msg_parent_to_node = NodeInterpolator(x, [1.0, 1.0],min_width=self.min_width)

                # integral message, which delivers to the node the positional information
                # from the complementary subtree
                res, res_t = NodeInterpolator.convolve(msg_parent_to_node, node.branch_length_interpolator,
                                                    max_or_integral='integral',
                                                    inverse_time=False,
                                                    n_grid_points = self.node_grid_points,
                                                    n_integral=self.n_integral,
                                                    rel_tol=self.rel_tol_refine)

                node.msg_from_parent = res
                if node.marginal_pos_Lx is None:
                    node.marginal_pos_LH = node.msg_from_parent
                else:
                    node.marginal_pos_LH = NodeInterpolator.multiply((node.msg_from_parent, node.subtree_distribution))

                self.logger('ClockTree._ml_t_root_to_leaves: computed convolution'
                                ' with %d points at node %s'%(len(res.x),node.name),4)

                if self.debug:
                    tmp = np.diff(res.y-res.peak_val)
                    nsign_changed = np.sum((tmp[1:]*tmp[:-1]<0)&(res.y[1:-1]-res.peak_val<500))
                    if nsign_changed>1:
                        import matplotlib.pyplot as plt
                        plt.ion()
                        plt.plot(res.x, res.y-res.peak_val, '-o')
                        plt.plot(res.peak_pos - node.branch_length_interpolator.x,
                                 node.branch_length_interpolator(node.branch_length_interpolator.x)-node.branch_length_interpolator.peak_val, '-o')
                        plt.plot(msg_parent_to_node.x,msg_parent_to_node.y-msg_parent_to_node.peak_val, '-o')
                        plt.ylim(0,100)
                        plt.xlim(-0.05, 0.05)
                        import ipdb; ipdb.set_trace()

            # assign positions of nodes and branch length only when desired
            # since marginal reconstruction can result in negative branch length
            if assign_dates:
                node.time_before_present = node.marginal_pos_LH.peak_pos
                if node.up:
                    node.clock_length = node.up.time_before_present - node.time_before_present
                    node.branch_length = node.clock_length

            # construct the inverse cumulant distribution to evaluate confidence intervals
            if node.marginal_pos_LH.is_delta:
                node.marginal_inverse_cdf=interp1d([0,1], node.marginal_pos_LH.peak_pos*np.ones(2), kind="linear")
            else:
                dt = np.diff(node.marginal_pos_LH.x)
                y = node.marginal_pos_LH.prob_relative(node.marginal_pos_LH.x)
                int_y = np.concatenate(([0], np.cumsum(dt*(y[1:]+y[:-1])/2.0)))
                int_y/=int_y[-1]
                node.marginal_inverse_cdf = interp1d(int_y, node.marginal_pos_LH.x, kind="linear")
                node.marginal_cdf = interp1d(node.marginal_pos_LH.x, int_y, kind="linear")

        if not self.debug:
            _cleanup()

        return


Instruction:
Can you tell what is the following Python 3 function doing
def branch_length_to_years(self):
        '''
        This function sets branch length to reflect the date differences between parent and child
        nodes measured in years. Should only be called after :py:meth:`timetree.ClockTree.convert_dates` has been called.

        Returns
        -------
         None
            All manipulations are done in place on the tree

        '''
        self.logger('ClockTree.branch_length_to_years: setting node positions in units of years', 2)
        if not hasattr(self.tree.root, 'numdate'):
            self.logger('ClockTree.branch_length_to_years: infer ClockTree first', 2,warn=True)
        self.tree.root.branch_length = 0.1
        for n in self.tree.find_clades(order='preorder'):
            if n.up is not None:
                n.branch_length = n.numdate - n.up.numdate

Response: This function sets the branch length to reflect the date differences between parent and child nodes measured in years.


Instruction:
Create a Python 3 function for
calculating the time tree estimation of evolutionary rates + / - one - time rate standard deviation form the ML estimate

Response:
def calc_rate_susceptibility(self, rate_std=None, params=None):
        """return the time tree estimation of evolutionary rates +/- one
        standard deviation form the ML estimate.

        Returns
        -------
        TreeTime.return_code : str
            success or failure
        """
        params = params or {}
        if rate_std is None:
            if not (self.clock_model['valid_confidence'] and 'cov' in self.clock_model):
                self.logger("ClockTree.calc_rate_susceptibility: need valid standard deviation of the clock rate to estimate dating error.", 1, warn=True)
                return ttconf.ERROR
            rate_std = np.sqrt(self.clock_model['cov'][0,0])

        current_rate = np.abs(self.clock_model['slope'])
        upper_rate = self.clock_model['slope'] + rate_std
        lower_rate = max(0.1*current_rate, self.clock_model['slope'] - rate_std)
        for n in self.tree.find_clades():
            if n.up:
                n._orig_gamma = n.branch_length_interpolator.gamma
                n.branch_length_interpolator.gamma = n._orig_gamma*upper_rate/current_rate

        self.logger("###ClockTree.calc_rate_susceptibility: run with upper bound of rate estimate", 1)
        self.make_time_tree(**params)
        self.logger("###ClockTree.calc_rate_susceptibility: rate: %f, LH:%f"%(upper_rate, self.tree.positional_joint_LH), 2)
        for n in self.tree.find_clades():
            n.numdate_rate_variation = [(upper_rate, n.numdate)]
            if n.up:
                n.branch_length_interpolator.gamma = n._orig_gamma*lower_rate/current_rate

        self.logger("###ClockTree.calc_rate_susceptibility: run with lower bound of rate estimate", 1)
        self.make_time_tree(**params)
        self.logger("###ClockTree.calc_rate_susceptibility: rate: %f, LH:%f"%(lower_rate, self.tree.positional_joint_LH), 2)
        for n in self.tree.find_clades():
            n.numdate_rate_variation.append((lower_rate, n.numdate))
            if n.up:
                n.branch_length_interpolator.gamma  = n._orig_gamma

        self.logger("###ClockTree.calc_rate_susceptibility: run with central rate estimate", 1)
        self.make_time_tree(**params)
        self.logger("###ClockTree.calc_rate_susceptibility: rate: %f, LH:%f"%(current_rate, self.tree.positional_joint_LH), 2)
        for n in self.tree.find_clades():
            n.numdate_rate_variation.append((current_rate, n.numdate))
            n.numdate_rate_variation.sort(key=lambda x:x[1]) # sort estimates for different rates by numdate

        return ttconf.SUCCESS


Instruction:
Make a summary of the following Python 3 code
def date_uncertainty_due_to_rate(self, node, interval=(0.05, 0.095)):
        if hasattr(node, "numdate_rate_variation"):
            from scipy.special import erfinv
            nsig = [np.sqrt(2.0)*erfinv(-1.0 + 2.0*x) if x*(1.0-x) else 0
                    for x in interval]
            l,c,u = [x[1] for x in node.numdate_rate_variation]
            return np.array([c + x*np.abs(y-c) for x,y in zip(nsig, (l,u))])

        else:
            return None

Response: estimate the uncertainty due to rate variation of a particular node


Instruction:
Here you have a function in Python 3, explain what it does
def get_max_posterior_region(self, node, fraction = 0.9):
        '''
        If temporal reconstruction was done using the marginal ML mode, the entire distribution of
        times is available. This function determines the interval around the highest
        posterior probability region that contains the specified fraction of the probability mass.
        In absense of marginal reconstruction, it will return uncertainty based on rate
        variation. If both are present, the wider interval will be returned.

        Parameters
        ----------

         node : PhyloTree.Clade
            The node for which the posterior region is to be calculated

         interval : float
            Float specifying who much of the posterior probability is
            to be contained in the region

        Returns
        -------
         max_posterior_region : numpy array
            Array with two numerical dates delineating the high posterior region

        '''
        if node.marginal_inverse_cdf=="delta":
            return np.array([node.numdate, node.numdate])

        min_max = (node.marginal_pos_LH.xmin, node.marginal_pos_LH.xmax)
        min_date, max_date = [self.date2dist.to_numdate(x) for x in min_max][::-1]
        if node.marginal_pos_LH.peak_pos == min_max[0]: #peak on the left
            return self.get_confidence_interval(node, (0, fraction))
        elif node.marginal_pos_LH.peak_pos == min_max[1]: #peak on the right
            return self.get_confidence_interval(node, (1.0-fraction ,1.0))
        else: # peak in the center of the distribution
            rate_contribution = self.date_uncertainty_due_to_rate(node, ((1-fraction)*0.5, 1.0-(1.0-fraction)*0.5))

            # construct height to position interpolators left and right of the peak
            # this assumes there is only one peak --- might fail in odd cases
            from scipy.interpolate import interp1d
            from scipy.optimize import minimize_scalar as minimize
            pidx = np.argmin(node.marginal_pos_LH.y)
            pval = np.min(node.marginal_pos_LH.y)
            left =  interp1d(node.marginal_pos_LH.y[:(pidx+1)]-pval, node.marginal_pos_LH.x[:(pidx+1)],
                            kind='linear', fill_value=min_max[0], bounds_error=False)
            right = interp1d(node.marginal_pos_LH.y[pidx:]-pval, node.marginal_pos_LH.x[pidx:],
                            kind='linear', fill_value=min_max[1], bounds_error=False)

            # function to minimize -- squared difference between prob mass and desired fracion
            def func(x, thres):
                interval = np.array([left(x), right(x)]).squeeze()
                return (thres - np.diff(node.marginal_cdf(np.array(interval))))**2

            # minimza and determine success
            sol = minimize(func, bracket=[0,10], args=(fraction,))
            if sol['success']:
                mutation_contribution = self.date2dist.to_numdate(np.array([right(sol['x']), left(sol['x'])]).squeeze())
            else: # on failure, return standard confidence interval
                mutation_contribution = None

            return self.combine_confidence(node.numdate, (min_date, max_date),
                                      c1=rate_contribution, c2=mutation_contribution)

Response: This function determines the interval around the highest posterior probability region that contains the specified fraction of the probability mass.