Export clock rate covariance matrix and std dev

Exports the clock rate covariance matrix and std dev from the
phylogenetic regression performed by TreeTime in augur refine. This
information was already available in a TreeTime data structure and it is
useful to users who do not know the std dev of their pathogen's clock
rate already.

Adds functional tests for behavior when no clock rate is provided by the
user and when one is. In the latter case, we shouldn't have a covariance
matrix.

augur/refine.py

@@ -259,6 +259,12 @@ def run(args):
         node_data['clock'] = {'rate': tt.date2dist.clock_rate,
                               'intercept': tt.date2dist.intercept,
                               'rtt_Tmrca': -tt.date2dist.intercept/tt.date2dist.clock_rate}
+        # Include the standard deviation of the clock rate, if the covariance
+        # matrix is available.
+        if hasattr(tt.date2dist, "cov") and tt.date2dist.cov is not None:
+            node_data["clock"]["cov"] = tt.date2dist.cov
+            node_data["clock"]["rate_std"] = np.sqrt(tt.date2dist.cov[0, 0])
+
         if args.coalescent=='skyline':
             try:
                 skyline, conf = tt.merger_model.skyline_inferred(gen=args.gen_per_year, confidence=2)

tests/functional/refine/cram/timetree.t

@@ -21,3 +21,23 @@ Confirm that TreeTime trees match expected topology and branch lengths.
 
   $ python3 "$TESTDIR/../../../../scripts/diff_trees.py" "$TESTDIR/../data/tree.nwk" tree.nwk --significant-digits 2
   {}
+
+Confirm that JSON output includes details about the clock rate.
+
+  $ grep -A 15 '\"clock\"' branch_lengths.json
+    "clock": {
+      "cov": [
+        [
+          .*, (re)
+          .* (re)
+        ],
+        [
+          .*, (re)
+          .* (re)
+        ]
+      ],
+      "intercept": .*, (re)
+      "rate": .*, (re)
+      "rate_std": .*, (re)
+      "rtt_Tmrca": .* (re)
+    },

tests/functional/refine/cram/timetree_with_fixed_clock_rate.t

@@ -0,0 +1,29 @@
+Setup
+
+  $ source "$TESTDIR"/_setup.sh
+
+Try building a time tree with a fixed clock rate and clock std dev.
+
+  $ ${AUGUR} refine \
+  >  --tree "$TESTDIR/../data/tree_raw.nwk" \
+  >  --alignment "$TESTDIR/../data/aligned.fasta" \
+  >  --metadata "$TESTDIR/../data/metadata.tsv" \
+  >  --output-tree tree.nwk \
+  >  --output-node-data branch_lengths.json \
+  >  --timetree \
+  >  --coalescent opt \
+  >  --date-confidence \
+  >  --date-inference marginal \
+  >  --clock-rate 0.0012 \
+  >  --clock-std-dev 0.0002 \
+  >  --clock-filter-iqd 4 \
+  >  --seed 314159 &> /dev/null
+
+Confirm that JSON output does not include information about the clock rate std dev, since it was provided by the user.
+
+  $ grep -A 4 '\"clock\"' branch_lengths.json
+    "clock": {
+      "intercept": .*, (re)
+      "rate": .*, (re)
+      "rtt_Tmrca": .* (re)
+    },