Downbeats: allow weighting of beats per bar

 * Optional parameter, implicitly defaults to ones for the array
 * Clean up the handling of lengths into the constructor, it was getting verbose
 * Check weights don't sum to zero, to avoid divide-by-zero pain.
 * Weight the HMM results in log space by normalised weight values, as suggested by @superbock
 * Add new test to prove that (sufficient, but arbitrary) weighting to 3-time (over 4-time)
   does indeed return 3-time beats results.

This fixes CPJKU#402.

madmom/features/downbeats.py

@@ -153,6 +153,11 @@ class DBNDownBeatTrackingProcessor(Processor):
         (down-)beat activation function).
     fps : float, optional
         Frames per second.
+    beats_per_bar_weights : list, optional
+        Weight the beats_per_bar list when choosing.
+        Higher numbers favour the beat number at the same index, e.g.
+        for beats_per_bar of [3, 4], a value here for [1, 2] will bias the
+        the choice towards 4 beats per bar.
 
     References
     ----------
@@ -200,11 +205,15 @@ class DBNDownBeatTrackingProcessor(Processor):
     def __init__(self, beats_per_bar, min_bpm=MIN_BPM, max_bpm=MAX_BPM,
                  num_tempi=NUM_TEMPI, transition_lambda=TRANSITION_LAMBDA,
                  observation_lambda=OBSERVATION_LAMBDA, threshold=THRESHOLD,
-                 correct=CORRECT, fps=None, **kwargs):
+                 correct=CORRECT, fps=None, beats_per_bar_weights=None,
+                 **kwargs):
         # pylint: disable=unused-argument
         # pylint: disable=no-name-in-module
         # expand arguments to arrays
         beats_per_bar = np.array(beats_per_bar, ndmin=1)
+        beats_per_bar_weights = (np.array(beats_per_bar_weights, ndmin=1)
+                                 if beats_per_bar_weights
+                                 else np.ones(beats_per_bar.shape))
         min_bpm = np.array(min_bpm, ndmin=1)
         max_bpm = np.array(max_bpm, ndmin=1)
         num_tempi = np.array(num_tempi, ndmin=1)
@@ -220,11 +229,14 @@ def __init__(self, beats_per_bar, min_bpm=MIN_BPM, max_bpm=MAX_BPM,
         if len(transition_lambda) != len(beats_per_bar):
             transition_lambda = np.repeat(transition_lambda,
                                           len(beats_per_bar))
-        if not (len(min_bpm) == len(max_bpm) == len(num_tempi) ==
-                len(beats_per_bar) == len(transition_lambda)):
-            raise ValueError('`min_bpm`, `max_bpm`, `num_tempi`, `num_beats` '
-                             'and `transition_lambda` must all have the same '
-                             'length.')
+        lengths = [len(a) for a in (min_bpm, max_bpm, num_tempi, beats_per_bar,
+                                    transition_lambda, beats_per_bar_weights)]
+        if not sum(beats_per_bar_weights):
+            raise ValueError("`beats_per_bar_weights` cannot total zero")
+        if np.var(lengths):
+            raise ValueError('`min_bpm`, `max_bpm`, `num_tempi`, `num_beats`, '
+                             '`beats_per_bar_weights` and `transition_lambda` '
+                             'must all have the same length.')
         # get num_threads from kwargs
         num_threads = min(len(beats_per_bar), kwargs.get('num_threads', 1))
         # init a pool of workers (if needed)
@@ -245,6 +257,7 @@ def __init__(self, beats_per_bar, min_bpm=MIN_BPM, max_bpm=MAX_BPM,
             self.hmms.append(HiddenMarkovModel(tm, om))
         # save variables
         self.beats_per_bar = beats_per_bar
+        self.beats_per_bar_weights = beats_per_bar_weights
         self.threshold = threshold
         self.correct = correct
         self.fps = fps
@@ -283,8 +296,10 @@ def process(self, activations, **kwargs):
         # (parallel) decoding of the activations with HMM
         results = list(self.map(_process_dbn, zip(self.hmms,
                                                   it.repeat(activations))))
-        # choose the best HMM (highest log probability)
-        best = np.argmax(np.asarray(results)[:, 1])
+        # choose the best HMM (highest log probability) after weighting
+        weights = self.beats_per_bar_weights
+        scores = np.asarray(results)[:, 1] + np.log(weights / np.sum(weights))
+        best = np.argmax(scores)
         # the best path through the state space
         path, _ = results[best]
         # the state space and observation model of the best HMM

tests/test_features_downbeats.py

@@ -101,6 +101,16 @@ def test_process(self):
         downbeats = self.processor(sample_downbeat_act)
         self.assertTrue(np.allclose(downbeats, np.empty((0, 2))))
 
+    def test_weighting_measure(self):
+        self.processor = DBNDownBeatTrackingProcessor(
+            [3, 4], fps=sample_downbeat_act.fps,
+            beats_per_bar_weights=[100, 1], correct=False)
+        downbeats = self.processor(sample_downbeat_act)
+        correct = np.array([[0.08, 1], [0.43, 2], [0.77, 3],
+                            [1.11, 1], [1.45, 2], [1.79, 3],
+                            [2.13, 1], [2.47, 2]])
+        self.assertTrue(np.allclose(downbeats, correct))
+
 
 class TestPatternTrackingProcessorClass(unittest.TestCase):