Optionally handle non-monotonic data

    * New load_xdf parameter: handle_non_monotonic (default: False)
      - None: disable monotonicity checking
      - False: check and warn only if non-monotonic data are detected
      - True: attempt to sort non-monotonic data

    * Additional tests for monotonicity

src/pyxdf/pyxdf.py

@@ -15,7 +15,7 @@
 import itertools
 import logging
 import struct
-from collections import OrderedDict, defaultdict
+from collections import OrderedDict, defaultdict, namedtuple
 from pathlib import Path
 from xml.etree.ElementTree import ParseError, fromstring
 
@@ -79,6 +79,7 @@ def load_xdf(
     select_streams=None,
     *,
     on_chunk=None,
+    handle_non_monotonic=False,
     synchronize_clocks=True,
     handle_clock_resets=True,
     dejitter_timestamps=True,
@@ -122,6 +123,13 @@ def load_xdf(
         verbose : Passing True will set logging level to DEBUG, False will set it to
           WARNING, and None will use root logger level. (default: None)
 
+        handle_non_monotonic : bool | None
+          Whether to warn only or sort samples that are not in ascending time
+          order. (default: False)
+          - bool : 'False' check only, warning when data are non-monotonic
+                   'True' check and sort non-monotonic data
+          - None : Disable non-monotonicity check
+
         synchronize_clocks : Whether to enable clock synchronization based on
           ClockOffset chunks. (default: true)
 
@@ -358,6 +366,33 @@ def load_xdf(
             else:
                 stream.time_series = np.zeros((0, stream.nchns))
 
+    # Perform initial non-monotonicity checks if requested
+    if handle_non_monotonic is None:
+        logger.debug("  skipping non-monotonicity check...")
+    else:
+        logger.info("  performing non-monotonicity check...")
+        mono_status = _check_monotonicity(temp)
+        # Are all time-values monotonic across all streams?
+        time_stamps_mono = all(mono_status["time_stamps"].values())
+        clock_times_mono = all(mono_status["clock_times"].values())
+        if time_stamps_mono and clock_times_mono:
+            # All streams are monotonic.
+            logger.info("All streams are monotonic, continuing...")
+        elif not handle_non_monotonic:
+            # Some data are non-monotonic, but we will not attempt to handle it.
+            if not synchronize_clocks and not clock_times_mono:
+                msg = (
+                    "Clock offsets are non-monotonic but clocks are not going to "
+                    "be synchronized. Consider loading with 'synchronize_clocks=True'."
+                )
+                logger.warning(msg)
+            else:
+                msg = (
+                    "Non-monotonic streams detected - "
+                    "consider loading with 'handle_non_monotonic=True'."
+                )
+                logger.warning(msg)
+
     # perform (fault-tolerant) clock synchronization if requested
     if synchronize_clocks:
         logger.info("  performing clock synchronization...")
@@ -371,6 +406,12 @@ def load_xdf(
             winsor_threshold,
         )
 
+    # perform non-monotonicity handling if requested
+    if handle_non_monotonic:
+        logger.info("  sorting non-monotonic data...")
+        for stream in temp.values():
+            _sort_stream_data(stream)
+
     # perform jitter removal if requested
     if dejitter_timestamps:
         logger.info("  performing jitter removal...")
@@ -547,6 +588,153 @@ def _scan_forward(f):
             return False
 
 
+# Named tuple to represent monotonicity information.
+Monotonicity = namedtuple("Monotonicity", ["result", "n", "dec_count", "eq_count"])
+# - result: bool - True if all pairwise values are equal or increasing.
+# - n: total number of pairwise values
+# - dec_count: number of pairwise decreasing values
+# - eq_count: number of pairwise equal values
+
+
+def _monotonic_increasing(a):
+    """Test for increasing (non-decreasing) monotonicity.
+
+    Parameters
+    ----------
+    a : array_like
+
+    Returns
+    -------
+    Monotonicity : namedtuple
+    """
+    # Intervals between successive values.
+    diffs = np.diff(a)
+
+    increasing = True
+    n = len(diffs)
+    dec_count = 0
+    eq_count = 0
+
+    # Count non-increasing intervals.
+    non_inc_count = np.sum(diffs <= 0)
+
+    if non_inc_count > 0:
+        # Count constant intervals.
+        eq_count = np.sum(diffs == 0).item()
+        dec_count = (non_inc_count - eq_count).item()
+
+        if dec_count > 0:
+            increasing = False
+    return Monotonicity(increasing, n, dec_count, eq_count)
+
+
+def _check_monotonicity(streams):
+    """Check monotonicity of all stream time values.
+
+    Parameters
+    ----------
+    streams : dict
+        Dictionary of stream_id: StreamData.
+
+    Returns
+    -------
+    mono_status : dict[dict]
+        Dictionary of attr: [stream_id: bool]
+        - attr: StreamData attribute name
+        - stream_id: Stream ID
+        - bool: stream attr data are monotonic
+    """
+    mono_status = {
+        "time_stamps": {},
+        "clock_times": {},
+    }
+
+    max_stream_id = max(streams.values(), key=lambda s: s.stream_id)
+    id_align = len(str(max_stream_id.stream_id))
+
+    for stream in streams.values():
+        for attr in mono_status.keys():
+            monotonic, n, dec_count, eq_count = _monotonic_increasing(
+                getattr(stream, attr)
+            )
+
+            mono_status[attr][stream.stream_id] = monotonic
+
+            msg = [
+                (
+                    f"Stream {stream.stream_id:>{id_align}}: {attr} are"
+                    f"{'' if monotonic else ' NOT'} monotonic"
+                )
+            ]
+
+            if dec_count > 0:
+                dec_pc = round(dec_count / n * 100, 1)
+                msg.append(f"dec={dec_count} ({'<0.1' if dec_pc < 0.1 else dec_pc}%)")
+
+            if eq_count > 0:
+                eq_pc = round(eq_count / n * 100, 1)
+                msg.append(f"eq={eq_count} ({'<0.1' if eq_pc < 0.1 else eq_pc}%)")
+
+            msg = ", ".join(msg)
+
+            if monotonic:
+                logger.info(msg)
+            else:
+                logger.warning(msg)
+    return mono_status
+
+
+def _sort_stream_data(stream):
+    """Sort stream data by ground truth timestamps.
+
+    Parameters
+    ----------
+    stream: StreamData (possibly non-monotonic)
+
+    Returns
+    -------
+    stream : StreamData (monotonic)
+        With sorted timestamps and timeseries data, if necessary.
+
+    Non-monotonic streams are stable sorted in ascending order of ground
+    truth timestamps. When clock resets have been detected sorting is
+    applied within each clock segment, but clock segments themselves are
+    not sorted.
+
+    Both timestamp and timeseries arrays are modified, keeping all
+    samples aligned with their original timestamp.
+
+    Monotonic streams/segments are not modified.
+
+    Stream may still contain identically timestamped samples, but these
+    can be handled by dejittering.
+    """
+    if len(stream.time_stamps) <= 1:
+        return stream
+    clock_segments = stream.clock_segments
+    if len(clock_segments) == 0:
+        # Clocks have not been synchronized.
+        clock_segments = [(0, len(stream.time_stamps) - 1)]  # inclusive
+    for start_i, end_i in clock_segments:
+        ts_slice = slice(start_i, end_i + 1)
+        if not _monotonic_increasing(stream.time_stamps[ts_slice]).result:
+            logger.info(
+                f"Sorting stream {stream.stream_id}: clock segment {start_i}-{end_i}."
+            )
+            # Determine monotonic timestamp ordering.
+            ind = np.argsort(stream.time_stamps[ts_slice], kind="stable")
+            # Reorder timestamps in place.
+            stream.time_stamps[ts_slice] = stream.time_stamps[ts_slice][ind]
+            # Reorder timeseries data.
+            if stream.fmt == "string":
+                stream.time_series[ts_slice] = np.array(stream.time_series[ts_slice])[
+                    ind
+                ].tolist()
+            else:
+                stream.time_series[ts_slice] = stream.time_series[ts_slice][ind]
+    return stream
+
+
 def _find_segment_indices(b_breaks):
     """Convert boundary breaks array to segment indices.