Module thunderfish.eventdetection

Detect and handle peaks and troughs as well as threshold crossings in data arrays.

Peak detection

Threshold crossings

Event manipulation

Threshold estimation

Snippets

  • snippets(): cut out data snippets around a list of indices.

Peak detection with dynamic threshold:

Expand source code 
"""Detect and handle peaks and troughs as well as threshold crossings in data arrays.

## Peak detection

- `detect_peaks()`: detect peaks and troughs using a relative threshold.
- `peak_width()`: compute width of each peak.
- `peak_size_width()`: compute size and width of each peak.

## Threshold crossings

- `threshold_crossings()`: detect crossings of an absolute threshold.
- `threshold_crossing_times()`: compute times of threshold crossings by linear interpolation.

## Event manipulation

- `trim()`: make the list of peaks and troughs the same length.
- `trim_to_peak()`: ensure that the peak is first.
- `trim_closest()`: ensure that peaks minus troughs is smallest.

- `merge_events()`: Merge events if they are closer than a minimum distance.
- `remove_events()`: Remove events that are too short or too long.
- `widen_events()`: Enlarge events on both sides without overlap.

## Threshold estimation

- `std_threshold()`: estimate detection threshold based on the standard deviation.
- `median_std_threshold()`: estimate detection threshold based on the median standard deviation of data snippets.
- `hist_threshold()`: esimate detection threshold based on a histogram of the data.
- `minmax_threshold()`: estimate detection threshold based on maximum minus minimum value.
- `percentile_threshold()`: estimate detection threshold based on interpercentile range.

## Snippets

- `snippets()`: cut out data snippets around a list of indices.

## Peak detection with dynamic threshold:

- `detect_dynamic_peaks()`: peak and trough detection with a dynamically adapted threshold.
- `accept_peak_size_threshold()`: adapt the dection threshold to the size of the detected peaks.
"""

import sys
import numpy as np
try:
    import matplotlib.pyplot as plt
except ImportError:
    pass

try:
    from numba import jit
except ImportError:
    def jit(*args, **kwargs):
        def decorator_jit(func):
            return func
        return decorator_jit


def detect_peaks(data, threshold):
    """Detect peaks and troughs using a relative threshold.

    This is an implementation of the algorithm by
    Bryan S. Todd and David C. Andrews (1999): The identification of peaks in physiological signals.
    Computers and Biomedical Research 32, 322-335.

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: float or array of floats
        A positive number or array of numbers setting the detection threshold,
        i.e. the minimum distance between peaks and troughs.
        In case of an array make sure that the threshold does not change faster
        than the expected intervals between peaks and troughs. 
    
    Returns
    -------
    peaks: array of ints
        Array of indices of detected peaks.
    troughs: array of ints
        Array of indices of detected troughs.

    Raises
    ------
    ValueError:
        If `threshold <= 0`.
    IndexError:
        If `data` and `threshold` arrays differ in length.
    """
    if np.isscalar(threshold):
        if threshold <= 0:
            raise ValueError('threshold value must be positive!')
        return detect_peaks_fixed(data, threshold)
    else:
        if len(data) != len(threshold):
            raise IndexError('input arrays data and threshold must have same length!')
        if np.min(threshold) <= 0:
            raise ValueError('threshold values must be positive!')
        return detect_peaks_array(data, threshold)


@jit(nopython=True)
def detect_peaks_fixed(data, threshold):
    """Detect peaks and troughs using a fixed, relative threshold.

    Helper function for detect_peaks().

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: float
        A positive number setting the detection threshold,
        i.e. the minimum distance between peaks and troughs.
    
    Returns
    -------
    peaks: array of ints
        Array of indices of detected peaks.
    troughs: array of ints
        Array of indices of detected troughs.
    """
    peaks = []
    troughs = []

    # initialize:
    direction = 0
    min_inx = 0
    max_inx = 0
    min_value = data[0]
    max_value = min_value

    # loop through the data:
    for index, value in enumerate(data):
        # rising?
        if direction > 0:
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            # otherwise, if the new value is falling below
            # the maximum value minus the threshold:
            # the maximum is a peak!
            elif value <= max_value - threshold:
                peaks.append(max_inx)
                # change direction:
                direction = -1
                # store minimum element:
                min_inx = index
                min_value = value

        # falling?
        elif direction < 0:
            if value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value
            # otherwise, if the new value is rising above
            # the minimum value plus the threshold:
            # the minimum is a trough!
            elif value >= min_value + threshold:
                troughs.append(min_inx)
                # change direction:
                direction = +1
                # store maximum element:
                max_inx = index
                max_value = value

        # don't know direction yet:
        else:
            if value <= max_value - threshold:
                direction = -1  # falling
            elif value >= min_value + threshold:
                direction = 1  # rising
                
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            elif value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value

    return np.asarray(peaks, dtype=np.int64), \
           np.asarray(troughs, dtype=np.int64)


@jit(nopython=True)
def detect_peaks_array(data, threshold):
    """Detect peaks and troughs using a variable relative threshold.

    Helper function for detect_peaks().

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: array
        A array of positive numbers setting the detection threshold,
        i.e. the minimum distance between peaks and troughs.
    
    Returns
    -------
    peaks: array of ints
        Array of indices of detected peaks.
    troughs: array of ints
        Array of indices of detected troughs.
    """    
    peaks = []
    troughs = []

    # initialize:
    direction = 0
    min_inx = 0
    max_inx = 0
    min_value = data[0]
    max_value = min_value

    # loop through the data:
    for index, value in enumerate(data):
        # rising?
        if direction > 0:
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            # otherwise, if the new value is falling below
            # the maximum value minus the threshold:
            # the maximum is a peak!
            elif value <= max_value - threshold[index]:
                peaks.append(max_inx)
                # change direction:
                direction = -1
                # store minimum element:
                min_inx = index
                min_value = value

        # falling?
        elif direction < 0:
            if value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value
            # otherwise, if the new value is rising above
            # the minimum value plus the threshold:
            # the minimum is a trough!
            elif value >= min_value + threshold[index]:
                troughs.append(min_inx)
                # change direction:
                direction = +1
                # store maximum element:
                max_inx = index
                max_value = value

        # don't know direction yet:
        else:
            if value <= max_value - threshold[index]:
                direction = -1  # falling
            elif value >= min_value + threshold[index]:
                direction = 1  # rising
                
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            elif value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value

    return np.asarray(peaks, dtype=np.int64), \
           np.asarray(troughs, dtype=np.int64)

    
def peak_width(time, data, peak_indices, trough_indices,
               peak_frac=0.5, base='max'):
    """Width of each peak.

    Peak width is computed from interpolated threshold crossings at
    `peak_frac` hieght of each peak.

    Parameters
    ----------
    time: array
        Time, must not be `None`.
    data: array
        The data with the peaks.
    peak_indices: array
        Indices of the peaks.
    trough_indices: array
        Indices of corresponding troughs.
    peak_frac: float
        Fraction of peak height where its width is measured.
    base: string
        Height and width of peak is measured relative to

        - 'left': trough to the left
        - 'right': trough to the right
        - 'min': the minimum of the two troughs to the left and to the right
        - 'max': the maximum of the two troughs to the left and to the right
        - 'mean': mean of the throughs to the left and to the rigth
        - 'closest': trough that is closest to peak
    
    Returns
    -------
    widths: array
        Width at `peak_frac` height of each peak.

    Raises
    ------
    ValueError:
        If an invalid value is passed to `base`.
    """
    def left_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] 
    def right_base(data, left_inx, right_inx, peak_inx):
        return data[right_inx] 
    def min_base(data, left_inx, right_inx, peak_inx):
        return min(data[left_inx], data[right_inx])
    def max_base(data, left_inx, right_inx, peak_inx):
        return max(data[left_inx], data[right_inx])
    def mean_base(data, left_inx, right_inx, peak_inx):
        return np.mean((data[left_inx], data[right_inx]))
    def closest_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] if peak_inx-left_inx <= right_inx-peak_inx else data[right_inx]
    
    widths = np.zeros(len(peak_indices))
    if len(peak_indices) == 0:
        return widths
    # we need a trough before and after each peak:
    peak_inx = np.asarray(peak_indices, dtype=int)
    trough_inx = np.asarray(trough_indices, dtype=int)
    if len(trough_inx) == 0 or peak_inx[0] < trough_inx[0]:
         trough_inx = np.hstack((0, trough_inx))
    if peak_inx[-1] > trough_inx[-1]:
         trough_inx = np.hstack((trough_inx, len(data)-1))
    # base for size of peaks:
    base_func = closest_base
    if base == 'left':
        base_func = left_base
    elif base == 'right':
        base_func = right_base
    elif base == 'min':
        base_func = min_base
    elif base == 'max':
        base_func = max_base
    elif base == 'mean':
        base_func = mean_base
    elif base == 'closest':
        base_func = closest_base
    else:
        raise ValueError(f'Invalid value for base ({base})')
    # width of peaks:
    for j in range(len(peak_inx)):
        li = trough_inx[j]
        ri = trough_inx[j+1]
        baseval = base_func(data, li, ri, peak_inx[j])
        thresh = baseval*(1.0-peak_frac) + data[peak_inx[j]]*peak_frac
        inx = li + np.argmax(data[li:ri] > thresh)
        if inx > 0:
            ti0 = np.interp(thresh, data[inx-1:inx+1], time[inx-1:inx+1])
        else:
            ti0 = time[0]
        inx = ri - np.argmax(data[ri:li:-1] > thresh)
        if inx+1 < len(data):
            ti1 = np.interp(thresh, data[inx+1:inx-1:-1], time[inx+1:inx-1:-1])
        else:
            ti1 = time[-1]
        widths[j] = ti1 - ti0
    return widths
    
    
def peak_size_width(time, data, peak_indices, trough_indices,
                    peak_frac=0.75, base='closest'):
    """Compute size and width of each peak.

    Parameters
    ----------
    time: array
        Time, must not be `None`.
    data: array
        The data with the peaks.
    peak_indices: array
        Indices of the peaks.
    trough_indices: array
        Indices of the troughs.
    peak_frac: float
        Fraction of peak height where its width is measured.
    base: string
        Height and width of peak is measured relative to

        - 'left': trough to the left
        - 'right': trough to the right
        - 'min': the minimum of the two troughs to the left and to the right
        - 'max': the maximum of the two troughs to the left and to the right
        - 'mean': mean of the throughs to the left and to the rigth
        - 'closest': trough that is closest to peak
    
    Returns
    -------
    peaks: 2-D array
        First dimension is the peak index. Second dimension is
        time, height (value of data at the peak),
        size (peak height minus height of closest trough),
        width (at `peak_frac` size), 0.0 (count) of the peak. See `peak_width()`.

    Raises
    ------
    ValueError:
        If an invalid value is passed to `base`.
    """
    def left_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] 
    def right_base(data, left_inx, right_inx, peak_inx):
        return data[right_inx] 
    def min_base(data, left_inx, right_inx, peak_inx):
        return min(data[left_inx], data[right_inx])
    def max_base(data, left_inx, right_inx, peak_inx):
        return max(data[left_inx], data[right_inx])
    def mean_base(data, left_inx, right_inx, peak_inx):
        return np.mean((data[left_inx], data[right_inx]))
    def closest_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] if peak_inx-left_inx <= right_inx-peak_inx else data[right_inx]
    
    peaks = np.zeros((len(peak_indices), 5))
    if len(peak_indices) == 0:
        return peaks
    # time point of peaks:
    peaks[:, 0] = time[peak_indices]
    # height of peaks:
    peaks[:, 1] = data[peak_indices]
    # we need a trough before and after each peak:
    peak_inx = np.asarray(peak_indices, dtype=int)
    trough_inx = np.asarray(trough_indices, dtype=int)
    if len(trough_inx) == 0 or peak_inx[0] < trough_inx[0]:
         trough_inx = np.hstack((0, trough_inx))

    if peak_inx[-1] > trough_inx[-1]:
         trough_inx = np.hstack((trough_inx, len(data)-1))
    # base for size of peaks:
    base_func = closest_base
    if base == 'left':
        base_func = left_base
    elif base == 'right':
        base_func = right_base
    elif base == 'min':
        base_func = min_base
    elif base == 'max':
        base_func = max_base
    elif base == 'mean':
        base_func = mean_base
    elif base == 'closest':
        base_func = closest_base

    else:
        raise ValueError('Invalid value for base ({base})')
    # size and width of peaks:
    for j, pi in enumerate(peak_inx):
        li = trough_inx[j]
        ri = trough_inx[j+1]
        baseval = base_func(data, li, ri, pi)
        thresh = baseval*(1.0-peak_frac) + data[pi]*peak_frac
        inx = li + np.argmax(data[li:ri] > thresh)
        if inx > 0:
            ti0 = np.interp(thresh, data[inx-1:inx+1], time[inx-1:inx+1])
        else:
            ti0 = time[0]
        inx = ri - np.argmax(data[ri:li:-1] > thresh)
        if inx+1 < len(data):
            ti1 = np.interp(thresh, data[inx+1:inx-1:-1], time[inx+1:inx-1:-1])
        else:
            ti1 = time[-1]
        if np.any(np.isfinite((data[pi], baseval))):
            peaks[j, 2] = data[pi] - baseval
        peaks[j, 3] = ti1 - ti0
    return peaks
    

def threshold_crossings(data, threshold):
    """Detect crossings of a threshold with positive and negative slope.

    Parameters
    ----------
    data: array
        An 1-D array of input data where threshold crossings are detected.
    threshold: float or array
        A number or array of numbers setting the threshold
        that needs to be crossed.
    
    Returns
    -------
    up_indices: array of ints
        A list of indices where the threshold is crossed with positive slope.
    down_indices: array of ints
        A list of indices where the threshold is crossed with negative slope.

    Raises
    ------
    IndexError:
        If `data` and `threshold` arrays differ in length.
    """
    if np.isscalar(threshold):
        up_indices = np.nonzero((data[1:]>threshold) & (data[:-1]<=threshold))[0]
        down_indices = np.nonzero((data[1:]<=threshold) & (data[:-1]>threshold))[0]
    else:
        if len(data) != len(threshold):
            raise IndexError('input arrays data and threshold must have same length!')
        up_indices = np.nonzero((data[1:]>threshold[1:]) & (data[:-1]<=threshold[:-1]))[0]
        down_indices = np.nonzero((data[1:]<=threshold[1:]) & (data[:-1]>threshold[:-1]))[0]
    return up_indices, down_indices

    
def threshold_crossing_times(time, data, threshold, up_indices, down_indices):
    """Compute times of threshold crossings by linear interpolation.

    Parameters
    ----------
    time: array
        Time, must not be `None`.
    data: array
        The data.
    threshold: float
        A number or array of numbers setting the threshold
        that was crossed.
    up_indices: array of ints
        A list of indices where the threshold is crossed with positive slope.
    down_indices: array of ints
        A list of indices where the threshold is crossed with negative slope.
    
    Returns
    -------
    up_times: array of floats
        Interpolated times where the threshold is crossed with positive slope.
    down_times: array of floats
        Interpolated times where the threshold is crossed with negative slope.
    """
    up_times = np.zeros(len(up_indices))
    for k, inx in enumerate(up_indices):
        up_times[k] = np.interp(threshold, data[inx:inx+2], time[inx:inx+2])
    down_times = np.zeros(len(down_indices))
    for k, inx in enumerate(down_indices):
        down_times[k] = np.interp(-threshold, -data[inx:inx+2], time[inx:inx+2])
    return up_times, down_times


def trim(peaks, troughs):
    """Trims the peaks and troughs arrays such that they have the same length.
    
    Parameters
    ----------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.

    Returns
    -------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.
    """
    # common len:
    n = min(len(peaks), len(troughs))
    # align arrays:
    return peaks[:n], troughs[:n]


def trim_to_peak(peaks, troughs):
    """Trims the peaks and troughs arrays such that they have the same length
    and the first peak comes first.
    
    Parameters
    ----------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.

    Returns
    -------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.
    """
    # start index for troughs:
    tidx = 0
    if len(peaks) > 0 and len(troughs) > 0 and troughs[0] < peaks[0]:
        tidx = 1
    # common len:
    n = min(len(peaks), len(troughs[tidx:]))
    # align arrays:
    return peaks[:n], troughs[tidx:tidx + n]


def trim_closest(peaks, troughs):
    """Trims the peaks and troughs arrays such that they have the same length
    and that peaks-troughs is on average as small as possible.
    
    Parameters
    ----------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.

    Returns
    -------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.
    """
    pidx = 0
    tidx = 0
    nn = min(len(peaks), len(troughs))
    if nn == 0:
        return np.array([]), np.array([])
    dist = np.abs(np.mean(peaks[:nn] - troughs[:nn]))
    if len(peaks) == 0 or len(troughs) == 0:
        nn = 0
    else:
        if peaks[0] < troughs[0]:
            nnp = min(len(peaks[1:]), len(troughs))
            distp = np.abs(np.mean(peaks[1:nnp] - troughs[:nnp - 1]))
            if distp < dist:
                pidx = 1
                nn = nnp
        else:
            nnt = min(len(peaks), len(troughs[1:]))
            distt = np.abs(np.mean(peaks[:nnt - 1] - troughs[1:nnt]))
            if distt < dist:
                tidx = 1
                nn = nnt
    # align arrays:
    return peaks[pidx:pidx + nn], troughs[tidx:tidx + nn]


def merge_events(onsets, offsets, min_distance):
    """Merge events if they are closer than a minimum distance.

    If the beginning of an event (onset, peak, or positive threshold crossing,
    is too close to the end of the previous event (offset, trough, or negative
    threshold crossing) the two events are merged into a single one that begins
    with the first one and ends with the second one.
    
    Parameters
    ----------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        as indices or times.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        as indices or times.
    min_distance: int or float
        The minimum distance between events. If the beginning of an event is separated
        from the end of the previous event by less than this distance then the two events
        are merged into one. If the event onsets and offsets are given in indices than
        min_distance is also in indices. 

    Returns
    -------
    merged_onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the merged events
        as indices or times according to onsets.
    merged_offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the merged events
        as indices or times according to offsets.
    """
    onsets, offsets = trim_to_peak(onsets, offsets)
    if len(onsets) == 0 or len(offsets) == 0:
        return np.array([]), np.array([])
    else:
        diff = onsets[1:] - offsets[:-1]
        indices = diff > min_distance
        merged_onsets = onsets[np.hstack([True, indices])]
        merged_offsets = offsets[np.hstack([indices, True])]
        return merged_onsets, merged_offsets

    
def remove_events(onsets, offsets, min_duration, max_duration=None):
    """Remove events that are too short or too long.

    If the length of an event, i.e. `offset` (offset, trough, or negative
    threshold crossing) minus `onset` (onset, peak, or positive threshold crossing),
    is shorter than `min_duration` or longer than `max_duration`, then this event is
    removed.
    
    Parameters
    ----------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        as indices or times.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        as indices or times.
    min_duration: int, float, or None
        The minimum duration of events. If the event offset minus the event onset
        is less than `min_duration`, then the event is removed from the lists.
        If the event onsets and offsets are given in indices than
        `min_duration` is also in indices. If `None` then this test is skipped.
    max_duration: int, float, or None
        The maximum duration of events. If the event offset minus the event onset
        is larger than `max_duration`, then the event is removed from the lists.
        If the event onsets and offsets are given in indices than
        `max_duration` is also in indices. If `None` then this test is skipped.

    Returns
    -------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        with too short and too long events removed as indices or times according to onsets.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        with too short and too long events removed as indices or times according to offsets.
    """
    onsets, offsets = trim_to_peak(onsets, offsets)
    if len(onsets) == 0 or len(offsets) == 0:
        return np.array([]), np.array([])
    elif min_duration is not None or max_duration is not None:
        diff = offsets - onsets
        if min_duration is not None and max_duration is not None:
            indices = (diff > min_duration) & (diff < max_duration)
        elif min_duration is not None:
            indices = diff > min_duration
        else:
            indices = diff < max_duration
        onsets = onsets[indices]
        offsets = offsets[indices]
    return onsets, offsets


def widen_events(onsets, offsets, max_time, duration):
    """Enlarge events on both sides without overlap.

    Subtracts `duration` from the `onsets` and adds `duration` to the offsets.
    If two succeeding events are separated by less than two times the
    `duration`, then the offset of the previous event and the onset of
    the following event are set at the center between the two events.
    
    Parameters
    ----------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        as indices or times.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        as indices or times.
    max_time: int or float
        The maximum value for the end of the last event.
        If the event onsets and offsets are given in indices than
        max_time is the maximum possible index, i.e. the len of the
        data array on which the events where detected.
    duration: int or float
        The number of indices or the time by which the events should
        be enlarged.
        If the event onsets and offsets are given in indices than
        duration is also in indices. 

    Returns
    -------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the enlarged events.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the enlarged events.

    """
    new_onsets = []
    new_offsets = []
    if len(onsets) > 0:
        on_idx = onsets[0]
        new_onsets.append(on_idx - duration if on_idx >= duration else 0)
    for off_idx, on_idx in zip(offsets[:-1], onsets[1:]):
        if on_idx - off_idx < 2*duration:
            mid_idx = (on_idx + off_idx)//2
            new_offsets.append(mid_idx)
            new_onsets.append(mid_idx)
        else:
            new_offsets.append(off_idx + duration)
            new_onsets.append(on_idx - duration)
    if len(offsets) > 0:
        off_idx = offsets[-1]
        new_offsets.append(off_idx + duration if off_idx + duration < max_time else max_time)
    return np.array(new_onsets, dtype=onsets.dtype), np.array(new_offsets, dtype=offsets.dtype)

    
def std_threshold(data, win_size=None, thresh_fac=5.0):
    """Estimates a threshold for peak detection based on the standard deviation of the data.

    The threshold is computed as the standard deviation of the data
    multiplied with `thresh_fac`.

    In case of Gaussian distributed data, setting `thresh_fac=2.0`
    (two standard deviations) captures 68% of the data,
    `thresh_fac=4.0` captures 95%, and `thresh_fac=6.0` 99.7%.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a `win_size` a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    thresh_fac: float
        Factor by which the standard deviation is multiplied to set the threshold.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.

    """

    if win_size:
        threshold = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            std = np.std(data[inx0:inx1], ddof=1)
            threshold[inx0:inx1] = std * thresh_fac
        return threshold
    else:
        return np.std(data, ddof=1) * thresh_fac

    
@jit(nopython=True)
def median_std_threshold(data, win_size=100, thresh_fac=6.0, n_snippets=1000):
    """Estimate a threshold for peak detection based on the median standard deviation of data snippets.

    On `n_snippets` snippets of `win_size` size the standard
    deviation of the data is estimated. The returned threshold is the
    median of these standard deviations that are larger than zero
    multiplied by `thresh_fac`.

    Parameters
    ----------
    data: 1-D array of float
        The data to be analysed.
    win_size: int
        Size of windows on which standarad deviations are computed.
    thresh_fac: float
        Factor by which the median standard deviation is multiplied to set the threshold.
    n_snippets: int
        Number of snippets on which the standard deviations are estimated.

    Returns
    -------
    threshold: float
        The computed threshold.
    """
    if win_size < 10:
        win_size = 10
    step = len(data)//n_snippets
    if step < win_size//2:
        step = win_size//2
    stds = np.array([np.std(data[i:i+win_size])
                     for i in range(0, len(data)-win_size, step)])
    return np.median(stds[stds>0])*thresh_fac

    
def hist_threshold(data, win_size=None, thresh_fac=5.0,
                   nbins=100, hist_height=1.0/np.sqrt(np.e)):
    """Estimate a threshold for peak detection based on a histogram of the data.

    The standard deviation of the data is estimated from half the
    width of the histogram of the data at `hist_height` relative
    height.  This estimates the data's standard deviation by ignoring
    tails of the distribution.

    However, you need enough data to robustly estimate the histogram.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a win_size a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    thresh_fac: float
        Factor by which the width of the histogram is multiplied to set the threshold.
    nbins: int or list of floats
        Number of bins or the bins for computing the histogram.
    hist_height: float
        Height between 0 and 1 at which the width of the histogram is computed.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.
    center: float or 1-D array
        The center (mean) of the width of the histogram.

    """
    if win_size:
        threshold = np.zeros(len(data))
        centers = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            std, center = hist_threshold(data[inx0:inx1], win_size=None,
                                         thresh_fac=thresh_fac, nbins=nbins,
                                         hist_height=hist_height)
            threshold[inx0:inx1] = std
            centers[inx0:inx1] = center
        return threshold, centers
    else:
        maxd = np.max(data)
        mind = np.min(data)
        contrast = np.abs((maxd - mind)/(maxd + mind))
        if contrast > 1e-8:
            hist, bins = np.histogram(data, nbins, density=False)
            inx = hist > np.max(hist) * hist_height
            lower = bins[0:-1][inx][0]
            upper = bins[1:][inx][-1]  # needs to return the next bin
            center = 0.5 * (lower + upper)
            std = 0.5 * (upper - lower)
        else:
            std = np.std(data)
            center = np.mean(data)
        return std * thresh_fac, center

    
def minmax_threshold(data, win_size=None, thresh_fac=0.8):
    """Estimate a threshold for peak detection based on minimum and maximum values of the data.

    The threshold is computed as the difference between maximum and
    minimum value of the data multiplied with `thresh_fac`.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a win_size a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    thresh_fac: float
        Factor by which the difference between minimum and maximum data value
        is multiplied to set the threshold.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.

    """
    if win_size:
        threshold = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            window_min = np.min(data[inx0:inx1])
            window_max = np.max(data[inx0:inx1])
            threshold[inx0:inx1] = (window_max - window_min) * thresh_fac
        return threshold

    else:
        return (np.max(data) - np.min(data)) * thresh_fac


def percentile_threshold(data, win_size=None, thresh_fac=1.0, percentile=1.0):
    """Estimate a threshold for peak detection based on an inter-percentile range of the data.

    The threshold is computed as the range between the percentile and
    100.0-percentile percentiles of the data multiplied with
    thresh_fac.

    For very small values of `percentile` the estimated threshold
    approaches the one returned by `minmax_threshold()` (for same
    values of `thresh_fac`). For `percentile=16.0` and Gaussian
    distributed data, the returned theshold is twice the one returned
    by `std_threshold()` or `hist_threshold()`, i.e. twice the
    standard deviation.

    If you have knowledge about how many data points are in the tails of
    the distribution, then this method is preferred over
    `hist_threshold()`. For example, if you expect peaks that you want
    to detect using `detect_peaks()` at an average rate of 10Hz and
    these peaks are about 1ms wide, then you have a 1ms peak per 100ms
    period, i.e. the peaks make up 1% of the distribution. So you should
    set `percentile=1.0` or lower. For much lower percentile values, you
    might choose `thresh_fac` slightly smaller than one to capture also
    smaller peaks. Setting `percentile` slightly higher might not change
    the estimated threshold too much, since you start incorporating the
    noise floor with a large density, but you may want to set
    `thresh_fac` larger than one to reduce false detections.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a win_size a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    percentile: float
        The interpercentile range is computed at percentile and
        100.0-percentile.
        If zero, compute maximum minus minimum data value as the
        interpercentile range.
    thresh_fac: float
        Factor by which the inter-percentile range of the data is
        multiplied to set the threshold.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.

    """
    if percentile < 1e-8:
        return minmax_threshold(data, win_size=win_size,
                                thresh_fac=thresh_fac)
    if win_size:
        threshold = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            threshold[inx0:inx1] = np.squeeze(np.abs(np.diff(
                np.percentile(data[inx0:inx1], [100.0 - percentile, percentile])))) * thresh_fac
        return threshold
    else:
        return np.squeeze(np.abs(np.diff(
            np.percentile(data, [100.0 - percentile, percentile])))) * thresh_fac


def snippets(data, indices, start=-10, stop=10):
    """Cut out data arround each position given in indices.

    Parameters
    ----------
    data: 1-D array
        Data array from which snippets are extracted.
    indices: list of int
        Indices around which snippets are cut out.
    start: int
        Each snippet starts at index + start.
    stop: int
        Each snippet ends at index + stop.
        
    Returns
    -------
    snippet_data: 2-D array
        The snippets: first index number of snippet, second index time.
    """
    idxs = indices[(indices>=-start) & (indices<len(data)-stop)]
    snippet_data = np.empty((len(idxs), stop-start))
    for k, idx in enumerate(idxs):
        snippet_data[k] = data[idx+start:idx+stop]
    # XXX alternative: check speed and behavior for empty idxs
    # snippets = np.vstack([data[idx+start:idx+stop] for idx in idxs])
    return snippet_data


def detect_dynamic_peaks(data, threshold, min_thresh, tau, time=None,
                         check_peak_func=None, check_trough_func=None, **kwargs):
    """Detect peaks and troughs using a relative threshold.

    The threshold decays dynamically towards min_thresh with time
    constant tau.  Use `check_peak_func` or `check_trough_func` to
    reset the threshold to an appropriate size.

    Based on Bryan S. Todd and David C. Andrews (1999): The
    identification of peaks in physiological signals.  Computers and
    Biomedical Research 32, 322-335.

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: float
        A positive number setting the minimum distance between peaks and troughs.
    min_thresh: float
        The minimum value the threshold is allowed to assume.
    tau: float
        The time constant of the the decay of the threshold value
        given in indices (`time` is None) or time units (`time` is not `None`).
    time: array
        The (optional) 1-D array with the time corresponding to the data values.
    check_peak_func: function
        An optional function to be used for further evaluating and analysing a peak.
        The signature of the function is
        
        ```
        r, th = check_peak_func(time, data, peak_inx, index, min_inx, threshold, **kwargs)
        ```
        
        with the arguments:
        
        - time (array): the full time array that might be None
        - data (array): the full data array
        - peak_inx (int): the index of the  detected peak
        - index (int): the current index
        - min_inx (int): the index of the trough preceeding the peak (might be 0)
        - threshold (float): the threshold value
        - min_thresh (float): the minimum value the threshold is allowed to assume.
        - tau (float): the time constant of the the decay of the threshold value
                       given in indices (time is None) or time units (time is not None)
        - **kwargs: further keyword arguments provided by the user
        - r (scalar or np.array): a single number or an array with properties of the peak or None to skip the peak
        - th (float): a new value for the threshold or None (to keep the original value)
    check_trough_func: function
        An optional function to be used for further evaluating and analysing a trough.
        The signature of the function is
        
        ```
        r, th = check_trough_func(time, data, trough_inx, index, max_inx, threshold, **kwargs)
        ```
        
        with the arguments:
        
        - time (array): the full time array that might be None
        - data (array): the full data array
        - trough_inx (int): the index of the  detected trough
        - index (int): the current index
        - max_inx (int): the index of the peak preceeding the trough (might be 0)
        - threshold (float): the threshold value
        - min_thresh (float): the minimum value the threshold is allowed to assume.
        - tau (float): the time constant of the the decay of the threshold value
                       given in indices (time is None) or time units (time is not None)
        - **kwargs: further keyword arguments provided by the user
        - r (scalar or np.array): a single number or an array with properties of the trough or None to skip the trough
        - th (float): a new value for the threshold or None (to keep the original value)            
    kwargs: key-word arguments
        Arguments passed on to `check_peak_func` and `check_trough_func`.
    
    Returns
    -------
    peak_list: array
        List of peaks.
    trough_list: array
        List of troughs.
        
    - If time is `None` and no `check_peak_func` is given,
      then these are lists of the indices where the peaks/troughs occur.
    - If `time` is given and no `check_peak_func`/`check_trough_func` is given,
      then these are lists of the times where the peaks/troughs occur.
    - If `check_peak_func` or `check_trough_func` is given,
      then these are lists of whatever `check_peak_func`/`check_trough_func` return.

    Raises
    ------
    ValueError:
        If `threshold <= 0` or `min_thresh <= 0` or `tau <= 0`.
    IndexError:
        If `data` and `time` arrays differ in length.

    """
    if threshold <= 0:
        raise ValueError('input argument threshold must be positive!')
    if min_thresh <= 0:
        raise ValueError('input argument min_thresh must be positive!')
    if tau <= 0:
        raise ValueError('input argument tau must be positive!')
    if time is not None and len(data) != len(time):
        raise IndexError('input arrays time and data must have same length!')

    peaks_list = list()
    troughs_list = list()

    # initialize:
    direction = 0
    min_inx = 0
    max_inx = 0
    min_value = data[0]
    max_value = min_value

    # loop through the data:
    for index, value in enumerate(data):

        # decaying threshold (first order low pass filter):
        if time is None:
            threshold += (min_thresh - threshold) / tau
        else:
            idx = index
            if idx + 1 >= len(data):
                idx = len(data) - 2
            threshold += (min_thresh - threshold) * (time[idx + 1] - time[idx]) / tau

        # rising?
        if direction > 0:
            # if the new value is bigger than the old maximum: set it as new maximum:
            if value > max_value:
                max_inx = index  # maximum element
                max_value = value

            # otherwise, if the new value is falling below the maximum value minus the threshold:
            # the maximum is a peak!
            elif max_value >= value + threshold:
                # check and update peak with the check_peak_func function:
                if check_peak_func:
                    r, th = check_peak_func(time, data, max_inx, index,
                                            min_inx, threshold,
                                            min_thresh=min_thresh, tau=tau, **kwargs)
                    if r is not None:
                        # this really is a peak:
                        peaks_list.append(r)
                    if th is not None:
                        threshold = th
                        if threshold < min_thresh:
                            threshold = min_thresh
                else:
                    # this is a peak:
                    if time is None:
                        peaks_list.append(max_inx)
                    else:
                        peaks_list.append(time[max_inx])

                # change direction:
                min_inx = index  # minimum element
                min_value = value
                direction = -1

        # falling?
        elif direction < 0:
            if value < min_value:
                min_inx = index  # minimum element
                min_value = value

            elif value >= min_value + threshold:
                # there was a trough:

                # check and update trough with the check_trough function:
                if check_trough_func:
                    r, th = check_trough_func(time, data, min_inx, index,
                                              max_inx, threshold,
                                              min_thresh=min_thresh, tau=tau, **kwargs)
                    if r is not None:
                        # this really is a trough:
                        troughs_list.append(r)
                    if th is not None:
                        threshold = th
                        if threshold < min_thresh:
                            threshold = min_thresh
                else:
                    # this is a trough:
                    if time is None:
                        troughs_list.append(min_inx)
                    else:
                        troughs_list.append(time[min_inx])

                # change direction:
                max_inx = index  # maximum element
                max_value = value
                direction = 1

        # don't know direction yet:
        else:
            if max_value >= value + threshold:
                direction = -1  # falling
            elif value >= min_value + threshold:
                direction = 1  # rising

            if max_value < value:
                max_inx = index  # maximum element
                max_value = value

            elif value < min_value:
                min_inx = index  # minimum element
                min_value = value

    return np.asarray(peaks_list), np.asarray(troughs_list)


def accept_peak_size_threshold(time, data, event_inx, index, min_inx, threshold,
                               min_thresh, tau, thresh_ampl_fac=0.75, thresh_weight=0.02):
    """Accept each detected peak/trough and return its index or time.
                               
    Adjust the threshold to the size of the detected peak.
    To be passed to the `detect_dynamic_peaks()` function.

    Parameters
    ----------
    time: array
        Time values, can be `None`.
    data: array
        The data in wich peaks and troughs are detected.
    event_inx: int
        Index of the current peak/trough.
    index: int
        Current index.
    min_inx: int
        Index of the previous trough/peak.
    threshold: float
        Threshold value.
    min_thresh: float
        The minimum value the threshold is allowed to assume..
    tau: float
        The time constant of the the decay of the threshold value
        given in indices (`time` is `None`) or time units (`time` is not `None`).
    thresh_ampl_fac: float
        The new threshold is `thresh_ampl_fac` times the size of the current peak.
    thresh_weight: float
        New threshold is weighted against current threshold with `thresh_weight`.

    Returns
    -------
    index: int
        Index of the peak/trough if `time` is `None`.
    time: int
        Time of the peak/trough if `time` is not `None`.
    threshold: float
        The new threshold to be used.
    """
    size = data[event_inx] - data[min_inx]
    threshold += thresh_weight * (thresh_ampl_fac * size - threshold)
    if time is None:
        return event_inx, threshold
    else:
        return time[event_inx], threshold


def main():
    print('Checking eventetection module ...')
    print('')
    # generate data:
    dt = 0.001
    time = np.arange(0.0, 10.0, dt)
    f = 2.0
    data = (0.5 * np.sin(2.0 * np.pi * f * time) + 0.5) ** 4.0
    data += -0.1 * time * (time - 10.0)
    data += 0.1 * np.random.randn(len(data))

    print(f'generated waveform with {int(np.round(time[-1] * f))} peaks')
    plt.plot(time, data)

    print('')
    print('check detect_peaks(data, 1.0)...')
    peaks, troughs = detect_peaks(data, 1.0)
    # print peaks:
    print(f'detected {len(peaks)} peaks with period {np.mean(np.diff(peaks)):.1f} that differs from the real frequency by {f - 1.0 / np.mean(np.diff(peaks)) / np.mean(np.diff(time)):.3f}')
    # print troughs:
    print(f'detected {len(troughs)} troughs with period {np.mean(np.diff(troughs)):.1f} that differs from the real frequency by {f - 1.0 / np.mean(np.diff(troughs)) / np.mean(np.diff(time)):.3f}')

    # plot peaks and troughs:
    plt.plot(time[peaks], data[peaks], '.r', ms=20)
    plt.plot(time[troughs], data[troughs], '.g', ms=20)

    # detect threshold crossings:
    onsets, offsets = threshold_crossings(data, 3.0)
    onsets, offsets = merge_events(onsets, offsets, int(0.5/f/dt))
    plt.plot(time, 3.0*np.ones(len(time)), 'k')
    plt.plot(time[onsets], data[onsets], '.c', ms=20)
    plt.plot(time[offsets], data[offsets], '.b', ms=20)

    plt.ylim(-0.5, 4.0)
    plt.show()

    # timing of the detect_peaks() algorithm:
    import timeit
    def wrapper(func, *args, **kwargs):
        def wrapped():
            return func(*args, **kwargs)
        return wrapped
    wrapped = wrapper(detect_peaks, data, 1.0)
    t1 = timeit.timeit(wrapped, number=200)
    print(t1)


if __name__ == '__main__':
    main()

Functions

def jit(*args, **kwargs)
Expand source code 
def jit(*args, **kwargs):
    def decorator_jit(func):
        return func
    return decorator_jit
def detect_peaks(data, threshold)

Detect peaks and troughs using a relative threshold.

This is an implementation of the algorithm by Bryan S. Todd and David C. Andrews (1999): The identification of peaks in physiological signals. Computers and Biomedical Research 32, 322-335.

Parameters

data : array
An 1-D array of input data where peaks are detected.
threshold : float or array of floats
A positive number or array of numbers setting the detection threshold, i.e. the minimum distance between peaks and troughs. In case of an array make sure that the threshold does not change faster than the expected intervals between peaks and troughs.

Returns

peaks : array of ints
Array of indices of detected peaks.
troughs : array of ints
Array of indices of detected troughs.

Raises

Valueerror

If threshold <= 0.

Indexerror

If data and threshold arrays differ in length.

Expand source code 
def detect_peaks(data, threshold):
    """Detect peaks and troughs using a relative threshold.

    This is an implementation of the algorithm by
    Bryan S. Todd and David C. Andrews (1999): The identification of peaks in physiological signals.
    Computers and Biomedical Research 32, 322-335.

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: float or array of floats
        A positive number or array of numbers setting the detection threshold,
        i.e. the minimum distance between peaks and troughs.
        In case of an array make sure that the threshold does not change faster
        than the expected intervals between peaks and troughs. 
    
    Returns
    -------
    peaks: array of ints
        Array of indices of detected peaks.
    troughs: array of ints
        Array of indices of detected troughs.

    Raises
    ------
    ValueError:
        If `threshold <= 0`.
    IndexError:
        If `data` and `threshold` arrays differ in length.
    """
    if np.isscalar(threshold):
        if threshold <= 0:
            raise ValueError('threshold value must be positive!')
        return detect_peaks_fixed(data, threshold)
    else:
        if len(data) != len(threshold):
            raise IndexError('input arrays data and threshold must have same length!')
        if np.min(threshold) <= 0:
            raise ValueError('threshold values must be positive!')
        return detect_peaks_array(data, threshold)
def detect_peaks_fixed(data, threshold)

Detect peaks and troughs using a fixed, relative threshold.

Helper function for detect_peaks().

Parameters

data : array
An 1-D array of input data where peaks are detected.
threshold : float
A positive number setting the detection threshold, i.e. the minimum distance between peaks and troughs.

Returns

peaks : array of ints
Array of indices of detected peaks.
troughs : array of ints
Array of indices of detected troughs.
Expand source code 
@jit(nopython=True)
def detect_peaks_fixed(data, threshold):
    """Detect peaks and troughs using a fixed, relative threshold.

    Helper function for detect_peaks().

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: float
        A positive number setting the detection threshold,
        i.e. the minimum distance between peaks and troughs.
    
    Returns
    -------
    peaks: array of ints
        Array of indices of detected peaks.
    troughs: array of ints
        Array of indices of detected troughs.
    """
    peaks = []
    troughs = []

    # initialize:
    direction = 0
    min_inx = 0
    max_inx = 0
    min_value = data[0]
    max_value = min_value

    # loop through the data:
    for index, value in enumerate(data):
        # rising?
        if direction > 0:
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            # otherwise, if the new value is falling below
            # the maximum value minus the threshold:
            # the maximum is a peak!
            elif value <= max_value - threshold:
                peaks.append(max_inx)
                # change direction:
                direction = -1
                # store minimum element:
                min_inx = index
                min_value = value

        # falling?
        elif direction < 0:
            if value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value
            # otherwise, if the new value is rising above
            # the minimum value plus the threshold:
            # the minimum is a trough!
            elif value >= min_value + threshold:
                troughs.append(min_inx)
                # change direction:
                direction = +1
                # store maximum element:
                max_inx = index
                max_value = value

        # don't know direction yet:
        else:
            if value <= max_value - threshold:
                direction = -1  # falling
            elif value >= min_value + threshold:
                direction = 1  # rising
                
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            elif value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value

    return np.asarray(peaks, dtype=np.int64), \
           np.asarray(troughs, dtype=np.int64)
def detect_peaks_array(data, threshold)

Detect peaks and troughs using a variable relative threshold.

Helper function for detect_peaks().

Parameters

data : array
An 1-D array of input data where peaks are detected.
threshold : array
A array of positive numbers setting the detection threshold, i.e. the minimum distance between peaks and troughs.

Returns

peaks : array of ints
Array of indices of detected peaks.
troughs : array of ints
Array of indices of detected troughs.
Expand source code 
@jit(nopython=True)
def detect_peaks_array(data, threshold):
    """Detect peaks and troughs using a variable relative threshold.

    Helper function for detect_peaks().

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: array
        A array of positive numbers setting the detection threshold,
        i.e. the minimum distance between peaks and troughs.
    
    Returns
    -------
    peaks: array of ints
        Array of indices of detected peaks.
    troughs: array of ints
        Array of indices of detected troughs.
    """    
    peaks = []
    troughs = []

    # initialize:
    direction = 0
    min_inx = 0
    max_inx = 0
    min_value = data[0]
    max_value = min_value

    # loop through the data:
    for index, value in enumerate(data):
        # rising?
        if direction > 0:
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            # otherwise, if the new value is falling below
            # the maximum value minus the threshold:
            # the maximum is a peak!
            elif value <= max_value - threshold[index]:
                peaks.append(max_inx)
                # change direction:
                direction = -1
                # store minimum element:
                min_inx = index
                min_value = value

        # falling?
        elif direction < 0:
            if value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value
            # otherwise, if the new value is rising above
            # the minimum value plus the threshold:
            # the minimum is a trough!
            elif value >= min_value + threshold[index]:
                troughs.append(min_inx)
                # change direction:
                direction = +1
                # store maximum element:
                max_inx = index
                max_value = value

        # don't know direction yet:
        else:
            if value <= max_value - threshold[index]:
                direction = -1  # falling
            elif value >= min_value + threshold[index]:
                direction = 1  # rising
                
            if value > max_value:
                # update maximum element:
                max_inx = index
                max_value = value
            elif value < min_value:
                # update minimum element:
                min_inx = index
                min_value = value

    return np.asarray(peaks, dtype=np.int64), \
           np.asarray(troughs, dtype=np.int64)
def peak_width(time, data, peak_indices, trough_indices, peak_frac=0.5, base='max')

Width of each peak.

Peak width is computed from interpolated threshold crossings at peak_frac hieght of each peak.

Parameters

time : array
Time, must not be None.
data : array
The data with the peaks.
peak_indices : array
Indices of the peaks.
trough_indices : array
Indices of corresponding troughs.
peak_frac : float
Fraction of peak height where its width is measured.
base : string

Height and width of peak is measured relative to

  • 'left': trough to the left
  • 'right': trough to the right
  • 'min': the minimum of the two troughs to the left and to the right
  • 'max': the maximum of the two troughs to the left and to the right
  • 'mean': mean of the throughs to the left and to the rigth
  • 'closest': trough that is closest to peak

Returns

widths : array
Width at peak_frac height of each peak.

Raises

Valueerror

If an invalid value is passed to base.

Expand source code 
def peak_width(time, data, peak_indices, trough_indices,
               peak_frac=0.5, base='max'):
    """Width of each peak.

    Peak width is computed from interpolated threshold crossings at
    `peak_frac` hieght of each peak.

    Parameters
    ----------
    time: array
        Time, must not be `None`.
    data: array
        The data with the peaks.
    peak_indices: array
        Indices of the peaks.
    trough_indices: array
        Indices of corresponding troughs.
    peak_frac: float
        Fraction of peak height where its width is measured.
    base: string
        Height and width of peak is measured relative to

        - 'left': trough to the left
        - 'right': trough to the right
        - 'min': the minimum of the two troughs to the left and to the right
        - 'max': the maximum of the two troughs to the left and to the right
        - 'mean': mean of the throughs to the left and to the rigth
        - 'closest': trough that is closest to peak
    
    Returns
    -------
    widths: array
        Width at `peak_frac` height of each peak.

    Raises
    ------
    ValueError:
        If an invalid value is passed to `base`.
    """
    def left_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] 
    def right_base(data, left_inx, right_inx, peak_inx):
        return data[right_inx] 
    def min_base(data, left_inx, right_inx, peak_inx):
        return min(data[left_inx], data[right_inx])
    def max_base(data, left_inx, right_inx, peak_inx):
        return max(data[left_inx], data[right_inx])
    def mean_base(data, left_inx, right_inx, peak_inx):
        return np.mean((data[left_inx], data[right_inx]))
    def closest_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] if peak_inx-left_inx <= right_inx-peak_inx else data[right_inx]
    
    widths = np.zeros(len(peak_indices))
    if len(peak_indices) == 0:
        return widths
    # we need a trough before and after each peak:
    peak_inx = np.asarray(peak_indices, dtype=int)
    trough_inx = np.asarray(trough_indices, dtype=int)
    if len(trough_inx) == 0 or peak_inx[0] < trough_inx[0]:
         trough_inx = np.hstack((0, trough_inx))
    if peak_inx[-1] > trough_inx[-1]:
         trough_inx = np.hstack((trough_inx, len(data)-1))
    # base for size of peaks:
    base_func = closest_base
    if base == 'left':
        base_func = left_base
    elif base == 'right':
        base_func = right_base
    elif base == 'min':
        base_func = min_base
    elif base == 'max':
        base_func = max_base
    elif base == 'mean':
        base_func = mean_base
    elif base == 'closest':
        base_func = closest_base
    else:
        raise ValueError(f'Invalid value for base ({base})')
    # width of peaks:
    for j in range(len(peak_inx)):
        li = trough_inx[j]
        ri = trough_inx[j+1]
        baseval = base_func(data, li, ri, peak_inx[j])
        thresh = baseval*(1.0-peak_frac) + data[peak_inx[j]]*peak_frac
        inx = li + np.argmax(data[li:ri] > thresh)
        if inx > 0:
            ti0 = np.interp(thresh, data[inx-1:inx+1], time[inx-1:inx+1])
        else:
            ti0 = time[0]
        inx = ri - np.argmax(data[ri:li:-1] > thresh)
        if inx+1 < len(data):
            ti1 = np.interp(thresh, data[inx+1:inx-1:-1], time[inx+1:inx-1:-1])
        else:
            ti1 = time[-1]
        widths[j] = ti1 - ti0
    return widths
def peak_size_width(time, data, peak_indices, trough_indices, peak_frac=0.75, base='closest')

Compute size and width of each peak.

Parameters

time : array
Time, must not be None.
data : array
The data with the peaks.
peak_indices : array
Indices of the peaks.
trough_indices : array
Indices of the troughs.
peak_frac : float
Fraction of peak height where its width is measured.
base : string

Height and width of peak is measured relative to

  • 'left': trough to the left
  • 'right': trough to the right
  • 'min': the minimum of the two troughs to the left and to the right
  • 'max': the maximum of the two troughs to the left and to the right
  • 'mean': mean of the throughs to the left and to the rigth
  • 'closest': trough that is closest to peak

Returns

peaks : 2-D array
First dimension is the peak index. Second dimension is time, height (value of data at the peak), size (peak height minus height of closest trough), width (at peak_frac size), 0.0 (count) of the peak. See peak_width().

Raises

Valueerror

If an invalid value is passed to base.

Expand source code 
def peak_size_width(time, data, peak_indices, trough_indices,
                    peak_frac=0.75, base='closest'):
    """Compute size and width of each peak.

    Parameters
    ----------
    time: array
        Time, must not be `None`.
    data: array
        The data with the peaks.
    peak_indices: array
        Indices of the peaks.
    trough_indices: array
        Indices of the troughs.
    peak_frac: float
        Fraction of peak height where its width is measured.
    base: string
        Height and width of peak is measured relative to

        - 'left': trough to the left
        - 'right': trough to the right
        - 'min': the minimum of the two troughs to the left and to the right
        - 'max': the maximum of the two troughs to the left and to the right
        - 'mean': mean of the throughs to the left and to the rigth
        - 'closest': trough that is closest to peak
    
    Returns
    -------
    peaks: 2-D array
        First dimension is the peak index. Second dimension is
        time, height (value of data at the peak),
        size (peak height minus height of closest trough),
        width (at `peak_frac` size), 0.0 (count) of the peak. See `peak_width()`.

    Raises
    ------
    ValueError:
        If an invalid value is passed to `base`.
    """
    def left_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] 
    def right_base(data, left_inx, right_inx, peak_inx):
        return data[right_inx] 
    def min_base(data, left_inx, right_inx, peak_inx):
        return min(data[left_inx], data[right_inx])
    def max_base(data, left_inx, right_inx, peak_inx):
        return max(data[left_inx], data[right_inx])
    def mean_base(data, left_inx, right_inx, peak_inx):
        return np.mean((data[left_inx], data[right_inx]))
    def closest_base(data, left_inx, right_inx, peak_inx):
        return data[left_inx] if peak_inx-left_inx <= right_inx-peak_inx else data[right_inx]
    
    peaks = np.zeros((len(peak_indices), 5))
    if len(peak_indices) == 0:
        return peaks
    # time point of peaks:
    peaks[:, 0] = time[peak_indices]
    # height of peaks:
    peaks[:, 1] = data[peak_indices]
    # we need a trough before and after each peak:
    peak_inx = np.asarray(peak_indices, dtype=int)
    trough_inx = np.asarray(trough_indices, dtype=int)
    if len(trough_inx) == 0 or peak_inx[0] < trough_inx[0]:
         trough_inx = np.hstack((0, trough_inx))

    if peak_inx[-1] > trough_inx[-1]:
         trough_inx = np.hstack((trough_inx, len(data)-1))
    # base for size of peaks:
    base_func = closest_base
    if base == 'left':
        base_func = left_base
    elif base == 'right':
        base_func = right_base
    elif base == 'min':
        base_func = min_base
    elif base == 'max':
        base_func = max_base
    elif base == 'mean':
        base_func = mean_base
    elif base == 'closest':
        base_func = closest_base

    else:
        raise ValueError('Invalid value for base ({base})')
    # size and width of peaks:
    for j, pi in enumerate(peak_inx):
        li = trough_inx[j]
        ri = trough_inx[j+1]
        baseval = base_func(data, li, ri, pi)
        thresh = baseval*(1.0-peak_frac) + data[pi]*peak_frac
        inx = li + np.argmax(data[li:ri] > thresh)
        if inx > 0:
            ti0 = np.interp(thresh, data[inx-1:inx+1], time[inx-1:inx+1])
        else:
            ti0 = time[0]
        inx = ri - np.argmax(data[ri:li:-1] > thresh)
        if inx+1 < len(data):
            ti1 = np.interp(thresh, data[inx+1:inx-1:-1], time[inx+1:inx-1:-1])
        else:
            ti1 = time[-1]
        if np.any(np.isfinite((data[pi], baseval))):
            peaks[j, 2] = data[pi] - baseval
        peaks[j, 3] = ti1 - ti0
    return peaks
def threshold_crossings(data, threshold)

Detect crossings of a threshold with positive and negative slope.

Parameters

data : array
An 1-D array of input data where threshold crossings are detected.
threshold : float or array
A number or array of numbers setting the threshold that needs to be crossed.

Returns

up_indices : array of ints
A list of indices where the threshold is crossed with positive slope.
down_indices : array of ints
A list of indices where the threshold is crossed with negative slope.

Raises

Indexerror

If data and threshold arrays differ in length.

Expand source code 
def threshold_crossings(data, threshold):
    """Detect crossings of a threshold with positive and negative slope.

    Parameters
    ----------
    data: array
        An 1-D array of input data where threshold crossings are detected.
    threshold: float or array
        A number or array of numbers setting the threshold
        that needs to be crossed.
    
    Returns
    -------
    up_indices: array of ints
        A list of indices where the threshold is crossed with positive slope.
    down_indices: array of ints
        A list of indices where the threshold is crossed with negative slope.

    Raises
    ------
    IndexError:
        If `data` and `threshold` arrays differ in length.
    """
    if np.isscalar(threshold):
        up_indices = np.nonzero((data[1:]>threshold) & (data[:-1]<=threshold))[0]
        down_indices = np.nonzero((data[1:]<=threshold) & (data[:-1]>threshold))[0]
    else:
        if len(data) != len(threshold):
            raise IndexError('input arrays data and threshold must have same length!')
        up_indices = np.nonzero((data[1:]>threshold[1:]) & (data[:-1]<=threshold[:-1]))[0]
        down_indices = np.nonzero((data[1:]<=threshold[1:]) & (data[:-1]>threshold[:-1]))[0]
    return up_indices, down_indices
def threshold_crossing_times(time, data, threshold, up_indices, down_indices)

Compute times of threshold crossings by linear interpolation.

Parameters

time : array
Time, must not be None.
data : array
The data.
threshold : float
A number or array of numbers setting the threshold that was crossed.
up_indices : array of ints
A list of indices where the threshold is crossed with positive slope.
down_indices : array of ints
A list of indices where the threshold is crossed with negative slope.

Returns

up_times : array of floats
Interpolated times where the threshold is crossed with positive slope.
down_times : array of floats
Interpolated times where the threshold is crossed with negative slope.
Expand source code 
def threshold_crossing_times(time, data, threshold, up_indices, down_indices):
    """Compute times of threshold crossings by linear interpolation.

    Parameters
    ----------
    time: array
        Time, must not be `None`.
    data: array
        The data.
    threshold: float
        A number or array of numbers setting the threshold
        that was crossed.
    up_indices: array of ints
        A list of indices where the threshold is crossed with positive slope.
    down_indices: array of ints
        A list of indices where the threshold is crossed with negative slope.
    
    Returns
    -------
    up_times: array of floats
        Interpolated times where the threshold is crossed with positive slope.
    down_times: array of floats
        Interpolated times where the threshold is crossed with negative slope.
    """
    up_times = np.zeros(len(up_indices))
    for k, inx in enumerate(up_indices):
        up_times[k] = np.interp(threshold, data[inx:inx+2], time[inx:inx+2])
    down_times = np.zeros(len(down_indices))
    for k, inx in enumerate(down_indices):
        down_times[k] = np.interp(-threshold, -data[inx:inx+2], time[inx:inx+2])
    return up_times, down_times
def trim(peaks, troughs)

Trims the peaks and troughs arrays such that they have the same length.

Parameters

peaks : array
List of peak indices or times.
troughs : array
List of trough indices or times.

Returns

peaks : array
List of peak indices or times.
troughs : array
List of trough indices or times.
Expand source code 
def trim(peaks, troughs):
    """Trims the peaks and troughs arrays such that they have the same length.
    
    Parameters
    ----------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.

    Returns
    -------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.
    """
    # common len:
    n = min(len(peaks), len(troughs))
    # align arrays:
    return peaks[:n], troughs[:n]
def trim_to_peak(peaks, troughs)

Trims the peaks and troughs arrays such that they have the same length and the first peak comes first.

Parameters

peaks : array
List of peak indices or times.
troughs : array
List of trough indices or times.

Returns

peaks : array
List of peak indices or times.
troughs : array
List of trough indices or times.
Expand source code 
def trim_to_peak(peaks, troughs):
    """Trims the peaks and troughs arrays such that they have the same length
    and the first peak comes first.
    
    Parameters
    ----------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.

    Returns
    -------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.
    """
    # start index for troughs:
    tidx = 0
    if len(peaks) > 0 and len(troughs) > 0 and troughs[0] < peaks[0]:
        tidx = 1
    # common len:
    n = min(len(peaks), len(troughs[tidx:]))
    # align arrays:
    return peaks[:n], troughs[tidx:tidx + n]
def trim_closest(peaks, troughs)

Trims the peaks and troughs arrays such that they have the same length and that peaks-troughs is on average as small as possible.

Parameters

peaks : array
List of peak indices or times.
troughs : array
List of trough indices or times.

Returns

peaks : array
List of peak indices or times.
troughs : array
List of trough indices or times.
Expand source code 
def trim_closest(peaks, troughs):
    """Trims the peaks and troughs arrays such that they have the same length
    and that peaks-troughs is on average as small as possible.
    
    Parameters
    ----------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.

    Returns
    -------
    peaks: array
        List of peak indices or times.
    troughs: array
        List of trough indices or times.
    """
    pidx = 0
    tidx = 0
    nn = min(len(peaks), len(troughs))
    if nn == 0:
        return np.array([]), np.array([])
    dist = np.abs(np.mean(peaks[:nn] - troughs[:nn]))
    if len(peaks) == 0 or len(troughs) == 0:
        nn = 0
    else:
        if peaks[0] < troughs[0]:
            nnp = min(len(peaks[1:]), len(troughs))
            distp = np.abs(np.mean(peaks[1:nnp] - troughs[:nnp - 1]))
            if distp < dist:
                pidx = 1
                nn = nnp
        else:
            nnt = min(len(peaks), len(troughs[1:]))
            distt = np.abs(np.mean(peaks[:nnt - 1] - troughs[1:nnt]))
            if distt < dist:
                tidx = 1
                nn = nnt
    # align arrays:
    return peaks[pidx:pidx + nn], troughs[tidx:tidx + nn]
def merge_events(onsets, offsets, min_distance)

Merge events if they are closer than a minimum distance.

If the beginning of an event (onset, peak, or positive threshold crossing, is too close to the end of the previous event (offset, trough, or negative threshold crossing) the two events are merged into a single one that begins with the first one and ends with the second one.

Parameters

onsets : 1-D array
The onsets (peaks, or positive threshold crossings) of the events as indices or times.
offsets : 1-D array
The offsets (troughs, or negative threshold crossings) of the events as indices or times.
min_distance : int or float
The minimum distance between events. If the beginning of an event is separated from the end of the previous event by less than this distance then the two events are merged into one. If the event onsets and offsets are given in indices than min_distance is also in indices.

Returns

merged_onsets : 1-D array
The onsets (peaks, or positive threshold crossings) of the merged events as indices or times according to onsets.
merged_offsets : 1-D array
The offsets (troughs, or negative threshold crossings) of the merged events as indices or times according to offsets.
Expand source code 
def merge_events(onsets, offsets, min_distance):
    """Merge events if they are closer than a minimum distance.

    If the beginning of an event (onset, peak, or positive threshold crossing,
    is too close to the end of the previous event (offset, trough, or negative
    threshold crossing) the two events are merged into a single one that begins
    with the first one and ends with the second one.
    
    Parameters
    ----------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        as indices or times.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        as indices or times.
    min_distance: int or float
        The minimum distance between events. If the beginning of an event is separated
        from the end of the previous event by less than this distance then the two events
        are merged into one. If the event onsets and offsets are given in indices than
        min_distance is also in indices. 

    Returns
    -------
    merged_onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the merged events
        as indices or times according to onsets.
    merged_offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the merged events
        as indices or times according to offsets.
    """
    onsets, offsets = trim_to_peak(onsets, offsets)
    if len(onsets) == 0 or len(offsets) == 0:
        return np.array([]), np.array([])
    else:
        diff = onsets[1:] - offsets[:-1]
        indices = diff > min_distance
        merged_onsets = onsets[np.hstack([True, indices])]
        merged_offsets = offsets[np.hstack([indices, True])]
        return merged_onsets, merged_offsets
def remove_events(onsets, offsets, min_duration, max_duration=None)

Remove events that are too short or too long.

If the length of an event, i.e. offset (offset, trough, or negative threshold crossing) minus onset (onset, peak, or positive threshold crossing), is shorter than min_duration or longer than max_duration, then this event is removed.

Parameters

onsets : 1-D array
The onsets (peaks, or positive threshold crossings) of the events as indices or times.
offsets : 1-D array
The offsets (troughs, or negative threshold crossings) of the events as indices or times.
min_duration : int, float, or None
The minimum duration of events. If the event offset minus the event onset is less than min_duration, then the event is removed from the lists. If the event onsets and offsets are given in indices than min_duration is also in indices. If None then this test is skipped.
max_duration : int, float, or None
The maximum duration of events. If the event offset minus the event onset is larger than max_duration, then the event is removed from the lists. If the event onsets and offsets are given in indices than max_duration is also in indices. If None then this test is skipped.

Returns

onsets : 1-D array
The onsets (peaks, or positive threshold crossings) of the events with too short and too long events removed as indices or times according to onsets.
offsets : 1-D array
The offsets (troughs, or negative threshold crossings) of the events with too short and too long events removed as indices or times according to offsets.
Expand source code 
def remove_events(onsets, offsets, min_duration, max_duration=None):
    """Remove events that are too short or too long.

    If the length of an event, i.e. `offset` (offset, trough, or negative
    threshold crossing) minus `onset` (onset, peak, or positive threshold crossing),
    is shorter than `min_duration` or longer than `max_duration`, then this event is
    removed.
    
    Parameters
    ----------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        as indices or times.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        as indices or times.
    min_duration: int, float, or None
        The minimum duration of events. If the event offset minus the event onset
        is less than `min_duration`, then the event is removed from the lists.
        If the event onsets and offsets are given in indices than
        `min_duration` is also in indices. If `None` then this test is skipped.
    max_duration: int, float, or None
        The maximum duration of events. If the event offset minus the event onset
        is larger than `max_duration`, then the event is removed from the lists.
        If the event onsets and offsets are given in indices than
        `max_duration` is also in indices. If `None` then this test is skipped.

    Returns
    -------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        with too short and too long events removed as indices or times according to onsets.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        with too short and too long events removed as indices or times according to offsets.
    """
    onsets, offsets = trim_to_peak(onsets, offsets)
    if len(onsets) == 0 or len(offsets) == 0:
        return np.array([]), np.array([])
    elif min_duration is not None or max_duration is not None:
        diff = offsets - onsets
        if min_duration is not None and max_duration is not None:
            indices = (diff > min_duration) & (diff < max_duration)
        elif min_duration is not None:
            indices = diff > min_duration
        else:
            indices = diff < max_duration
        onsets = onsets[indices]
        offsets = offsets[indices]
    return onsets, offsets
def widen_events(onsets, offsets, max_time, duration)

Enlarge events on both sides without overlap.

Subtracts duration from the onsets and adds duration to the offsets. If two succeeding events are separated by less than two times the duration, then the offset of the previous event and the onset of the following event are set at the center between the two events.

Parameters

onsets : 1-D array
The onsets (peaks, or positive threshold crossings) of the events as indices or times.
offsets : 1-D array
The offsets (troughs, or negative threshold crossings) of the events as indices or times.
max_time : int or float
The maximum value for the end of the last event. If the event onsets and offsets are given in indices than max_time is the maximum possible index, i.e. the len of the data array on which the events where detected.
duration : int or float
The number of indices or the time by which the events should be enlarged. If the event onsets and offsets are given in indices than duration is also in indices.

Returns

onsets : 1-D array
The onsets (peaks, or positive threshold crossings) of the enlarged events.
offsets : 1-D array
The offsets (troughs, or negative threshold crossings) of the enlarged events.
Expand source code 
def widen_events(onsets, offsets, max_time, duration):
    """Enlarge events on both sides without overlap.

    Subtracts `duration` from the `onsets` and adds `duration` to the offsets.
    If two succeeding events are separated by less than two times the
    `duration`, then the offset of the previous event and the onset of
    the following event are set at the center between the two events.
    
    Parameters
    ----------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the events
        as indices or times.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the events
        as indices or times.
    max_time: int or float
        The maximum value for the end of the last event.
        If the event onsets and offsets are given in indices than
        max_time is the maximum possible index, i.e. the len of the
        data array on which the events where detected.
    duration: int or float
        The number of indices or the time by which the events should
        be enlarged.
        If the event onsets and offsets are given in indices than
        duration is also in indices. 

    Returns
    -------
    onsets: 1-D array
        The onsets (peaks, or positive threshold crossings) of the enlarged events.
    offsets: 1-D array
        The offsets (troughs, or negative threshold crossings) of the enlarged events.

    """
    new_onsets = []
    new_offsets = []
    if len(onsets) > 0:
        on_idx = onsets[0]
        new_onsets.append(on_idx - duration if on_idx >= duration else 0)
    for off_idx, on_idx in zip(offsets[:-1], onsets[1:]):
        if on_idx - off_idx < 2*duration:
            mid_idx = (on_idx + off_idx)//2
            new_offsets.append(mid_idx)
            new_onsets.append(mid_idx)
        else:
            new_offsets.append(off_idx + duration)
            new_onsets.append(on_idx - duration)
    if len(offsets) > 0:
        off_idx = offsets[-1]
        new_offsets.append(off_idx + duration if off_idx + duration < max_time else max_time)
    return np.array(new_onsets, dtype=onsets.dtype), np.array(new_offsets, dtype=offsets.dtype)
def std_threshold(data, win_size=None, thresh_fac=5.0)

Estimates a threshold for peak detection based on the standard deviation of the data.

The threshold is computed as the standard deviation of the data multiplied with thresh_fac.

In case of Gaussian distributed data, setting thresh_fac=2.0 (two standard deviations) captures 68% of the data, thresh_fac=4.0 captures 95%, and thresh_fac=6.0 99.7%.

If win_size is given, then the threshold is computed for half-overlapping windows of size win_size separately. In this case the returned threshold is an array of the same size as data. Without a win_size a single threshold value determined from the whole data array is returned.

Parameters

data : 1-D array
The data to be analyzed.
win_size : int or None
Size of window in which a threshold value is computed.
thresh_fac : float
Factor by which the standard deviation is multiplied to set the threshold.

Returns

threshold : float or 1-D array
The computed threshold.
Expand source code 
def std_threshold(data, win_size=None, thresh_fac=5.0):
    """Estimates a threshold for peak detection based on the standard deviation of the data.

    The threshold is computed as the standard deviation of the data
    multiplied with `thresh_fac`.

    In case of Gaussian distributed data, setting `thresh_fac=2.0`
    (two standard deviations) captures 68% of the data,
    `thresh_fac=4.0` captures 95%, and `thresh_fac=6.0` 99.7%.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a `win_size` a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    thresh_fac: float
        Factor by which the standard deviation is multiplied to set the threshold.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.

    """

    if win_size:
        threshold = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            std = np.std(data[inx0:inx1], ddof=1)
            threshold[inx0:inx1] = std * thresh_fac
        return threshold
    else:
        return np.std(data, ddof=1) * thresh_fac
def median_std_threshold(data, win_size=100, thresh_fac=6.0, n_snippets=1000)

Estimate a threshold for peak detection based on the median standard deviation of data snippets.

On n_snippets snippets of win_size size the standard deviation of the data is estimated. The returned threshold is the median of these standard deviations that are larger than zero multiplied by thresh_fac.

Parameters

data : 1-D array of float
The data to be analysed.
win_size : int
Size of windows on which standarad deviations are computed.
thresh_fac : float
Factor by which the median standard deviation is multiplied to set the threshold.
n_snippets : int
Number of snippets on which the standard deviations are estimated.

Returns

threshold : float
The computed threshold.
Expand source code 
@jit(nopython=True)
def median_std_threshold(data, win_size=100, thresh_fac=6.0, n_snippets=1000):
    """Estimate a threshold for peak detection based on the median standard deviation of data snippets.

    On `n_snippets` snippets of `win_size` size the standard
    deviation of the data is estimated. The returned threshold is the
    median of these standard deviations that are larger than zero
    multiplied by `thresh_fac`.

    Parameters
    ----------
    data: 1-D array of float
        The data to be analysed.
    win_size: int
        Size of windows on which standarad deviations are computed.
    thresh_fac: float
        Factor by which the median standard deviation is multiplied to set the threshold.
    n_snippets: int
        Number of snippets on which the standard deviations are estimated.

    Returns
    -------
    threshold: float
        The computed threshold.
    """
    if win_size < 10:
        win_size = 10
    step = len(data)//n_snippets
    if step < win_size//2:
        step = win_size//2
    stds = np.array([np.std(data[i:i+win_size])
                     for i in range(0, len(data)-win_size, step)])
    return np.median(stds[stds>0])*thresh_fac
def hist_threshold(data, win_size=None, thresh_fac=5.0, nbins=100, hist_height=0.6065306597126334)

Estimate a threshold for peak detection based on a histogram of the data.

The standard deviation of the data is estimated from half the width of the histogram of the data at hist_height relative height. This estimates the data's standard deviation by ignoring tails of the distribution.

However, you need enough data to robustly estimate the histogram.

If win_size is given, then the threshold is computed for half-overlapping windows of size win_size separately. In this case the returned threshold is an array of the same size as data. Without a win_size a single threshold value determined from the whole data array is returned.

Parameters

data : 1-D array
The data to be analyzed.
win_size : int or None
Size of window in which a threshold value is computed.
thresh_fac : float
Factor by which the width of the histogram is multiplied to set the threshold.
nbins : int or list of floats
Number of bins or the bins for computing the histogram.
hist_height : float
Height between 0 and 1 at which the width of the histogram is computed.

Returns

threshold : float or 1-D array
The computed threshold.
center : float or 1-D array
The center (mean) of the width of the histogram.
Expand source code 
def hist_threshold(data, win_size=None, thresh_fac=5.0,
                   nbins=100, hist_height=1.0/np.sqrt(np.e)):
    """Estimate a threshold for peak detection based on a histogram of the data.

    The standard deviation of the data is estimated from half the
    width of the histogram of the data at `hist_height` relative
    height.  This estimates the data's standard deviation by ignoring
    tails of the distribution.

    However, you need enough data to robustly estimate the histogram.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a win_size a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    thresh_fac: float
        Factor by which the width of the histogram is multiplied to set the threshold.
    nbins: int or list of floats
        Number of bins or the bins for computing the histogram.
    hist_height: float
        Height between 0 and 1 at which the width of the histogram is computed.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.
    center: float or 1-D array
        The center (mean) of the width of the histogram.

    """
    if win_size:
        threshold = np.zeros(len(data))
        centers = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            std, center = hist_threshold(data[inx0:inx1], win_size=None,
                                         thresh_fac=thresh_fac, nbins=nbins,
                                         hist_height=hist_height)
            threshold[inx0:inx1] = std
            centers[inx0:inx1] = center
        return threshold, centers
    else:
        maxd = np.max(data)
        mind = np.min(data)
        contrast = np.abs((maxd - mind)/(maxd + mind))
        if contrast > 1e-8:
            hist, bins = np.histogram(data, nbins, density=False)
            inx = hist > np.max(hist) * hist_height
            lower = bins[0:-1][inx][0]
            upper = bins[1:][inx][-1]  # needs to return the next bin
            center = 0.5 * (lower + upper)
            std = 0.5 * (upper - lower)
        else:
            std = np.std(data)
            center = np.mean(data)
        return std * thresh_fac, center
def minmax_threshold(data, win_size=None, thresh_fac=0.8)

Estimate a threshold for peak detection based on minimum and maximum values of the data.

The threshold is computed as the difference between maximum and minimum value of the data multiplied with thresh_fac.

If win_size is given, then the threshold is computed for half-overlapping windows of size win_size separately. In this case the returned threshold is an array of the same size as data. Without a win_size a single threshold value determined from the whole data array is returned.

Parameters

data : 1-D array
The data to be analyzed.
win_size : int or None
Size of window in which a threshold value is computed.
thresh_fac : float
Factor by which the difference between minimum and maximum data value is multiplied to set the threshold.

Returns

threshold : float or 1-D array
The computed threshold.
Expand source code 
def minmax_threshold(data, win_size=None, thresh_fac=0.8):
    """Estimate a threshold for peak detection based on minimum and maximum values of the data.

    The threshold is computed as the difference between maximum and
    minimum value of the data multiplied with `thresh_fac`.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a win_size a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    thresh_fac: float
        Factor by which the difference between minimum and maximum data value
        is multiplied to set the threshold.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.

    """
    if win_size:
        threshold = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            window_min = np.min(data[inx0:inx1])
            window_max = np.max(data[inx0:inx1])
            threshold[inx0:inx1] = (window_max - window_min) * thresh_fac
        return threshold

    else:
        return (np.max(data) - np.min(data)) * thresh_fac
def percentile_threshold(data, win_size=None, thresh_fac=1.0, percentile=1.0)

Estimate a threshold for peak detection based on an inter-percentile range of the data.

The threshold is computed as the range between the percentile and 100.0-percentile percentiles of the data multiplied with thresh_fac.

For very small values of percentile the estimated threshold approaches the one returned by minmax_threshold() (for same values of thresh_fac). For percentile=16.0 and Gaussian distributed data, the returned theshold is twice the one returned by std_threshold() or hist_threshold(), i.e. twice the standard deviation.

If you have knowledge about how many data points are in the tails of the distribution, then this method is preferred over hist_threshold(). For example, if you expect peaks that you want to detect using detect_peaks() at an average rate of 10Hz and these peaks are about 1ms wide, then you have a 1ms peak per 100ms period, i.e. the peaks make up 1% of the distribution. So you should set percentile=1.0 or lower. For much lower percentile values, you might choose thresh_fac slightly smaller than one to capture also smaller peaks. Setting percentile slightly higher might not change the estimated threshold too much, since you start incorporating the noise floor with a large density, but you may want to set thresh_fac larger than one to reduce false detections.

If win_size is given, then the threshold is computed for half-overlapping windows of size win_size separately. In this case the returned threshold is an array of the same size as data. Without a win_size a single threshold value determined from the whole data array is returned.

Parameters

data : 1-D array
The data to be analyzed.
win_size : int or None
Size of window in which a threshold value is computed.
percentile : float
The interpercentile range is computed at percentile and 100.0-percentile. If zero, compute maximum minus minimum data value as the interpercentile range.
thresh_fac : float
Factor by which the inter-percentile range of the data is multiplied to set the threshold.

Returns

threshold : float or 1-D array
The computed threshold.
Expand source code 
def percentile_threshold(data, win_size=None, thresh_fac=1.0, percentile=1.0):
    """Estimate a threshold for peak detection based on an inter-percentile range of the data.

    The threshold is computed as the range between the percentile and
    100.0-percentile percentiles of the data multiplied with
    thresh_fac.

    For very small values of `percentile` the estimated threshold
    approaches the one returned by `minmax_threshold()` (for same
    values of `thresh_fac`). For `percentile=16.0` and Gaussian
    distributed data, the returned theshold is twice the one returned
    by `std_threshold()` or `hist_threshold()`, i.e. twice the
    standard deviation.

    If you have knowledge about how many data points are in the tails of
    the distribution, then this method is preferred over
    `hist_threshold()`. For example, if you expect peaks that you want
    to detect using `detect_peaks()` at an average rate of 10Hz and
    these peaks are about 1ms wide, then you have a 1ms peak per 100ms
    period, i.e. the peaks make up 1% of the distribution. So you should
    set `percentile=1.0` or lower. For much lower percentile values, you
    might choose `thresh_fac` slightly smaller than one to capture also
    smaller peaks. Setting `percentile` slightly higher might not change
    the estimated threshold too much, since you start incorporating the
    noise floor with a large density, but you may want to set
    `thresh_fac` larger than one to reduce false detections.

    If `win_size` is given, then the threshold is computed for
    half-overlapping windows of size `win_size` separately.  In this
    case the returned threshold is an array of the same size as data.
    Without a win_size a single threshold value determined from the
    whole data array is returned.

    Parameters
    ----------
    data: 1-D array
        The data to be analyzed.
    win_size: int or None
        Size of window in which a threshold value is computed.
    percentile: float
        The interpercentile range is computed at percentile and
        100.0-percentile.
        If zero, compute maximum minus minimum data value as the
        interpercentile range.
    thresh_fac: float
        Factor by which the inter-percentile range of the data is
        multiplied to set the threshold.

    Returns
    -------
    threshold: float or 1-D array
        The computed threshold.

    """
    if percentile < 1e-8:
        return minmax_threshold(data, win_size=win_size,
                                thresh_fac=thresh_fac)
    if win_size:
        threshold = np.zeros(len(data))
        for inx0 in range(0, len(data) - win_size//2, win_size//2):
            inx1 = inx0 + win_size
            threshold[inx0:inx1] = np.squeeze(np.abs(np.diff(
                np.percentile(data[inx0:inx1], [100.0 - percentile, percentile])))) * thresh_fac
        return threshold
    else:
        return np.squeeze(np.abs(np.diff(
            np.percentile(data, [100.0 - percentile, percentile])))) * thresh_fac
def snippets(data, indices, start=-10, stop=10)

Cut out data arround each position given in indices.

Parameters

data : 1-D array
Data array from which snippets are extracted.
indices : list of int
Indices around which snippets are cut out.
start : int
Each snippet starts at index + start.
stop : int
Each snippet ends at index + stop.

Returns

snippet_data : 2-D array
The snippets: first index number of snippet, second index time.
Expand source code 
def snippets(data, indices, start=-10, stop=10):
    """Cut out data arround each position given in indices.

    Parameters
    ----------
    data: 1-D array
        Data array from which snippets are extracted.
    indices: list of int
        Indices around which snippets are cut out.
    start: int
        Each snippet starts at index + start.
    stop: int
        Each snippet ends at index + stop.
        
    Returns
    -------
    snippet_data: 2-D array
        The snippets: first index number of snippet, second index time.
    """
    idxs = indices[(indices>=-start) & (indices<len(data)-stop)]
    snippet_data = np.empty((len(idxs), stop-start))
    for k, idx in enumerate(idxs):
        snippet_data[k] = data[idx+start:idx+stop]
    # XXX alternative: check speed and behavior for empty idxs
    # snippets = np.vstack([data[idx+start:idx+stop] for idx in idxs])
    return snippet_data
def detect_dynamic_peaks(data, threshold, min_thresh, tau, time=None, check_peak_func=None, check_trough_func=None, **kwargs)

Detect peaks and troughs using a relative threshold.

The threshold decays dynamically towards min_thresh with time constant tau. Use check_peak_func or check_trough_func to reset the threshold to an appropriate size.

Based on Bryan S. Todd and David C. Andrews (1999): The identification of peaks in physiological signals. Computers and Biomedical Research 32, 322-335.

Parameters

data : array
An 1-D array of input data where peaks are detected.
threshold : float
A positive number setting the minimum distance between peaks and troughs.
min_thresh : float
The minimum value the threshold is allowed to assume.
tau : float
The time constant of the the decay of the threshold value given in indices (time is None) or time units (time is not None).
time : array
The (optional) 1-D array with the time corresponding to the data values.
check_peak_func : function

An optional function to be used for further evaluating and analysing a peak. The signature of the function is

r, th = check_peak_func(time, data, peak_inx, index, min_inx, threshold, **kwargs)

with the arguments:

  • time (array): the full time array that might be None
  • data (array): the full data array
  • peak_inx (int): the index of the detected peak
  • index (int): the current index
  • min_inx (int): the index of the trough preceeding the peak (might be 0)
  • threshold (float): the threshold value
  • min_thresh (float): the minimum value the threshold is allowed to assume.
  • tau (float): the time constant of the the decay of the threshold value given in indices (time is None) or time units (time is not None)
  • **kwargs: further keyword arguments provided by the user
  • r (scalar or np.array): a single number or an array with properties of the peak or None to skip the peak
  • th (float): a new value for the threshold or None (to keep the original value)
check_trough_func : function

An optional function to be used for further evaluating and analysing a trough. The signature of the function is

r, th = check_trough_func(time, data, trough_inx, index, max_inx, threshold, **kwargs)

with the arguments:

  • time (array): the full time array that might be None
  • data (array): the full data array
  • trough_inx (int): the index of the detected trough
  • index (int): the current index
  • max_inx (int): the index of the peak preceeding the trough (might be 0)
  • threshold (float): the threshold value
  • min_thresh (float): the minimum value the threshold is allowed to assume.
  • tau (float): the time constant of the the decay of the threshold value given in indices (time is None) or time units (time is not None)
  • **kwargs: further keyword arguments provided by the user
  • r (scalar or np.array): a single number or an array with properties of the trough or None to skip the trough
  • th (float): a new value for the threshold or None (to keep the original value)
kwargs : key-word arguments
Arguments passed on to check_peak_func and check_trough_func.

Returns

peak_list : array
List of peaks.
trough_list : array
List of troughs.
  • If time is None and no check_peak_func is given, then these are lists of the indices where the peaks/troughs occur.
  • If time is given and no check_peak_func/check_trough_func is given, then these are lists of the times where the peaks/troughs occur.
  • If check_peak_func or check_trough_func is given, then these are lists of whatever check_peak_func/check_trough_func return.

Raises

Valueerror

If threshold <= 0 or min_thresh <= 0 or tau <= 0.

Indexerror

If data and time arrays differ in length.

Expand source code 
def detect_dynamic_peaks(data, threshold, min_thresh, tau, time=None,
                         check_peak_func=None, check_trough_func=None, **kwargs):
    """Detect peaks and troughs using a relative threshold.

    The threshold decays dynamically towards min_thresh with time
    constant tau.  Use `check_peak_func` or `check_trough_func` to
    reset the threshold to an appropriate size.

    Based on Bryan S. Todd and David C. Andrews (1999): The
    identification of peaks in physiological signals.  Computers and
    Biomedical Research 32, 322-335.

    Parameters
    ----------
    data: array
        An 1-D array of input data where peaks are detected.
    threshold: float
        A positive number setting the minimum distance between peaks and troughs.
    min_thresh: float
        The minimum value the threshold is allowed to assume.
    tau: float
        The time constant of the the decay of the threshold value
        given in indices (`time` is None) or time units (`time` is not `None`).
    time: array
        The (optional) 1-D array with the time corresponding to the data values.
    check_peak_func: function
        An optional function to be used for further evaluating and analysing a peak.
        The signature of the function is
        
        ```
        r, th = check_peak_func(time, data, peak_inx, index, min_inx, threshold, **kwargs)
        ```
        
        with the arguments:
        
        - time (array): the full time array that might be None
        - data (array): the full data array
        - peak_inx (int): the index of the  detected peak
        - index (int): the current index
        - min_inx (int): the index of the trough preceeding the peak (might be 0)
        - threshold (float): the threshold value
        - min_thresh (float): the minimum value the threshold is allowed to assume.
        - tau (float): the time constant of the the decay of the threshold value
                       given in indices (time is None) or time units (time is not None)
        - **kwargs: further keyword arguments provided by the user
        - r (scalar or np.array): a single number or an array with properties of the peak or None to skip the peak
        - th (float): a new value for the threshold or None (to keep the original value)
    check_trough_func: function
        An optional function to be used for further evaluating and analysing a trough.
        The signature of the function is
        
        ```
        r, th = check_trough_func(time, data, trough_inx, index, max_inx, threshold, **kwargs)
        ```
        
        with the arguments:
        
        - time (array): the full time array that might be None
        - data (array): the full data array
        - trough_inx (int): the index of the  detected trough
        - index (int): the current index
        - max_inx (int): the index of the peak preceeding the trough (might be 0)
        - threshold (float): the threshold value
        - min_thresh (float): the minimum value the threshold is allowed to assume.
        - tau (float): the time constant of the the decay of the threshold value
                       given in indices (time is None) or time units (time is not None)
        - **kwargs: further keyword arguments provided by the user
        - r (scalar or np.array): a single number or an array with properties of the trough or None to skip the trough
        - th (float): a new value for the threshold or None (to keep the original value)            
    kwargs: key-word arguments
        Arguments passed on to `check_peak_func` and `check_trough_func`.
    
    Returns
    -------
    peak_list: array
        List of peaks.
    trough_list: array
        List of troughs.
        
    - If time is `None` and no `check_peak_func` is given,
      then these are lists of the indices where the peaks/troughs occur.
    - If `time` is given and no `check_peak_func`/`check_trough_func` is given,
      then these are lists of the times where the peaks/troughs occur.
    - If `check_peak_func` or `check_trough_func` is given,
      then these are lists of whatever `check_peak_func`/`check_trough_func` return.

    Raises
    ------
    ValueError:
        If `threshold <= 0` or `min_thresh <= 0` or `tau <= 0`.
    IndexError:
        If `data` and `time` arrays differ in length.

    """
    if threshold <= 0:
        raise ValueError('input argument threshold must be positive!')
    if min_thresh <= 0:
        raise ValueError('input argument min_thresh must be positive!')
    if tau <= 0:
        raise ValueError('input argument tau must be positive!')
    if time is not None and len(data) != len(time):
        raise IndexError('input arrays time and data must have same length!')

    peaks_list = list()
    troughs_list = list()

    # initialize:
    direction = 0
    min_inx = 0
    max_inx = 0
    min_value = data[0]
    max_value = min_value

    # loop through the data:
    for index, value in enumerate(data):

        # decaying threshold (first order low pass filter):
        if time is None:
            threshold += (min_thresh - threshold) / tau
        else:
            idx = index
            if idx + 1 >= len(data):
                idx = len(data) - 2
            threshold += (min_thresh - threshold) * (time[idx + 1] - time[idx]) / tau

        # rising?
        if direction > 0:
            # if the new value is bigger than the old maximum: set it as new maximum:
            if value > max_value:
                max_inx = index  # maximum element
                max_value = value

            # otherwise, if the new value is falling below the maximum value minus the threshold:
            # the maximum is a peak!
            elif max_value >= value + threshold:
                # check and update peak with the check_peak_func function:
                if check_peak_func:
                    r, th = check_peak_func(time, data, max_inx, index,
                                            min_inx, threshold,
                                            min_thresh=min_thresh, tau=tau, **kwargs)
                    if r is not None:
                        # this really is a peak:
                        peaks_list.append(r)
                    if th is not None:
                        threshold = th
                        if threshold < min_thresh:
                            threshold = min_thresh
                else:
                    # this is a peak:
                    if time is None:
                        peaks_list.append(max_inx)
                    else:
                        peaks_list.append(time[max_inx])

                # change direction:
                min_inx = index  # minimum element
                min_value = value
                direction = -1

        # falling?
        elif direction < 0:
            if value < min_value:
                min_inx = index  # minimum element
                min_value = value

            elif value >= min_value + threshold:
                # there was a trough:

                # check and update trough with the check_trough function:
                if check_trough_func:
                    r, th = check_trough_func(time, data, min_inx, index,
                                              max_inx, threshold,
                                              min_thresh=min_thresh, tau=tau, **kwargs)
                    if r is not None:
                        # this really is a trough:
                        troughs_list.append(r)
                    if th is not None:
                        threshold = th
                        if threshold < min_thresh:
                            threshold = min_thresh
                else:
                    # this is a trough:
                    if time is None:
                        troughs_list.append(min_inx)
                    else:
                        troughs_list.append(time[min_inx])

                # change direction:
                max_inx = index  # maximum element
                max_value = value
                direction = 1

        # don't know direction yet:
        else:
            if max_value >= value + threshold:
                direction = -1  # falling
            elif value >= min_value + threshold:
                direction = 1  # rising

            if max_value < value:
                max_inx = index  # maximum element
                max_value = value

            elif value < min_value:
                min_inx = index  # minimum element
                min_value = value

    return np.asarray(peaks_list), np.asarray(troughs_list)
def accept_peak_size_threshold(time, data, event_inx, index, min_inx, threshold, min_thresh, tau, thresh_ampl_fac=0.75, thresh_weight=0.02)

Accept each detected peak/trough and return its index or time.

Adjust the threshold to the size of the detected peak. To be passed to the detect_dynamic_peaks() function.

Parameters

time : array
Time values, can be None.
data : array
The data in wich peaks and troughs are detected.
event_inx : int
Index of the current peak/trough.
index : int
Current index.
min_inx : int
Index of the previous trough/peak.
threshold : float
Threshold value.
min_thresh : float
The minimum value the threshold is allowed to assume..
tau : float
The time constant of the the decay of the threshold value given in indices (time is None) or time units (time is not None).
thresh_ampl_fac : float
The new threshold is thresh_ampl_fac times the size of the current peak.
thresh_weight : float
New threshold is weighted against current threshold with thresh_weight.

Returns

index : int
Index of the peak/trough if time is None.
time : int
Time of the peak/trough if time is not None.
threshold : float
The new threshold to be used.
Expand source code 
def accept_peak_size_threshold(time, data, event_inx, index, min_inx, threshold,
                               min_thresh, tau, thresh_ampl_fac=0.75, thresh_weight=0.02):
    """Accept each detected peak/trough and return its index or time.
                               
    Adjust the threshold to the size of the detected peak.
    To be passed to the `detect_dynamic_peaks()` function.

    Parameters
    ----------
    time: array
        Time values, can be `None`.
    data: array
        The data in wich peaks and troughs are detected.
    event_inx: int
        Index of the current peak/trough.
    index: int
        Current index.
    min_inx: int
        Index of the previous trough/peak.
    threshold: float
        Threshold value.
    min_thresh: float
        The minimum value the threshold is allowed to assume..
    tau: float
        The time constant of the the decay of the threshold value
        given in indices (`time` is `None`) or time units (`time` is not `None`).
    thresh_ampl_fac: float
        The new threshold is `thresh_ampl_fac` times the size of the current peak.
    thresh_weight: float
        New threshold is weighted against current threshold with `thresh_weight`.

    Returns
    -------
    index: int
        Index of the peak/trough if `time` is `None`.
    time: int
        Time of the peak/trough if `time` is not `None`.
    threshold: float
        The new threshold to be used.
    """
    size = data[event_inx] - data[min_inx]
    threshold += thresh_weight * (thresh_ampl_fac * size - threshold)
    if time is None:
        return event_inx, threshold
    else:
        return time[event_inx], threshold
def main()
Expand source code 
def main():
    print('Checking eventetection module ...')
    print('')
    # generate data:
    dt = 0.001
    time = np.arange(0.0, 10.0, dt)
    f = 2.0
    data = (0.5 * np.sin(2.0 * np.pi * f * time) + 0.5) ** 4.0
    data += -0.1 * time * (time - 10.0)
    data += 0.1 * np.random.randn(len(data))

    print(f'generated waveform with {int(np.round(time[-1] * f))} peaks')
    plt.plot(time, data)

    print('')
    print('check detect_peaks(data, 1.0)...')
    peaks, troughs = detect_peaks(data, 1.0)
    # print peaks:
    print(f'detected {len(peaks)} peaks with period {np.mean(np.diff(peaks)):.1f} that differs from the real frequency by {f - 1.0 / np.mean(np.diff(peaks)) / np.mean(np.diff(time)):.3f}')
    # print troughs:
    print(f'detected {len(troughs)} troughs with period {np.mean(np.diff(troughs)):.1f} that differs from the real frequency by {f - 1.0 / np.mean(np.diff(troughs)) / np.mean(np.diff(time)):.3f}')

    # plot peaks and troughs:
    plt.plot(time[peaks], data[peaks], '.r', ms=20)
    plt.plot(time[troughs], data[troughs], '.g', ms=20)

    # detect threshold crossings:
    onsets, offsets = threshold_crossings(data, 3.0)
    onsets, offsets = merge_events(onsets, offsets, int(0.5/f/dt))
    plt.plot(time, 3.0*np.ones(len(time)), 'k')
    plt.plot(time[onsets], data[onsets], '.c', ms=20)
    plt.plot(time[offsets], data[offsets], '.b', ms=20)

    plt.ylim(-0.5, 4.0)
    plt.show()

    # timing of the detect_peaks() algorithm:
    import timeit
    def wrapper(func, *args, **kwargs):
        def wrapped():
            return func(*args, **kwargs)
        return wrapped
    wrapped = wrapper(detect_peaks, data, 1.0)
    t1 = timeit.timeit(wrapped, number=200)
    print(t1)