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Module « scipy.signal »

Fonction peak_widths - module scipy.signal

Signature de la fonction peak_widths

def peak_widths(x, peaks, rel_height=0.5, prominence_data=None, wlen=None) 

Description

help(scipy.signal.peak_widths)

Calculate the width of each peak in a signal.

This function calculates the width of a peak in samples at a relative
distance to the peak's height and prominence.

Parameters
----------
x : sequence
    A signal with peaks.
peaks : sequence
    Indices of peaks in `x`.
rel_height : float, optional
    Chooses the relative height at which the peak width is measured as a
    percentage of its prominence. 1.0 calculates the width of the peak at
    its lowest contour line while 0.5 evaluates at half the prominence
    height. Must be at least 0. See notes for further explanation.
prominence_data : tuple, optional
    A tuple of three arrays matching the output of `peak_prominences` when
    called with the same arguments `x` and `peaks`. This data are calculated
    internally if not provided.
wlen : int, optional
    A window length in samples passed to `peak_prominences` as an optional
    argument for internal calculation of `prominence_data`. This argument
    is ignored if `prominence_data` is given.

Returns
-------
widths : ndarray
    The widths for each peak in samples.
width_heights : ndarray
    The height of the contour lines at which the `widths` where evaluated.
left_ips, right_ips : ndarray
    Interpolated positions of left and right intersection points of a
    horizontal line at the respective evaluation height.

Raises
------
ValueError
    If `prominence_data` is supplied but doesn't satisfy the condition
    ``0 <= left_base <= peak <= right_base < x.shape[0]`` for each peak,
    has the wrong dtype, is not C-contiguous or does not have the same
    shape.

Warns
-----
PeakPropertyWarning
    Raised if any calculated width is 0. This may stem from the supplied
    `prominence_data` or if `rel_height` is set to 0.

Warnings
--------
This function may return unexpected results for data containing NaNs. To
avoid this, NaNs should either be removed or replaced.

See Also
--------
find_peaks
    Find peaks inside a signal based on peak properties.
peak_prominences
    Calculate the prominence of peaks.

Notes
-----
The basic algorithm to calculate a peak's width is as follows:

* Calculate the evaluation height :math:`h_{eval}` with the formula
  :math:`h_{eval} = h_{Peak} - P \cdot R`, where :math:`h_{Peak}` is the
  height of the peak itself, :math:`P` is the peak's prominence and
  :math:`R` a positive ratio specified with the argument `rel_height`.
* Draw a horizontal line at the evaluation height to both sides, starting at
  the peak's current vertical position until the lines either intersect a
  slope, the signal border or cross the vertical position of the peak's
  base (see `peak_prominences` for an definition). For the first case,
  intersection with the signal, the true intersection point is estimated
  with linear interpolation.
* Calculate the width as the horizontal distance between the chosen
  endpoints on both sides. As a consequence of this the maximal possible
  width for each peak is the horizontal distance between its bases.

As shown above to calculate a peak's width its prominence and bases must be
known. You can supply these yourself with the argument `prominence_data`.
Otherwise, they are internally calculated (see `peak_prominences`).

.. versionadded:: 1.1.0

Examples
--------
>>> import numpy as np
>>> from scipy.signal import chirp, find_peaks, peak_widths
>>> import matplotlib.pyplot as plt

Create a test signal with two overlaid harmonics

>>> x = np.linspace(0, 6 * np.pi, 1000)
>>> x = np.sin(x) + 0.6 * np.sin(2.6 * x)

Find all peaks and calculate their widths at the relative height of 0.5
(contour line at half the prominence height) and 1 (at the lowest contour
line at full prominence height).

>>> peaks, _ = find_peaks(x)
>>> results_half = peak_widths(x, peaks, rel_height=0.5)
>>> results_half[0]  # widths
array([ 64.25172825,  41.29465463,  35.46943289, 104.71586081,
        35.46729324,  41.30429622, 181.93835853,  45.37078546])
>>> results_full = peak_widths(x, peaks, rel_height=1)
>>> results_full[0]  # widths
array([181.9396084 ,  72.99284945,  61.28657872, 373.84622694,
    61.78404617,  72.48822812, 253.09161876,  79.36860878])

Plot signal, peaks and contour lines at which the widths where calculated

>>> plt.plot(x)
>>> plt.plot(peaks, x[peaks], "x")
>>> plt.hlines(*results_half[1:], color="C2")
>>> plt.hlines(*results_full[1:], color="C3")
>>> plt.show()

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