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def find_peaks(x, height=None, threshold=None, distance=None, prominence=None, width=None, wlen=None, rel_height=0.5, plateau_size=None)
Find peaks inside a signal based on peak properties.
This function takes a 1-D array and finds all local maxima by
simple comparison of neighboring values. Optionally, a subset of these
peaks can be selected by specifying conditions for a peak's properties.
Parameters
----------
x : sequence
A signal with peaks.
height : number or ndarray or sequence, optional
Required height of peaks. Either a number, ``None``, an array matching
`x` or a 2-element sequence of the former. The first element is
always interpreted as the minimal and the second, if supplied, as the
maximal required height.
threshold : number or ndarray or sequence, optional
Required threshold of peaks, the vertical distance to its neighboring
samples. Either a number, ``None``, an array matching `x` or a
2-element sequence of the former. The first element is always
interpreted as the minimal and the second, if supplied, as the maximal
required threshold.
distance : number, optional
Required minimal horizontal distance (>= 1) in samples between
neighbouring peaks. Smaller peaks are removed first until the condition
is fulfilled for all remaining peaks.
prominence : number or ndarray or sequence, optional
Required prominence of peaks. Either a number, ``None``, an array
matching `x` or a 2-element sequence of the former. The first
element is always interpreted as the minimal and the second, if
supplied, as the maximal required prominence.
width : number or ndarray or sequence, optional
Required width of peaks in samples. Either a number, ``None``, an array
matching `x` or a 2-element sequence of the former. The first
element is always interpreted as the minimal and the second, if
supplied, as the maximal required width.
wlen : int, optional
Used for calculation of the peaks prominences, thus it is only used if
one of the arguments `prominence` or `width` is given. See argument
`wlen` in `peak_prominences` for a full description of its effects.
rel_height : float, optional
Used for calculation of the peaks width, thus it is only used if `width`
is given. See argument `rel_height` in `peak_widths` for a full
description of its effects.
plateau_size : number or ndarray or sequence, optional
Required size of the flat top of peaks in samples. Either a number,
``None``, an array matching `x` or a 2-element sequence of the former.
The first element is always interpreted as the minimal and the second,
if supplied as the maximal required plateau size.
.. versionadded:: 1.2.0
Returns
-------
peaks : ndarray
Indices of peaks in `x` that satisfy all given conditions.
properties : dict
A dictionary containing properties of the returned peaks which were
calculated as intermediate results during evaluation of the specified
conditions:
* 'peak_heights'
If `height` is given, the height of each peak in `x`.
* 'left_thresholds', 'right_thresholds'
If `threshold` is given, these keys contain a peaks vertical
distance to its neighbouring samples.
* 'prominences', 'right_bases', 'left_bases'
If `prominence` is given, these keys are accessible. See
`peak_prominences` for a description of their content.
* 'widths', 'width_heights', 'left_ips', 'right_ips'
If `width` is given, these keys are accessible. See `peak_widths`
for a description of their content.
* 'plateau_sizes', left_edges', 'right_edges'
If `plateau_size` is given, these keys are accessible and contain
the indices of a peak's edges (edges are still part of the
plateau) and the calculated plateau sizes.
.. versionadded:: 1.2.0
To calculate and return properties without excluding peaks, provide the
open interval ``(None, None)`` as a value to the appropriate argument
(excluding `distance`).
Warns
-----
PeakPropertyWarning
Raised if a peak's properties have unexpected values (see
`peak_prominences` and `peak_widths`).
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_cwt
Find peaks using the wavelet transformation.
peak_prominences
Directly calculate the prominence of peaks.
peak_widths
Directly calculate the width of peaks.
Notes
-----
In the context of this function, a peak or local maximum is defined as any
sample whose two direct neighbours have a smaller amplitude. For flat peaks
(more than one sample of equal amplitude wide) the index of the middle
sample is returned (rounded down in case the number of samples is even).
For noisy signals the peak locations can be off because the noise might
change the position of local maxima. In those cases consider smoothing the
signal before searching for peaks or use other peak finding and fitting
methods (like `find_peaks_cwt`).
Some additional comments on specifying conditions:
* Almost all conditions (excluding `distance`) can be given as half-open or
closed intervals, e.g., ``1`` or ``(1, None)`` defines the half-open
interval :math:`[1, \infty]` while ``(None, 1)`` defines the interval
:math:`[-\infty, 1]`. The open interval ``(None, None)`` can be specified
as well, which returns the matching properties without exclusion of peaks.
* The border is always included in the interval used to select valid peaks.
* For several conditions the interval borders can be specified with
arrays matching `x` in shape which enables dynamic constrains based on
the sample position.
* The conditions are evaluated in the following order: `plateau_size`,
`height`, `threshold`, `distance`, `prominence`, `width`. In most cases
this order is the fastest one because faster operations are applied first
to reduce the number of peaks that need to be evaluated later.
* While indices in `peaks` are guaranteed to be at least `distance` samples
apart, edges of flat peaks may be closer than the allowed `distance`.
* Use `wlen` to reduce the time it takes to evaluate the conditions for
`prominence` or `width` if `x` is large or has many local maxima
(see `peak_prominences`).
.. versionadded:: 1.1.0
Examples
--------
To demonstrate this function's usage we use a signal `x` supplied with
SciPy (see `scipy.datasets.electrocardiogram`). Let's find all peaks (local
maxima) in `x` whose amplitude lies above 0.
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.datasets import electrocardiogram
>>> from scipy.signal import find_peaks
>>> x = electrocardiogram()[2000:4000]
>>> peaks, _ = find_peaks(x, height=0)
>>> plt.plot(x)
>>> plt.plot(peaks, x[peaks], "x")
>>> plt.plot(np.zeros_like(x), "--", color="gray")
>>> plt.show()
We can select peaks below 0 with ``height=(None, 0)`` or use arrays matching
`x` in size to reflect a changing condition for different parts of the
signal.
>>> border = np.sin(np.linspace(0, 3 * np.pi, x.size))
>>> peaks, _ = find_peaks(x, height=(-border, border))
>>> plt.plot(x)
>>> plt.plot(-border, "--", color="gray")
>>> plt.plot(border, ":", color="gray")
>>> plt.plot(peaks, x[peaks], "x")
>>> plt.show()
Another useful condition for periodic signals can be given with the
`distance` argument. In this case, we can easily select the positions of
QRS complexes within the electrocardiogram (ECG) by demanding a distance of
at least 150 samples.
>>> peaks, _ = find_peaks(x, distance=150)
>>> np.diff(peaks)
array([186, 180, 177, 171, 177, 169, 167, 164, 158, 162, 172])
>>> plt.plot(x)
>>> plt.plot(peaks, x[peaks], "x")
>>> plt.show()
Especially for noisy signals peaks can be easily grouped by their
prominence (see `peak_prominences`). E.g., we can select all peaks except
for the mentioned QRS complexes by limiting the allowed prominence to 0.6.
>>> peaks, properties = find_peaks(x, prominence=(None, 0.6))
>>> properties["prominences"].max()
0.5049999999999999
>>> plt.plot(x)
>>> plt.plot(peaks, x[peaks], "x")
>>> plt.show()
And, finally, let's examine a different section of the ECG which contains
beat forms of different shape. To select only the atypical heart beats, we
combine two conditions: a minimal prominence of 1 and width of at least 20
samples.
>>> x = electrocardiogram()[17000:18000]
>>> peaks, properties = find_peaks(x, prominence=1, width=20)
>>> properties["prominences"], properties["widths"]
(array([1.495, 2.3 ]), array([36.93773946, 39.32723577]))
>>> plt.plot(x)
>>> plt.plot(peaks, x[peaks], "x")
>>> plt.vlines(x=peaks, ymin=x[peaks] - properties["prominences"],
... ymax = x[peaks], color = "C1")
>>> plt.hlines(y=properties["width_heights"], xmin=properties["left_ips"],
... xmax=properties["right_ips"], color = "C1")
>>> plt.show()
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