def test_create_detrended_rri_class(self):
detrended_rri = [
-87.98470401, -88.22253018, -49.46831978, -109.69798458,
-181.90892056
]
rri_time = [0, 1, 2, 3, 4]
det_rri_obj = RRiDetrended(detrended_rri, time=rri_time)
assert det_rri_obj.detrended
assert not det_rri_obj.interpolated
def sg_detrend(rri, window_length=51, polyorder=3, *args, **kwargs):
"""
Remove the low-frequency components of the RRi series with the low-pass
filter developed by Savitzky-Golay
Parameters
----------
rri : array_like
sequence containing the RRi series
window_length: integer, optional
The length of the filter window (i.e. the number of coefficients).
`window_length` must be a positive odd integer. If `mode` is 'interp',
`window_length` must be less than or equal to the size of `x`.
Defaults to 51
polyorder: integer, optional
The order of the polynomial used to fit the samples. `polyorder` must
be less than `window_length`. Defauts to 3
See scipy.signal.savgol_filter for more information
Returns
-------
results : RRi array
instance of the RRi Detrended class containing the detrended RRi values
See Also
-------
polynomial_detrend, smoothness_priors
Examples
--------
>>> from hrv.detrend import sg_detrend
>>> from hrv.sampledata import load_rest_rri
>>> rri = load_rest_rri()
>>> sg_detrend(rri)
RRi array([5.07722695e+01, 4.16090643e+01, ..., -1.26297542e+01])
"""
if isinstance(rri, RRi):
time = rri.time
rri = rri.values
else:
time = _create_time_array(rri)
trend = savgol_filter(rri,
window_length=window_length,
polyorder=polyorder,
*args,
**kwargs)
return RRiDetrended(rri - trend, time=time, detrended=True)
def test_frequency_domain_with_welch_and_detrended_rri(
self, _interpolate_rri, _welch, _auc):
_interpolate_rri.return_value = [1, 2, 3, 4]
fake_rri = RRiDetrended([-1, -2, -3, -4], time=[5, 6, 7, 8])
frequency_domain(fake_rri, time=fake_rri.time, fs=4,
method='welch', nperseg=256, noverlap=128,
window='hanning')
_welch.assert_called_once_with(
x=[1, 2, 3, 4],
fs=4,
detrend=False,
noverlap=128,
nperseg=256,
window='hanning'
)
def test_frequency_domain_with_welch_and_detrended_rri_and_interp(
self, _interpolate_rri, _welch, _auc):
fake_rri = RRiDetrended(
[-1, -2, -3, -4], time=[5, 6, 7, 8], interpolated=True
)
frequency_domain(fake_rri, time=fake_rri.time, fs=4,
method='welch', nperseg=256, noverlap=128,
window='hanning')
_interpolate_rri.assert_not_called()
_welch.assert_called_once_with(
x=fake_rri,
fs=4,
detrend=False,
noverlap=128,
nperseg=256,
window='hanning'
)
def polynomial_detrend(rri, degree=1):
"""
Fits a polynomial function with degree=`degree` in the RRi series
and then subtract it from the signal.
Parameters
----------
rri : array_like
sequence containing the RRi series
degree: integer, optional
degree of the polynomial function to be fitted in the RRi series.
Defaults to 1
Returns
-------
results : RRi array
instance of the RRi Detrended class containing the detrended RRi values
See Also
-------
smoothness_priors, sg_detrend
Examples
--------
>>> from hrv.detrend import polynomial_detrend
>>> from hrv.sampledata import load_rest_rri
>>> rri = load_rest_rri()
>>> polynomial_detrend(rri)
RRi array([ 5.60099763e+01, 5.50082903e+01, ..., 8.00667554e+00])
"""
if isinstance(rri, RRi):
time = rri.time
rri = rri.values
else:
time = _create_time_array(rri)
coef = np.polyfit(time, rri, deg=degree)
polynomial = np.polyval(coef, time)
detrended_rri = rri - polynomial
return RRiDetrended(detrended_rri, time=time)
def smoothness_priors(rri, l=500, fs=4.0):
"""
Estimates the stationary part of the resampled RRi series and subtracts it
from the signal. The RRi series must have equal time-space between
adjacents RRi values, therefore the original RRi is interpolated and then
resampled.
Parameters
----------
rri : array_like
sequence containing the RRi series
l: integer, optional
the regularization parameter
Defaults to 500
fs: integer, optional
sampling frequency in each the RRi series will be resampled after
cubic interpolation. Defaults to 4
.. math::
The estimated stationary component of the RRi can represented as:
z_stat = (I - (l**2 @ D2.T @ D2)**2) @ z
where I is the identity matrix; D2 is the second order difference
matrix and z is the evenly spaced RRi series (containing both
stationaty and trend components)
Returns
-------
results : RRi array
instance of the RRi Detrended class containing the detrended RRi values
See Also
-------
polynomial_detrend, sg_detrend
References
----------
- M.P. Tarvainen, P.O. Ranta-aho and P.A. Karjalainen, An advanced
detrending method with application to HRV analysis, IEEE
Transaction on Biomedical Engineering 49 (2002), 172–175.
Examples
--------
>>> from hrv.detrend import smoothness_priors
>>> from hrv.sampledata import load_rest_rri
>>> rri = load_rest_rri()
>>> smoothness_priors(rri)
RRi array([27.17281349, 46.12837695, 51.21922892, ..., 1042.86845282])
"""
if isinstance(rri, RRi):
time = rri.time
rri = rri.values
else:
time = _create_time_array(rri)
# TODO: only interp if not interpolated yet
cubic_spline = CubicSpline(time, rri)
time_interp = np.arange(time[0], time[-1], 1.0 / fs)
rri_interp = cubic_spline(time_interp)
N = len(rri_interp)
identity = np.eye(N)
B = np.dot(np.ones((N - 2, 1)), np.array([[1, -2, 1]]))
D_2 = dia_matrix((B.T, [0, 1, 2]), shape=(N - 2, N))
inv = np.linalg.inv(identity + l**2 * D_2.T @ D_2)
z_stat = ((identity - np.linalg.inv(identity + l**2 * D_2.T @ D_2)))\
@ rri_interp
rri_interp_detrend = np.squeeze(np.asarray(rri_interp - z_stat))
return RRiDetrended(rri_interp - rri_interp_detrend,
time=time_interp,
detrended=True,
interpolated=True)