# Source code for sensormotion.gait

```"""
Calculate gait dynamics.

Functions for the calculation of variance gait dynamics from acceleration
"""

from __future__ import print_function, division

import numpy as np

"""
Calculate cadence of the current signal.

Cadence (steps per minute) can be estimated by detecting peaks in the
acceleration vector. Given 1) the duration of the signal and 2) the number
of steps/peaks in the signal, we can calculate an estimate of steps per
minute.

Peak detection provides number of steps within the time frame of the
signal. This is then extrapolated from milliseconds to minutes to estimate

Parameters
----------
time : ndarray
Time vector of the original acceleration signal. Used to calculate
duration of the input signal.
peak_times : ndarray
Time of each peak, returned by :func:`sensormotion.peak.find_peaks`.
This provides the number of steps within the timeframe of the signal.
time_units : {'ms', 's'}, optional
Units of the time signal.

Returns
-------
Estimated cadence for the input signal.
"""

n = step_count(peak_times)

# Convert duration to seconds
if time_units == "ms":
duration = (time.max() - time.min()) / 1000
elif time_units == "s":
duration = time.max() - time.min()

steps_per_min = (n / duration) * 60

return steps_per_min

[docs]def step_count(peak_times):
"""
Count total number of steps in the signal.

This is simply the number of peaks detected in the signal.

Parameters
----------
peak_times : ndarray
Times of the peaks detected by :func:`sensormotion.peak.find_peaks`.

Returns
-------
step_count : int
Number of steps/peaks in the signal.
"""

return len(peak_times)

[docs]def step_regularity(autocorr_peak_values):
"""
Calculate step and stride regularity from autocorrelation peak values.

Step and stride regularity measures based on
`Moe-Nilssen (2004) - Estimation of gait cycle characteristics by trunk
accelerometry
<http://www.jbiomech.com/article/S0021-9290(03)00233-1/abstract>`_.

If calculating regularity from acceleration in the vertical axis, this
function receives the detected peaks from the vertical axis
autocorrelation.

However, if calculating regularity from lateral axis
acceleration, you should pass in *both* peaks and valleys from the
autocorrelation of the lateral axis.

**Step regularity:**

Perfect step regularity will be 1.0 for vertical axis autocorrelation
(the larger the better, capped at 1.0).

For the lateral axis, perfect regularity is -1.0 (the smaller the
better, capped at -1.0).

**Stride regularity:**

Perfect stride regularity will be 1.0 for vertical axis autocorrelation
(the larger the better, capped at 1.0).

Lateral axis sign and interpretation are the same as the vertical axis.

Parameters
----------
autocorr_peak_values : ndarray
Values of the autocorrelation peaks/valleys detected by
:func:`sensormotion.peak.find_peaks`. This should contain only peak
values when looking at the vertical axis, and both peak and valley
values when looking at the lateral axis.

Returns
-------
step_reg : float
Step regularity. Value is capped at 1.0 or -1.0 depending on the
axis of interest.
stride_reg : float
Stride regularity. Capped at 1.0 for both vertical and lateral axes.
"""

peaks_half = autocorr_peak_values[autocorr_peak_values.size // 2 :]

assert len(peaks_half) >= 3, (
"Not enough autocorrelation peaks detected. Plot the "
"autocorrelation signal to visually inspect peaks"
)

ac_lag0 = peaks_half  # autocorrelation value at lag 0
ac_d1 = peaks_half  # first dominant period i.e. a step (left-right)
ac_d2 = peaks_half  # second dominant period i.e. a stride (left-left)

step_reg = ac_d1 / ac_lag0
stride_reg = ac_d2 / ac_lag0

return step_reg, stride_reg

[docs]def step_symmetry(autocorr_peak_values):
"""
Calculate step symmetry from autocorrelation peak values.

Step symmetry measures based on `Moe-Nilssen (2004) - Estimation of gait
cycle characteristics by trunk accelerometry
<http://www.jbiomech.com/article/S0021-9290(03)00233-1/abstract>`_.

If calculating symmetry from acceleration in the vertical axis, this
function receives the detected peaks from the vertical axis
autocorrelation.

However, if calculating symmetry from lateral axis
acceleration, you should pass in *both* peaks and valleys from the
autocorrelation of the lateral axis.

Perfect step symmetry is 1.0 for the vertical axis - larger values are
more symmetric, capped at 1.0.

Perfect step symmetry is -1.0 for the lateral axis - smaller values are
more symmetric, capped at -1.0.

Parameters
----------
autocorr_peak_values : ndarray
Values of the autocorrelation peaks/valleys detected by
:func:`sensormotion.peak.find_peaks`. This should contain only peak
values when looking at the vertical axis, and both peak and valley
values when looking at the lateral axis.

Returns
-------
step_sym : float
Step symmetry. Value is capped at 1.0 or -1.0 depending on the
axis of interest.
"""

peaks_half = autocorr_peak_values[autocorr_peak_values.size // 2 :]

assert len(peaks_half) >= 3, (
"Not enough autocorrelation peaks detected. Plot the "
"autocorrelation signal to visually inspect peaks"
)

ac_d1 = peaks_half  # first dominant period i.e. a step (left-right)
ac_d2 = peaks_half  # second dominant period i.e. a stride (left-left)

# Always divide smaller peak by the larger peak
if abs(ac_d1) > abs(ac_d2):
step_sym = ac_d2 / ac_d1  # Preserve sign by not using abs()
else:
step_sym = ac_d1 / ac_d2  # Preserve sign by not using abs()

return step_sym

[docs]def step_time(peak_times):
"""
Calculate step timing information.

Step timing can be calculated from the peak times of the original
acceleration signal. This includes mean time between steps,
standard deviation of step time, and the coefficient of
variation (sd/mean).

Parameters
----------
peak_times : ndarray
Times of the peaks detected by :func:`sensormotion.peak.find_peaks`.

Returns
-------
step_time_mean : float
Mean time between all steps/peaks in the signal.
step_time_sd : float
Standard deviation of the distribution of step times in the signal.
step_time_cov : float
Coefficient of variation. Calculated as sd/mean.
"""

peak_time_differences = np.diff(peak_times)
peak_time_mean = np.mean(peak_time_differences)
peak_time_sd = np.std(peak_time_differences)
peak_time_cov = peak_time_sd / peak_time_mean

return peak_time_mean, peak_time_sd, peak_time_cov
```