def _compute_natural_frequencies(freqs, n, t, avg = False):
'''
Computes the natural frequencies omega_0 of a matrix of frequencies. In
this calculation, we assume the natural frequency is that which is maximal.
Arguments
=========
freqs: The M x N frequency data matrix.
n: Number of frames.
t: Framerate.
avg: Boolean flag indicating whether we want to average the columns of "freqs"
together into a single vector, or compute the parameters for all the rows.
Returns
=======
natural_frequencies: Natural frequencies of each pixel (either length M or 1)
nu: Indices at which the natural frequencies are found in the FFT data. (M or 1)
'''
# Do some indexing voodoo to prevent the 0th index from ever being
# the maximum frequency of the entire dataset (since it never should be!).
nu = None
if avg:
nu = np.argmax(frequency.average_frequencies(np.absolute(freqs))[1:])
else:
nu = np.argmax(np.absolute(freqs[:, 1:]), axis = 1)
nu += 1
natural_frequencies = 2 * np.pi * (nu / (n * t))
return [natural_frequencies, nu]
def _compute_force_avg(freqs, n, t):
'''
Averages the frequencies of each component together before performing
the force analysis.
Arguments
=========
frequencies: Frequency embedding of the original displacement data. M x N.
n: Number of frames.
t: Framerate.
Returns
=======
natural_frequencies: 1 natural frequency.
damping_coefficients: 1 damping coefficient.
F_mvs: N force/mass ratios (freq domain).
phase: N force/mass phase angles.
f_mvs: N force/mass ratios (time domain).
'''
# First, compute the natural frequency.
natural_frequency, index = _compute_natural_frequencies(freqs, n, t, avg = True)
# Next, compute the damping coefficient.
avg_freqs = frequency.average_frequencies(freqs)
damping_coefficient = _compute_damping_coefficient(avg_freqs, index, n, t)
# Then, compute the force for each point in the dataset.
F_mv = _force_equation(avg_freqs, natural_frequency, damping_coefficient, n, t)
# Compute the phase angle associated with each force in the dataset.
phase = _phase_angle_equation(avg_freqs, natural_frequency, damping_coefficient, n, t)
# Finally, compute the time domain representation of force of contractility
f_mv = _time_domain(F_mv, phase, n)
# All done.
return [natural_frequency, damping_coefficient, F_mv, phase, f_mv]
