# yasa.transition_matrix¶

yasa.transition_matrix(hypno)[source]

Create a state-transition matrix from an hypnogram.

New in version 0.1.9.

Parameters
hypnoarray_like

Hypnogram. The dtype of hypno must be integer (e.g. [0, 2, 2, 1, 1, 1, …]). The sampling frequency must be the original one, i.e. 1 value per 30 seconds if the staging was done in 30 seconds epochs. Using an upsampled hypnogram will result in an incorrect transition matrix. For best results, we recommend using an hypnogram cropped to either the time in bed (TIB) or the sleep period time (SPT), without any artefact / unscored epochs.

Returns
countspandas.DataFrame

Counts transition matrix (number of transitions from stage A to stage B). The pre-transition states are the rows and the post-transition states are the columns.

probspandas.DataFrame

Conditional probability transition matrix, i.e. given that current state is A, what is the probability that the next state is B. probs is a right stochastic matrix, i.e. each row sums to 1.

Examples

>>> import numpy as np
>>> from yasa import transition_matrix
>>> a = [0, 0, 0, 1, 1, 0, 1, 2, 2, 3, 3, 2, 3, 3, 0, 2, 2, 1, 2, 2, 3, 3]
>>> counts, probs = transition_matrix(a)
>>> counts
0  1  2  3
Stage
0      2  2  1  0
1      1  1  2  0
2      0  1  3  3
3      1  0  1  3

>>> probs.round(2)
0     1     2     3
Stage
0      0.40  0.40  0.20  0.00
1      0.25  0.25  0.50  0.00
2      0.00  0.14  0.43  0.43
3      0.20  0.00  0.20  0.60


Several metrics of sleep fragmentation can be calculated from the probability matrix. For example, the stability of sleep stages can be calculated by taking the average of the diagonal values (excluding Wake and N1 sleep):

>>> np.diag(probs.loc[2:, 2:]).mean().round(3)
0.514


Finally, we can plot the transition matrix using seaborn.heatmap()

>>> import numpy as np
>>> import seaborn as sns
>>> import matplotlib.pyplot as plt
>>> from yasa import transition_matrix
>>> # Calculate probability matrix
>>> a = [1, 1, 1, 0, 0, 2, 2, 0, 2, 0, 1, 1, 0, 0]
>>> _, probs = transition_matrix(a)
>>> # Start the plot
>>> grid_kws = {"height_ratios": (.9, .05), "hspace": .1}
>>> f, (ax, cbar_ax) = plt.subplots(2, gridspec_kw=grid_kws,
...                                 figsize=(5, 5))
>>> sns.heatmap(probs, ax=ax, square=False, vmin=0, vmax=1, cbar=True,
...             cbar_ax=cbar_ax, cmap='YlOrRd', annot=True, fmt='.2f',
...             cbar_kws={"orientation": "horizontal", "fraction": 0.1,
...                       "label": "Transition probability"})
>>> ax.set_xlabel("To sleep stage")
>>> ax.xaxis.tick_top()
>>> ax.set_ylabel("From sleep stage")
>>> ax.xaxis.set_label_position('top')