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muap_comp

Functions to compute MUAP similarity and distance metrics

get_highest_iqr_ch 

get_highest_iqr_ch(muap: ndarray) -> np.ndarray

Compute the highest interquartile range (IQR) channels.

Parameters:

Name Type Description Default
muap ndarray

Motor unit action potential with shape (ch_rows, ch_cols, samples)

 required

Returns:

Name Type Description
ndarray ndarray

A boolean mask indicating the channels with the highest IQR.
Source code in motor_unit_toolbox/muap_comp.py 
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def get_highest_iqr_ch(muap: np.ndarray) -> np.ndarray:
    """Compute the highest interquartile range (IQR) channels.

    Args:
        muap (ndarray): Motor unit action potential with shape
            (ch_rows, ch_cols, samples)

    Returns:
        ndarray: A boolean mask indicating the channels with the highest IQR.
    """

    peak_amps = np.amax(np.abs(muap), axis=-1)
    peak_amps = np.reshape(peak_amps, (-1))
    q1 = np.percentile(peak_amps, 25)
    q3 = np.percentile(peak_amps, 75)
    iqr = q3 - q1
    whis = 1.5
    outliers = peak_amps > q3 + whis * iqr
    ch_mask = np.reshape(outliers, (muap.shape[0], muap.shape[1]))
    return ch_mask

get_percentile_ch 

get_percentile_ch(muap: ndarray, thr: Optional[int] = 90) -> np.ndarray

Compute the channels that exceed a certain percentile threshold.

Parameters:

Name Type Description Default
muap ndarray

Motor unit action potential with shape (ch_rows, ch_cols, samples)

 required
thr int

The percentile threshold. Defaults to 90.

 90

Returns:

Name Type Description
ndarray ndarray

A boolean mask indicating the channels that exceed the specified percentile threshold.
Source code in motor_unit_toolbox/muap_comp.py 
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def get_percentile_ch(
    muap: np.ndarray,
    thr: Optional[int] = 90
) -> np.ndarray:
    """Compute the channels that exceed a certain percentile threshold.

    Args:
        muap (ndarray): Motor unit action potential with shape
            (ch_rows, ch_cols, samples)
        thr (int, optional): The percentile threshold. Defaults to 90.

    Returns:
        ndarray: A boolean mask indicating the channels that exceed the
            specified percentile threshold.
    """
    peak_amps = np.amax(np.abs(muap), axis=-1)
    peak_amps = np.reshape(peak_amps, (-1))
    outliers = peak_amps > np.percentile(peak_amps, thr)
    ch_mask = np.reshape(outliers, (muap.shape[0], muap.shape[1]))
    return ch_mask

get_highest_iqr_ptp_ch 

get_highest_iqr_ptp_ch(muap: ndarray) -> np.ndarray

Compute the channels with the highest peak-to-peak (PTP) amplitude.

Parameters:

Name Type Description Default
muap ndarray

Motor unit action potential with shape (ch_rows, ch_cols, samples)

 required

Returns:

Type Description
ndarray

np.ndarray: A boolean mask indicating the channels with the highest PTP amplitude.
Source code in motor_unit_toolbox/muap_comp.py 
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def get_highest_iqr_ptp_ch(muap: np.ndarray) -> np.ndarray:
    """Compute the channels with the highest peak-to-peak (PTP) amplitude.

    Args:
        muap (np.ndarray): Motor unit action potential with shape
            (ch_rows, ch_cols, samples)

    Returns:
        np.ndarray: A boolean mask indicating the channels with the highest
            PTP amplitude.
    """

    peak_amps = np.ptp(muap, axis=-1)
    peak_amps = np.reshape(peak_amps, (-1))
    q1 = np.percentile(peak_amps, 25)
    q3 = np.percentile(peak_amps, 75)
    iqr = q3 - q1
    whis = 1.5
    outliers = peak_amps > q3 + whis * iqr
    ch_mask = np.reshape(outliers, (muap.shape[0], muap.shape[1]))
    return ch_mask

get_highest_amp_ch 

get_highest_amp_ch(muap: ndarray) -> np.ndarray

Compute the channels with the highest amplitude.

Parameters:

Name Type Description Default
muap ndarray

Motor unit action potential with shape (ch_rows, ch_cols, samples)

 required

Returns:

Name Type Description
ndarray ndarray

A boolean mask indicating the channels with the highest amplitude.
Source code in motor_unit_toolbox/muap_comp.py 
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def get_highest_amp_ch(muap: np.ndarray) -> np.ndarray:
    """Compute the channels with the highest amplitude.

    Args:
        muap (ndarray): Motor unit action potential with shape
            (ch_rows, ch_cols, samples)

    Returns:
        ndarray: A boolean mask indicating the channels with the highest
            amplitude.
    """
    peak_amps = np.amax(np.abs(muap), axis=-1)
    amp_thr = 3 * np.std(peak_amps)
    ch_mask = peak_amps > amp_thr
    return ch_mask

get_highest_ptp_ch 

get_highest_ptp_ch(muap: ndarray) -> np.ndarray

Compute the channels with the highest peak-to-peak (PTP) amplitude.

Parameters:

Name Type Description Default
muap ndarray

Motor unit action potential with shape (ch_rows, ch_cols, samples)

 required

Returns:

Type Description
ndarray

np.ndarray: A boolean mask indicating the channels with the highest PTP amplitude.
Source code in motor_unit_toolbox/muap_comp.py 
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def get_highest_ptp_ch(muap: np.ndarray) -> np.ndarray:
    """Compute the channels with the highest peak-to-peak (PTP) amplitude.

    Args:
        muap (np.ndarray): Motor unit action potential with shape
            (ch_rows, ch_cols, samples)

    Returns:
        np.ndarray: A boolean mask indicating the channels with the highest
            PTP amplitude.
    """
    ptp_amps = np.ptp(muap, axis=-1)
    amp_thr = 2 * np.std(ptp_amps)
    ch_mask = ptp_amps > amp_thr
    return ch_mask

nmse 

nmse(muap1: ndarray, muap2: ndarray) -> float

Compute the normalized mean squared error (NMSE) between two MUAPs.

Parameters:

Name Type Description Default
muap1 ndarray

First motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
muap2 ndarray

Second motor unit action potential with shape (ch_rows, ch_cols, samples).

 required

Returns:

Name Type Description
float float

The NMSE between the two MUAPs.
Source code in motor_unit_toolbox/muap_comp.py 
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def nmse(muap1: np.ndarray, muap2: np.ndarray) -> float:
    """Compute the normalized mean squared error (NMSE) between two MUAPs.

    Args:
        muap1 (np.ndarray): First motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        muap2 (np.ndarray): Second motor unit action potential with shape
            (ch_rows, ch_cols, samples).

    Returns:
        float: The NMSE between the two MUAPs.
    """
    mse = np.power(np.linalg.norm(muap1 - muap2), 2)
    m_energy = np.mean(
        np.power(np.linalg.norm(muap1), 2) + np.power(np.linalg.norm(muap2), 2)
    )

    return mse / m_energy

norm_farina_distance 

norm_farina_distance(muap1: ndarray, muap2: ndarray) -> float

Compute the normalized Farina distance between two MUAPs.

Parameters:

Name Type Description Default
muap1 ndarray

First motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
muap2 ndarray

Second motor unit action potential with shape (ch_rows, ch_cols, samples).

 required

Returns:

Name Type Description
float float

The normalized Farina distance between the two MUAPs.
Source code in motor_unit_toolbox/muap_comp.py 
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def norm_farina_distance(muap1: np.ndarray, muap2: np.ndarray) -> float:
    """Compute the normalized Farina distance between two MUAPs.

    Args:
        muap1 (np.ndarray): First motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        muap2 (np.ndarray): Second motor unit action potential with shape
            (ch_rows, ch_cols, samples).

    Returns:
        float: The normalized Farina distance between the two MUAPs.
    """
    # Check dimensions
    if len(muap1.shape) == 1:
        muap1 = np.expand_dims(muap1, axis=0)
    if len(muap2.shape) == 1:
        muap2 = np.expand_dims(muap2, axis=0)

    # Compute means
    muap1_mean = np.mean(muap1, axis=-1)
    muap2_mean = np.mean(muap2, axis=-1)

    # Compute norms
    muap1_l2 = np.linalg.norm(muap1, 2)
    muap2_l2 = np.linalg.norm(muap2, 2)

    # Normalise muaps
    muap1_norm = (muap1 - muap1_mean[:, None]) / muap1_l2
    muap2_norm = (muap2 - muap2_mean[:, None]) / muap2_l2

    # Compute energy
    muap1_energy = np.sum(np.power(muap1_norm, 2))
    muap2_energy = np.sum(np.power(muap2_norm, 2))

    # Compute normalized farina distance
    muaps_nfd = (2 * np.sum(np.power(muap1_norm - muap2_norm, 2))) / (
        muap1_energy + muap2_energy
    )

    return muaps_nfd

get_alignment 

get_alignment(muap1: ndarray, muap2: ndarray, flag_debug: Optional[bool] = False) -> int

Compute the alignment lag between two MUAPs.

Parameters:

Name Type Description Default
muap1 ndarray

First motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
muap2 ndarray

Second motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
flag_debug bool

Flag to enable debug mode. Defaults to False.

 False

Returns:

Name Type Description
int int

The alignment lag between the two MUAPs.
Source code in motor_unit_toolbox/muap_comp.py 
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def get_alignment(
        muap1: np.ndarray,
        muap2: np.ndarray,
        flag_debug: Optional[bool] = False
        ) -> int:
    """Compute the alignment lag between two MUAPs.

    Args:
        muap1 (np.ndarray): First motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        muap2 (np.ndarray): Second motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        flag_debug (bool, optional): Flag to enable debug mode. Defaults to
            False.

    Returns:
        int: The alignment lag between the two MUAPs.
    """
    # Get the muap length
    muap_length = muap1.shape[-1]

    # Flatten muaps for the correlation
    muap1_flat = muap1.flatten()
    muap2_flat = muap2.flatten()

    # Compute correlation and lags
    corr = signal.correlate(muap1_flat, muap2_flat, mode="full")
    lags = signal.correlation_lags(len(muap1_flat), len(muap2_flat), mode="full")

    # Bound both to half the muap length in each direction
    boundary_mask = np.nonzero(
        np.logical_and(lags >= -muap_length // 2, lags <= muap_length // 2)
    )[0]
    bounded_corr = corr[boundary_mask]
    bounded_lags = lags[boundary_mask]
    muaps_lag = bounded_lags[np.argmax(np.abs(bounded_corr))].astype(int)

    if not np.isscalar(muaps_lag):
        # If there is more than one possible lag, choose the minimum
        muaps_lag = np.amin(muaps_lag)

    if flag_debug:
        _, axs = plt.subplots(3, 1)

        axs[0].plot(bounded_lags, bounded_corr)
        axs[0].plot(muaps_lag, bounded_corr[np.argmax(np.abs(bounded_corr))], "ro")
        axs[0].set_ylabel("Correlation")
        axs[0].set_xlabel("Lags")
        axs[0].grid(True)
        axs[0].set_xlim([bounded_lags[0], bounded_lags[-1]])
        axs[0].set_title(f"max_corr = {np.amax(bounded_corr):.3f} at lag = {muaps_lag}")

        axs[1].plot(muap1_flat)
        axs[1].plot(muap2_flat)
        axs[1].grid(True)
        axs[1].set_xlim([0, len(muap1_flat)])
        axs[1].set_title("Before alignment")

        axs[2].plot(muap1_flat)
        axs[2].plot(np.roll(muap2_flat, muaps_lag, axis=-1))
        axs[2].grid(True)
        axs[2].set_xlim([0, len(muap1_flat)])
        axs[2].set_title(f"After alignment (lag = {muaps_lag})")

        plt.tight_layout()
        plt.show()

    return muaps_lag

compute_muaps_similarity 

compute_muaps_similarity(muap1: ndarray, muap2: ndarray, sel_chs_by: Literal['iqr', 'iqr_ptp', 'max_abs', 'ptp'] = 'iqr', metric: Literal['corr', 'cosine', 'nmse', 'nfd'] = 'nmse') -> Tuple[float, int]

Compute the similarity between two MUAPs.

Parameters:

Name Type Description Default
muap1 ndarray

First motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
muap2 ndarray

Second motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
sel_chs_by str

Method for selecting significant amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

 'iqr'
metric str

Similarity metric to compute: "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".

 'nmse'

Returns:

Type Description
Tuple[float, int]

Tuple[float, int]: The similarity between the two MUAPs and the alignment lag.
Source code in motor_unit_toolbox/muap_comp.py 
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def compute_muaps_similarity(
    muap1: np.ndarray,
    muap2: np.ndarray,
    sel_chs_by: Literal["iqr", "iqr_ptp", "max_abs", "ptp"] = "iqr",
    metric: Literal["corr", "cosine", "nmse", "nfd"] = "nmse"
) -> Tuple[float, int]:
    """Compute the similarity between two MUAPs.

    Args:
        muap1 (np.ndarray): First motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        muap2 (np.ndarray): Second motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        sel_chs_by (str, optional): Method for selecting significant
            amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".
        metric (str, optional): Similarity metric to compute:
            "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".

    Returns:
        Tuple[float, int]: The similarity between the two MUAPs and the
            alignment lag.
    """
    # Get significant amplitude channels
    if sel_chs_by == "max_abs":
        muap1_ch_mask = get_highest_amp_ch(muap1)
        muap2_ch_mask = get_highest_amp_ch(muap2)
    elif sel_chs_by == "ptp":
        muap1_ch_mask = get_highest_ptp_ch(muap1)
        muap2_ch_mask = get_highest_ptp_ch(muap2)
    elif sel_chs_by == "iqr":
        muap1_ch_mask = get_highest_iqr_ch(muap1)
        muap2_ch_mask = get_highest_iqr_ch(muap2)
    elif sel_chs_by == "iqr_ptp":
        muap1_ch_mask = get_highest_iqr_ptp_ch(muap1)
        muap2_ch_mask = get_highest_iqr_ptp_ch(muap2)

    # Check if channel masks are empty
    if not np.any(muap1_ch_mask):
        muap1_ch_mask = np.empty(muap1.shape[0:2])
    if not np.any(muap2_ch_mask):
        muap2_ch_mask = np.empty(muap2.shape[0:2])

    # Apply the channel selection to the muaps and correct for the lag
    sel_chs = np.nonzero(np.logical_or(muap1_ch_mask, muap2_ch_mask))
    if not np.any(sel_chs):
        sel_chs = np.ones_like(muap1).astype(bool)

    muap1_sel = np.array(muap1[sel_chs])
    muap2_sel = np.array(muap2[sel_chs])

    # Align signals based on the selected channels
    muaps_lag = get_alignment(muap1_sel, muap2_sel)
    muap2_sel = np.roll(muap2_sel, muaps_lag, axis=-1)

    # Compute metric
    if metric == "corr":
        muaps_sim = stats.pearsonr(muap1_sel.flatten(), muap2_sel.flatten())[0]
    elif metric == "cosine":
        muaps_sim = 1 - spatial.distance.cosine(
            muap1_sel.flatten(), muap2_sel.flatten()
        )
    elif metric == "nmse":
        muaps_sim = 1 - nmse(muap1_sel.flatten(), muap2_sel.flatten())
    elif metric == "nfd":
        muaps_sim = 1 - norm_farina_distance(muap1_sel.flatten(), muap2_sel.flatten())

    return muaps_sim, muaps_lag

compute_muaps_dist 

compute_muaps_dist(muap1: ndarray, muap2: ndarray, sel_chs_by: Literal['iqr', 'iqr_ptp', 'max_abs', 'ptp'] = 'iqr', metric: Literal['corr', 'cosine', 'nmse', 'nfd'] = 'nmse') -> Tuple[float, int]

Compute the distance between two MUAPs.

Parameters:

Name Type Description Default
muap1 ndarray

First motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
muap2 ndarray

Second motor unit action potential with shape (ch_rows, ch_cols, samples).

 required
sel_chs_by str

Method for selecting significant amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

 'iqr'
metric str

Distance metric to compute: "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".

 'nmse'

Returns:

Type Description
Tuple[float, int]

Tuple[float, int]: The distance between the two MUAPs and the alignment lag.
Source code in motor_unit_toolbox/muap_comp.py 
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def compute_muaps_dist(
        muap1: np.ndarray,
        muap2: np.ndarray,
        sel_chs_by: Literal["iqr", "iqr_ptp", "max_abs", "ptp"] = "iqr",
        metric: Literal["corr", "cosine", "nmse", "nfd"] = "nmse"
        ) -> Tuple[float, int]:
    """Compute the distance between two MUAPs.

    Args:
        muap1 (np.ndarray): First motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        muap2 (np.ndarray): Second motor unit action potential with shape
            (ch_rows, ch_cols, samples).
        sel_chs_by (str, optional): Method for selecting significant
            amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".
        metric (str, optional): Distance metric to compute:
            "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".

    Returns:
        Tuple[float, int]: The distance between the two MUAPs and the
            alignment lag.
    """

    # Get significant amplitude channels
    if sel_chs_by == "max_abs":
        muap1_ch_mask = get_highest_amp_ch(muap1)
        muap2_ch_mask = get_highest_amp_ch(muap2)
    elif sel_chs_by == "ptp":
        muap1_ch_mask = get_highest_ptp_ch(muap1)
        muap2_ch_mask = get_highest_ptp_ch(muap2)
    elif sel_chs_by == "iqr":
        muap1_ch_mask = get_highest_iqr_ch(muap1)
        muap2_ch_mask = get_highest_iqr_ch(muap2)
    elif sel_chs_by == "iqr_ptp":
        muap1_ch_mask = get_highest_iqr_ptp_ch(muap1)
        muap2_ch_mask = get_highest_iqr_ptp_ch(muap2)

    # Check if channel masks are empty
    if not np.any(muap1_ch_mask):
        muap1_ch_mask = np.empty(muap1.shape[0:2])
    if not np.any(muap2_ch_mask):
        muap2_ch_mask = np.empty(muap2.shape[0:2])

    # Apply the channel selection to the muaps and correct for the lag
    sel_chs = np.nonzero(np.logical_or(muap1_ch_mask, muap2_ch_mask))
    if not np.any(sel_chs):
        sel_chs = np.ones_like(muap1).astype(bool)

    muap1_sel = np.array(muap1[sel_chs])
    muap2_sel = np.array(muap2[sel_chs])

    # Align signals based on the selected channels
    muaps_lag = get_alignment(muap1_sel, muap2_sel)
    muap2_sel = np.roll(muap2_sel, muaps_lag, axis=-1)

    # Compute metric
    if metric == "corr":
        muaps_dist = 1 - stats.pearsonr(muap1_sel.flatten(), muap2_sel.flatten())[0]
    elif metric == "cosine":
        muaps_dist = spatial.distance.cosine(muap1_sel.flatten(), muap2_sel.flatten())
    elif metric == "nmse":
        muaps_dist = nmse(muap1_sel.flatten(), muap2_sel.flatten())
    elif metric == "nfd":
        muaps_dist = norm_farina_distance(muap1_sel.flatten(), muap2_sel.flatten())

    return muaps_dist, muaps_lag

compute_muaps_dist_sets 

compute_muaps_dist_sets(muaps1: ndarray, muaps2: ndarray, dist_metric: Literal['corr', 'cosine', 'nmse', 'nfd'] = 'nmse', sel_chs_method: Literal['iqr', 'iqr_ptp', 'max_abs', 'ptp'] = 'iqr') -> Tuple[np.ndarray, np.ndarray]

Compute the distance between sets of MUAPs.

Parameters:

Name Type Description Default
muaps1 ndarray

First set of motor unit action potentials with shape (n_units1, ch_rows, ch_cols, samples).

 required
muaps2 ndarray

Second set of motor unit action potentials with shape (n_units2, ch_rows, ch_cols, samples).

 required
dist_metric str

Distance metric to compute: "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".

 'nmse'
sel_chs_method str

Method for selecting significant amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

 'iqr'

Returns:

Type Description
Tuple[ndarray, ndarray]

Tuple[np.ndarray, np.ndarray]: The distance matrix between the two sets of MUAPs and the alignment lag matrix.
Source code in motor_unit_toolbox/muap_comp.py 
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def compute_muaps_dist_sets(
    muaps1: np.ndarray,
    muaps2: np.ndarray,
    dist_metric: Literal["corr", "cosine", "nmse", "nfd"] = "nmse",
    sel_chs_method: Literal["iqr", "iqr_ptp", "max_abs", "ptp"] = "iqr"
) -> Tuple[np.ndarray, np.ndarray]:
    """Compute the distance between sets of MUAPs.

    Args:
        muaps1 (np.ndarray): First set of motor unit action potentials with shape
            (n_units1, ch_rows, ch_cols, samples).
        muaps2 (np.ndarray): Second set of motor unit action potentials with shape
            (n_units2, ch_rows, ch_cols, samples).
        dist_metric (str, optional): Distance metric to compute:
            "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".
        sel_chs_method (str, optional): Method for selecting significant
            amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

    Returns:
        Tuple[np.ndarray, np.ndarray]: The distance matrix between the two sets of
            MUAPs and the alignment lag matrix.
    """

    # Check muaps size
    if np.any([len(muaps1) == 0, len(muaps2) == 0]):
        # No units
        all_muaps_dist = np.empty(0)
        all_muaps_lags = np.empty(0)
    else:
        # Check units sizes
        if len(muaps1.shape) < 4:
            muaps1 = np.expand_dims(muaps1, axis=0)

        if len(muaps2.shape) < 4:
            muaps2 = np.expand_dims(muaps2, axis=0)

        # Initialise variables
        n_units1 = muaps1.shape[0]
        n_units2 = muaps2.shape[0]

        # Initialise output
        all_muaps_dist = np.zeros((n_units1, n_units2))
        all_muaps_lags = np.zeros((n_units1, n_units2))

        # Fill correlation matrix for each unique pair comparison
        for unit1, unit2 in itertools.product(range(n_units1), range(n_units2)):

            # Select motor units
            muap1 = muaps1[unit1]
            muap2 = muaps2[unit2]

            # Compute correlation and lags
            curr_muaps_dist, curr_muaps_lag = compute_muaps_dist(
                muap1, muap2, sel_chs_by=sel_chs_method, metric=dist_metric
            )

            # Fill matrices
            all_muaps_dist[unit1, unit2] = curr_muaps_dist
            all_muaps_lags[unit1, unit2] = curr_muaps_lag

    return all_muaps_dist, all_muaps_lags.astype(int)

compute_all_muaps_dist 

compute_all_muaps_dist(muaps: ndarray, dist_metric: Literal['corr', 'cosine', 'nmse', 'nfd'] = 'nmse', sel_chs_method: Literal['iqr', 'iqr_ptp', 'max_abs', 'ptp'] = 'iqr') -> Tuple[np.ndarray, np.ndarray]

Compute the distance between all pairs of MUAPs.

Parameters:

Name Type Description Default
muaps ndarray

Motor unit action potentials with shape (n_units, ch_rows, ch_cols, samples).

 required
dist_metric str

Distance metric to compute: "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".

 'nmse'
sel_chs_method str

Method for selecting significant amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

 'iqr'

Returns:

Type Description
Tuple[ndarray, ndarray]

Tuple[np.ndarray, np.ndarray]: The distance matrix between all pairs of MUAPs and the alignment lag matrix.
Source code in motor_unit_toolbox/muap_comp.py 
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def compute_all_muaps_dist(
    muaps: np.ndarray,
    dist_metric: Literal["corr", "cosine", "nmse", "nfd"] = "nmse",
    sel_chs_method: Literal["iqr", "iqr_ptp", "max_abs", "ptp"] = "iqr"
    ) -> Tuple[np.ndarray, np.ndarray]:
    """Compute the distance between all pairs of MUAPs.

    Args:
        muaps (np.ndarray): Motor unit action potentials with shape
            (n_units, ch_rows, ch_cols, samples).
        dist_metric (str, optional): Distance metric to compute:
            "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".
        sel_chs_method (str, optional): Method for selecting significant
            amplitude channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

    Returns:
        Tuple[np.ndarray, np.ndarray]: The distance matrix between all pairs of MUAPs
            and the alignment lag matrix.
    """

    # Check muaps size
    if len(muaps) == 0:
        # No units
        all_muaps_dist = np.empty(0)
        all_muaps_lags = np.empty(0)
    else:
        # There are units
        if len(muaps.shape) < 4:
            muaps = np.expand_dims(muaps, axis=0)

        # Initialise variables
        n_units = muaps.shape[0]

        if n_units == 1:
            # Only one unit
            all_muaps_dist = np.array([0])
            all_muaps_lags = np.array([0])
        else:
            # More than one unit, so initialise pair combinations
            pairs = itertools.combinations(range(n_units), 2)
            all_muaps_dist = np.zeros((n_units, n_units))
            all_muaps_lags = np.zeros((n_units, n_units))

            # Fill correlation matrix for each unique pair comparison
            for pair in pairs:
                # Select motor units
                muap1 = muaps[pair[0]]
                muap2 = muaps[pair[1]]

                # Compute correlation and lags
                curr_muaps_dist, curr_muaps_lag = compute_muaps_dist(
                    muap1, muap2, sel_chs_by=sel_chs_method, metric=dist_metric
                )

                # Fill matrices
                all_muaps_dist[pair[0], pair[1]] = curr_muaps_dist
                all_muaps_dist[pair[1], pair[0]] = curr_muaps_dist

                all_muaps_lags[pair[0], pair[1]] = curr_muaps_lag
                all_muaps_lags[pair[1], pair[0]] = curr_muaps_lag

    return all_muaps_dist, all_muaps_lags.astype(int)

mask_within_trial_dist 

mask_within_trial_dist(all_muaps_dist: ndarray, trial_labels: ndarray, fill_value: Optional[float] = None) -> np.ndarray

Set the distance between different MUAPs of the same trial to a large value.

Units identified in the same trial that are different motor units, should not be matched together. The diagonal (each unit with itself) is left at 0.

Parameters:

Name Type Description Default
all_muaps_dist ndarray

Distance matrix between all pairs of MUAPs with shape (n_units, n_units).

 required
trial_labels ndarray

Trial label of each MUAP, with shape (n_units).

 required
fill_value float

Distance assigned to pairs from the same trial. Defaults to 1 + the largest distance in the matrix.

 None

Returns:

Type Description
ndarray

np.ndarray: A masked copy of the distance matrix. The input is not modified.
Source code in motor_unit_toolbox/muap_comp.py 
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def mask_within_trial_dist(
    all_muaps_dist: np.ndarray,
    trial_labels: np.ndarray,
    fill_value: Optional[float] = None,
) -> np.ndarray:
    """Set the distance between different MUAPs of the same trial to a large value.

    Units identified in the same trial that are different motor units, should
    not be matched together. The diagonal (each unit with itself) is left at 0.

    Args:
        all_muaps_dist (np.ndarray): Distance matrix between all pairs of MUAPs
            with shape (n_units, n_units).
        trial_labels (np.ndarray): Trial label of each MUAP, with shape (n_units).
        fill_value (float, optional): Distance assigned to pairs from the same
            trial. Defaults to 1 + the largest distance in the matrix.

    Returns:
        np.ndarray: A masked copy of the distance matrix. The input is not modified.
    """
    trial_labels = np.asarray(trial_labels)
    if trial_labels.shape != (all_muaps_dist.shape[0],):
        raise ValueError(
            f"trial_labels has shape {trial_labels.shape}, expected "
            f"({all_muaps_dist.shape[0]},) to match the distance matrix."
        )
    if fill_value is None:
        fill_value = np.nanmax(all_muaps_dist) + 1

    same_trial = trial_labels[:, None] == trial_labels[None, :]
    np.fill_diagonal(same_trial, False)

    masked_dist = np.array(all_muaps_dist, dtype=float)
    masked_dist[same_trial] = fill_value
    return masked_dist

cluster_muaps 

cluster_muaps(all_muaps_dist: ndarray, cluster_method: Literal['single', 'complete', 'average', 'weighted', 'centroid', 'median', 'ward'] = 'ward', dist_metric: Literal['corr', 'cosine', 'nmse', 'nfd'] = 'corr', sel_chs_method: Literal['iqr', 'iqr_ptp', 'max_abs', 'ptp'] = 'iqr_ptp', thr_vals: Optional[ndarray] = np.arange(0, 2.0001, 0.001), flag_plot: Optional[bool] = True, *, trial_labels: Optional[ndarray] = None) -> Tuple[pd.DataFrame, Dict[str, np.ndarray]]

Cluster MUAPs based on distance matrix.

Parameters:

Name Type Description Default
all_muaps_dist ndarray

Distance matrix between all pairs of MUAPs.

 required
cluster_method str

Linkage method passed to scipy.cluster.hierarchy.linkage. Defaults to "ward".

 'ward'
dist_metric str

Distance metric used to build all_muaps_dist (stored in the output only). Defaults to "corr".

 'corr'
sel_chs_method str

Channel selection method used to build all_muaps_dist (stored in the output only). Defaults to "iqr_ptp".

 'iqr_ptp'
thr_vals ndarray

Threshold values for clustering. Defaults to np.arange(0, 2.0001, 0.001).

 arange(0, 2.0001, 0.001)
flag_plot bool

Flag to plot clustering metrics. Defaults to True.

 True
trial_labels ndarray

Trial label of each MUAP, with shape (n_units). If given, MUAPs from the same trial are made maximally distant before clustering (see mask_within_trial_dist), so they are not grouped together. Only "complete" linkage guarantees this; with other methods a warning lists any same-trial units merged at the selected threshold. The clustering metrics are always computed on the original distances. Defaults to None (no trial constraint).

 None

Returns:

Type Description
Tuple[DataFrame, Dict[str, ndarray]]

Tuple[pd.DataFrame, Dict[str, np.ndarray]]: Optimal threshold information and clustering metrics. The dictionary contains the following keys: - "cluster_method" (str): The clustering method used. - "dist_metric" (str): The distance metric used. - "sel_chs_method" (str): The method used for selecting significant amplitude channels. - "labels" (np.ndarray): The cluster labels for each threshold value. - "n_clusters" (np.ndarray): The number of clusters for each threshold value. - "sil" (np.ndarray): The silhouette scores for each threshold value. - "chi" (np.ndarray): The Calinski-Harabasz scores for each threshold value. - "dbi" (np.ndarray): The Davies-Bouldin scores for each threshold value. - "w_dist_mean" (np.ndarray): The mean within-cluster distances for each threshold value. - "w_dist_std" (np.ndarray): The standard deviation of within-cluster distances for each threshold value. - "b_dist_mean" (np.ndarray): The mean between-cluster distances for each threshold value. - "b_dist_std" (np.ndarray): The standard deviation of between-cluster distances for each threshold value.
Source code in motor_unit_toolbox/muap_comp.py 
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def cluster_muaps(
    all_muaps_dist: np.ndarray,
    cluster_method: Literal[
        "single", "complete", "average", "weighted", "centroid", "median", "ward"
    ] = "ward",
    dist_metric: Literal["corr", "cosine", "nmse", "nfd"] = "corr",
    sel_chs_method: Literal["iqr", "iqr_ptp", "max_abs", "ptp"] = "iqr_ptp",
    thr_vals: Optional[np.ndarray] = np.arange(0, 2.0001, 0.001),  # noqa: B008 (read-only)
    flag_plot: Optional[bool] = True,
    *,
    trial_labels: Optional[np.ndarray] = None,
) -> Tuple[pd.DataFrame, Dict[str, np.ndarray]]:
    """Cluster MUAPs based on distance matrix.

    Args:
        all_muaps_dist (np.ndarray): Distance matrix between all pairs of MUAPs.
        cluster_method (str, optional): Linkage method passed to
            scipy.cluster.hierarchy.linkage. Defaults to "ward".
        dist_metric (str, optional): Distance metric used to build
            all_muaps_dist (stored in the output only). Defaults to "corr".
        sel_chs_method (str, optional): Channel selection method used to
            build all_muaps_dist (stored in the output only). Defaults to "iqr_ptp".
        thr_vals (np.ndarray, optional): Threshold values for clustering. Defaults to
            np.arange(0, 2.0001, 0.001).
        flag_plot (bool, optional): Flag to plot clustering metrics. Defaults to True.
        trial_labels (np.ndarray, optional): Trial label of each MUAP, with shape
            (n_units). If given, MUAPs from the same trial are made maximally distant
            before clustering (see `mask_within_trial_dist`), so they are not grouped
            together. Only "complete" linkage guarantees this; with other methods a
            warning lists any same-trial units merged at the selected threshold.
            The clustering metrics are always computed on the original distances.
            Defaults to None (no trial constraint).

    Returns:
        Tuple[pd.DataFrame, Dict[str, np.ndarray]]: Optimal threshold information and
            clustering metrics. The dictionary contains the following keys:
            - "cluster_method" (str): The clustering method used.
            - "dist_metric" (str): The distance metric used.
            - "sel_chs_method" (str): The method used for selecting significant amplitude
                channels.
            - "labels" (np.ndarray): The cluster labels for each threshold value.
            - "n_clusters" (np.ndarray): The number of clusters for each threshold value.
            - "sil" (np.ndarray): The silhouette scores for each threshold value.
            - "chi" (np.ndarray): The Calinski-Harabasz scores for each threshold value.
            - "dbi" (np.ndarray): The Davies-Bouldin scores for each threshold value.
            - "w_dist_mean" (np.ndarray): The mean within-cluster distances for each
                threshold value.
            - "w_dist_std" (np.ndarray): The standard deviation of within-cluster distances
                for each threshold value.
            - "b_dist_mean" (np.ndarray): The mean between-cluster distances for each
                threshold value.
            - "b_dist_std" (np.ndarray): The standard deviation of between-cluster distances
                for each threshold value.
    """

    # Initialise variables
    n_units = all_muaps_dist.shape[0]

    # Keep units from the same trial apart (only affects the linkage, not the metrics)
    link_dist = all_muaps_dist
    if trial_labels is not None:
        trial_labels = np.asarray(trial_labels)
        link_dist = mask_within_trial_dist(
            all_muaps_dist,
            trial_labels,
            fill_value=max(np.nanmax(all_muaps_dist), np.max(thr_vals)) + 1,
        )

    # Transform distance from redundant form into condensed form
    all_muaps_dist_cond = spatial.distance.squareform(link_dist)

    # Build linkage between
    link = cluster.hierarchy.linkage(all_muaps_dist_cond, method=cluster_method)

    # Initialise outputs
    cluster_out = {
        "cluster_method": cluster_method,
        "dist_metric": dist_metric,
        "sel_chs_method": sel_chs_method,
        "labels": np.empty((len(thr_vals), n_units)),
        "n_clusters": np.empty(len(thr_vals)),
        "sil": np.empty(len(thr_vals)),
        "chi": np.empty(len(thr_vals)),
        "dbi": np.empty(len(thr_vals)),
        "w_dist_mean": np.empty(len(thr_vals)),
        "w_dist_std": np.empty(len(thr_vals)),
        "b_dist_mean": np.empty(len(thr_vals)),
        "b_dist_std": np.empty(len(thr_vals)),
    }

    for i, thr in enumerate(thr_vals):

        # Apply hierarchical/agglomerative clustering
        cluster_out["labels"][i] = cluster.hierarchy.fcluster(
            link, t=thr, criterion="distance"
        )

        # Number of clusters
        cluster_out["n_clusters"][i] = np.amax(cluster_out["labels"][i])

        # Clustering metrics
        if (cluster_out["n_clusters"][i] > 1) & (
            cluster_out["n_clusters"][i] < n_units
        ):
            cluster_out["sil"][i] = metrics.silhouette_score(
                all_muaps_dist, cluster_out["labels"][i], metric="precomputed"
            )
            cluster_out["chi"][i] = metrics.calinski_harabasz_score(
                all_muaps_dist, cluster_out["labels"][i]
            )
            cluster_out["dbi"][i] = metrics.davies_bouldin_score(
                all_muaps_dist, cluster_out["labels"][i]
            )
        else:
            cluster_out["sil"][i] = np.nan
            cluster_out["chi"][i] = np.nan
            cluster_out["dbi"][i] = np.nan

        # Between and within cluster distance stats
        w_dist_mean = []
        w_dist_std = []
        b_dist_mean = []
        b_dist_std = []
        np.fill_diagonal(all_muaps_dist, np.nan)

        for curr_cluster in np.unique(cluster_out["labels"][i]):
            curr_cluster_mask = cluster_out["labels"][i] == curr_cluster

            # Single-unit clusters have no within distances and a single cluster has
            # no between distances: these are NaN (skipped quietly, not warned about)
            within_dists = all_muaps_dist[np.ix_(curr_cluster_mask, curr_cluster_mask)]
            between_dists = all_muaps_dist[
                np.ix_(curr_cluster_mask, np.logical_not(curr_cluster_mask))
            ]
            w_dist_mean.append(_nanmean_or_nan(within_dists))
            w_dist_std.append(_nanstd_or_nan(within_dists))
            b_dist_mean.append(_nanmean_or_nan(between_dists))
            b_dist_std.append(_nanstd_or_nan(between_dists))

        cluster_out["w_dist_mean"][i] = _nanmean_or_nan(w_dist_mean)
        cluster_out["w_dist_std"][i] = _nanmean_or_nan(w_dist_std)
        cluster_out["b_dist_mean"][i] = _nanmean_or_nan(b_dist_mean)
        cluster_out["b_dist_std"][i] = _nanmean_or_nan(b_dist_std)

        np.fill_diagonal(all_muaps_dist, 0)

    # Find maximum sil
    opt_sil_idx = np.nanargmax(cluster_out["sil"])
    opt_thr = thr_vals[opt_sil_idx]
    opt_sil = cluster_out["sil"][opt_sil_idx]
    opt_n_clusters = cluster_out["n_clusters"][opt_sil_idx]

    # Check the trial constraint held at the selected threshold
    if trial_labels is not None:
        _warn_same_trial_clusters(cluster_out["labels"][opt_sil_idx], trial_labels, opt_thr)

    # Store output in a dataframe
    opt_thr_info = pd.DataFrame(
        {
            "cluster_method": [cluster_method],
            "dist_metric": [dist_metric],
            "sel_chs_method": [sel_chs_method],
            "opt_sil": [opt_sil],
            "opt_idx": [opt_sil_idx],
            "opt_thr": [opt_thr],
            "opt_n_clusters": [opt_n_clusters],
        }
    )

    if flag_plot:
        # Plot metrics
        _, axs = plt.subplots(6, 1, figsize=(10, 10))
        axs = np.ravel(axs)

        cluster.hierarchy.dendrogram(
            link.tolist(),
            ax=axs[0],
            color_threshold=opt_thr_info["opt_thr"].values[0],
            leaf_font_size=12,
        )
        axs[0].set_title(
            f"{cluster_method}" +
            f"max sil = {opt_thr_info['opt_sil'].values[0]:.3f}, " +
            f"thr = {opt_thr_info['opt_thr'].values[0]:.3f}"
        )
        axs[0].set_xlabel("Motor units")
        axs[0].set_ylabel("Linkage distance")

        axs[1].plot(thr_vals, cluster_out["n_clusters"])
        axs[1].axvline(opt_thr_info["opt_thr"].values[0], color="r")
        axs[1].grid(True)
        axs[1].set_xlim([thr_vals[0], thr_vals[-1]])
        axs[1].set_xlabel("Distance thresholds")
        axs[1].set_ylabel("Number of clusters")

        axs[2].plot(thr_vals, cluster_out["w_dist_mean"], "-", label="w_dist")
        axs[2].fill_between(
            thr_vals,
            cluster_out["w_dist_mean"] - cluster_out["w_dist_std"],
            cluster_out["w_dist_mean"] + cluster_out["w_dist_std"],
            alpha=0.2,
            label=None,
        )
        axs[2].plot(thr_vals, cluster_out["b_dist_mean"], "-", label="b_dist")
        axs[2].fill_between(
            thr_vals,
            cluster_out["b_dist_mean"] - cluster_out["b_dist_std"],
            cluster_out["b_dist_mean"] + cluster_out["b_dist_std"],
            alpha=0.2,
            label=None,
        )
        axs[2].axvline(opt_thr_info["opt_thr"].values[0], color="r", label="opt_thr")
        axs[2].legend(bbox_to_anchor=(1.1, 1))
        axs[2].grid(True)
        axs[2].set_xlim([thr_vals[0], thr_vals[-1]])
        axs[2].set_xlabel("Distance thresholds")
        axs[2].set_ylabel("Distance")

        axs[3].plot(thr_vals, cluster_out["sil"])
        axs[3].plot(
            opt_thr_info["opt_thr"].values[0],
            opt_thr_info["opt_sil"].values[0],
            "ro",
            markersize=6,
        )
        axs[3].axvline(opt_thr_info["opt_thr"].values[0], color="r")
        axs[3].grid(True)
        axs[3].set_xlim([thr_vals[0], thr_vals[-1]])
        axs[3].set_xlabel("Distance thresholds")
        axs[3].set_ylabel("silhouette\n(maximise)")

        axs[4].plot(thr_vals, cluster_out["dbi"])
        axs[4].axvline(opt_thr_info["opt_thr"].values[0], color="r")
        axs[4].grid(True)
        axs[4].set_xlim([thr_vals[0], thr_vals[-1]])
        axs[4].set_xlabel("Distance thresholds")
        axs[4].set_ylabel("Davies-Bouldin\n(minimise)")

        axs[5].plot(thr_vals, cluster_out["chi"])
        axs[5].axvline(opt_thr_info["opt_thr"].values[0], color="r")
        axs[5].grid(True)
        axs[5].set_xlim([thr_vals[0], thr_vals[-1]])
        axs[5].set_xlabel("Distance thresholds")
        axs[5].set_ylabel("Calinski-Harabasz\n(maximise)")

        plt.tight_layout()
        plt.show()

    return opt_thr_info, cluster_out

pairwise 

pairwise(iterable: Iterable) -> Iterable[Tuple]

pairwise(iterable) --> AB BC CD DE EF FG

Returns an iterable of tuples containing adjacent pairs of elements from the input iterable.

Parameters:

Name Type Description Default
iterable Iterable

The input iterable.

 required

Yields:

Type Description
Iterable[Tuple]

A tuple containing adjacent pairs of elements from the input iterable.
Example

list(pairwise('ABCDEFG')) [('A', 'B'), ('B', 'C'), ('C', 'D'), ('D', 'E'), ('E', 'F'), ('F', 'G')]

Source code in motor_unit_toolbox/muap_comp.py 
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def pairwise(iterable: Iterable) -> Iterable[Tuple]:
    """
    pairwise(iterable) --> AB BC CD DE EF FG

    Returns an iterable of tuples containing adjacent pairs of elements from the input iterable.

    Args:
        iterable: The input iterable.

    Yields:
        A tuple containing adjacent pairs of elements from the input iterable.

    Example:
        >>> list(pairwise('ABCDEFG'))
        [('A', 'B'), ('B', 'C'), ('C', 'D'), ('D', 'E'), ('E', 'F'), ('F', 'G')]
    """
    a, b = itertools.tee(iterable)
    next(b, None)
    return zip(a, b, strict=False)

mark_groups 

mark_groups(rows: List[int], cols: List[int], idx_i: List[int], idx_j: List[int], curr_dist_mat: ndarray, trial_labels: List[int], out_dict: Dict, graph: DiGraph) -> Tuple[Dict, nx.DiGraph]

Mark groups based on the given rows and columns.

Parameters:

Name Type Description Default
rows List[int]

The list of row indices.

 required
cols List[int]

The list of column indices.

 required
idx_i List[int]

The list of unit indices for rows.

 required
idx_j List[int]

The list of unit indices for columns.

 required
curr_dist_mat ndarray

The current distance matrix.

 required
trial_labels List[int]

The list of trial labels.

 required
out_dict Dict

The output dictionary containing the following keys: - "unit1" (List[int]): The list of unit indices from the first group. - "unit2" (List[int]): The list of unit indices from the second group. - "label1" (List[int]): The list of trial labels for the units in the first group. - "label2" (List[int]): The list of trial labels for the units in the second group. - "link_dist" (List[float]): The list of linkage distances between the units. - "no_link_dist" (List[List[float]]): The list of distances between each unit and all other units in the same group.

 required
graph DiGraph

The directed graph.

 required

Returns:

Type Description
Tuple[Dict, DiGraph]

Tuple[Dict, nx.DiGraph]: The updated output dictionary and graph.
Source code in motor_unit_toolbox/muap_comp.py 
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def mark_groups(
    rows: List[int],
    cols: List[int],
    idx_i: List[int],
    idx_j: List[int],
    curr_dist_mat: np.ndarray,
    trial_labels: List[int],
    out_dict: Dict,
    graph: nx.DiGraph
) -> Tuple[Dict, nx.DiGraph]:
    """
    Mark groups based on the given rows and columns.

    Args:
        rows (List[int]): The list of row indices.
        cols (List[int]): The list of column indices.
        idx_i (List[int]): The list of unit indices for rows.
        idx_j (List[int]): The list of unit indices for columns.
        curr_dist_mat (np.ndarray): The current distance matrix.
        trial_labels (List[int]): The list of trial labels.
        out_dict (Dict): The output dictionary containing the following keys:
            - "unit1" (List[int]): The list of unit indices from the first group.
            - "unit2" (List[int]): The list of unit indices from the second group.
            - "label1" (List[int]): The list of trial labels for the units in the
                first group.
            - "label2" (List[int]): The list of trial labels for the units in the
                second group.
            - "link_dist" (List[float]): The list of linkage distances between the
                units.
            - "no_link_dist" (List[List[float]]): The list of distances between
                each unit and all other units in the same group.
        graph (nx.DiGraph): The directed graph.

    Returns:
        Tuple[Dict, nx.DiGraph]: The updated output dictionary and graph.
    """

    if len(rows) < 1 or len(cols) < 1:
        return out_dict, graph

    for row, col in zip(rows, cols, strict=True):
        #  Get dist_mat values
        row_list, col_list = list(range(len(idx_i))), list(range(len(idx_j)))
        row_list.remove(row)
        col_list.remove(col)
        no_link_dist = np.concatenate(
            (curr_dist_mat[row_list, col], curr_dist_mat[row, col_list])
        )

        #  Update output
        out_dict['unit1'].append(idx_i[row])
        out_dict['unit2'].append(idx_j[col])
        out_dict['label1'].append(trial_labels[idx_i[row]])
        out_dict['label2'].append(trial_labels[idx_j[col]])
        out_dict['link_dist'].append(curr_dist_mat[row, col])
        out_dict['no_link_dist'].append(no_link_dist.tolist())

        # Update graph
        graph.add_edge(idx_i[row], idx_j[col], weight=curr_dist_mat[row, col])

    return out_dict, graph

generate_group_sets 

generate_group_sets(graph: DiGraph) -> List[List[int]]

Generate group sets based on the given directed graph.

Parameters:

Name Type Description Default
graph DiGraph

A directed graph representing the connections between units.

 required

Returns:

Type Description
List

A list of group sets, where each group set is a list of unit indices.
Example

graph = nx.DiGraph() graph.add_edge(1, 2) graph.add_edge(2, 3) graph.add_edge(3, 4) generate_group_sets(graph) [[1, 2, 3, 4]]

Source code in motor_unit_toolbox/muap_comp.py 
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def generate_group_sets(graph: nx.DiGraph) -> List[List[int]]:
    """
    Generate group sets based on the given directed graph.

    Args:
        graph (nx.DiGraph): A directed graph representing the connections between
            units.

    Returns:
        (List): A list of group sets, where each group set is a list of unit indices.

    Example:
        >>> graph = nx.DiGraph()
        >>> graph.add_edge(1, 2)
        >>> graph.add_edge(2, 3)
        >>> graph.add_edge(3, 4)
        >>> generate_group_sets(graph)
        [[1, 2, 3, 4]]
    """

    # Get all possible sources
    possible_sources = [node for node, in_degree in graph.in_degree() if in_degree == 0]

    #  Initialise group sets
    group_sets = []
    for source in possible_sources:
        #  Get successors
        curr_successor = list(graph.successors(source))

        #  If there are no successors, just add the source
        if len(curr_successor) < 1:
            group_sets.append([source])
            continue

        #  While the are successors add them to the path
        path = [source, curr_successor[0]]
        while list(graph.successors(curr_successor[0])):
            curr_successor = list(graph.successors(curr_successor[0]))
            path.append(curr_successor[0])
        #  Append path to set
        group_sets.append(path)

    # Sort by size
    group_counts = list(map(len, group_sets))
    idxs = np.argsort(group_counts)[::-1]

    return [group_sets[i] for i in idxs]

generate_group_labels 

generate_group_labels(group_sets: List[List[int]]) -> List[int]

Generate group labels based on the given group sets.

Parameters:

Name Type Description Default
group_sets List

A list of group sets, where each group set is a list of unit indices. Unit indices must be 0-based and cover every unit (0 to n_units - 1), as produced by generate_group_sets.

 required

Returns:

Type Description
List

A list of group labels (starting at 1), where each label corresponds to a unit index.
Example

generate_group_labels([[0, 2, 3], [1]]) [1, 2, 1, 1]

Source code in motor_unit_toolbox/muap_comp.py 
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def generate_group_labels(group_sets: List[List[int]]) -> List[int]:
    """
    Generate group labels based on the given group sets.

    Args:
        group_sets (List): A list of group sets, where each group set is a list of
            unit indices. Unit indices must be 0-based and cover every unit
            (0 to n_units - 1), as produced by generate_group_sets.

    Returns:
        (List): A list of group labels (starting at 1), where each label
            corresponds to a unit index.

    Example:
        >>> generate_group_labels([[0, 2, 3], [1]])
        [1, 2, 1, 1]
    """
    units = len(np.concatenate(group_sets))
    groups = np.zeros(units).astype(int)
    for i, path in enumerate(group_sets):
        groups[path] = i + 1
    tracker = np.amax(groups) + 1
    idxs = np.nonzero(groups == 0)[0]
    for i, idx in enumerate(idxs):
        groups[idx] = tracker + i
    return groups

apply_hungarian_algorithm 

apply_hungarian_algorithm(curr_dist_mat: ndarray, dist_thr: float) -> Tuple[np.ndarray, np.ndarray]

Apply the Hungarian algorithm for association based on the given distance matrix.

Parameters:

Name Type Description Default
curr_dist_mat ndarray

The distance matrix.

 required
dist_thr float

The distance threshold.

 required

Returns:

Type Description
Tuple

containing the rows and columns that meet the distance threshold.
Example

apply_hungarian_algorithm(curr_dist_mat, dist_thr) (array([0, 1, 2]), array([0, 1, 2]))

Source code in motor_unit_toolbox/muap_comp.py 
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def apply_hungarian_algorithm(
    curr_dist_mat: np.ndarray,
    dist_thr: float
) -> Tuple[np.ndarray, np.ndarray]:
    """
    Apply the Hungarian algorithm for association based on the given distance matrix.

    Args:
        curr_dist_mat (np.ndarray): The distance matrix.
        dist_thr (float): The distance threshold.

    Returns:
        (Tuple): containing the rows and columns that meet the distance threshold.

    Example:
        >>> apply_hungarian_algorithm(curr_dist_mat, dist_thr)
        (array([0, 1, 2]), array([0, 1, 2]))
    """
    rows, cols = optimize.linear_sum_assignment(curr_dist_mat)

    # Keep only the rows and cols that meet the threshold
    valid_idxs = curr_dist_mat[rows, cols] <= dist_thr
    rows, cols = rows[valid_idxs], cols[valid_idxs]
    return rows, cols

apply_sorted_grid_search(curr_dist_mat: ndarray, dist_thr: float) -> Tuple[List[int], List[int]]

Apply a sorted grid search to find possible matches for each row in the distance matrix.

Parameters:

Name Type Description Default
curr_dist_mat ndarray

The distance matrix.

 required
dist_thr float

The distance threshold.

 required

Returns:

Type Description
Tuple

containing the rows and columns that meet the distance threshold.
Example

apply_sorted_grid_search(curr_dist_mat, dist_thr) ([0, 1, 2], [0, 1, 2])

Source code in motor_unit_toolbox/muap_comp.py 
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def apply_sorted_grid_search(
        curr_dist_mat: np.ndarray,
        dist_thr: float,
) -> Tuple[List[int], List[int]]:
    """
    Apply a sorted grid search to find possible matches for each row in the
    distance matrix.

    Args:
        curr_dist_mat (np.ndarray): The distance matrix.
        dist_thr (float): The distance threshold.

    Returns:
        (Tuple): containing the rows and columns that meet the distance threshold.

    Example:
        >>> apply_sorted_grid_search(curr_dist_mat, dist_thr)
        ([0, 1, 2], [0, 1, 2])
    """

    #  Search for possible matches for each row
    rows, cols = [], []
    for i in range(curr_dist_mat.shape[0]):

        # Get the minimum distance for that row
        min_dist_i = np.min(curr_dist_mat[i, :])
        if min_dist_i > dist_thr:
            continue

        # If it is a valid hit, make sure it is also the best assignment for the column
        j = np.argmin(curr_dist_mat[i, :])
        if min_dist_i > np.min(curr_dist_mat[:, j]):
            continue

        #  If it is, then mark it as a match
        rows.append(i)
        cols.append(j)

    return rows, cols

assign_muaps_across_seq_trials 

assign_muaps_across_seq_trials(dist_mat: ndarray, trial_labels: ndarray, trial_set: List[int], assign_method: Literal['hungarian', 'grid-search'] = 'grid-search', dist_thr: Optional[float] = 0.3) -> Tuple[Dict[str, List], nx.DiGraph, np.ndarray]

Assign MUAPs across sequential trials based on the given distance matrix.

Parameters:

Name Type Description Default
dist_mat ndarray

The distance matrix.

 required
trial_labels ndarray

All trial labels.

 required
trial_set List[int]

The trial labels present in the distance matrix.

 required
assign_method str

The method to use for assignment: "hungarian" or "grid-search". Defaults to "grid-search".

 'grid-search'
dist_thr float

The distance threshold. Defaults to 0.3.

 0.3

Returns:

Type Description
Tuple[Dict[str, List], DiGraph, ndarray]

Tuple[Dict[str, List], nx.DiGraph, np.ndarray]: A tuple containing the output dictionary, the graph, and the updated distance matrix.
Source code in motor_unit_toolbox/muap_comp.py 
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def assign_muaps_across_seq_trials(
    dist_mat: np.ndarray,
    trial_labels: np.ndarray,
    trial_set: List[int],
    assign_method: Literal["hungarian", "grid-search"] = "grid-search",
    dist_thr: Optional[float] = 0.3
) -> Tuple[Dict[str, List], nx.DiGraph, np.ndarray]:
    """
    Assign MUAPs across sequential trials based on the given distance matrix.

    Args:
        dist_mat (np.ndarray): The distance matrix.
        trial_labels (np.ndarray): All trial labels.
        trial_set (List[int]): The trial labels present in the distance matrix.
        assign_method (str, optional): The method to use for assignment:
            "hungarian" or "grid-search". Defaults to "grid-search".
        dist_thr (float, optional): The distance threshold. Defaults to 0.3.

    Returns:
        Tuple[Dict[str, List], nx.DiGraph, np.ndarray]: A tuple containing the
            output dictionary, the graph, and the updated distance matrix.
    """

    #  Initialise outputs
    keys = ["unit1", "unit2", "label1", "label2", "group", "link_dist", "no_link_dist"]
    out_dict = edict({key: [] for key in keys})

    # Generate nodes
    subset_sizes = [np.sum(trial_labels == trial) for trial in trial_set]
    extents = nx.utils.pairwise(itertools.accumulate([0,] + subset_sizes))
    layers = [range(start, end) for start, end in extents]

    #  Generate graph
    graph = nx.DiGraph()
    for trial, layer in zip(trial_set, layers, strict=True):
        graph.add_nodes_from(layer, layer=trial)

    # Find adjacent neighbours
    # ------------------------
    for trial_i, trial_j in pairwise(trial_set):

        # Get indexes of the trials
        idx_i = np.nonzero(trial_labels == trial_i)[0]
        idx_j = np.nonzero(trial_labels == trial_j)[0]

        #  If there are no units in any of the trials, skip
        if len(idx_i) < 1 or len(idx_j) < 1:
            continue

        #  Assign units
        curr_dist_mat = dist_mat[np.ix_(idx_i, idx_j)]
        if assign_method == "hungarian":
            rows, cols = apply_hungarian_algorithm(curr_dist_mat, dist_thr)
        elif assign_method == "grid-search":
            rows, cols = apply_sorted_grid_search(curr_dist_mat, dist_thr)

        #  If there are no valid matches, all units are unique
        if len(rows) < 1:
            continue

        #  Mark the groups
        out_dict, graph = mark_groups(
            rows, cols, idx_i, idx_j, curr_dist_mat, trial_labels, out_dict, graph
        )

        # Once a trial has been explored, mask it
        dist_mat[np.ix_(idx_i, idx_j)] = 2

    return out_dict, graph, dist_mat

assign_muaps_all_trials 

assign_muaps_all_trials(muaps: ndarray, trial_labels: ndarray, trial_set: List[int], assign_method: Literal['hungarian', 'grid-search'] = 'hungarian', dist_metric: Literal['corr', 'cosine', 'nmse', 'nfd'] = 'nmse', dist_thr: float = 0.3, sel_chs_method: Literal['iqr', 'iqr_ptp', 'max_abs', 'ptp'] = 'iqr') -> Tuple[List[int], List[List[int]], pd.DataFrame, nx.DiGraph]

Assign MUAPs across all trials based on the given distance matrix.

Parameters:

Name Type Description Default
muaps ndarray

MUAPs with shape (units, ch_rows, ch_cols, samples).

 required
trial_labels ndarray

All trial labels.

 required
trial_set List[int]

The trial labels of the MUAPs.

 required
assign_method str

The method to use for assignment: "hungarian" or "grid-search". Defaults to "hungarian".

 'hungarian'
dist_metric str

The distance metric: "corr", "cosine", "nmse" or "nfd". Defaults to "nmse".

 'nmse'
dist_thr float

The distance threshold. Defaults to 0.3.

 0.3
sel_chs_method str

The method to use for selecting channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

 'iqr'

Returns:

Type Description
Tuple[List[int], List[List[int]], DataFrame, DiGraph]

Tuple[List[int], List[List[int]], pd.DataFrame, nx.DiGraph]: A tuple containing the group labels, group sets, link information dataframe, and the graph.
Source code in motor_unit_toolbox/muap_comp.py 
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def assign_muaps_all_trials(
    muaps: np.ndarray,
    trial_labels: np.ndarray,
    trial_set: List[int],
    assign_method: Literal["hungarian", "grid-search"] = "hungarian",
    dist_metric: Literal["corr", "cosine", "nmse", "nfd"] = "nmse",
    dist_thr: float = 0.3,
    sel_chs_method: Literal["iqr", "iqr_ptp", "max_abs", "ptp"] = "iqr",
) -> Tuple[List[int], List[List[int]], pd.DataFrame, nx.DiGraph]:
    """
    Assign MUAPs across all trials based on the given distance matrix.

    Args:
        muaps (np.ndarray): MUAPs with shape (units, ch_rows, ch_cols, samples).
        trial_labels (np.ndarray): All trial labels.
        trial_set (List[int]): The trial labels of the MUAPs.
        assign_method (str, optional): The method to use for assignment:
            "hungarian" or "grid-search". Defaults to "hungarian".
        dist_metric (str, optional): The distance metric: "corr", "cosine", "nmse" or "nfd".
            Defaults to "nmse".
        dist_thr (float, optional): The distance threshold. Defaults to 0.3.
        sel_chs_method (str, optional): The method to use for selecting
            channels: "iqr", "iqr_ptp", "max_abs" or "ptp". Defaults to "iqr".

    Returns:
        Tuple[List[int], List[List[int]], pd.DataFrame, nx.DiGraph]: A tuple
            containing the group labels, group sets, link information dataframe,
            and the graph.
    """

    #  Compute distances between muaps
    #  -------------------------------
    dist_mat, _ = compute_all_muaps_dist(
        muaps, sel_chs_method=sel_chs_method, dist_metric=dist_metric
    )

    # Discard connections between the same trial
    idx_tril = np.tril_indices(dist_mat.shape[0])
    dist_mat[idx_tril] = 2
    for trial in np.unique(trial_labels):
        trial_idxs = np.nonzero(trial_labels == trial)[0]
        dist_mat[np.ix_(trial_idxs, trial_idxs)] = 2

    # fig, axs = plt.subplots(1,3, figsize=(12,4), layout='constrained', dpi=200)
    # g = sns.heatmap(dist_mat, annot=False, ax=axs[0])
    # g.set(title='Initial')

    out_dict, graph, dist_mat = assign_muaps_across_seq_trials(
        dist_mat, trial_labels, trial_set, assign_method, dist_thr
    )

    # g = sns.heatmap(dist_mat, annot=False, ax=axs[1])
    # g.set(title='After adjacent')

    # Find distant neighbours
    # -----------------------
    #  Find distant hits
    rows, cols = np.nonzero(dist_mat <= dist_thr)
    distant_dists = dist_mat[rows, cols]

    #  Sort based on distant metric
    sort_idxs = np.argsort(distant_dists)
    rows, cols = rows[sort_idxs], cols[sort_idxs]

    # Get the unique trial combinations to perform the hungarian algorithm
    distant_trials = [
        (trial_labels[row], trial_labels[col]) for row, col in zip(rows, cols, strict=True)
    ]
    trial_comb = list(dict.fromkeys(distant_trials))

    #  Apply hungarian algorithm
    for trial_i, trial_j in trial_comb:

        # Get indexes of the trials
        idx_i = np.nonzero(trial_labels == trial_i)[0]
        idx_j = np.nonzero(trial_labels == trial_j)[0]

        #  Select source units within trial_i (no output edges)
        idx_i = [idx for idx in idx_i if graph.out_degree(idx) == 0]
        #  Select target units within trial_j (no input edges)
        idx_j = [idx for idx in idx_j if graph.in_degree(idx) == 0]

        if len(idx_i) < 1 or len(idx_j) < 1:
            # Once a trial has been explored, mask it
            dist_mat[np.ix_(idx_i, idx_j)] = 2
            continue

        #  Assign units
        curr_dist_mat = dist_mat[np.ix_(idx_i, idx_j)]
        if assign_method == "hungarian":
            rows, cols = apply_hungarian_algorithm(curr_dist_mat, dist_thr)
        elif assign_method == "grid-search":
            rows, cols = apply_sorted_grid_search(curr_dist_mat, dist_thr)

        #  If there are no valid matches, all units are unique
        if len(rows) < 1:
            continue

        #  Mark the groups
        out_dict, graph = mark_groups(
            rows, cols, idx_i, idx_j, curr_dist_mat, trial_labels, out_dict, graph
        )

        # Once a trial has been explored, mask it
        dist_mat[np.ix_(idx_i, idx_j)] = 2

    # g = sns.heatmap(dist_mat, annot=False, ax=axs[2])
    # g.set(title='After distant')
    # plt.show()

    #  Generate group sets and labels
    group_sets = generate_group_sets(graph)
    group_labels = generate_group_labels(group_sets)

    #  Fill groups in out_dict
    for unit in out_dict.unit1:
        out_dict.group.append(group_labels[unit])
    df_link_info = pd.DataFrame(out_dict)

    return group_labels, group_sets, df_link_info, graph