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Loaders

Contains functions to load transition matrices from arrays or predefined csv's.

load_from_data(data, normalizer=standard_row_normalization)

Based on a Gaussian similarity matrix, create a transition matrix for the data as given in the array.

Parameters:

  • data (ndarray) –

    Array in which the rows represent data points.

  • normalizer (Callable[[ndarray], ndarray], default: standard_row_normalization ) –

    Normalization function used to create a stochastic matrix from the Gaussian similarity matrix, by default standard_row_normalization. See normalizers.py for pre-defined options.

Returns:

  • ndarray –

    Transition matrix of a Markov chain for the given data.

Source code in pykda\loaders.py 
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def load_from_data(
    data: np.ndarray, normalizer: _normalizer_type = standard_row_normalization
) -> np.ndarray:
    """
    Based on a Gaussian similarity matrix, create a transition matrix for
    the data as given in the array.

    Parameters
    ----------
    data : np.ndarray
        Array in which the rows represent data points.
    normalizer : Callable[[np.ndarray], np.ndarray], optional
        Normalization function used to create a stochastic matrix from the
        Gaussian similarity matrix, by default standard_row_normalization.
        See normalizers.py for pre-defined options.

    Returns
    -------
    np.ndarray
        Transition matrix of a Markov chain for the given data.
    """

    return load_transition_matrix(Gaussian_similarity(data), normalizer)

load_predefined_transition_matrix(name, normalizer=standard_row_normalization)

Load a predefined csv file from the data folder as transition matrix. The data is normalized when needed.

Parameters:

  • name (str) –

    Name of the transition matrix to be loaded.

  • normalizer (Callable[[ndarray], ndarray], default: standard_row_normalization ) –

    Normalization function used to create a stochastic matrix from a matrix A, by default standard_row_normalization. See normalizers.py for pre-defined options.

Returns:

  • ndarray –

    Transition matrix of a Markov chain.

Source code in pykda\loaders.py 
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def load_predefined_transition_matrix(
    name: str, normalizer: _normalizer_type = standard_row_normalization
) -> np.ndarray:
    """
    Load a predefined csv file from the data folder as transition matrix. The
    data is normalized when needed.

    Parameters
    ----------
    name : str
        Name of the transition matrix to be loaded.
    normalizer : Callable[[np.ndarray], np.ndarray], optional
        Normalization function used to create a stochastic matrix from a matrix
        A, by default standard_row_normalization. See normalizers.py for
        pre-defined options.

    Returns
    -------
    np.ndarray
        Transition matrix of a Markov chain.

    """

    csv_string = read_text("pykda.data", f"{name}.csv")
    csv_file = StringIO(csv_string)
    data = np.genfromtxt(csv_file, delimiter=",")

    return load_transition_matrix(data, normalizer)

load_transition_matrix(A, normalizer=standard_row_normalization)

Load a transition matrix from a given array. If the array is not a stochastic matrix, the function will try to normalize it.

Parameters:

  • A (Union[ndarray, list[list]]) –

    Array to be loaded as a Markov chain transition matrix.

  • normalizer (Callable[[ndarray], ndarray], default: standard_row_normalization ) –

    Normalization function used to create a stochastic matrix from a matrix A, by default standard_row_normalization. See normalizers.py for pre-defined options.

Returns:

  • ndarray –

    Transition matrix of a Markov chain.

Source code in pykda\loaders.py 
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def load_transition_matrix(
    A: np.ndarray | list[list],
    normalizer: _normalizer_type = standard_row_normalization,
) -> np.ndarray:
    """
    Load a transition matrix from a given array. If the array is not a
    stochastic matrix, the function will try to normalize it.

    Parameters
    ----------
    A : Union[np.ndarray, list[list]]
        Array to be loaded as a Markov chain transition matrix.
    normalizer : Callable[[np.ndarray], np.ndarray], optional
        Normalization function used to create a stochastic matrix from a matrix
        A, by default standard_row_normalization. See normalizers.py for
        pre-defined options.

    Returns
    -------
    np.ndarray
        Transition matrix of a Markov chain.

    """

    if not isinstance(A, np.ndarray):
        A = np.array(A)

    if is_stochastic_matrix(A):
        return A

    if PRINT_NORMALIZATION_WARNINGS:
        print("The given matrix is not stochastic: trying to normalize it.")

    if not is_nonnegative_matrix(A):
        if PRINT_NORMALIZATION_WARNINGS:
            print("Negative elements in matrix replaced by zeros.")
        A[A < 0] = 0

    if not has_positive_row_sums(A):
        if PRINT_NORMALIZATION_WARNINGS:
            print("Some row sums were zero: added self-loops.")
        rows_zero_sums = A.sum(axis=1) == 0
        A[rows_zero_sums, rows_zero_sums] = 1

    return normalizer(A)