distance_metric

Complexity

Total Complexity

8

Size/Duplication

Total Lines	76
Duplicated Lines	0 %

Importance

Changes

0

2 Methods

Rating	Name	Duplication	Size	Complexity
A	__init__()	0	16	1
C	__call__()	0	30	7

"""!


@brief Module provides various distance metrics - abstraction of the notion of distance in a metric space.


@authors Andrei Novikov (pyclustering@yandex.ru)

@date 2014-2018

@copyright GNU Public License


@cond GNU_PUBLIC_LICENSE

    PyClustering is free software: you can redistribute it and/or modify

    it under the terms of the GNU General Public License as published by

    the Free Software Foundation, either version 3 of the License, or

    (at your option) any later version.


    PyClustering is distributed in the hope that it will be useful,

    but WITHOUT ANY WARRANTY; without even the implied warranty of

    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

    GNU General Public License for more details.


    You should have received a copy of the GNU General Public License

    along with this program.  If not, see <http://www.gnu.org/licenses/>.

@endcond


"""



from enum import IntEnum;



class type_metric(IntEnum):

    """!

    @brief Enumeration of supported metrics in the module for distance calculation between two points.


    """


    ## Euclidean distance, for more information see function 'euclidean_distance'.

    EUCLIDEAN = 0;


    ## Square Euclidean distance, for more information see function 'euclidean_distance_square'.

    EUCLIDEAN_SQUARE = 1;


    ## Manhattan distance, for more information see function 'manhattan_distance'.

    MANHATTAN = 2;


    ## Chebyshev distance, for more information see function 'chebyshev_distance'.

    CHEBYSHEV = 3;


    ## Minkowski distance, for more information see function 'minkowski_distance'.

    MINKOWSKI = 4;


    ## User defined function for distance calculation between two points.

    USER_DEFINED = 1000;



class distance_metric:

    """!

    @brief Distance metric performs distance calculation between two points in line with encapsulated function, for

            example, euclidean distance or chebyshev distance, or even user-defined.


    @details


    Example of Euclidean distance metric:

    @code

        metric = distance_metric(type_metric.EUCLIDEAN);

        distance = metric([1.0, 2.5], [-1.2, 3.4]);

    @endcode


    In following example additional argument should be specified (generally, 'degree' is a optional argument that is

     equal to '2' by default) that is specific for Minkowski distance:

    @code

        metric = distance_metric(type_metric.MINKOWSKI, degree=4);

        distance = metric([4.0, 9.2, 1.0], [3.4, 2.5, 6.2]);

    @endcode


    User may define its own function for distance calculation:

    @code

        user_function = lambda point1, point2: point1[0] + point2[0] + 2;

        metric = distance_metric(type_metric.USER_DEFINED, func=user_function);

        distance = metric([2.0, 3.0], [1.0, 3.0]);

    @endcode


    """

    def __init__(self, type, **kwargs):

        """!

        @brief Creates distance metric instance for calculation distance between two points.


        @param[in] type (type_metric):

        @param[in] **kwargs: Arbitrary keyword arguments (available arguments: 'func' and corresponding additional argument for

                    for specific metric types).


        Keyword Args:

            func (callable): Callable object with two arguments (point #1 and point #2) that is used only if metric is 'type_metric.USER_DEFINED'.

            degree (numeric): Only for 'type_metric.MINKOWSKI' - degree of Minkowski equation.


        """

        self.__type = type;

        self.__args = kwargs;

        self.__func = self.__args.get('func', None);



    def __call__(self, point1, point2):

        """!

        @brief Calculates distance between two points.


        @param[in] point1 (list): The first point.

        @param[in] point2 (list): The second point.


        @return (double) Distance between two points.


        """

        if self.__type == type_metric.EUCLIDEAN:

            return euclidean_distance(point1, point2);


        elif self.__type == type_metric.EUCLIDEAN_SQUARE:

            return euclidean_distance_square(point1, point2);


        elif self.__type == type_metric.MANHATTAN:

            return manhattan_distance(point1, point2);


        elif self.__type == type_metric.CHEBYSHEV:

            return chebyshev_distance(point1, point2);


        elif self.__type == type_metric.MINKOWSKI:

            return minkowski_distance(point1, point2, self.__args.get('degree', 2));


        elif self.__type == type_metric.USER_DEFINED:

            return self.__func(point1, point2);


        else:

            raise ValueError("Unknown type of metric: '%d'", self.__type);



def euclidean_distance(point1, point2):

    """!

A suspicious escape sequence \s was found. Did you maybe forget to add an r prefix?

    @brief Calculate Euclidean distance between two vectors.

    @details The Euclidean between vectors (points) a and b is calculated by following formula:


    \f[

    dist(a, b) = \sqrt{ \sum_{i=0}^{N}(a_{i} - b_{i})^{2} };

    \f]


    Where N is a length of each vector.


    @param[in] point1 (list): The first vector.

    @param[in] point2 (list): The second vector.


    @return (double) Euclidean distance between two vectors.


    @see euclidean_distance_square, manhattan_distance, chebyshev_distance


    """

    distance = euclidean_distance_square(point1, point2);

    return distance ** 0.5;



def euclidean_distance_square(point1, point2):

    """!

A suspicious escape sequence \s was found. Did you maybe forget to add an r prefix?

    @brief Calculate square Euclidean distance between two vectors.


    \f[

    dist(a, b) = \sum_{i=0}^{N}(a_{i} - b_{i})^{2};

    \f]


    @param[in] point1 (list): The first vector.

    @param[in] point2 (list): The second vector.


    @return (double) Square Euclidean distance between two vectors.


    @see euclidean_distance, manhattan_distance, chebyshev_distance


    """

    distance = 0.0;

    for i in range(len(point1)):

        distance += (point1[i] - point2[i]) ** 2.0;


    return distance;



def manhattan_distance(point1, point2):

    """!

A suspicious escape sequence \s was found. Did you maybe forget to add an r prefix?

A suspicious escape sequence \l was found. Did you maybe forget to add an r prefix?

    @brief Calculate Manhattan distance between between two vectors.


    \f[

    dist(a, b) = \sum_{i=0}^{N}\left | a_{i} - b_{i} \right |;

    \f]


    @param[in] point1 (list): The first vector.

    @param[in] point2 (list): The second vector.


    @return (double) Manhattan distance between two vectors.


    @see euclidean_distance_square, euclidean_distance, chebyshev_distance


    """

    distance = 0.0;

    dimension = len(point1);


    for i in range(dimension):

        distance += abs(point1[i] - point2[i]);


    return distance;



def chebyshev_distance(point1, point2):

    """!

A suspicious escape sequence \m was found. Did you maybe forget to add an r prefix?

A suspicious escape sequence \l was found. Did you maybe forget to add an r prefix?

    @brief Calculate Chebyshev distance between between two vectors.


    \f[

    dist(a, b) = \max_{}i\left (\left | a_{i} - b_{i} \right |\right );

    \f]


    @param[in] point1 (list): The first vector.

    @param[in] point2 (list): The second vector.


    @return (double) Chebyshev distance between two vectors.


    @see euclidean_distance_square, euclidean_distance, minkowski_distance


    """

    distance = 0.0;

    dimension = len(point1);


    for i in range(dimension):

        distance = max(distance, abs(point1[i] - point2[i]));


    return distance;



def minkowski_distance(point1, point2, degree=2):

    """!

A suspicious escape sequence \s was found. Did you maybe forget to add an r prefix?

A suspicious escape sequence \l was found. Did you maybe forget to add an r prefix?

    @brief Calculate Minkowski distance between two vectors.


    \f[

    dist(a, b) = \sqrt[p]{ \sum_{i=0}^{N}\left(a_{i} - b_{i}\right)^{p} };

    \f]


    @param[in] point1 (list): The first vector.

    @param[in] point2 (list): The second vector.

    @param[in] degree (numeric): Degree of that is used for Minkowski distance.


    @return (double) Minkowski distance between two vectors.


    @see euclidean_distance


    """

    distance = 0.0;

    for i in range(len(point1)):

        distance += (point1[i] - point2[i]) ** degree;


    return distance ** (1.0 / degree);