pymcdm.helpers

pymcdm.helpers.correlation_matrix(rankings, method, columns=False)

Creates a correlation matrix for given vectors from the numpy array.

Parameters:

  • rankings (ndarray) – Vectors for which the correlation matrix is to be calculated.

  • method (callable) – Function to calculate the correlation matrix.

  • columns (bool) – If the column value is set to true then the correlation matrix will be calculated for the columns. Otherwise the matrix will be calculated for the rows.

Returns:

Correlation between two rankings vectors.

Return type:

ndarray

pymcdm.helpers.leave_one_out_rr(method, matrix, weights, types, corr_function, ideal_corr_value=1, only_rr=True)

Function which implements the procedure similar to leave one out cross validation. This function calculates N rankings from N decision matrices created by removing one of N alternatives from original one. This function returns the array of rankings build in following way: [original_ranking, w/o A1, w/o A2, …, w/o AN, original_ranking].

This function will insert in the ranking value 0 instead of removed alternative position. E.g. original ranking is [1, 2, 3, 4], ranking without A1 will looks like [0, 1, 2, 3].

This function main purpose is to prepare data for rankings_flow visualization function.

Parameters:

  • method (MCDA_method) – MCDA method which should be used to calculate rankings.

  • matrix (ndarray) – Decision matrix / alternatives data. Alternatives are in rows and Criteria are in columns.

  • weights (ndarray) – Criteria weights. Sum of the weights should be 1. (e.g. sum(weights) == 1)

  • types (ndarray) – Array with definitions of criteria types: 1 if criteria is profit and -1 if criteria is cost for each criteria in matrix.

  • corr_function (Callable) – Correlation function to calculate correlation value between rankings.

  • ideal_corr_value (float) – Correlation value for ideal ranking. Default is 1. Use it if correlation function you use has different value for two same rankings (e.g. 0).

  • only_rr (bool) – Include in returned collections only rankings in which rank reversal occurs. If rank reversal do not occured the list of two original rankings will be returned. Default is True.

Returns:

  • rankings (ndarray) – Matrix of rankings obtained when removing different alternatives. Instead of removed alternatives 0 is placed.

  • correlations (list) – List of correlation values calculated for rankings in rankings matrix.

  • labels (list) – Names of the created rankings. It will looks like [‘None’, ‘w/o A_1’, ‘w/o A_2’, … ‘None’], where ‘w/o A_i’ means that this ranking was build without alternative A_i.

Examples

>>> import numpy as np
>>> import pymcdm as pm
>>> matrix = np.array([
...     [1, 9, 3, 4, 2],
...     [3, 2, 1, 6, 1],
...     [4, 6, 3, 2, 1],
...     [1, 2, 3, 4, 7],
...     [3, 2, 4, 5, 1]
... ])
>>> topsis = pm.methods.TOPSIS()
>>> weights = np.ones(5)/5
>>> types = np.ones(5)
>>> rankings, cors, labels = leave_one_out_rr(
...         topsis,
...         matrix,
...         weights,
...         types,
...         pm.correlations.weighted_spearman,
...         only_rr=False)
>>> print(labels, cors, rankings)
pymcdm.helpers.normalize_matrix(matrix: ndarray | list | tuple, method: Callable, criteria_types: Iterable[int]) → ndarray

Normalize each column in matrix, using method`normalization function according to `criteria_types.

Parameters:

  • matrix (np.ndarray | list | tuple) – Decision matrix representation. The rows are considered as alternatives and the columns are considered as criteria.

  • method (Callable or Iterable[Callable] or str or Iterable[str]) – Function or Functions which should be used to normalize matrix columns. Functions should match signature foo(x, cost), where x is a vector which would be normalized and cost is a bool variable which says if x is a cost or profit criteria. In case of providing list or tuple of the functions, number of functions should be the same as number of criteria in matrix (columns) and same as the lenght of the criteria_types.

  • criteria_types (None or Iterable[int]) – Describes criteria types. 1 if criteria is profit and -1 if criteria is cost for each criteria in matrix. If None all criteria are considered as profit

Returns:

Normalized copy of the input matrix.

Return type:

ndarray

Raises:

ValueError – If criteria_types and matrix has different number of criteria.

pymcdm.helpers.rankdata(a, reverse=False)

Assign ranks to data in vector a.

Ranks begin at 1. Tied elements get average rank (see Examples below).

Ranking starts from smaller values, e.g. the smaller element get the first position. The reverse argument reverse posisions, e.g. the largest element get first position.

Parameters:

  • a (iterable) – The array of values to be ranked.

  • reverse (bool, optional) – If True, larger elements get first posisions in ranking. If False, smaller elements get first positions in ranking.

Returns:

An array of rank scores for the input data.

Return type:

ndarray

Examples

>>> from pymcdm.helpers import rankdata
>>> rankdata([0, 3, 2, 5])
array([1, 3, 2, 4])
>>> rankdata([0, 3, 2, 5], reverse=True)
array([4, 2, 3, 1])
>>> rankdata([0, 3, 2, 3])
array([1. , 3.5, 2. , 3.5])
>>> rankdata([0, 3, 2, 3], reverse=True)
array([4. , 1.5, 3. , 1.5])
pymcdm.helpers.rrankdata(a)

Alias to rankdata(a, reverse=True). See rankdata for details.