#!/usr/bin/env python
# -*- coding: utf-8 -*-

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# =============================================================================
# FUTURE & DOCS
# =============================================================================

from __future__ import unicode_literals

__doc__ = """Methods based on an aggregating function representing
“closeness to the ideal”.

"""

__all__ = ['TOPSIS']

# =============================================================================
# IMPORTS
# =============================================================================

import numpy as np

from .. import rank
from ..validate import MIN, MAX
from ..utils.doc_inherit import doc_inherit

from ._dmaker import DecisionMaker

# =============================================================================
# Function
# =============================================================================

def topsis(nmtx, ncriteria, nweights):

# apply weights
wmtx = np.multiply(nmtx, nweights)

# extract mins and maxes
mins = np.min(wmtx, axis=0)
maxs = np.max(wmtx, axis=0)

# create the ideal and the anti ideal arrays
ideal = np.where(ncriteria == MAX, maxs, mins)
anti_ideal = np.where(ncriteria == MIN, maxs, mins)

# calculate distances
d_better = np.sqrt(np.sum(np.power(wmtx - ideal, 2), axis=1))
d_worst = np.sqrt(np.sum(np.power(wmtx - anti_ideal, 2), axis=1))

# relative closeness
closeness = d_worst / (d_better + d_worst)

# compute the rank and return the result
return rank.rankdata(closeness, reverse=True), ideal, anti_ideal, closeness

# =============================================================================
# OO
# =============================================================================

[docs]class TOPSIS(DecisionMaker):
"""TOPSIS is based on the concept that the chosen alternative should have
the shortest geometric distance from the ideal solution
and the longest euclidean distance from the worst solution.

An assumption of TOPSIS is that the criteria are monotonically increasing
or decreasing, and also allow trade-offs between criteria, where a poor
result in one criterion can be negated by a good result in another
criterion.

Parameters
----------

mnorm : string, callable, optional (default="vector")
Normalization method for the alternative matrix.

wnorm : string, callable, optional (default="sum")
Normalization method for the weights array.

Returns
-------

Decision : :py:class:skcriteria.madm.Decision
With values:

- **kernel_**: None
- **rank_**: A ranking (start at 1) where the i-nth element represent
the position of the i-nth alternative.
- **best_alternative_**: The index of the best alternative.
- **alpha_solution_**: True
- **beta_solution_**: False
- **gamma_solution_**: True
- **e_**: Particular data created by this method.

- **e_.closeness**: Array where the i-nth element represent the
closenees of the i-nth alternative to ideal and worst solution.

References
----------

.. [1] Yoon, K., & Hwang, C. L. (1981). Multiple attribute decision
making: methods and applications. SPRINGER-VERLAG BERLIN AN.
.. [2] TOPSIS. In Wikipedia, The Free Encyclopedia. Retrieved
from https://en.wikipedia.org/wiki/TOPSIS
.. [3] Tzeng, G. H., & Huang, J. J. (2011). Multiple attribute decision
making: methods and applications. CRC press.

"""

def __init__(self, mnorm="vector", wnorm="sum"):
super(TOPSIS, self).__init__(mnorm=mnorm, wnorm=wnorm)

[docs]    @doc_inherit
def solve(self, ndata):
nmtx, ncriteria, nweights = ndata.mtx, ndata.criteria, ndata.weights
rank, ideal, anti_ideal, closeness = topsis(nmtx, ncriteria, nweights)
extra = {
"ideal": ideal,
"anti_ideal": anti_ideal,
"closeness": closeness}
return None, rank, extra