concordance and discordance

skcriteria/common/util.py

@@ -51,9 +51,40 @@ def criteriarr(criteria):
 
 def is_mtx(mtx, size=None):
     try:
-        a, b = mtx.shape
+        a, b = mtx.shapeW
         if size and (a, b) != size:
             return False
     except:
         return False
     return True
+
+
+def nearest(array, value, side=None):
+    # based on: http://stackoverflow.com/a/2566508
+    #           http://stackoverflow.com/a/3230123
+    #           http://stackoverflow.com/a/17119267
+    if side not in (None, "gt", "lt"):
+        msg = "'side' must be None, 'gt' or 'lt'. Found {}".format(side)
+        raise ValueError(msg)
+
+    raveled = np.ravel(array)
+    cleaned = raveled[~np.isnan(raveled)]
+
+    if side is None:
+        idx = np.argmin(np.abs(cleaned-value))
+
+    else:
+        masker, decisor = (
+            (np.ma.less_equal,  np.argmin)
+            if side == "gt" else
+            (np.ma.greater_equal, np.argmax))
+
+        diff = cleaned - value
+        mask = masker(diff, 0)
+        if np.all(mask):
+            return None
+
+        masked_diff = np.ma.masked_array(diff, mask)
+        idx = decisor(masked_diff)
+
+    return cleaned[idx]

skcriteria/electre.py

@@ -0,0 +1,108 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+# License: 3 Clause BSD
+# http://scikit-criteria.org/
+
+
+# =============================================================================
+# FUTURE
+# =============================================================================
+
+from __future__ import unicode_literals
+
+
+__doc__ = """
+
+Data from Tzeng and Huang et al, 2011 [TZENG2011]_
+
+References
+----------
+
+.. [TZENG2011] Tzeng, G. H., & Huang, J. J. (2011). Multiple
+   attribute decision making: methods and applications. CRC press.
+
+"""
+
+
+# =============================================================================
+# IMPORTS
+# =============================================================================
+
+import numpy as np
+
+from skcriteria.common import norm, util, rank
+
+
+# =============================================================================
+# UTILS
+# =============================================================================
+
+def concordance(nmtx, ncriteria, nweights):
+
+    mtx_criteria = np.tile(ncriteria, (len(nmtx), 1))
+    mtx_weight = np.tile(nweights, (len(nmtx), 1))
+    mtx_concordance = np.empty((len(nmtx), len(nmtx)))
+
+    for idx, row in enumerate(nmtx):
+        difference = row - nmtx
+        outrank = (
+            ((mtx_criteria == util.MAX) & (difference >= 0)) |
+            ((mtx_criteria == util.MIN) & (difference <= 0))
+        )
+        filter_weights = mtx_weight * outrank.astype(int)
+        new_row = np.sum(filter_weights, axis=1)
+        mtx_concordance[idx] = new_row
+
+    np.fill_diagonal(mtx_concordance, np.nan)
+    mean = np.nanmean(mtx_concordance)
+    p = util.nearest(mtx_concordance, mean, side="gt")
+
+    return mtx_concordance, mean, p
+
+
+def discordance(nmtx, ncriteria, nweights):
+
+    mtx_criteria = np.tile(ncriteria, (len(nmtx), 1))
+    mtx_weight = np.tile(nweights, (len(nmtx), 1))
+    mtx_discordance = np.empty((len(nmtx), len(nmtx)))
+    ranges = np.max(nmtx, axis=0) - np.min(nmtx, axis=0)
+
+    for idx, row in enumerate(nmtx):
+        difference = nmtx - row
+        worsts = (
+            ((mtx_criteria == util.MAX) & (difference >= 0)) |
+            ((mtx_criteria == util.MIN) & (difference <= 0))
+        )
+        filter_difference = np.abs(difference * worsts)
+        delta = filter_difference / ranges
+        new_row = np.max(delta, axis=1)
+        mtx_discordance[idx] = new_row
+
+    np.fill_diagonal(mtx_discordance, np.nan)
+    mean = np.nanmean(mtx_discordance)
+    q = util.nearest(mtx_discordance, mean, side="lt")
+
+    return mtx_discordance, mean, q
+
+
+# =============================================================================
+# ELECTRE
+# =============================================================================
+
+def electre1(mtx, criteria, weights=1):
+
+    # This guarantee the criteria array consistency
+    ncriteria = util.criteriarr(criteria)
+
+    # validate the matrix is the matrix
+    nmtx = np.asarray(mtx)
+    if not util.is_mtx(nmtx):
+        raise ValueError("'mtx' is not a matrix")
+
+    # normalize weights
+    nweights = norm.sum(weights) if weights is not None else 1
+
+    # get the concordance matrix
+    mtx_concordance = concordance(nmtx, nweights)
+

skcriteria/tests/test_electre.py

@@ -0,0 +1,122 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+# License: 3 Clause BSD
+# http://scikit-criteria.org/
+
+
+# =============================================================================
+# FUTURE
+# =============================================================================
+
+from __future__ import unicode_literals
+
+
+# =============================================================================
+# DOC
+# =============================================================================
+
+__doc__ = """test electre methods"""
+
+
+# =============================================================================
+# IMPORTS
+# =============================================================================
+
+import random
+
+import numpy as np
+
+from . import core
+
+from ..common import norm, util
+from .. import electre
+
+
+# =============================================================================
+# BASE CLASS
+# =============================================================================
+
+class ElectreTest(core.SKCriteriaTestCase):
+
+    def test_concordance(self):
+
+        # Data From:
+        # Cebrián, L. I. G., & Porcar, A. M. (2009). Localización empresarial
+        # en Aragón: Una aplicación empírica de la ayuda a la decisión
+        # multicriterio tipo ELECTRE I y III. Robustez de los resultados
+        # obtenidos.
+        # Revista de Métodos Cuantitativos para la Economía y la Empresa,
+        # (7), 31-56.
+        nmtx = norm.sum([
+            [6, 5, 28, 5, 5],
+            [4, 2, 25, 10, 9],
+            [5, 7, 35, 9, 6],
+            [6, 1, 27, 6, 7],
+            [6, 8, 30, 7, 9],
+            [5, 6, 26, 4, 8]
+        ], axis=0)
+        ncriteria = util.criteriarr([1, 1, -1, 1, 1])
+        nweights = norm.sum([0.25, 0.25, 0.1, 0.2, 0.2])
+        results = [
+            [np.nan, 0.5000, 0.3500, 0.5000, 0.3500, 0.4500],
+            [0.5000, np.nan, 0.5000, 0.7500, 0.5000, 0.5000],
+            [0.6500, 0.5000, np.nan, 0.4500, 0.2000, 0.7000],
+            [0.7500, 0.2500, 0.5500, np.nan, 0.3500, 0.4500],
+            [0.9000, 0.7000, 0.8000, 0.9000, np.nan, 0.9000],
+            [0.5500, 0.5000, 0.5500, 0.5500, 0.1000, np.nan]
+        ]
+        result_mean, result_p = 0.5400, 0.5500
+        concordance, mean, p = electre.concordance(nmtx, ncriteria, nweights)
+        self.assertAllClose(concordance, results, atol=1.e-3)
+        self.assertAllClose(mean, result_mean, atol=1.e-3)
+        self.assertAllClose(p, result_p, atol=1.e-3)
+
+    def test_discordance(self):
+        # Data From:
+        # Cebrián, L. I. G., & Porcar, A. M. (2009). Localización empresarial
+        # en Aragón: Una aplicación empírica de la ayuda a la decisión
+        # multicriterio tipo ELECTRE I y III. Robustez de los resultados
+        # obtenidos.
+        # Revista de Métodos Cuantitativos para la Economía y la Empresa,
+        # (7), 31-56.
+        nmtx = norm.sum([
+            [6, 5, 28, 5, 5],
+            [4, 2, 25, 10, 9],
+            [5, 7, 35, 9, 6],
+            [6, 1, 27, 6, 7],
+            [6, 8, 30, 7, 9],
+            [5, 6, 26, 4, 8]
+        ], axis=0)
+        ncriteria = util.criteriarr([1, 1, -1, 1, 1])
+        nweights = norm.sum([0.25, 0.25, 0.1, 0.2, 0.2])
+        results = [
+            [np.nan, 1.0000, 0.6667, 0.5000, 1.0000, 0.7500],
+            [1.0000, np.nan, 0.7143, 1.0000, 1.0000, 0.5714],
+            [0.7000, 1.0000, np.nan, 0.8000, 0.7500, 0.9000],
+            [0.5714, 0.6667, 0.8571, np.nan, 1.0000, 0.7143],
+            [0.2000, 0.5000, 0.3333, 0.3000, np.nan, 0.4000],
+            [0.5000, 1.0000, 0.8333, 0.5000, 0.5000, np.nan]
+        ]
+        result_mean, result_p = 0.7076, 0.70
+        discordance, mean, p = electre.discordance(nmtx, ncriteria, nweights)
+        self.assertAllClose(discordance, results, atol=1.e-3)
+        self.assertAllClose(mean, result_mean, atol=1.e-3)
+        self.assertAllClose(p, result_p, atol=1.e-3)
+
+    def _test_electre1(self):
+        #~ Data from:
+        #~ Tzeng, G. H., & Huang, J. J. (2011). Multiple
+        #~ attribute decision making: methods and applications. CRC press.
+        VD, D, U, S, VS = 1, 2, 3, 4, 5
+        mtx = [
+            [U, D, S, VS],
+            [D, VS, D, S],
+            [D, VD, S, D],
+            [U, VS, U, S]
+        ]
+        criteria = [1, 1, 1, 1]
+        weights = [.35, .15, .20, .30]
+        electre.electre1(mtx, criteria, weights)
+
+