#! /usr/bin/env python
#
# Author: Damian Eads
# Date: April 17, 2008
#
# Copyright (C) 2008 Damian Eads
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
#    notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above
#    copyright notice, this list of conditions and the following
#    disclaimer in the documentation and/or other materials provided
#    with the distribution.
#
# 3. The name of the author may not be used to endorse or promote
#    products derived from this software without specific prior
#    written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
from __future__ import division, print_function, absolute_import

import os.path

import numpy as np
from numpy.testing import TestCase, run_module_suite, dec, assert_raises

from scipy.lib.six import xrange
from scipy.lib.six import u

import scipy.cluster.hierarchy
from scipy.cluster.hierarchy import (
    linkage, from_mlab_linkage, to_mlab_linkage,
    num_obs_linkage, inconsistent, cophenet, fclusterdata, fcluster,
    is_isomorphic, single, complete, weighted, centroid, leaders,
    correspond, is_monotonic, maxdists, maxinconsts, maxRstat,
    is_valid_linkage, is_valid_im, to_tree, leaves_list, dendrogram)
from scipy.spatial.distance import squareform, pdist


# Matplotlib is not a scipy dependency but is optionally used in dendrogram, so
# check if it's available
try:
    # import matplotlib
    import matplotlib
    # and set the backend to be Agg (no gui)
    matplotlib.use('Agg')
    # before importing pyplot
    import matplotlib.pyplot as plt
    have_matplotlib = True
except:
    have_matplotlib = False


_tdist = np.array([[0, 662, 877, 255, 412, 996],
                   [662, 0, 295, 468, 268, 400],
                   [877, 295, 0, 754, 564, 138],
                   [255, 468, 754, 0, 219, 869],
                   [412, 268, 564, 219, 0, 669],
                   [996, 400, 138, 869, 669, 0]], dtype='double')

_ytdist = squareform(_tdist)


eo = {}

_filenames = ["iris.txt",
              "Q-X.txt",
              "fclusterdata-maxclusts-2.txt",
              "fclusterdata-maxclusts-3.txt",
              "fclusterdata-maxclusts-4.txt",
              "linkage-single-tdist.txt",
              "linkage-complete-tdist.txt",
              "linkage-average-tdist.txt",
              "linkage-weighted-tdist.txt",
              "inconsistent-Q-single-1.txt",
              "inconsistent-Q-single-2.txt",
              "inconsistent-Q-single-3.txt",
              "inconsistent-Q-single-4.txt",
              "inconsistent-Q-single-5.txt",
              "inconsistent-Q-single-6.txt",
              "inconsistent-complete-tdist-depth-1.txt",
              "inconsistent-complete-tdist-depth-2.txt",
              "inconsistent-complete-tdist-depth-3.txt",
              "inconsistent-complete-tdist-depth-4.txt",
              "inconsistent-single-tdist-depth-0.txt",
              "inconsistent-single-tdist-depth-1.txt",
              "inconsistent-single-tdist-depth-2.txt",
              "inconsistent-single-tdist-depth-3.txt",
              "inconsistent-single-tdist-depth-4.txt",
              "inconsistent-single-tdist-depth-5.txt",
              "inconsistent-single-tdist.txt",
              "inconsistent-weighted-tdist-depth-1.txt",
              "inconsistent-weighted-tdist-depth-2.txt",
              "inconsistent-weighted-tdist-depth-3.txt",
              "inconsistent-weighted-tdist-depth-4.txt",
              "linkage-Q-average.txt",
              "linkage-Q-complete.txt",
              "linkage-Q-single.txt",
              "linkage-Q-weighted.txt",
              "linkage-Q-centroid.txt",
              "linkage-Q-median.txt",
              "linkage-Q-ward.txt"
              ]


def load_testing_files():
    for fn in _filenames:
        name = fn.replace(".txt", "").replace("-ml", "")
        fqfn = os.path.join(os.path.dirname(__file__), fn)
        eo[name] = np.loadtxt(fqfn)

load_testing_files()


class TestLinkage(TestCase):
    def test_linkage_empty_distance_matrix(self):
        # Tests linkage(Y) where Y is a 0x4 linkage matrix. Exception expected.
        y = np.zeros((0,))
        self.assertRaises(ValueError, linkage, y)

    ################### linkage
    def test_linkage_single_tdist(self):
        # Tests linkage(Y, 'single') on the tdist data set.
        Z = linkage(_ytdist, 'single')
        Zmlab = eo['linkage-single-tdist']
        eps = 1e-10
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    def test_linkage_complete_tdist(self):
        # Tests linkage(Y, 'complete') on the tdist data set.
        Z = linkage(_ytdist, 'complete')
        Zmlab = eo['linkage-complete-tdist']
        eps = 1e-10
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    def test_linkage_average_tdist(self):
        # Tests linkage(Y, 'average') on the tdist data set.
        Z = linkage(_ytdist, 'average')
        Zmlab = eo['linkage-average-tdist']
        eps = 1e-05
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    def test_linkage_weighted_tdist(self):
        # Tests linkage(Y, 'weighted') on the tdist data set.
        Z = linkage(_ytdist, 'weighted')
        Zmlab = eo['linkage-weighted-tdist']
        eps = 1e-10
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    def test_linkage_with_unicode_method_name(self):
        # Tests linkage(Y, u'single') on the tdist data set.
        Z = linkage(_ytdist, u('single'))
        Zmlab = eo['linkage-single-tdist']
        eps = 1e-10
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    ################### linkage on Q
    def test_linkage_single_q(self):
        # Tests linkage(Y, 'single') on the Q data set.
        X = eo['Q-X']
        Z = single(X)
        Zmlab = eo['linkage-Q-single']
        eps = 1e-06
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    def test_linkage_complete_q(self):
        # Tests linkage(Y, 'complete') on the Q data set.
        X = eo['Q-X']
        Z = complete(X)
        Zmlab = eo['linkage-Q-complete']
        eps = 1e-07
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    def test_linkage_centroid_q(self):
        # Tests linkage(Y, 'centroid') on the Q data set.
        X = eo['Q-X']
        Z = centroid(X)
        Zmlab = eo['linkage-Q-centroid']
        eps = 1e-07
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))

    def test_linkage_weighted_q(self):
        # Tests linkage(Y, 'weighted') on the Q data set.
        X = eo['Q-X']
        Z = weighted(X)
        Zmlab = eo['linkage-Q-weighted']
        eps = 1e-07
        expectedZ = from_mlab_linkage(Zmlab)
        self.assertTrue(within_tol(Z, expectedZ, eps))


class TestInconsistent(TestCase):
    def test_single_inconsistent_tdist_1(self):
        # Tests inconsistency matrix calculation (depth=1) on a single linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'single')
        R = inconsistent(Z, 1)
        Rright = eo['inconsistent-single-tdist-depth-1']
        eps = 1e-15
        self.assertTrue(within_tol(R, Rright, eps))

    def test_single_inconsistent_tdist_2(self):
        # Tests inconsistency matrix calculation (depth=2) on a single linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'single')
        R = inconsistent(Z, 2)
        Rright = eo['inconsistent-single-tdist-depth-2']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))

    def test_single_inconsistent_tdist_3(self):
        # Tests inconsistency matrix calculation (depth=3) on a single linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'single')
        R = inconsistent(Z, 3)
        Rright = eo['inconsistent-single-tdist-depth-3']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))

    def test_single_inconsistent_tdist_4(self):
        # Tests inconsistency matrix calculation (depth=4) on a single linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'single')
        R = inconsistent(Z, 4)
        Rright = eo['inconsistent-single-tdist-depth-4']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))

    # with complete linkage...
    def test_complete_inconsistent_tdist_1(self):
        # Tests inconsistency matrix calculation (depth=1) on a complete linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'complete')
        R = inconsistent(Z, 1)
        Rright = eo['inconsistent-complete-tdist-depth-1']
        eps = 1e-15
        self.assertTrue(within_tol(R, Rright, eps))

    def test_complete_inconsistent_tdist_2(self):
        # Tests inconsistency matrix calculation (depth=2) on a complete linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'complete')
        R = inconsistent(Z, 2)
        Rright = eo['inconsistent-complete-tdist-depth-2']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))

    def test_complete_inconsistent_tdist_3(self):
        # Tests inconsistency matrix calculation (depth=3) on a complete linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'complete')
        R = inconsistent(Z, 3)
        Rright = eo['inconsistent-complete-tdist-depth-3']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))

    def test_complete_inconsistent_tdist_4(self):
        # Tests inconsistency matrix calculation (depth=4) on a complete linkage.
        Y = squareform(_tdist)
        Z = linkage(Y, 'complete')
        R = inconsistent(Z, 4)
        Rright = eo['inconsistent-complete-tdist-depth-4']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))

    # with single linkage and Q data set
    def test_single_inconsistent_Q_1(self):
        # Tests inconsistency matrix calculation (depth=1, dataset=Q) with single linkage.
        X = eo['Q-X']
        Z = linkage(X, 'single', 'euclidean')
        R = inconsistent(Z, 1)
        Rright = eo['inconsistent-Q-single-1']
        eps = 1e-06
        self.assertTrue(within_tol(R, Rright, eps))

    def test_single_inconsistent_Q_2(self):
        # Tests inconsistency matrix calculation (depth=2, dataset=Q) with single linkage.
        X = eo['Q-X']
        Z = linkage(X, 'single', 'euclidean')
        R = inconsistent(Z, 2)
        Rright = eo['inconsistent-Q-single-2']
        eps = 1e-06
        self.assertTrue(within_tol(R, Rright, eps))

    def test_single_inconsistent_Q_3(self):
        # Tests inconsistency matrix calculation (depth=3, dataset=Q) with single linkage.
        X = eo['Q-X']
        Z = linkage(X, 'single', 'euclidean')
        R = inconsistent(Z, 3)
        Rright = eo['inconsistent-Q-single-3']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))

    def test_single_inconsistent_Q_4(self):
        # Tests inconsistency matrix calculation (depth=4, dataset=Q) with single linkage.
        X = eo['Q-X']
        Z = linkage(X, 'single', 'euclidean')
        R = inconsistent(Z, 4)
        Rright = eo['inconsistent-Q-single-4']
        eps = 1e-05
        self.assertTrue(within_tol(R, Rright, eps))


class TestCopheneticDistance(TestCase):
    def test_linkage_cophenet_tdist_Z(self):
        # Tests cophenet(Z) on tdist data set.
        expectedM = np.array([268, 295, 255, 255, 295, 295, 268, 268, 295, 295,
                              295, 138, 219, 295, 295])
        Z = linkage(_ytdist, 'single')
        M = cophenet(Z)
        eps = 1e-10
        self.assertTrue(within_tol(M, expectedM, eps))

    def test_linkage_cophenet_tdist_Z_Y(self):
        # Tests cophenet(Z, Y) on tdist data set.
        Z = linkage(_ytdist, 'single')
        (c, M) = cophenet(Z, _ytdist)
        expectedM = np.array([268, 295, 255, 255, 295, 295, 268, 268, 295, 295,
                              295, 138, 219, 295, 295])
        expectedc = 0.639931296433393415057366837573
        eps = 1e-10
        self.assertTrue(np.abs(c - expectedc) <= eps)
        self.assertTrue(within_tol(M, expectedM, eps))


class TestFromMLabLinkage(TestCase):
    def test_from_mlab_linkage_empty(self):
        # Tests from_mlab_linkage on empty linkage array.
        X = np.asarray([])
        R = from_mlab_linkage([])
        self.assertTrue((R == X).all())

    def test_from_mlab_linkage_single_row(self):
        # Tests from_mlab_linkage on linkage array with single row.
        expectedZP = np.asarray([[0., 1., 3., 2.]])
        Z = [[1,2,3]]
        ZP = from_mlab_linkage(Z)
        return self.assertTrue((ZP == expectedZP).all())

    def test_from_mlab_linkage_multiple_rows(self):
        # Tests from_mlab_linkage on linkage array with multiple rows.
        Z = np.asarray([[3, 6, 138], [4, 5, 219],
                        [1, 8, 255], [2, 9, 268], [7, 10, 295]])
        expectedZS = np.array([[2., 5., 138., 2.],
                               [3., 4., 219., 2.],
                               [0., 7., 255., 3.],
                               [1., 8., 268., 4.],
                               [6., 9., 295., 6.]],
                              dtype=np.double)
        ZS = from_mlab_linkage(Z)
        self.assertTrue((expectedZS == ZS).all())


class TestToMLabLinkage(TestCase):
    def test_to_mlab_linkage_empty(self):
        # Tests to_mlab_linkage on empty linkage array.
        X = np.asarray([])
        R = to_mlab_linkage([])
        self.assertTrue((R == X).all())

    def test_to_mlab_linkage_single_row(self):
        # Tests to_mlab_linkage on linkage array with single row.
        Z = np.asarray([[0., 1., 3., 2.]])
        expectedZP = np.asarray([[1,2,3]])
        ZP = to_mlab_linkage(Z)
        return self.assertTrue((ZP == expectedZP).all())

    def test_from_mlab_linkage_multiple_rows(self):
        # Tests to_mlab_linkage on linkage array with multiple rows.
        expectedZM = np.asarray([[3, 6, 138], [4, 5, 219],
                        [1, 8, 255], [2, 9, 268], [7, 10, 295]])
        Z = np.array([[2., 5., 138., 2.],
                      [3., 4., 219., 2.],
                      [0., 7., 255., 3.],
                      [1., 8., 268., 4.],
                      [6., 9., 295., 6.]],
                     dtype=np.double)
        ZM = to_mlab_linkage(Z)
        self.assertTrue((expectedZM == ZM).all())


class TestFcluster(TestCase):
    def test_fclusterdata_maxclusts_2(self):
        # Tests fclusterdata(X, criterion='maxclust', t=2) on a random 3-cluster data set.
        expectedT = np.int_(eo['fclusterdata-maxclusts-2'])
        X = eo['Q-X']
        T = fclusterdata(X, criterion='maxclust', t=2)
        self.assertTrue(is_isomorphic(T, expectedT))

    def test_fclusterdata_maxclusts_3(self):
        # Tests fclusterdata(X, criterion='maxclust', t=3) on a random 3-cluster data set.
        expectedT = np.int_(eo['fclusterdata-maxclusts-3'])
        X = eo['Q-X']
        T = fclusterdata(X, criterion='maxclust', t=3)
        self.assertTrue(is_isomorphic(T, expectedT))

    def test_fclusterdata_maxclusts_4(self):
        # Tests fclusterdata(X, criterion='maxclust', t=4) on a random 3-cluster data set.
        expectedT = np.int_(eo['fclusterdata-maxclusts-4'])
        X = eo['Q-X']
        T = fclusterdata(X, criterion='maxclust', t=4)
        self.assertTrue(is_isomorphic(T, expectedT))

    def test_fcluster_maxclusts_2(self):
        # Tests fcluster(Z, criterion='maxclust', t=2) on a random 3-cluster data set.
        expectedT = np.int_(eo['fclusterdata-maxclusts-2'])
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(Y)
        T = fcluster(Z, criterion='maxclust', t=2)
        self.assertTrue(is_isomorphic(T, expectedT))

    def test_fcluster_maxclusts_3(self):
        # Tests fcluster(Z, criterion='maxclust', t=3) on a random 3-cluster data set.
        expectedT = np.int_(eo['fclusterdata-maxclusts-3'])
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(Y)
        T = fcluster(Z, criterion='maxclust', t=3)
        self.assertTrue(is_isomorphic(T, expectedT))

    def test_fcluster_maxclusts_4(self):
        # Tests fcluster(Z, criterion='maxclust', t=4) on a random 3-cluster data set.
        expectedT = np.int_(eo['fclusterdata-maxclusts-4'])
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(Y)
        T = fcluster(Z, criterion='maxclust', t=4)
        self.assertTrue(is_isomorphic(T, expectedT))


class TestLeaders(TestCase):
    def test_leaders_single(self):
        # Tests leaders using a flat clustering generated by single linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(Y)
        T = fcluster(Z, criterion='maxclust', t=3)
        Lright = (np.array([53, 55, 56]), np.array([2, 3, 1]))
        L = leaders(Z, T)
        self.assertTrue((L[0] == Lright[0]).all() and (L[1] == Lright[1]).all())


class TestIsIsomorphic(TestCase):
    def test_is_isomorphic_1(self):
        # Tests is_isomorphic on test case #1 (one flat cluster, different labellings)
        a = [1, 1, 1]
        b = [2, 2, 2]
        self.assertTrue(is_isomorphic(a, b) == True)
        self.assertTrue(is_isomorphic(b, a) == True)

    def test_is_isomorphic_2(self):
        # Tests is_isomorphic on test case #2 (two flat clusters, different labelings)
        a = [1, 7, 1]
        b = [2, 3, 2]
        self.assertTrue(is_isomorphic(a, b) == True)
        self.assertTrue(is_isomorphic(b, a) == True)

    def test_is_isomorphic_3(self):
        # Tests is_isomorphic on test case #3 (no flat clusters)
        a = []
        b = []
        self.assertTrue(is_isomorphic(a, b) == True)

    def test_is_isomorphic_4A(self):
        # Tests is_isomorphic on test case #4A (3 flat clusters, different labelings, isomorphic)
        a = [1, 2, 3]
        b = [1, 3, 2]
        self.assertTrue(is_isomorphic(a, b) == True)
        self.assertTrue(is_isomorphic(b, a) == True)

    def test_is_isomorphic_4B(self):
        # Tests is_isomorphic on test case #4B (3 flat clusters, different labelings, nonisomorphic)
        a = [1, 2, 3, 3]
        b = [1, 3, 2, 3]
        self.assertTrue(is_isomorphic(a, b) == False)
        self.assertTrue(is_isomorphic(b, a) == False)

    def test_is_isomorphic_4C(self):
        # Tests is_isomorphic on test case #4C (3 flat clusters, different labelings, isomorphic)
        a = [7, 2, 3]
        b = [6, 3, 2]
        self.assertTrue(is_isomorphic(a, b) == True)
        self.assertTrue(is_isomorphic(b, a) == True)

    def test_is_isomorphic_5A(self):
        # Tests is_isomorphic on test case #5A (1000 observations, 2 random clusters,
        # random permutation of the labeling). Run 3 times.
        for k in xrange(0, 3):
            self.help_is_isomorphic_randperm(1000, 2)

    def test_is_isomorphic_5B(self):
        # Tests is_isomorphic on test case #5B (1000 observations, 3 random
        # clusters, random permutation of the labeling). Run 3 times.
        for k in xrange(0, 3):
            self.help_is_isomorphic_randperm(1000, 3)

    def test_is_isomorphic_5C(self):
        # Tests is_isomorphic on test case #5C (1000 observations, 5 random
        # clusters, random permutation of the labeling). Run 3 times.
        for k in xrange(0, 3):
            self.help_is_isomorphic_randperm(1000, 5)

    def test_is_isomorphic_6A(self):
        # Tests is_isomorphic on test case #5A (1000 observations, 2 random
        # clusters, random permutation of the labeling, slightly
        # nonisomorphic.) Run 3 times.
        for k in xrange(0, 3):
            self.help_is_isomorphic_randperm(1000, 2, True, 5)

    def test_is_isomorphic_6B(self):
        # Tests is_isomorphic on test case #5B (1000 observations, 3 random
        # clusters, random permutation of the labeling, slightly
        # nonisomorphic.) Run 3 times.
        for k in xrange(0, 3):
            self.help_is_isomorphic_randperm(1000, 3, True, 5)

    def test_is_isomorphic_6C(self):
        # Tests is_isomorphic on test case #5C (1000 observations, 5 random
        # clusters, random permutation of the labeling, slightly
        # non-isomorphic.) Run 3 times.
        for k in xrange(0, 3):
            self.help_is_isomorphic_randperm(1000, 5, True, 5)

    def help_is_isomorphic_randperm(self, nobs, nclusters, noniso=False, nerrors=0):
        a = np.int_(np.random.rand(nobs) * nclusters)
        b = np.zeros(a.size, dtype=np.int_)
        q = {}
        P = np.random.permutation(nclusters)
        for i in xrange(0, a.shape[0]):
            b[i] = P[a[i]]
        if noniso:
            Q = np.random.permutation(nobs)
            b[Q[0:nerrors]] += 1
            b[Q[0:nerrors]] %= nclusters
        self.assertTrue(is_isomorphic(a, b) == (not noniso))
        self.assertTrue(is_isomorphic(b, a) == (not noniso))


class TestIsValidLinkage(TestCase):
    def test_is_valid_linkage_int_type(self):
        # Tests is_valid_linkage(Z) with integer type.
        Z = np.asarray([[0, 1, 3.0, 2],
                        [3, 2, 4.0, 3]], dtype=np.int)
        self.assertTrue(is_valid_linkage(Z) == False)
        self.assertRaises(TypeError, is_valid_linkage, Z, throw=True)

    def test_is_valid_linkage_5_columns(self):
        # Tests is_valid_linkage(Z) with 5 columns.
        Z = np.asarray([[0, 1, 3.0, 2, 5],
                        [3, 2, 4.0, 3, 3]], dtype=np.double)
        self.assertTrue(is_valid_linkage(Z) == False)
        self.assertRaises(ValueError, is_valid_linkage, Z, throw=True)

    def test_is_valid_linkage_3_columns(self):
        # Tests is_valid_linkage(Z) with 3 columns.
        Z = np.asarray([[0, 1, 3.0],
                        [3, 2, 4.0]], dtype=np.double)
        self.assertTrue(is_valid_linkage(Z) == False)
        self.assertRaises(ValueError, is_valid_linkage, Z, throw=True)

    def test_is_valid_linkage_empty(self):
        # Tests is_valid_linkage(Z) with empty linkage.
        Z = np.zeros((0, 4), dtype=np.double)
        self.assertTrue(is_valid_linkage(Z) == False)
        self.assertRaises(ValueError, is_valid_linkage, Z, throw=True)

    def test_is_valid_linkage_1x4(self):
        # Tests is_valid_linkage(Z) on linkage over 2 observations.
        Z = np.asarray([[0, 1, 3.0, 2]], dtype=np.double)
        self.assertTrue(is_valid_linkage(Z) == True)

    def test_is_valid_linkage_2x4(self):
        # Tests is_valid_linkage(Z) on linkage over 3 observations.
        Z = np.asarray([[0, 1, 3.0, 2],
                        [3, 2, 4.0, 3]], dtype=np.double)
        self.assertTrue(is_valid_linkage(Z) == True)

    def test_is_valid_linkage_4_and_up(self):
        # Tests is_valid_linkage(Z) on linkage on observation sets between
        # sizes 4 and 15 (step size 3).
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            self.assertTrue(is_valid_linkage(Z) == True)

    def test_is_valid_linkage_4_and_up_neg_index_left(self):
        # Tests is_valid_linkage(Z) on linkage on observation sets between
        # sizes 4 and 15 (step size 3) with negative indices (left).
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            Z[i//2,0] = -2
            self.assertTrue(is_valid_linkage(Z) == False)
            self.assertRaises(ValueError, is_valid_linkage, Z, throw=True)

    def test_is_valid_linkage_4_and_up_neg_index_right(self):
        # Tests is_valid_linkage(Z) on linkage on observation sets between
        # sizes 4 and 15 (step size 3) with negative indices (right).
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            Z[i//2,1] = -2
            self.assertTrue(is_valid_linkage(Z) == False)
            self.assertRaises(ValueError, is_valid_linkage, Z, throw=True)

    def test_is_valid_linkage_4_and_up_neg_dist(self):
        # Tests is_valid_linkage(Z) on linkage on observation sets between
        # sizes 4 and 15 (step size 3) with negative distances.
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            Z[i//2,2] = -0.5
            self.assertTrue(is_valid_linkage(Z) == False)
            self.assertRaises(ValueError, is_valid_linkage, Z, throw=True)

    def test_is_valid_linkage_4_and_up_neg_counts(self):
        # Tests is_valid_linkage(Z) on linkage on observation sets between
        # sizes 4 and 15 (step size 3) with negative counts.
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            Z[i//2,3] = -2
            self.assertTrue(is_valid_linkage(Z) == False)
            self.assertRaises(ValueError, is_valid_linkage, Z, throw=True)


class TestIsValidInconsistent(TestCase):
    def test_is_valid_im_int_type(self):
        # Tests is_valid_im(R) with integer type.
        R = np.asarray([[0, 1, 3.0, 2],
                        [3, 2, 4.0, 3]], dtype=np.int)
        self.assertTrue(is_valid_im(R) == False)
        self.assertRaises(TypeError, is_valid_im, R, throw=True)

    def test_is_valid_im_5_columns(self):
        # Tests is_valid_im(R) with 5 columns.
        R = np.asarray([[0, 1, 3.0, 2, 5],
                        [3, 2, 4.0, 3, 3]], dtype=np.double)
        self.assertTrue(is_valid_im(R) == False)
        self.assertRaises(ValueError, is_valid_im, R, throw=True)

    def test_is_valid_im_3_columns(self):
        # Tests is_valid_im(R) with 3 columns.
        R = np.asarray([[0, 1, 3.0],
                        [3, 2, 4.0]], dtype=np.double)
        self.assertTrue(is_valid_im(R) == False)
        self.assertRaises(ValueError, is_valid_im, R, throw=True)

    def test_is_valid_im_empty(self):
        # Tests is_valid_im(R) with empty inconsistency matrix.
        R = np.zeros((0, 4), dtype=np.double)
        self.assertTrue(is_valid_im(R) == False)
        self.assertRaises(ValueError, is_valid_im, R, throw=True)

    def test_is_valid_im_1x4(self):
        # Tests is_valid_im(R) on im over 2 observations.
        R = np.asarray([[0, 1, 3.0, 2]], dtype=np.double)
        self.assertTrue(is_valid_im(R) == True)

    def test_is_valid_im_2x4(self):
        # Tests is_valid_im(R) on im over 3 observations.
        R = np.asarray([[0, 1, 3.0, 2],
                        [3, 2, 4.0, 3]], dtype=np.double)
        self.assertTrue(is_valid_im(R) == True)

    def test_is_valid_im_4_and_up(self):
        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
        # (step size 3).
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            R = inconsistent(Z)
            self.assertTrue(is_valid_im(R) == True)

    def test_is_valid_im_4_and_up_neg_index_left(self):
        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
        # (step size 3) with negative link height means.
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            R = inconsistent(Z)
            R[i//2,0] = -2.0
            self.assertTrue(is_valid_im(R) == False)
            self.assertRaises(ValueError, is_valid_im, R, throw=True)

    def test_is_valid_im_4_and_up_neg_index_right(self):
        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
        # (step size 3) with negative link height standard deviations.
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            R = inconsistent(Z)
            R[i//2,1] = -2.0
            self.assertTrue(is_valid_im(R) == False)
            self.assertRaises(ValueError, is_valid_im, R, throw=True)

    def test_is_valid_im_4_and_up_neg_dist(self):
        # Tests is_valid_im(R) on im on observation sets between sizes 4 and 15
        # (step size 3) with negative link counts.
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            R = inconsistent(Z)
            R[i//2,2] = -0.5
            self.assertTrue(is_valid_im(R) == False)
            self.assertRaises(ValueError, is_valid_im, R, throw=True)


class TestNumObsLinkage(TestCase):
    def test_num_obs_linkage_empty(self):
        # Tests num_obs_linkage(Z) with empty linkage.
        Z = np.zeros((0, 4), dtype=np.double)
        self.assertRaises(ValueError, num_obs_linkage, Z)

    def test_num_obs_linkage_1x4(self):
        # Tests num_obs_linkage(Z) on linkage over 2 observations.
        Z = np.asarray([[0, 1, 3.0, 2]], dtype=np.double)
        self.assertTrue(num_obs_linkage(Z) == 2)

    def test_num_obs_linkage_2x4(self):
        # Tests num_obs_linkage(Z) on linkage over 3 observations.
        Z = np.asarray([[0, 1, 3.0, 2],
                        [3, 2, 4.0, 3]], dtype=np.double)
        self.assertTrue(num_obs_linkage(Z) == 3)

    def test_num_obs_linkage_4_and_up(self):
        # Tests num_obs_linkage(Z) on linkage on observation sets between sizes
        # 4 and 15 (step size 3).
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            self.assertTrue(num_obs_linkage(Z) == i)


class TestLeavesList(TestCase):
    def test_leaves_list_1x4(self):
        # Tests leaves_list(Z) on a 1x4 linkage.
        Z = np.asarray([[0, 1, 3.0, 2]], dtype=np.double)
        node = to_tree(Z)
        self.assertTrue((leaves_list(Z) == [0, 1]).all())

    def test_leaves_list_2x4(self):
        # Tests leaves_list(Z) on a 2x4 linkage.
        Z = np.asarray([[0, 1, 3.0, 2],
                        [3, 2, 4.0, 3]], dtype=np.double)
        node = to_tree(Z)
        self.assertTrue((leaves_list(Z) == [0, 1, 2]).all())

    def test_leaves_list_iris_single(self):
        # Tests leaves_list(Z) on the Iris data set using single linkage.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'single')
        node = to_tree(Z)
        self.assertTrue((node.pre_order() == leaves_list(Z)).all())

    def test_leaves_list_iris_complete(self):
        # Tests leaves_list(Z) on the Iris data set using complete linkage.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'complete')
        node = to_tree(Z)
        self.assertTrue((node.pre_order() == leaves_list(Z)).all())

    def test_leaves_list_iris_centroid(self):
        # Tests leaves_list(Z) on the Iris data set using centroid linkage.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'centroid')
        node = to_tree(Z)
        self.assertTrue((node.pre_order() == leaves_list(Z)).all())

    def test_leaves_list_iris_median(self):
        # Tests leaves_list(Z) on the Iris data set using median linkage.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'median')
        node = to_tree(Z)
        self.assertTrue((node.pre_order() == leaves_list(Z)).all())

    def test_leaves_list_iris_ward(self):
        # Tests leaves_list(Z) on the Iris data set using ward linkage.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'ward')
        node = to_tree(Z)
        self.assertTrue((node.pre_order() == leaves_list(Z)).all())

    def test_leaves_list_iris_average(self):
        # Tests leaves_list(Z) on the Iris data set using average linkage.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'average')
        node = to_tree(Z)
        self.assertTrue((node.pre_order() == leaves_list(Z)).all())

    def test_iris_subtree_pre_order(self):
        # Tests that pre_order() works when called on sub-trees.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'single')
        node = to_tree(Z)
        self.assertTrue(node.pre_order() == (node.get_left().pre_order()
                                             + node.get_right().pre_order()))


class TestCorrespond(TestCase):
    def test_correspond_empty(self):
        # Tests correspond(Z, y) with empty linkage and condensed distance matrix.
        y = np.zeros((0,))
        Z = np.zeros((0,4))
        self.assertRaises(ValueError, correspond, Z, y)

    def test_correspond_2_and_up(self):
        # Tests correspond(Z, y) on linkage and CDMs over observation sets of
        # different sizes.
        for i in xrange(2, 4):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            self.assertTrue(correspond(Z, y))
        for i in xrange(4, 15, 3):
            y = np.random.rand(i*(i-1)//2)
            Z = linkage(y)
            self.assertTrue(correspond(Z, y))

    def test_correspond_4_and_up(self):
        # Tests correspond(Z, y) on linkage and CDMs over observation sets of
        # different sizes. Correspondance should be false.
        for (i, j) in (list(zip(list(range(2, 4)), list(range(3, 5)))) +
                       list(zip(list(range(3, 5)), list(range(2, 4))))):
            y = np.random.rand(i*(i-1)//2)
            y2 = np.random.rand(j*(j-1)//2)
            Z = linkage(y)
            Z2 = linkage(y2)
            self.assertTrue(correspond(Z, y2) == False)
            self.assertTrue(correspond(Z2, y) == False)

    def test_correspond_4_and_up_2(self):
        # Tests correspond(Z, y) on linkage and CDMs over observation sets of
        # different sizes. Correspondance should be false.
        for (i, j) in (list(zip(list(range(2, 7)), list(range(16, 21)))) +
                       list(zip(list(range(2, 7)), list(range(16, 21))))):
            y = np.random.rand(i*(i-1)//2)
            y2 = np.random.rand(j*(j-1)//2)
            Z = linkage(y)
            Z2 = linkage(y2)
            self.assertTrue(correspond(Z, y2) == False)
            self.assertTrue(correspond(Z2, y) == False)

    def test_num_obs_linkage_multi_matrix(self):
        # Tests num_obs_linkage with observation matrices of multiple sizes.
        for n in xrange(2, 10):
            X = np.random.rand(n, 4)
            Y = pdist(X)
            Z = linkage(Y)
            self.assertTrue(num_obs_linkage(Z) == n)


class TestIsMonotonic(TestCase):
    def test_is_monotonic_empty(self):
        # Tests is_monotonic(Z) on an empty linkage.
        Z = np.zeros((0, 4))
        self.assertRaises(ValueError, is_monotonic, Z)

    def test_is_monotonic_1x4(self):
        # Tests is_monotonic(Z) on 1x4 linkage. Expecting True.
        Z = np.asarray([[0, 1, 0.3, 2]], dtype=np.double)
        self.assertTrue(is_monotonic(Z) == True)

    def test_is_monotonic_2x4_T(self):
        # Tests is_monotonic(Z) on 2x4 linkage. Expecting True.
        Z = np.asarray([[0, 1, 0.3, 2],
                        [2, 3, 0.4, 3]], dtype=np.double)
        self.assertTrue(is_monotonic(Z) == True)

    def test_is_monotonic_2x4_F(self):
        # Tests is_monotonic(Z) on 2x4 linkage. Expecting False.
        Z = np.asarray([[0, 1, 0.4, 2],
                        [2, 3, 0.3, 3]], dtype=np.double)
        self.assertTrue(is_monotonic(Z) == False)

    def test_is_monotonic_3x4_T(self):
        # Tests is_monotonic(Z) on 3x4 linkage. Expecting True.
        Z = np.asarray([[0, 1, 0.3, 2],
                        [2, 3, 0.4, 2],
                        [4, 5, 0.6, 4]], dtype=np.double)
        self.assertTrue(is_monotonic(Z) == True)

    def test_is_monotonic_3x4_F1(self):
        # Tests is_monotonic(Z) on 3x4 linkage (case 1). Expecting False.
        Z = np.asarray([[0, 1, 0.3, 2],
                        [2, 3, 0.2, 2],
                        [4, 5, 0.6, 4]], dtype=np.double)
        self.assertTrue(is_monotonic(Z) == False)

    def test_is_monotonic_3x4_F2(self):
        # Tests is_monotonic(Z) on 3x4 linkage (case 2). Expecting False.
        Z = np.asarray([[0, 1, 0.8, 2],
                        [2, 3, 0.4, 2],
                        [4, 5, 0.6, 4]], dtype=np.double)
        self.assertTrue(is_monotonic(Z) == False)

    def test_is_monotonic_3x4_F3(self):
        # Tests is_monotonic(Z) on 3x4 linkage (case 3). Expecting False
        Z = np.asarray([[0, 1, 0.3, 2],
                        [2, 3, 0.4, 2],
                        [4, 5, 0.2, 4]], dtype=np.double)
        self.assertTrue(is_monotonic(Z) == False)

    def test_is_monotonic_tdist_linkage1(self):
        # Tests is_monotonic(Z) on clustering generated by single linkage on
        # tdist data set. Expecting True.
        Z = linkage(_ytdist, 'single')
        self.assertTrue(is_monotonic(Z) == True)

    def test_is_monotonic_tdist_linkage2(self):
        # Tests is_monotonic(Z) on clustering generated by single linkage on
        # tdist data set. Perturbing. Expecting False.
        Z = linkage(_ytdist, 'single')
        Z[2,2] = 0.0
        self.assertTrue(is_monotonic(Z) == False)

    def test_is_monotonic_iris_linkage(self):
        # Tests is_monotonic(Z) on clustering generated by single linkage on
        # Iris data set. Expecting True.
        X = eo['iris']
        Y = pdist(X)
        Z = linkage(X, 'single')
        self.assertTrue(is_monotonic(Z) == True)


class TestMaxDists(TestCase):
    def test_maxdists_empty_linkage(self):
        # Tests maxdists(Z) on empty linkage. Expecting exception.
        Z = np.zeros((0, 4), dtype=np.double)
        self.assertRaises(ValueError, maxdists, Z)

    def test_maxdists_one_cluster_linkage(self):
        # Tests maxdists(Z) on linkage with one cluster.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        MD = maxdists(Z)
        eps = 1e-15
        expectedMD = calculate_maximum_distances(Z)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxdists_Q_linkage_single(self):
        # Tests maxdists(Z) on the Q data set using single linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'single')
        MD = maxdists(Z)
        eps = 1e-15
        expectedMD = calculate_maximum_distances(Z)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxdists_Q_linkage_complete(self):
        # Tests maxdists(Z) on the Q data set using complete linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'complete')
        MD = maxdists(Z)
        eps = 1e-15
        expectedMD = calculate_maximum_distances(Z)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxdists_Q_linkage_ward(self):
        # Tests maxdists(Z) on the Q data set using Ward linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'ward')
        MD = maxdists(Z)
        eps = 1e-15
        expectedMD = calculate_maximum_distances(Z)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxdists_Q_linkage_centroid(self):
        # Tests maxdists(Z) on the Q data set using centroid linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'centroid')
        MD = maxdists(Z)
        eps = 1e-15
        expectedMD = calculate_maximum_distances(Z)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxdists_Q_linkage_median(self):
        # Tests maxdists(Z) on the Q data set using median linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'median')
        MD = maxdists(Z)
        eps = 1e-15
        expectedMD = calculate_maximum_distances(Z)
        self.assertTrue(within_tol(MD, expectedMD, eps))


class TestMaxInconsts(TestCase):
    def test_maxinconsts_empty_linkage(self):
        # Tests maxinconsts(Z, R) on empty linkage. Expecting exception.
        Z = np.zeros((0, 4), dtype=np.double)
        R = np.zeros((0, 4), dtype=np.double)
        self.assertRaises(ValueError, maxinconsts, Z, R)

    def test_maxinconsts_difrow_linkage(self):
        # Tests maxinconsts(Z, R) on linkage and inconsistency matrices with
        # different numbers of clusters. Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.random.rand(2, 4)
        self.assertRaises(ValueError, maxinconsts, Z, R)

    def test_maxinconsts_one_cluster_linkage(self):
        # Tests maxinconsts(Z, R) on linkage with one cluster.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        MD = maxinconsts(Z, R)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxinconsts_Q_linkage_single(self):
        # Tests maxinconsts(Z, R) on the Q data set using single linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'single')
        R = inconsistent(Z)
        MD = maxinconsts(Z, R)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxinconsts_Q_linkage_complete(self):
        # Tests maxinconsts(Z, R) on the Q data set using complete linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'complete')
        R = inconsistent(Z)
        MD = maxinconsts(Z, R)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxinconsts_Q_linkage_ward(self):
        # Tests maxinconsts(Z, R) on the Q data set using Ward linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'ward')
        R = inconsistent(Z)
        MD = maxinconsts(Z, R)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxinconsts_Q_linkage_centroid(self):
        # Tests maxinconsts(Z, R) on the Q data set using centroid linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'centroid')
        R = inconsistent(Z)
        MD = maxinconsts(Z, R)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxinconsts_Q_linkage_median(self):
        # Tests maxinconsts(Z, R) on the Q data set using median linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'median')
        R = inconsistent(Z)
        MD = maxinconsts(Z, R)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R)
        self.assertTrue(within_tol(MD, expectedMD, eps))


class TestMaxRStat(TestCase):
    def test_maxRstat_float_index(self):
        # Tests maxRstat(Z, R, 3.3). Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        self.assertRaises(TypeError, maxRstat, Z, R, 3.3)

    def test_maxRstat_neg_index(self):
        # Tests maxRstat(Z, R, -1). Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        self.assertRaises(ValueError, maxRstat, Z, R, -1)

    def test_maxRstat_oob_pos_index(self):
        # Tests maxRstat(Z, R, 4). Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        self.assertRaises(ValueError, maxRstat, Z, R, 4)

    def test_maxRstat_0_empty_linkage(self):
        # Tests maxRstat(Z, R, 0) on empty linkage. Expecting exception.
        Z = np.zeros((0, 4), dtype=np.double)
        R = np.zeros((0, 4), dtype=np.double)
        self.assertRaises(ValueError, maxRstat, Z, R, 0)

    def test_maxRstat_0_difrow_linkage(self):
        # Tests maxRstat(Z, R, 0) on linkage and inconsistency matrices with
        # different numbers of clusters. Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.random.rand(2, 4)
        self.assertRaises(ValueError, maxRstat, Z, R, 0)

    def test_maxRstat_0_one_cluster_linkage(self):
        # Tests maxRstat(Z, R, 0) on linkage with one cluster.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        MD = maxRstat(Z, R, 0)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 0)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_0_Q_linkage_single(self):
        # Tests maxRstat(Z, R, 0) on the Q data set using single linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'single')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 0)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 0)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_0_Q_linkage_complete(self):
        # Tests maxRstat(Z, R, 0) on the Q data set using complete linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'complete')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 0)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 0)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_0_Q_linkage_ward(self):
        # Tests maxRstat(Z, R, 0) on the Q data set using Ward linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'ward')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 0)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 0)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_0_Q_linkage_centroid(self):
        # Tests maxRstat(Z, R, 0) on the Q data set using centroid linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'centroid')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 0)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 0)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_0_Q_linkage_median(self):
        # Tests maxRstat(Z, R, 0) on the Q data set using median linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'median')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 0)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 0)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_1_empty_linkage(self):
        # Tests maxRstat(Z, R, 1) on empty linkage. Expecting exception.
        Z = np.zeros((0, 4), dtype=np.double)
        R = np.zeros((0, 4), dtype=np.double)
        self.assertRaises(ValueError, maxRstat, Z, R, 0)

    def test_maxRstat_1_difrow_linkage(self):
        # Tests maxRstat(Z, R, 1) on linkage and inconsistency matrices with
        # different numbers of clusters. Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.random.rand(2, 4)
        self.assertRaises(ValueError, maxRstat, Z, R, 0)

    def test_maxRstat_1_one_cluster_linkage(self):
        # Tests maxRstat(Z, R, 1) on linkage with one cluster.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        MD = maxRstat(Z, R, 1)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 1)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_1_Q_linkage_single(self):
        # Tests maxRstat(Z, R, 1) on the Q data set using single linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'single')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 1)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 1)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_1_Q_linkage_complete(self):
        # Tests maxRstat(Z, R, 1) on the Q data set using complete linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'complete')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 1)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 1)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_1_Q_linkage_ward(self):
        # Tests maxRstat(Z, R, 1) on the Q data set using Ward linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'ward')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 1)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 1)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_1_Q_linkage_centroid(self):
        # Tests maxRstat(Z, R, 1) on the Q data set using centroid linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'centroid')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 1)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 1)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_1_Q_linkage_median(self):
        # Tests maxRstat(Z, R, 1) on the Q data set using median linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'median')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 1)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 1)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_2_empty_linkage(self):
        # Tests maxRstat(Z, R, 2) on empty linkage. Expecting exception.
        Z = np.zeros((0, 4), dtype=np.double)
        R = np.zeros((0, 4), dtype=np.double)
        self.assertRaises(ValueError, maxRstat, Z, R, 2)

    def test_maxRstat_2_difrow_linkage(self):
        # Tests maxRstat(Z, R, 2) on linkage and inconsistency matrices with
        # different numbers of clusters. Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.random.rand(2, 4)
        self.assertRaises(ValueError, maxRstat, Z, R, 2)

    def test_maxRstat_2_one_cluster_linkage(self):
        # Tests maxRstat(Z, R, 2) on linkage with one cluster.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        MD = maxRstat(Z, R, 2)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 2)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_2_Q_linkage_single(self):
        # Tests maxRstat(Z, R, 2) on the Q data set using single linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'single')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 2)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 2)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_2_Q_linkage_complete(self):
        # Tests maxRstat(Z, R, 2) on the Q data set using complete linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'complete')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 2)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 2)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_2_Q_linkage_ward(self):
        # Tests maxRstat(Z, R, 2) on the Q data set using Ward linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'ward')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 2)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 2)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_2_Q_linkage_centroid(self):
        # Tests maxRstat(Z, R, 2) on the Q data set using centroid linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'centroid')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 2)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 2)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_2_Q_linkage_median(self):
        # Tests maxRstat(Z, R, 2) on the Q data set using median linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'median')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 2)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 2)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_3_empty_linkage(self):
        # Tests maxRstat(Z, R, 3) on empty linkage. Expecting exception.
        Z = np.zeros((0, 4), dtype=np.double)
        R = np.zeros((0, 4), dtype=np.double)
        self.assertRaises(ValueError, maxRstat, Z, R, 3)

    def test_maxRstat_3_difrow_linkage(self):
        # Tests maxRstat(Z, R, 3) on linkage and inconsistency matrices with
        # different numbers of clusters. Expecting exception.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.random.rand(2, 4)
        self.assertRaises(ValueError, maxRstat, Z, R, 3)

    def test_maxRstat_3_one_cluster_linkage(self):
        # Tests maxRstat(Z, R, 3) on linkage with one cluster.
        Z = np.asarray([[0, 1, 0.3, 4]], dtype=np.double)
        R = np.asarray([[0, 0, 0, 0.3]], dtype=np.double)
        MD = maxRstat(Z, R, 3)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 3)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_3_Q_linkage_single(self):
        # Tests maxRstat(Z, R, 3) on the Q data set using single linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'single')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 3)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 3)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_3_Q_linkage_complete(self):
        # Tests maxRstat(Z, R, 3) on the Q data set using complete linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'complete')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 3)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 3)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_3_Q_linkage_ward(self):
        # Tests maxRstat(Z, R, 3) on the Q data set using Ward linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'ward')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 3)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 3)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_3_Q_linkage_centroid(self):
        # Tests maxRstat(Z, R, 3) on the Q data set using centroid linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'centroid')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 3)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 3)
        self.assertTrue(within_tol(MD, expectedMD, eps))

    def test_maxRstat_3_Q_linkage_median(self):
        # Tests maxRstat(Z, R, 3) on the Q data set using median linkage.
        X = eo['Q-X']
        Y = pdist(X)
        Z = linkage(X, 'median')
        R = inconsistent(Z)
        MD = maxRstat(Z, R, 3)
        eps = 1e-15
        expectedMD = calculate_maximum_inconsistencies(Z, R, 3)
        self.assertTrue(within_tol(MD, expectedMD, eps))


class TestDendrogram(TestCase):
    def test_dendrogram_single_linkage_tdist(self):
        # Tests dendrogram calculation on single linkage of the tdist data set.
        Z = linkage(_ytdist, 'single')
        R = dendrogram(Z, no_plot=True)
        leaves = R["leaves"]
        self.assertEqual(leaves, [2, 5, 1, 0, 3, 4])

    @dec.skipif(not have_matplotlib)
    def test_dendrogram_plot(self):
        # Tests dendrogram plotting.
        Z = linkage(_ytdist, 'single')

        fig = plt.figure()
        ax = fig.add_subplot(111)

        # test that dendrogram accepts ax keyword
        R1 = dendrogram(Z, ax=ax)
        plt.close()

        # test plotting to gca (will import pylab)
        R2 = dendrogram(Z)
        plt.close()


def calculate_maximum_distances(Z):
    # Used for testing correctness of maxdists.
    n = Z.shape[0] + 1
    B = np.zeros((n-1,))
    q = np.zeros((3,))
    for i in xrange(0, n - 1):
        q[:] = 0.0
        left = Z[i, 0]
        right = Z[i, 1]
        if left >= n:
            q[0] = B[int(left) - n]
        if right >= n:
            q[1] = B[int(right) - n]
        q[2] = Z[i, 2]
        B[i] = q.max()
    return B


def calculate_maximum_inconsistencies(Z, R, k=3):
    # Used for testing correctness of maxinconsts.
    n = Z.shape[0] + 1
    B = np.zeros((n-1,))
    q = np.zeros((3,))
    for i in xrange(0, n - 1):
        q[:] = 0.0
        left = Z[i, 0]
        right = Z[i, 1]
        if left >= n:
            q[0] = B[int(left) - n]
        if right >= n:
            q[1] = B[int(right) - n]
        q[2] = R[i, k]
        B[i] = q.max()
    return B


def within_tol(a, b, tol):
    return np.abs(a - b).max() < tol


def test_euclidean_linkage_value_error():
    for method in scipy.cluster.hierarchy._cpy_euclid_methods:
        assert_raises(ValueError,
                linkage, [[1, 1], [1, 1]], method=method, metric='cityblock')


if __name__ == "__main__":
    run_module_suite()
