├── .gitignore
├── BDeuScore.py
├── FGES-py_Jupyter_Tutorial.ipynb
├── SEMScore.py
├── SemEstimator.py
├── __init__.py
├── data
    ├── 40_random.txt
    ├── 50_edges.txt
    ├── 50_fully_connected.txt
    ├── HCP.tsv
    ├── collider_1.txt
    ├── collider_2.txt
    ├── collider_3.txt
    ├── collider_4.txt
    ├── collider_5.txt
    ├── data1.txt
    ├── linear_1.txt
    ├── params_1.txt
    ├── params_1_graph.txt
    ├── single_edge_1.txt
    ├── single_edge_2.txt
    └── single_edge_3.txt
├── fges.py
├── graph_util.py
├── knowledge.py
├── meekrules.py
├── runner.py
├── search_util.py
└── tests
    ├── __init__.py
    ├── fges_tests.py
    ├── test_graph_util.py
    ├── test_meek_rules.py
    ├── test_search_util.py
    └── test_util.py


/.gitignore:
--------------------------------------------------------------------------------
 1 | __pycache__/
 2 | .vscode
 3 | .Python
 4 | *.json
 5 | include/
 6 | share/
 7 | lib/
 8 | bin/
 9 | .idea
10 | *.pkl
11 | *.pyc
12 | *.npy
13 | *.ipynb
14 | .DS_store
15 | */.DS_store
16 | 


--------------------------------------------------------------------------------
/BDeuScore.py:
--------------------------------------------------------------------------------
  1 | import numpy as np
  2 | from numpy.linalg import inv
  3 | import math
  4 | from scipy import special
  5 | 
  6 | 
  7 | class BDeuScore:
  8 |     def __init__(self, dataset, variables, sample_prior=1,
  9 |                  structure_prior=1):
 10 |         """Initialize the BDeuScore object.
 11 | 
 12 |         :param dataset: 2D np.array, with a row for each data
 13 |                         point and a column for each variable.
 14 |         :param variables: np.array containing the variable ids
 15 |         :param sample_prior: sample prior
 16 |         :param structure_prior: structure prior
 17 |         """
 18 | 
 19 |         assert len(dataset.shape) == 2, "Dataset must be 2-dimensional."
 20 |         # defining attributes
 21 |         self.dataset = dataset
 22 |         self.variables = variables
 23 |         self.sampleSize = dataset.shape[0]
 24 | 
 25 |         # note that the sample prior is set by the
 26 |         # sparsity parameter in runner.py
 27 |         self.sample_prior = sample_prior
 28 |         self.structure_prior = structure_prior
 29 | 
 30 |         # num_categories is always 2 for binary data
 31 |         # (TODO: if data is not binary we must create
 32 |         # a method which computes the number
 33 |         # of categories for each variable)
 34 |         self.num_categories = np.full(len(self.variables), 2)
 35 | 
 36 |     def local_score(self, node, parents):
 37 |         """
 38 |         Method to compute the score associated to having
 39 |         a certain set of parents associated to a node.
 40 | 
 41 |         :param node: int representing the node in question.
 42 |         :param parents: np.array of ints representing the parent nodes.
 43 |         """
 44 |         # number of categories of this node
 45 |         c = self.num_categories[node]
 46 | 
 47 |         # number of categories of the parent nodes
 48 |         dims = self.num_categories[parents]
 49 | 
 50 |         # number of parent states (i.e. multiplying the number of
 51 |         # categories of each variable together)
 52 |         r = np.prod(dims)
 53 | 
 54 |         # conditional cell coeffs for node given parents (node)
 55 |         n_jk = np.zeros((r, c))
 56 |         n_j = np.zeros(r)
 57 |         my_parents = self.dataset[:, parents]
 58 |         my_child = self.dataset[:, node]
 59 | 
 60 |         # populate the conditional cell coeffs
 61 |         for i in range(self.sampleSize):
 62 |             parent_values = my_parents[i]
 63 |             child_value = my_child[i]
 64 |             row_index = self.get_row_index(dims, parent_values)
 65 | 
 66 |             n_jk[row_index][child_value] += 1
 67 |             n_j[row_index] += 1
 68 | 
 69 |         # finally compute the score
 70 |         score = self.get_prior_for_structure(len(parents))
 71 | 
 72 |         cell_prior = self.sample_prior / (c*r)
 73 |         row_prior = self.sample_prior / r
 74 | 
 75 |         for j in range(r):
 76 |             score -= special.loggamma(row_prior + n_j[j])
 77 |             for k in range(c):
 78 |                 score += special.loggamma(cell_prior + n_jk[j][k])
 79 | 
 80 |         score += r * special.loggamma(row_prior)
 81 |         score -= c * r * special.loggamma(cell_prior)
 82 | 
 83 |         return score
 84 | 
 85 |     def get_prior_for_structure(self, num_parents):
 86 |         """
 87 |         Method that returns the initial score value
 88 |         as defined by the structure prior.
 89 | 
 90 |         :param num_parents: int representing the number of
 91 |                             nodes in the parents np.array.
 92 |         """
 93 |         e = self.structure_prior
 94 |         vm = self.dataset.shape[0] - 1
 95 |         return num_parents*np.log(e/vm) + (vm - num_parents) * np.log(1-(e/vm))
 96 | 
 97 |     def get_row_index(self, dims, values):
 98 |         """
 99 |         Method that returns the index to increment in
100 |         the cell coeffs.
101 | 
102 |         :param dims: np.array containing the number of categories
103 |                      adopted by each node in the parents np.array.
104 |         :param values: value of parent nodes at a specific time instant.
105 |         """
106 |         row_index = 0
107 |         for i in range(len(dims)):
108 |             row_index *= dims[i]
109 |             row_index += values[i]
110 |         return row_index
111 | 
112 |     def local_score_diff_parents(self, node1, node2, parents):
113 |         """
114 |         Method to compute the change in score resulting
115 |         from adding node1 to the list of parents.
116 | 
117 |         :param node1: int representing the node to add
118 |                       to list of parents.
119 |         :param node2: int representing the node in question.
120 |         :param parents: list of ints representing the parent nodes.
121 |         """
122 |         return self.local_score(node2, parents + [node1]) - self.local_score(node2, parents)
123 | 
124 |     def local_score_diff(self, node1, node2):
125 |         """
126 |         Method to compute the change in score resulting
127 |         from having node1 as a parent.
128 | 
129 |         :param node1: int representing the parent node.
130 |         :param node2: int representing the node in question.
131 |         """
132 |         return self.local_score_diff_parents(node1, node2, [])
133 | 


--------------------------------------------------------------------------------
/FGES-py_Jupyter_Tutorial.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "This tutorial is intended to show proper usage of the `fges-py` library. "
  8 |    ]
  9 |   },
 10 |   {
 11 |    "cell_type": "markdown",
 12 |    "metadata": {},
 13 |    "source": [
 14 |     "`fges-py` is a full python implementation of the Fast Greedy Equivalence Search algorithm, which is described [here](https://www.ncbi.nlm.nih.gov/pubmed/28393106)."
 15 |    ]
 16 |   },
 17 |   {
 18 |    "cell_type": "markdown",
 19 |    "metadata": {},
 20 |    "source": [
 21 |     "First we will install the necessary dependencies:"
 22 |    ]
 23 |   },
 24 |   {
 25 |    "cell_type": "code",
 26 |    "execution_count": null,
 27 |    "metadata": {},
 28 |    "outputs": [],
 29 |    "source": [
 30 |     "!pip3 install numpy\n",
 31 |     "!pip3 install scipy\n",
 32 |     "!pip3 install sortedcontainers\n",
 33 |     "!pip3 install dill\n",
 34 |     "!pip3 install argparse\n",
 35 |     "!pip3 install networkx"
 36 |    ]
 37 |   },
 38 |   {
 39 |    "cell_type": "markdown",
 40 |    "metadata": {},
 41 |    "source": [
 42 |     "The entry point of the algorithm is in the `runner.py` file. The algorithm takes three arguments as input: \n",
 43 |     "* a dataset which is formatted as a text file with a row for each datapoint and a column for each variable, \n",
 44 |     "* a save name\n",
 45 |     "* a sparsity level, which acts as a limit on output graph complexity (set to 1 below)"
 46 |    ]
 47 |   },
 48 |   {
 49 |    "cell_type": "markdown",
 50 |    "metadata": {},
 51 |    "source": [
 52 |     "For example, the code may be run with the following command (this will take about 1min for sparsity 4 on the HCP.tsv data). Make sure to adjust the path appropriately:"
 53 |    ]
 54 |   },
 55 |   {
 56 |    "cell_type": "code",
 57 |    "execution_count": null,
 58 |    "metadata": {},
 59 |    "outputs": [],
 60 |    "source": [
 61 |     "!python3.6 ~/<FILL IN PATH TO>/fges-py/runner.py ~/<FILL IN PATH TO>/fges-py/data/HCP.tsv demo_save_name 4"
 62 |    ]
 63 |   },
 64 |   {
 65 |    "cell_type": "markdown",
 66 |    "metadata": {},
 67 |    "source": [
 68 |     "This data will be stored under `demo_save_name` in the folder where this notebook is running. To load the graph, we can load this file using `pickle`:"
 69 |    ]
 70 |   },
 71 |   {
 72 |    "cell_type": "code",
 73 |    "execution_count": null,
 74 |    "metadata": {
 75 |     "collapsed": true
 76 |    },
 77 |    "outputs": [],
 78 |    "source": [
 79 |     "import numpy as np\n",
 80 |     "import pickle\n",
 81 |     "with open('demo_save_name.pkl', 'rb') as f:\n",
 82 |     "    result = pickle.load(f)"
 83 |    ]
 84 |   },
 85 |   {
 86 |    "cell_type": "markdown",
 87 |    "metadata": {},
 88 |    "source": [
 89 |     "We can view a list of the edges in the loaded graph like so:"
 90 |    ]
 91 |   },
 92 |   {
 93 |    "cell_type": "code",
 94 |    "execution_count": null,
 95 |    "metadata": {},
 96 |    "outputs": [],
 97 |    "source": [
 98 |     "result['graph'].edges()"
 99 |    ]
100 |   },
101 |   {
102 |    "cell_type": "code",
103 |    "execution_count": null,
104 |    "metadata": {
105 |     "collapsed": true
106 |    },
107 |    "outputs": [],
108 |    "source": []
109 |   }
110 |  ],
111 |  "metadata": {
112 |   "kernelspec": {
113 |    "display_name": "Python 3",
114 |    "language": "python",
115 |    "name": "python3"
116 |   },
117 |   "language_info": {
118 |    "codemirror_mode": {
119 |     "name": "ipython",
120 |     "version": 3
121 |    },
122 |    "file_extension": ".py",
123 |    "mimetype": "text/x-python",
124 |    "name": "python",
125 |    "nbconvert_exporter": "python",
126 |    "pygments_lexer": "ipython3",
127 |    "version": "3.6.1"
128 |   }
129 |  },
130 |  "nbformat": 4,
131 |  "nbformat_minor": 2
132 | }
133 | 


--------------------------------------------------------------------------------
/SEMScore.py:
--------------------------------------------------------------------------------
  1 | import numpy as np
  2 | from numpy.linalg import inv
  3 | import math
  4 | 
  5 | 
  6 | class SEMBicScore:
  7 | 
  8 |     def __init__(self, penalty_discount,
  9 |                  dataset=None,
 10 |                  corrs=None, dataset_size=None,
 11 |                  cache_interval=1):
 12 |         """Initialize the SEMBicScore object.
 13 | 
 14 |         Must specify either the dataset or the correlation matrix and dataset size.
 15 | 
 16 |         :param penalty_discount: Sparsity parameter
 17 |         :param dataset: 2D np.array, with a row for each data point and a column for each variable
 18 |         :param corrs: 2D square np.array, the correlation coefficients
 19 |         :param dataset_size: the number of data points
 20 |         :param cache_interval: parameter to limit how many partial correlations are cached
 21 |         """
 22 |         self.penalty = penalty_discount
 23 |         self.cache = {}
 24 |         self.cache_interval = cache_interval
 25 | 
 26 |         if dataset is not None:
 27 |             assert corrs is None and dataset_size is None, \
 28 |                 "SEMBicScore: must specify either dataset or {corrs, dataset_size}"
 29 |             assert len(dataset.shape) == 2
 30 |             self.corrcoef = np.corrcoef(dataset.transpose())
 31 |             self.sample_size = dataset.shape[0]
 32 | 
 33 |         elif corrs is not None and dataset_size is not None:
 34 |             assert len(corrs.shape) == 2
 35 |             assert corrs.shape[0] == corrs.shape[1]
 36 |             self.corrcoef = corrs
 37 |             self.sample_size = dataset_size
 38 | 
 39 |         else:
 40 |             raise AssertionError("SEMBicScore: must specify either dataset or {corrs, dataset_size}")
 41 | 
 42 |     # def partial_corr(self, x, y, Z):
 43 |     #     """
 44 |     #     Returns the partial correlation coefficients between elements of X controlling for the elements in Z.
 45 |     #     """
 46 |     #     x_data = self.dataset[:,x]
 47 |     #     y_data = self.dataset[:,y]
 48 |     #     if Z == []:
 49 |     #         return self.corrcoef[x, y]
 50 |     #     Z_data = self.dataset[:,Z]
 51 |     #
 52 |     #     beta_i = np.linalg.lstsq(Z_data, x_data)[0]
 53 |     #     beta_j = np.linalg.lstsq(Z_data, y_data)[0]
 54 |     #
 55 |     #     res_j = x_data - Z_data.dot(beta_i)
 56 |     #     res_i = y_data - Z_data.dot(beta_j)
 57 |     #
 58 |     #     return np.corrcoef(res_i, res_j)[0, 1]
 59 | 
 60 |     def recursive_partial_corr(self, x, y, Z):
 61 |         if len(Z) == 0:
 62 |             return self.corrcoef[x, y]
 63 |         else:
 64 |             z0 = min(Z)
 65 |             Z1 = Z - {z0}
 66 |             key1 = (frozenset({x, y}), Z1)
 67 |             if key1 not in self.cache:
 68 |                 term1 = self.recursive_partial_corr(x, y, Z1)
 69 |                 if len(Z1) > 0 and len(Z1) % self.cache_interval == 0:
 70 |                     self.cache[key1] = term1
 71 |             else:
 72 |                 term1 = self.cache[key1]
 73 | 
 74 |             key2 = (frozenset({x, z0}), Z1)
 75 |             if key2 not in self.cache:
 76 |                 term2 = self.recursive_partial_corr(x, z0, Z1)
 77 |                 if len(Z1) > 0 and len(Z1) % self.cache_interval == 0:
 78 |                     self.cache[key2] = term2
 79 |             else:
 80 |                 term2 = self.cache[key2]
 81 | 
 82 |             key3 = (frozenset({y, z0}), Z1)
 83 |             if key3 not in self.cache:
 84 |                 term3 = self.recursive_partial_corr(y, z0, Z1)
 85 |                 if len(Z1) > 0 and len(Z1) % self.cache_interval == 0:
 86 |                     self.cache[key3] = term3
 87 |             else:
 88 |                 term3 = self.cache[key3]
 89 | 
 90 |             return (term1 - (term2 * term3)) / math.sqrt((1 - (term2 * term2)) * (1 - (term3 * term3)))
 91 | 
 92 |     # def local_score(self, node, parents):
 93 |     #     """ `node` is an int index """
 94 |     #     #print("Node:", node, "Parents:", parents)
 95 |     #     variance = self.cov[node][node]
 96 |     #     p = len(parents)
 97 |     #
 98 |     #     # np.ix_(rowIndices, colIndices)
 99 |     #
100 |     #     covxx = self.cov[np.ix_(parents, parents)]
101 |     #     covxx_inv = inv(covxx)
102 |     #
103 |     #     if (p == 0):
104 |     #         covxy = []
105 |     #     else:
106 |     #         # vector
107 |     #         covxy = self.cov[np.ix_(parents, [node])]
108 |     #
109 |     #     b = np.dot(covxx_inv, covxy)
110 |     #
111 |     #     variance -= np.dot(np.transpose(covxy), b)
112 |     #
113 |     #     if variance <= 0:
114 |     #         return None
115 |     #
116 |     #     returnval = self.score(variance, p)
117 |     #     return returnval
118 | 
119 |     # def local_score_no_parents(self, node):
120 |     #     """ if node has no parents """
121 |     #     variance = self.cov[node][node]
122 |     #
123 |     #     if variance <= 0:
124 |     #         return None
125 |     #
126 |     #     return self.score(variance)
127 | 
128 |     # def score(self, variance, parents_len=0):
129 |     #     bic = - self.sample_size * math.log(variance) - parents_len * self.penalty * math.log(self.sample_size)
130 |     #     # TODO: Struct prior?
131 |     #     return bic
132 | 
133 |     def local_score_diff_parents(self, node1, node2, parents):
134 |         parents = frozenset(parents)
135 |         r = self.recursive_partial_corr(node1, node2, parents)
136 |         return -self.sample_size * math.log(1.0 - r * r) - self.penalty * math.log(self.sample_size)
137 |         #return self.local_score(node2, parents + [node1]) - self.local_score(node2, parents)
138 | 
139 |     def local_score_diff(self, node1, node2):
140 |         return self.local_score_diff_parents(node1, node2, [])
141 | 


--------------------------------------------------------------------------------
/SemEstimator.py:
--------------------------------------------------------------------------------
 1 | 
 2 | from fges import FGES
 3 | from SEMScore import SEMBicScore
 4 | from search_util import *
 5 | import numpy as np
 6 | 
 7 | class SemEstimator:
 8 | 
 9 |     def __init__(self, dataset, sparsity=2, savename=None):
10 |         ''' Initialize a SEM Estimator '''
11 |         self.dataset = dataset
12 |         self.sparsity = sparsity
13 |         self.savename = savename
14 | 
15 |         self.pattern = None
16 |         self.dag = None
17 |         self.penalty = None
18 |         self.params = None
19 |         self.residuals = None
20 |         self.graph_cov = None
21 |         self.true_cov = np.cov(dataset.transpose())
22 | 
23 |     def set_pattern(self, pattern):
24 |         self.pattern = pattern
25 |         self.dag = None
26 | 
27 |     def search(self, verbose=False, cache_interval=1):
28 |         ''' Run an FGES search '''
29 |         score = SEMBicScore(self.sparsity, dataset=self.dataset, cache_interval=cache_interval)
30 |         self._fges = FGES(list(range(self.dataset.shape[1])), score, save_name=self.savename, verbose=verbose)
31 |         self._fges.search()
32 |         self.set_pattern(self._fges.graph)
33 | 
34 |     def get_dag(self):
35 |         if self.dag is None:
36 |             if self.pattern is None:
37 |                 self.search()
38 |             self.dag, self.penalty = dagFromPatternWithColliders(self.pattern)
39 |         return self.dag
40 | 
41 |     def estimate(self):
42 |         ''' Estimate edge weights '''
43 |         self.get_dag()
44 | 
45 |         self.params, self.residuals = estimate_parameters(self.dag, self.dataset)
46 |         self.graph_cov = get_covariance_matrix(self.params, self.residuals)
47 | 


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/__init__.py:
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https://raw.githubusercontent.com/eberharf/fges-py/961188a48b8689ae451861a7232262adffb46d45/__init__.py


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/data/collider_1.txt:
--------------------------------------------------------------------------------
   1 | X1	X2	X3
   2 | 1.7869	0.7324	-1.3530
   3 | 0.2002	-0.2018	0.9317
   4 | 1.7231	-2.9502	-1.7968
   5 | -1.4848	-2.7838	6.9764
   6 | 0.4706	-1.9414	1.7225
   7 | 1.1321	1.0168	-4.0000
   8 | 1.0335	1.7365	-0.3499
   9 | 1.3195	-0.2100	-1.0427
  10 | 0.8520	-1.9769	-1.0067
  11 | 0.0231	0.7298	-1.7389
  12 | 0.7401	-0.8008	3.3581
  13 | -2.0537	1.6676	4.0060
  14 | -0.9154	-1.2341	2.2162
  15 | -1.6451	-0.4509	2.0177
  16 | 0.3636	0.0461	-1.6078
  17 | 0.2437	-2.5463	0.7920
  18 | -0.1690	-3.1754	3.0947
  19 | 1.5954	0.0517	-4.0841
  20 | 0.0703	2.4978	-1.1081
  21 | 0.2150	1.8194	-2.1761
  22 | 1.1456	-1.0914	-1.4977
  23 | -0.2050	-0.4743	0.1768
  24 | -0.3693	-1.8408	2.7590
  25 | -1.6631	-1.6655	3.3695
  26 | 0.5112	0.0581	-2.9762
  27 | -1.0575	2.7114	0.1417
  28 | -0.3196	4.1104	-3.1743
  29 | 1.5595	0.2065	-3.5248
  30 | 0.5565	1.5530	-1.5917
  31 | -0.1730	1.6696	1.8385
  32 | -0.9016	-4.3590	0.8092
  33 | -0.0597	1.9776	-3.0717
  34 | -2.3203	0.7434	1.3621
  35 | -2.0180	-0.6351	0.3855
  36 | 0.3707	-0.0434	-1.2272
  37 | 0.1867	1.4426	0.7999
  38 | 1.9659	-1.1257	-0.8178
  39 | 0.6937	0.2871	-0.4287
  40 | 0.1094	-1.9184	-1.7470
  41 | -0.6720	0.8403	-0.4589
  42 | -2.0260	0.9793	0.2502
  43 | 0.0112	0.8090	0.3828
  44 | -0.5451	-0.9364	0.2744
  45 | -0.2377	-1.1349	-0.0804
  46 | 0.1039	0.7324	-1.1734
  47 | 2.1091	-0.3180	-2.7315
  48 | 0.9179	0.6004	-3.7155
  49 | -1.2495	0.4416	-1.4304
  50 | 1.2848	-1.9496	-0.4651
  51 | 0.8130	-1.0275	1.2244
  52 | 0.5241	1.0444	-5.1213
  53 | 0.7677	-2.0094	1.2068
  54 | -0.6001	1.4905	0.8852
  55 | 0.0494	-0.8477	-0.9638
  56 | -0.5612	4.1986	0.9903
  57 | 0.4128	-0.9873	0.2324
  58 | -0.4003	-1.9122	1.9089
  59 | 0.1913	1.7060	-0.6234
  60 | -0.8396	0.3556	2.8150
  61 | -0.8113	-0.7999	3.7927
  62 | 0.2494	-1.7425	1.7554
  63 | -0.7097	-1.4981	2.6692
  64 | 1.7416	0.3273	-0.3035
  65 | 0.0171	-0.0577	0.5227
  66 | -0.3970	1.0340	1.6731
  67 | 0.7704	0.3947	-0.9166
  68 | 0.0089	-1.8546	-0.6948
  69 | -0.6254	-2.1146	3.0955
  70 | 0.0562	1.2452	1.2660
  71 | -0.6090	-4.0589	2.0583
  72 | -0.2539	-1.1119	0.8132
  73 | -0.8492	-0.2565	1.1412
  74 | -2.4110	-2.0078	5.0902
  75 | 1.2268	3.0729	-4.1854
  76 | 0.4469	-1.5657	0.2821
  77 | 0.8737	1.4921	-2.9592
  78 | -0.5416	2.2367	0.7982
  79 | 0.3844	0.6844	0.2547
  80 | -0.4471	1.0137	-0.0131
  81 | 1.2902	-0.8576	-1.2759
  82 | -0.8763	0.3283	0.3094
  83 | 0.6502	1.7117	-1.8099
  84 | -1.1329	2.3970	-1.0835
  85 | -1.4376	0.0565	3.2165
  86 | -0.0448	-1.8356	0.5852
  87 | 0.8885	1.7652	-1.2521
  88 | 1.2195	0.5618	-3.8167
  89 | -1.1410	-2.0937	2.5047
  90 | -0.7690	0.3086	-0.1310
  91 | 0.9377	0.7832	-5.6508
  92 | 0.3557	2.0159	-1.6169
  93 | 1.3387	-2.8972	3.8145
  94 | -0.2658	-1.3369	-0.5513
  95 | 1.4862	0.4709	-3.2630
  96 | -0.1584	0.8209	-0.8450
  97 | 1.8754	-1.3959	-1.5557
  98 | -1.1411	-1.6410	2.6862
  99 | 0.4618	-2.9149	0.4402
 100 | -0.1771	2.0952	-1.1855
 101 | -0.6951	2.3902	-2.8638
 102 | 0.4207	-0.5683	0.8444
 103 | -1.0481	-1.5666	3.1244
 104 | -0.6390	0.9374	-2.6336
 105 | -0.1162	-1.8180	1.0340
 106 | 0.4252	1.7579	-5.3201
 107 | -0.0659	1.4474	-1.5221
 108 | 1.5783	-0.6044	-1.8706
 109 | 0.4085	-2.2673	1.5970
 110 | -1.0080	-1.6561	4.6537
 111 | -1.5243	0.4395	3.3762
 112 | -1.0513	0.9479	1.1395
 113 | 1.2884	0.4872	-5.0845
 114 | -1.7691	-2.7462	7.0158
 115 | -0.1646	0.1660	-1.8695
 116 | -0.5608	1.5979	-0.9791
 117 | 0.0833	1.3112	2.3391
 118 | 0.9282	2.9746	-2.7005
 119 | -0.8619	-1.8532	2.0282
 120 | 0.2194	-0.6242	1.9738
 121 | -0.7177	-0.2136	4.1886
 122 | 0.9801	-0.2637	-2.7088
 123 | 0.5917	-3.7915	-0.2654
 124 | -0.8467	1.9818	0.0430
 125 | -0.1049	-0.3922	1.1507
 126 | -0.3125	1.0905	-0.4396
 127 | 0.4858	-2.4832	1.6491
 128 | 1.3427	2.9294	-3.6810
 129 | -0.4561	2.4764	-0.4867
 130 | 0.1062	0.6147	0.2877
 131 | 0.3248	-1.2016	-3.0802
 132 | -1.3053	-0.4456	2.6331
 133 | -0.2907	-2.6172	4.0340
 134 | 1.5716	0.8792	-4.3413
 135 | 0.9572	1.7511	-3.3209
 136 | -0.7328	0.1276	-1.2009
 137 | 0.1071	0.6390	-0.6346
 138 | 0.8121	1.4646	0.8150
 139 | -1.2583	-2.2225	4.2728
 140 | -1.0548	-0.4006	0.0034
 141 | 0.5080	-1.7327	-0.6728
 142 | -0.9592	2.9405	0.2514
 143 | -1.0381	1.6122	0.1085
 144 | 0.3157	-2.5547	2.5072
 145 | 1.2096	-2.4331	1.3065
 146 | 0.0464	1.8003	-4.7052
 147 | -0.3487	-0.9287	-0.0025
 148 | 0.1806	0.2905	-0.7372
 149 | 0.1073	0.1160	-0.4185
 150 | -1.8923	0.8333	3.8903
 151 | -0.1192	1.6664	-0.7852
 152 | -1.5308	1.4819	5.2034
 153 | 0.5341	-2.3791	-0.6181
 154 | 0.7881	0.0017	-1.9870
 155 | -0.6032	1.3141	-1.8618
 156 | -2.0672	1.3850	0.8187
 157 | 0.1798	-0.2190	-3.2475
 158 | -1.3655	0.0234	5.6586
 159 | 1.0018	-0.2115	0.9231
 160 | 1.7195	-1.4766	-1.5319
 161 | 1.2638	-3.1002	1.2036
 162 | 0.9321	1.1860	-2.6442
 163 | 1.2227	-2.3994	0.5310
 164 | -0.2515	-5.3342	1.9025
 165 | 1.0665	-0.7613	-0.1345
 166 | -0.0583	-1.5093	0.4274
 167 | 0.8051	-0.4880	0.7087
 168 | 0.0231	-1.4349	2.4960
 169 | -0.9150	-1.9873	1.7107
 170 | -0.4536	0.8591	-0.2222
 171 | 0.1395	0.4868	1.1484
 172 | -1.2535	-1.0900	0.5993
 173 | 0.0594	-0.6554	-0.2438
 174 | -1.5875	2.7220	-0.1970
 175 | 0.2899	-0.1024	-1.8767
 176 | -0.4134	1.4748	0.2624
 177 | -0.7932	-0.8163	5.0096
 178 | -0.4748	1.2958	-0.2950
 179 | 0.8918	1.1687	-2.7910
 180 | 1.1756	0.6599	-0.4933
 181 | -1.5564	-0.4579	-0.9636
 182 | -0.0554	1.5534	2.1558
 183 | 0.5922	2.4285	-0.4728
 184 | 1.5552	-0.6070	-2.5137
 185 | 0.4447	-3.4539	-1.9230
 186 | 0.2578	2.9765	-0.6720
 187 | -1.1542	1.1036	2.9265
 188 | 1.6134	-0.2445	-1.5788
 189 | -0.4735	-1.8173	4.8565
 190 | -0.6493	-0.8774	1.6265
 191 | 1.1198	-2.2061	1.3041
 192 | 0.4390	-0.6128	0.4360
 193 | 0.6428	0.1244	-1.8335
 194 | -0.2877	-0.6256	-0.5758
 195 | -0.0332	-0.7172	1.9901
 196 | 1.4647	-0.1540	-1.7222
 197 | -1.5485	0.1268	1.2300
 198 | 0.1722	-0.8336	-0.4094
 199 | 0.3725	1.0658	-0.5911
 200 | -0.5635	1.6244	-0.0049
 201 | 0.8429	-2.3537	1.3145
 202 | -0.6351	4.8859	-2.9705
 203 | -0.1606	-0.4731	-1.8537
 204 | -1.1716	0.8000	2.3647
 205 | 1.0954	-2.0969	0.6080
 206 | -0.7566	2.7822	0.2100
 207 | 1.6547	-1.5476	-4.1702
 208 | 0.2338	-1.3415	3.4062
 209 | 0.2400	0.5223	0.8405
 210 | 0.4120	2.4207	-0.3113
 211 | -0.9919	-0.0903	2.2016
 212 | 0.6102	1.6538	-1.2869
 213 | -0.4561	0.5274	-1.0341
 214 | -2.6669	-1.7821	5.1306
 215 | -1.8143	-1.0073	2.6571
 216 | 0.9375	0.1752	-0.9418
 217 | -0.6463	1.6371	-0.3831
 218 | 1.0973	1.7363	-2.0831
 219 | -1.9110	-0.0486	4.2968
 220 | 1.1857	-0.9300	-4.1763
 221 | 1.4180	1.7297	-1.4599
 222 | -1.1575	1.6216	-0.8415
 223 | 1.4692	-0.2405	-3.8994
 224 | 1.6632	0.8512	-4.2538
 225 | -0.4709	0.4166	0.1549
 226 | 0.4590	1.2725	-1.9841
 227 | 1.7829	-0.3209	-0.0152
 228 | -3.1483	-2.7843	4.7948
 229 | 0.3914	-2.7283	-0.6944
 230 | -1.6485	-0.5400	4.9442
 231 | 1.1054	1.0559	-1.5166
 232 | 0.7875	-1.6138	0.8181
 233 | 1.2075	0.5971	-3.3946
 234 | 0.0481	-1.0770	3.2600
 235 | -0.3120	-2.5160	0.1285
 236 | 1.1049	1.2375	-4.1662
 237 | -2.3846	-2.2740	5.3708
 238 | 1.2088	1.8491	-1.8488
 239 | -0.4573	0.8092	-0.6449
 240 | -1.8452	0.8789	1.4066
 241 | -0.0849	-1.0167	-0.4697
 242 | -0.7194	-0.3555	-1.6535
 243 | -0.7408	-0.2844	1.4166
 244 | -0.8514	2.2618	1.3513
 245 | -1.2948	0.7566	1.6170
 246 | 0.2009	0.7139	-1.1601
 247 | -1.1279	0.9647	2.9146
 248 | -0.0719	0.5783	1.6962
 249 | 0.5571	2.9849	-4.8461
 250 | 0.1562	-2.0022	-2.1049
 251 | -0.0146	0.1885	-0.7663
 252 | 0.3506	1.9329	-3.3834
 253 | 0.4855	-1.1695	2.2794
 254 | 1.0628	0.8436	-1.1688
 255 | -0.5770	-0.9973	3.1523
 256 | 0.8991	1.1788	-1.6000
 257 | -0.7910	-1.2222	2.1015
 258 | -0.2998	0.4506	-3.3165
 259 | -1.6281	1.6956	-0.7569
 260 | 0.6715	0.6107	-2.8276
 261 | -2.2684	-0.9542	3.3964
 262 | -1.1286	0.9167	-0.5281
 263 | -1.7539	-1.9550	6.4621
 264 | -0.8511	-2.0431	4.4231
 265 | -0.8910	-2.2755	1.0011
 266 | -0.3430	-0.8275	2.2324
 267 | 1.2703	-1.4539	-1.0729
 268 | 0.6159	-0.0833	1.8975
 269 | 1.0449	2.4196	-2.9273
 270 | 1.0669	0.3589	-3.8964
 271 | 0.5818	0.3147	0.1133
 272 | -1.6035	-1.2709	3.4055
 273 | 0.4309	2.8284	-0.8090
 274 | 2.6141	0.3865	-9.2050
 275 | -0.6463	1.9626	-0.7736
 276 | -1.4384	-1.9595	-0.6811
 277 | 1.5436	-1.1574	-3.0688
 278 | 1.8669	1.4194	-3.1750
 279 | 1.1345	-0.6882	0.2532
 280 | 0.0854	-2.6606	1.1112
 281 | -0.1720	-2.3260	0.2972
 282 | -0.3926	0.7879	0.3247
 283 | 0.8083	-3.2362	1.5536
 284 | -0.1682	2.4801	2.8603
 285 | 0.4801	-0.0235	-1.2122
 286 | -1.5012	0.7613	1.5672
 287 | 0.3312	-0.6185	1.7271
 288 | -0.0401	-1.1222	1.4906
 289 | 1.6597	-0.6408	-1.1032
 290 | -0.4155	1.0243	0.3208
 291 | 0.2066	-2.6770	3.3956
 292 | -0.5702	-1.8649	6.2854
 293 | -1.4871	-0.5066	1.3696
 294 | 0.0925	0.6615	3.2616
 295 | -0.0374	5.1540	-2.0315
 296 | 0.0198	-3.1432	2.6538
 297 | 0.1480	-4.4698	3.5394
 298 | -0.4085	-0.7235	1.2393
 299 | 1.0391	-2.0578	-0.3743
 300 | 0.3165	3.1746	-2.6325
 301 | 0.3703	-1.9943	0.6294
 302 | -1.3916	-0.7983	3.8962
 303 | 0.4689	1.3203	-5.0496
 304 | 0.8284	-0.6041	-1.1944
 305 | 0.2891	1.8654	-1.4758
 306 | -0.1384	2.9615	-0.4725
 307 | 0.4141	0.5954	-3.0110
 308 | 0.1640	-1.5880	0.4547
 309 | 0.6119	-0.3221	0.3216
 310 | -0.5101	-1.5410	2.5111
 311 | -0.8468	-0.7400	1.5122
 312 | -0.4789	0.4370	-2.4775
 313 | -0.3572	0.5304	-3.2562
 314 | 0.2958	2.4149	-4.1287
 315 | -0.3468	-0.7577	0.9154
 316 | 1.0863	-1.1519	-3.8317
 317 | 0.6774	1.8903	-2.4271
 318 | 0.8669	1.4571	-0.3616
 319 | 0.6380	-1.3982	0.4040
 320 | 1.6229	3.7827	-3.7928
 321 | 0.6180	-1.0817	0.6754
 322 | 0.5975	0.0743	-1.1124
 323 | 0.9848	-1.9926	-0.2306
 324 | -0.4918	1.6793	-5.2187
 325 | 0.6661	-1.2915	1.1944
 326 | 0.9091	-0.8969	1.7042
 327 | 1.2932	-1.9601	-1.1354
 328 | -0.6403	1.1810	0.4146
 329 | -0.3454	-3.3770	-0.8429
 330 | 0.4655	-0.0792	-0.7019
 331 | 0.6916	-0.2152	0.6124
 332 | 0.1932	-3.3264	-1.7663
 333 | 0.1276	2.8836	0.2860
 334 | 1.0330	-0.0114	0.1287
 335 | 2.1294	1.1047	-3.3294
 336 | -0.4547	-0.7981	2.8040
 337 | -2.3857	1.1539	2.5673
 338 | 1.0912	1.8221	-1.4017
 339 | 0.2812	0.2672	-2.6632
 340 | 1.0693	-2.0563	0.6294
 341 | -0.8581	1.9287	0.2015
 342 | 1.9535	-0.2910	-0.7864
 343 | -0.8387	-1.5061	3.9909
 344 | 0.2096	-0.9250	1.2090
 345 | -0.0067	-0.6426	-2.1973
 346 | -0.1780	0.0720	1.4560
 347 | 1.2410	-0.7656	-0.5719
 348 | -0.2986	-0.7402	1.2599
 349 | 0.1591	-0.0210	-0.8006
 350 | -0.4653	-0.2880	3.1089
 351 | -1.3267	-1.0366	4.3198
 352 | -0.4697	3.0419	-1.6195
 353 | 0.4295	2.3728	-3.0471
 354 | -2.1790	-0.1630	4.3953
 355 | 0.7159	2.5533	-1.0698
 356 | -0.1122	-0.7493	1.4854
 357 | 0.4300	-0.8002	-0.3326
 358 | 1.5860	-0.8260	1.0649
 359 | 0.0778	-2.3349	-1.0456
 360 | -0.0402	0.2427	2.5070
 361 | -1.2811	-2.2916	5.7929
 362 | 1.1994	2.6350	-4.4608
 363 | 0.6597	-0.0881	-0.1552
 364 | -0.2025	1.8555	-1.3619
 365 | -1.3432	0.0759	-0.6736
 366 | 0.2502	1.1461	-2.9861
 367 | -2.1706	-3.7867	6.5889
 368 | 2.4333	-1.9673	-3.3208
 369 | 0.6870	-2.2446	-1.4866
 370 | 0.5404	-0.4650	-4.0648
 371 | -1.6682	1.6766	2.4133
 372 | 0.4277	1.6586	-1.3622
 373 | 1.0438	-0.0137	-0.6785
 374 | -1.1358	0.3702	3.5342
 375 | 0.8216	-1.2839	-0.2569
 376 | 0.2810	2.4699	-0.4829
 377 | -0.7446	2.0014	1.1952
 378 | 1.2329	2.0325	-2.3723
 379 | 0.1032	1.2384	1.7391
 380 | -0.2749	1.5353	1.7235
 381 | -0.0651	-2.5584	2.1093
 382 | -0.2994	-1.2258	-1.2295
 383 | -0.2105	-0.6036	0.9689
 384 | -1.2442	-2.9778	3.6765
 385 | 0.1908	-1.7405	1.1137
 386 | -2.6488	2.6077	0.5376
 387 | 1.1462	-2.2203	-0.2591
 388 | 0.1388	-0.6665	0.9629
 389 | -1.3173	-2.8530	5.8211
 390 | -0.7899	-0.2697	-0.8084
 391 | 0.5339	0.9325	-0.7124
 392 | 1.9070	1.8827	-4.3889
 393 | 0.5013	2.3157	-1.9965
 394 | 0.9845	0.0388	-1.4837
 395 | 0.4612	-0.0371	-2.6803
 396 | -0.5751	-1.2993	2.6914
 397 | -0.2021	4.3234	-1.6120
 398 | -0.8848	1.3533	-1.7043
 399 | -0.6569	0.6357	-2.1913
 400 | -1.6452	-2.1025	2.1872
 401 | 0.6464	2.0386	-2.9907
 402 | -0.4624	-2.6273	1.6440
 403 | -1.1890	0.9753	0.8833
 404 | -0.3300	0.5924	-2.1506
 405 | -1.2778	-3.1344	1.5452
 406 | 1.5365	4.1925	-4.7739
 407 | -0.2632	1.4513	-1.0609
 408 | 0.0544	0.3655	-1.3904
 409 | -0.9648	0.9959	-0.7428
 410 | -0.5898	-0.1139	-1.0399
 411 | 0.3746	0.4611	-1.3967
 412 | -0.9379	-1.5389	1.1238
 413 | -2.1790	-1.1781	4.3100
 414 | -1.6313	0.2044	0.4496
 415 | 0.1758	-0.3579	-0.7308
 416 | 1.5968	-0.4743	0.2432
 417 | -1.2300	-2.8925	4.8259
 418 | 1.2658	-3.2168	-2.8706
 419 | 0.4950	-3.0301	-1.1687
 420 | 0.7963	2.1001	-1.8573
 421 | 1.8884	0.2927	-2.0411
 422 | -0.4692	-0.9602	-0.1438
 423 | 1.2058	-1.2745	-2.7944
 424 | 1.6075	3.5572	-1.4841
 425 | -0.8645	1.8739	1.0835
 426 | -1.3855	0.9809	1.3192
 427 | 0.6242	-0.1499	-0.8700
 428 | -0.9104	3.1818	-2.4417
 429 | -0.6415	1.1610	-0.3276
 430 | 0.2158	0.4422	-1.1135
 431 | 0.7915	-1.7099	0.1015
 432 | 0.5905	2.6152	0.1373
 433 | -0.0253	0.2464	-2.3093
 434 | -0.1664	1.7852	-1.9109
 435 | 0.8606	0.6717	-1.3015
 436 | 0.8204	-1.4269	2.2200
 437 | -1.1497	1.5552	1.8907
 438 | -0.3445	0.0489	3.9985
 439 | 0.4223	0.5194	1.8082
 440 | 0.1046	0.4591	0.8633
 441 | -0.2287	-0.9487	-0.9906
 442 | -0.1950	2.7155	-3.1638
 443 | 0.7087	-0.0344	-1.0680
 444 | -0.4453	0.6127	-1.2194
 445 | 0.1784	-2.0133	2.4828
 446 | -0.0183	0.1248	-0.1537
 447 | -0.6184	-1.1293	-0.6803
 448 | -0.3319	-1.9442	1.1947
 449 | 0.7692	-0.5753	2.2391
 450 | 0.2290	-0.3237	2.0731
 451 | -0.2196	0.7089	0.3223
 452 | -0.2203	-0.9883	-1.4272
 453 | -0.9488	-0.7320	1.7130
 454 | 0.4083	-0.1487	1.5533
 455 | -0.4852	3.3702	-1.9793
 456 | 1.5201	2.4664	-5.1262
 457 | -1.1208	1.2902	-2.0578
 458 | 0.9481	-2.2838	-2.4577
 459 | 0.6235	0.6463	-2.8842
 460 | -0.7729	2.6839	-0.0764
 461 | -0.2645	-0.9074	0.7823
 462 | 0.4640	-0.8680	1.8650
 463 | -1.1709	1.9996	2.7479
 464 | 1.0273	3.4896	-3.7911
 465 | 0.4416	-0.9429	-0.7547
 466 | 1.0910	-0.9689	1.5874
 467 | -0.5646	-3.4024	4.3258
 468 | -0.5387	0.2589	2.0970
 469 | -0.4505	2.0285	-4.1134
 470 | 0.1675	-1.8904	1.6573
 471 | 0.6169	1.9289	-3.1132
 472 | 0.3192	2.1870	-2.7918
 473 | -0.6641	-0.0641	-0.8257
 474 | -0.5469	2.4057	-2.7569
 475 | 0.2235	-4.1247	1.6703
 476 | -0.6467	-0.7809	-2.2825
 477 | 0.8814	0.3799	-1.4891
 478 | 0.8237	0.6553	-2.0749
 479 | -0.2850	0.3540	-1.9830
 480 | 0.7647	0.1544	-0.5801
 481 | -1.0707	-0.7453	3.4260
 482 | 0.7154	1.6495	-3.7736
 483 | 1.6398	-0.8718	-5.6711
 484 | 1.2405	-2.6132	-1.1999
 485 | 0.2836	2.2006	-3.6808
 486 | 1.0014	0.4414	-5.2846
 487 | -1.2752	0.1004	4.5937
 488 | -1.4588	-0.7642	1.6818
 489 | 0.7518	-2.3086	0.9225
 490 | -0.5522	-0.6260	1.3166
 491 | 1.9177	1.0950	-2.9098
 492 | 1.4974	2.2717	-1.6559
 493 | -0.7023	1.0229	2.7253
 494 | -0.1116	0.2732	-2.4855
 495 | 0.4669	-0.4499	-2.5797
 496 | 0.3958	-3.0181	1.9327
 497 | -0.4935	-0.3747	4.6344
 498 | 0.5913	1.6317	1.2920
 499 | -0.8185	-3.7028	5.4694
 500 | 0.8361	3.2535	-2.2691
 501 | 0.5415	-1.3667	2.6463
 502 | -0.4509	1.3289	-1.2549
 503 | 0.7739	-2.2089	-1.2263
 504 | 0.2150	-2.7797	1.9605
 505 | -0.1637	-1.1095	-2.6037
 506 | -0.8775	-0.8985	1.1150
 507 | -1.7226	0.8263	1.4060
 508 | -0.2978	0.9788	-2.1521
 509 | -0.6078	0.6851	1.4465
 510 | -1.1650	-0.4656	0.3401
 511 | 0.1487	-0.5398	-3.3908
 512 | -1.0622	0.7272	-0.2478
 513 | 0.1922	0.4832	-1.3308
 514 | 0.1079	-3.6846	1.2910
 515 | 0.3141	-1.0516	1.0399
 516 | -0.8150	-1.4273	-1.0252
 517 | -0.7152	-2.4567	3.2242
 518 | -0.6325	-0.3451	1.3740
 519 | 0.0710	-0.9154	1.0856
 520 | 0.4938	0.2255	-1.5967
 521 | -1.0549	0.3084	1.1880
 522 | 1.0308	1.6365	-1.7080
 523 | -0.0811	-1.9413	4.2238
 524 | 1.8943	-0.5163	-2.1074
 525 | 1.2982	2.2106	-2.8454
 526 | 0.6853	-1.7521	0.5694
 527 | 0.9868	3.0256	-6.3787
 528 | -0.2478	0.7401	-1.1251
 529 | -0.2467	-0.2407	3.2768
 530 | -0.5183	-3.0655	3.0077
 531 | 0.2530	-1.3720	-2.2107
 532 | 0.5794	-1.8065	3.1796
 533 | 0.6162	-1.3585	2.3748
 534 | -0.5111	0.6423	1.1155
 535 | -0.7469	2.6513	-2.0013
 536 | -0.2207	-1.9255	1.6286
 537 | 0.5455	-0.6783	-1.6092
 538 | 0.6988	-0.4853	2.3551
 539 | 0.4803	-0.3657	0.6331
 540 | 2.0743	-1.3677	-4.7342
 541 | 0.3783	-1.0920	1.4240
 542 | -0.0932	-0.0217	0.3739
 543 | 0.2728	0.7739	1.0233
 544 | -0.9578	-0.0145	1.1852
 545 | -2.4568	-0.5410	2.9504
 546 | 0.0230	-2.5967	3.8437
 547 | 0.4373	0.9590	-2.0637
 548 | 0.2506	-1.4241	-0.4418
 549 | 0.0413	-0.6673	2.1263
 550 | 0.1768	-0.1341	-0.9899
 551 | 0.8697	0.7261	-1.1168
 552 | 0.1950	-1.3376	-0.4102
 553 | -0.4583	0.1420	1.1097
 554 | 0.0155	-1.1614	2.8213
 555 | 0.5059	-1.5232	0.1309
 556 | 1.7822	-0.9151	-1.5728
 557 | 0.3096	1.5285	0.1236
 558 | 0.5556	-2.6425	1.4175
 559 | 1.8673	-0.5856	-3.3362
 560 | -0.3276	-0.6244	0.4465
 561 | 1.5438	1.6947	-1.0373
 562 | -0.1274	-0.2081	2.2012
 563 | -0.5049	-0.1579	2.8369
 564 | 0.1906	1.7033	-0.5680
 565 | -0.2628	1.5870	-0.9232
 566 | -0.3910	0.9559	-0.9153
 567 | -0.6484	1.8158	-2.1426
 568 | 0.1473	-3.5035	5.0981
 569 | 0.4438	0.3112	-3.5197
 570 | 0.6517	-0.4179	-0.2370
 571 | 1.0049	-0.0248	-0.2713
 572 | -1.1612	-0.8286	0.9597
 573 | 0.2419	-2.0804	2.5810
 574 | -2.3153	2.7316	0.9517
 575 | -0.5788	-1.0377	1.8383
 576 | -0.1556	0.7674	-1.1798
 577 | -1.3739	1.7094	1.6150
 578 | 0.9814	0.0228	-3.6819
 579 | 0.8729	0.6398	-2.6539
 580 | 0.2840	-2.3410	2.3134
 581 | 0.8667	0.4650	-4.8674
 582 | -0.9838	-1.5919	2.5063
 583 | -1.4401	-3.8133	4.8801
 584 | -0.5777	-1.5795	2.3883
 585 | 1.9790	-1.4779	-2.2336
 586 | 0.9375	2.0041	-1.4884
 587 | 0.0656	2.4027	2.8385
 588 | 0.7733	3.0587	-3.9030
 589 | 0.1741	0.9626	5.9147
 590 | 1.1150	0.7841	-1.7055
 591 | 0.9798	4.8975	-7.3795
 592 | -0.6698	3.3083	-3.2202
 593 | 0.2300	-2.1966	-0.1216
 594 | -2.6676	0.7031	5.5294
 595 | -1.2745	0.7297	-1.4866
 596 | 1.1822	3.7891	-2.1930
 597 | -0.1746	-2.8679	1.6286
 598 | 1.1952	-1.0631	-1.6999
 599 | 0.6704	1.4330	-2.1902
 600 | 1.5429	1.3379	-1.2086
 601 | -0.0351	-0.8557	0.5519
 602 | 0.6895	-2.6485	0.7767
 603 | 0.7803	-1.2256	0.3235
 604 | 0.3055	1.3072	-3.9902
 605 | -0.1756	-0.7634	1.0970
 606 | -0.7536	-2.0827	1.4243
 607 | -1.1052	2.0448	2.2416
 608 | -1.4000	0.9058	3.5352
 609 | -0.8692	-1.7300	1.1478
 610 | -1.2025	0.6942	-0.7769
 611 | -0.0365	2.3204	-1.5813
 612 | -1.8495	-2.8573	1.8544
 613 | -1.0105	-0.3134	0.9502
 614 | -0.6439	-2.4703	0.1816
 615 | 0.9972	-2.6184	-0.3202
 616 | -0.5734	0.2049	0.0031
 617 | 0.1244	-1.7542	0.8802
 618 | 0.4374	-0.1089	-2.3017
 619 | -0.4450	2.5659	-1.6431
 620 | -0.7072	-0.0062	0.2109
 621 | 0.5190	0.9093	-1.7209
 622 | 1.0734	0.5563	-1.6107
 623 | -0.2107	-0.8682	0.5814
 624 | 0.4868	-0.3298	-1.6871
 625 | -0.4298	-2.1308	2.3678
 626 | -0.0694	1.3934	-2.6284
 627 | -2.6336	-0.8871	5.4283
 628 | 1.2523	-0.2803	0.4606
 629 | 0.1284	2.7203	-1.5365
 630 | -1.8639	-0.2804	0.0393
 631 | -0.1486	2.9866	-1.9920
 632 | -0.1094	-3.4008	0.5404
 633 | 0.6211	-3.2399	0.4168
 634 | -0.4276	0.5230	0.0031
 635 | -0.9022	-0.5562	0.4336
 636 | 0.7592	1.1529	-0.1710
 637 | -0.8159	0.3365	1.8838
 638 | -0.9976	1.9248	-0.8289
 639 | -0.8504	3.3659	-1.5923
 640 | -0.6081	-1.2964	-1.1133
 641 | 0.6894	-3.8735	3.7577
 642 | 0.0044	-0.0889	0.3707
 643 | 0.2268	-2.3111	0.8408
 644 | -0.1891	-1.0543	-0.6226
 645 | 0.0845	-1.4012	-0.6607
 646 | 0.4259	-2.0616	-0.5494
 647 | 1.3966	-1.4942	-3.4130
 648 | 0.4081	0.1873	0.3694
 649 | 1.0640	2.3934	-5.1100
 650 | -0.8545	1.4081	0.6680
 651 | -0.0320	0.8642	1.4850
 652 | 0.8599	-0.8230	-0.5073
 653 | 1.2790	0.4386	-2.5647
 654 | 0.5557	-0.8829	-2.6852
 655 | 0.2331	-0.2212	1.1722
 656 | -0.4563	-1.5572	4.0192
 657 | -0.3626	0.4691	1.5748
 658 | -0.5601	-0.2652	2.0080
 659 | 0.8532	-1.2277	0.5873
 660 | 0.4932	-0.9124	-2.1526
 661 | -0.2782	0.9147	-0.9315
 662 | 2.2660	2.2636	-5.7953
 663 | -1.0375	-0.0867	1.2309
 664 | 0.0116	1.7813	-1.7751
 665 | 0.4562	-2.8420	2.1352
 666 | -1.3965	0.7735	-1.7720
 667 | 2.0985	1.0871	-4.1825
 668 | 0.0824	0.4299	-1.2516
 669 | -1.0092	2.4983	-1.6641
 670 | 1.3047	2.2322	-5.2020
 671 | 0.6167	-0.1650	-1.2714
 672 | -0.5355	-0.9141	1.1169
 673 | 0.3670	1.0032	-3.0471
 674 | -0.7900	-0.0528	1.9038
 675 | -1.8485	-0.8856	2.6529
 676 | 0.5623	-3.5773	4.5523
 677 | -0.3771	1.0861	2.2947
 678 | 1.1178	-0.7161	0.5287
 679 | 0.1910	-2.5372	0.3618
 680 | 0.3544	-2.1499	0.8273
 681 | -1.0067	-0.2087	4.6531
 682 | 1.2778	-4.0693	1.8174
 683 | 2.1474	-1.6038	0.6734
 684 | 0.8705	0.5140	-1.7869
 685 | 2.4142	1.1991	-5.9608
 686 | 1.2389	-1.1693	-2.5197
 687 | -1.8546	0.2106	3.1319
 688 | -0.8854	0.1236	-0.7367
 689 | 0.8929	0.1395	-1.6198
 690 | -0.7508	-0.2234	-0.6322
 691 | -0.0002	0.6225	0.3548
 692 | -1.3097	0.5854	2.9335
 693 | 0.0325	1.1051	-1.1795
 694 | 1.2889	-0.6834	-0.4149
 695 | -0.7575	0.2540	-0.8255
 696 | 1.2961	0.5673	-3.1792
 697 | 2.0716	0.8915	-3.4760
 698 | -0.7617	-1.6051	2.9135
 699 | -0.8960	-0.7453	1.4793
 700 | 0.5429	1.0775	-4.2415
 701 | 0.7043	-1.0076	2.4761
 702 | -0.3767	-1.1713	2.4143
 703 | -0.2667	-2.4308	3.2064
 704 | -1.6363	0.5189	1.0895
 705 | -0.3399	-3.7093	3.2907
 706 | 0.0196	-0.9340	-0.0856
 707 | -0.7335	-2.7772	3.8713
 708 | -0.4590	-2.6285	2.7894
 709 | -0.0492	0.3481	-1.2482
 710 | 1.3318	0.7238	-1.4188
 711 | 0.2145	0.4124	-1.3504
 712 | 2.0645	-1.0724	-1.5921
 713 | -0.6721	-0.9178	3.1087
 714 | 0.5456	2.0196	-2.4957
 715 | 0.5227	-1.2729	1.8078
 716 | -0.3891	-1.9340	1.8406
 717 | -0.9420	-3.0726	2.4798
 718 | -2.1882	0.1092	1.6957
 719 | 0.2972	-1.1200	3.2561
 720 | -0.3789	2.6302	0.7057
 721 | 0.4286	-2.2846	3.8287
 722 | -2.0772	0.1328	1.7194
 723 | 0.9892	2.0309	-3.6449
 724 | 0.0070	-2.9022	1.1377
 725 | 1.4908	-2.1473	-2.7900
 726 | 0.2737	0.6679	-1.2748
 727 | -0.8114	1.6084	-2.3816
 728 | 0.3064	1.2581	-0.1413
 729 | 0.2756	-4.3317	3.3299
 730 | 1.9740	-3.6888	-0.2313
 731 | 1.7097	-0.9592	-0.0399
 732 | 0.6661	-0.6771	1.1470
 733 | 0.0479	0.2881	1.8357
 734 | 1.1871	1.4205	-2.3936
 735 | 0.0801	-1.4284	-0.8818
 736 | 1.8179	1.3108	-2.8368
 737 | 0.7342	1.2448	-1.4105
 738 | -1.1004	-0.8228	1.4999
 739 | -0.6732	0.2717	3.7674
 740 | -0.1942	-0.6086	-1.2368
 741 | 0.4372	-4.3730	3.3812
 742 | 0.0910	1.4168	0.4345
 743 | 0.1469	-2.4516	2.4109
 744 | 0.3307	0.8454	0.8855
 745 | -0.2353	4.5001	-0.1819
 746 | -2.0366	-0.4386	4.0323
 747 | -0.7039	-2.6787	2.5227
 748 | 1.7392	-2.8947	-2.8208
 749 | 0.9721	1.8310	-6.1813
 750 | 0.1271	-1.3028	-0.1038
 751 | 1.6030	4.3398	-6.2278
 752 | -0.2170	-0.0743	1.1493
 753 | -0.2027	0.3025	-0.2173
 754 | 1.1804	1.5617	-5.5390
 755 | -0.6188	-0.2099	2.5412
 756 | -0.9972	1.4982	0.5328
 757 | -0.6462	2.8395	0.5079
 758 | -0.1213	1.5612	-1.8062
 759 | -0.7791	-0.5228	2.0555
 760 | 0.0876	-0.5901	-1.3081
 761 | 0.3937	1.8899	-3.1028
 762 | 2.3646	0.7403	-5.5173
 763 | 0.1992	1.4604	-3.4213
 764 | -0.8743	1.8549	-2.1294
 765 | 0.9433	-2.3873	2.8670
 766 | 0.6889	-0.1076	-0.7907
 767 | -0.5686	-1.6047	3.0658
 768 | 1.2103	-2.0370	-3.1381
 769 | 0.3702	-0.1917	0.7730
 770 | 0.8753	2.5134	-2.8666
 771 | -1.2284	-1.4720	4.7505
 772 | -1.2080	5.4442	-3.3891
 773 | 1.2385	0.6956	-1.6249
 774 | -0.6339	1.9172	-0.6977
 775 | 0.4940	2.0313	-0.9569
 776 | 0.5507	-2.9352	2.3622
 777 | -1.2344	2.2320	-0.3269
 778 | 0.3940	-0.5095	-1.3472
 779 | -0.2165	0.7620	-1.8072
 780 | -0.4519	-0.7435	4.0167
 781 | -0.2831	-2.1187	2.7310
 782 | -1.5735	-2.9911	5.8275
 783 | 0.3633	0.6216	-1.0455
 784 | 0.0882	0.4901	-0.0306
 785 | 0.4161	0.3398	-0.6149
 786 | 1.5518	-0.3676	-0.0961
 787 | 0.5984	1.1960	-0.9847
 788 | 0.1869	-1.0560	-1.4569
 789 | 0.2263	-1.6788	2.6386
 790 | -1.1469	0.7425	-0.1019
 791 | 1.6637	0.8959	-2.8419
 792 | -0.1515	1.3152	-0.9111
 793 | -1.4014	4.1367	0.3908
 794 | -0.0044	0.4976	1.7605
 795 | -1.2940	1.8854	0.7262
 796 | -0.3246	1.0976	0.4036
 797 | 0.0625	-1.0852	0.5678
 798 | -0.7272	4.8726	-2.7230
 799 | 0.4228	0.0614	0.4666
 800 | 0.0607	-3.0197	2.9111
 801 | -0.4947	-1.0641	1.9963
 802 | -1.4132	1.3150	1.0277
 803 | -0.0992	-0.0679	-0.7884
 804 | 1.1419	1.0097	-5.4861
 805 | 1.0228	0.3323	-2.3881
 806 | -0.2902	1.1148	-1.1814
 807 | -0.0430	0.3129	-0.8216
 808 | -1.1122	1.7525	3.1786
 809 | 1.2206	1.4444	-1.9224
 810 | -1.1267	0.5041	3.3534
 811 | -0.0701	-1.9973	2.5239
 812 | 0.4053	-0.9926	1.2551
 813 | -0.0375	-0.0384	-0.6804
 814 | 0.0823	0.4185	-3.8865
 815 | -0.5544	-4.0449	4.6323
 816 | -1.4217	0.8489	2.0305
 817 | 1.3316	2.9226	-5.5131
 818 | -2.1504	-4.5697	5.0449
 819 | -0.0574	2.1042	-1.5029
 820 | 0.5682	1.2154	-4.3737
 821 | -1.3171	0.2025	0.9887
 822 | 0.0851	-2.7432	3.0755
 823 | 0.4372	-1.0720	1.3697
 824 | 0.5203	1.3457	-3.2778
 825 | 0.5634	-3.1488	3.9998
 826 | -0.2095	2.9142	-1.3116
 827 | -0.9101	0.2031	0.5608
 828 | 0.6400	2.4870	-1.5830
 829 | -1.7463	-0.3120	1.3487
 830 | -2.2135	0.0323	4.5797
 831 | 0.6014	2.2321	-5.5287
 832 | -1.6896	-0.3941	3.5481
 833 | -0.9000	0.3726	0.8896
 834 | 1.6125	-2.1033	-0.2021
 835 | 1.2224	1.2172	-0.7842
 836 | 0.4437	2.7468	-4.2819
 837 | 0.4386	1.9135	-2.2470
 838 | -0.5949	3.5965	-4.7408
 839 | -0.5280	1.7752	-0.7169
 840 | 0.2093	0.3187	-0.9048
 841 | -0.8402	2.1019	0.5080
 842 | 0.0979	-1.4626	0.4036
 843 | 0.6453	-0.1291	-0.8761
 844 | -1.9177	-0.9365	6.0281
 845 | 0.6057	-2.0078	1.4632
 846 | 0.3993	2.8601	-2.9472
 847 | -0.0491	0.8524	1.9755
 848 | -0.1295	0.8009	2.4826
 849 | -1.1988	2.1601	-0.4097
 850 | 0.5628	0.0442	-2.4073
 851 | 0.1473	1.0974	-0.1966
 852 | 0.0374	1.5049	0.2982
 853 | 0.0159	0.6225	0.6155
 854 | -0.4851	0.5514	0.6441
 855 | 0.7190	-1.2295	-3.7323
 856 | 1.7101	1.8781	-3.7144
 857 | 0.1029	0.5478	0.6940
 858 | -0.5656	0.5632	-2.5533
 859 | -0.3323	0.1008	2.1883
 860 | -0.2746	1.8912	-0.0072
 861 | -2.9762	-3.0520	5.6880
 862 | 0.9627	1.0573	-1.7740
 863 | 0.4069	-0.4520	-3.1970
 864 | 0.9892	-1.1602	-0.3896
 865 | 0.2400	1.4736	-0.5366
 866 | -0.0979	2.3615	-2.9847
 867 | -1.2266	0.2490	2.6118
 868 | 1.2510	1.7774	-3.2399
 869 | -1.7885	1.5466	-1.5805
 870 | 0.7856	0.6086	-1.1472
 871 | 1.0047	0.6843	-4.6216
 872 | -0.8928	1.8376	-0.1201
 873 | 1.9743	1.4277	-4.0594
 874 | -1.1952	0.9800	-0.5345
 875 | 1.1390	-1.4877	-0.4946
 876 | -0.0966	1.1006	-0.8143
 877 | -2.6498	1.2714	0.7561
 878 | -1.3700	1.4884	-2.6752
 879 | -0.7631	0.1441	0.9364
 880 | -0.4335	-1.7927	3.5638
 881 | -0.3094	0.9619	-2.6675
 882 | -1.3941	-0.5125	-0.2600
 883 | -0.2657	0.8864	-0.3590
 884 | -0.0028	-0.5612	1.9069
 885 | 0.5031	-2.7019	3.7896
 886 | 1.2540	3.1087	-3.8960
 887 | 0.9532	1.9237	-4.3669
 888 | 0.9420	-1.2149	-2.8146
 889 | 1.0953	-1.0769	-1.0557
 890 | 1.0606	-0.9607	-1.8553
 891 | -0.6265	-2.4699	2.9370
 892 | -0.6039	1.0831	-2.8658
 893 | -0.0425	1.1346	-1.3895
 894 | -0.1429	0.1193	-0.7477
 895 | 0.5607	2.0749	-2.4954
 896 | -0.1667	1.5844	0.0921
 897 | 1.7477	3.3760	-4.9921
 898 | 0.4839	3.9617	-3.0886
 899 | 0.3367	-4.4135	2.4641
 900 | -0.3804	0.3135	-0.4265
 901 | 2.4944	0.6615	-3.5929
 902 | -1.8550	1.1602	0.9342
 903 | 2.0130	-1.1951	-1.8099
 904 | 0.4184	-1.2231	-0.3721
 905 | -0.5746	-3.3731	3.8456
 906 | -0.0271	1.9273	-2.5786
 907 | 0.8176	1.8801	-0.8791
 908 | 0.6807	1.1615	-0.6308
 909 | 1.2910	1.5704	-3.5147
 910 | -1.0358	0.0871	1.6014
 911 | 0.7847	2.4066	-3.9717
 912 | 0.9113	0.2255	-2.5213
 913 | 0.0092	-0.2948	1.2037
 914 | 1.9317	2.1325	-3.3859
 915 | 1.1510	1.2650	-3.0147
 916 | -0.4157	-0.9435	2.4275
 917 | 0.0129	0.8263	-0.4513
 918 | 1.7694	0.5046	-1.1824
 919 | -0.8860	-1.2893	-0.9090
 920 | -0.6377	1.4092	-1.3271
 921 | 0.5750	-2.2653	-1.4286
 922 | -0.2121	-1.2086	1.2617
 923 | 0.1116	-0.1609	1.6958
 924 | 0.5416	-0.8037	-1.6919
 925 | 1.2403	-2.3281	0.2951
 926 | -0.4888	1.9170	-1.5866
 927 | 1.6430	0.4885	-5.8927
 928 | 1.7829	1.6126	-2.9355
 929 | 1.4157	1.3246	-5.0875
 930 | -0.0829	-2.6627	4.8165
 931 | 0.4704	-2.2992	2.2848
 932 | -0.0168	2.2702	-1.2156
 933 | -1.0543	-0.6726	-0.3825
 934 | -0.2448	2.8178	-1.7861
 935 | 0.4240	3.3976	-2.1006
 936 | -0.1584	2.2219	0.5450
 937 | 0.0894	-0.1042	-0.6320
 938 | 0.0710	-0.3543	-0.5467
 939 | 0.3269	-1.0989	2.2095
 940 | 0.6743	0.7929	-3.5553
 941 | -0.3011	1.0315	4.5546
 942 | -0.7979	0.7749	-2.2280
 943 | 1.5191	3.4595	-8.6227
 944 | -0.3539	-2.8257	0.6184
 945 | 1.1973	-2.9076	0.6748
 946 | 2.0218	-2.3325	-1.9215
 947 | 0.9058	0.6329	3.0691
 948 | 0.6626	0.5451	-0.3513
 949 | -0.3561	0.4800	0.2932
 950 | -0.7267	-0.8662	2.6447
 951 | -0.8789	-1.0501	1.6011
 952 | -0.0146	0.6406	-0.7848
 953 | 0.9903	2.5993	-4.8354
 954 | -0.9992	-2.3783	0.6957
 955 | 0.7439	-2.1535	1.1709
 956 | 0.3018	-0.1487	4.6337
 957 | -1.1614	-0.4968	1.7557
 958 | -0.5196	-1.2995	2.9900
 959 | 0.6166	-1.8249	-0.3863
 960 | -1.6423	-0.3793	0.0888
 961 | 1.0838	1.7636	-2.1946
 962 | -0.4569	-0.9040	0.9600
 963 | 0.2669	-3.8707	1.1191
 964 | 0.9581	3.0635	-2.6265
 965 | -0.8461	-0.6187	1.0651
 966 | 0.6063	-1.6857	-0.0578
 967 | -0.0815	1.6645	1.0141
 968 | -0.3193	-0.3253	-0.2656
 969 | 1.6110	2.1848	-3.4172
 970 | -0.6893	2.2022	-2.1822
 971 | 0.9476	-1.5016	-0.7381
 972 | -0.8235	-1.0771	3.8707
 973 | 0.7756	1.4879	-1.6864
 974 | -0.4442	-0.5738	0.9628
 975 | 0.1257	-0.1919	-0.6149
 976 | -1.6379	0.3830	4.8343
 977 | 0.8200	-0.9686	-2.4793
 978 | -1.0920	-0.6631	-0.3192
 979 | -0.4553	-0.4915	-1.1676
 980 | -0.6804	1.9010	0.6671
 981 | -2.2468	2.1263	2.4203
 982 | 0.4163	-0.8516	1.6201
 983 | -0.5521	-3.0539	3.4095
 984 | 0.3359	-2.1168	0.3021
 985 | -2.0478	1.9609	3.6934
 986 | -0.4933	-2.4007	1.9448
 987 | 0.3634	-1.4716	1.4597
 988 | 1.6697	2.8742	-2.2917
 989 | -1.1754	-0.7956	0.4925
 990 | -1.8815	0.8858	2.4103
 991 | 1.2236	0.2958	-0.8644
 992 | -0.1010	-2.6666	-0.6651
 993 | -0.4549	-2.0165	1.0625
 994 | 0.7573	-0.1949	-0.6306
 995 | 0.6815	1.8460	-2.2371
 996 | 2.3622	1.4018	-5.8440
 997 | 0.4919	0.8900	-0.7791
 998 | -2.5604	0.5772	1.1980
 999 | 0.4326	-1.1828	1.1779
1000 | 0.6565	-0.4224	1.2812
1001 | 0.1774	-2.9787	1.3059
1002 | 


--------------------------------------------------------------------------------
/data/collider_5.txt:
--------------------------------------------------------------------------------
  1 | X1	X2	X3	X4
  2 | 0.3411	2.4042	-2.7309	-0.7160
  3 | 0.7290	1.2013	-2.9588	-0.5622
  4 | 1.6729	0.3517	-1.9430	-3.0258
  5 | 0.3096	-1.4417	0.1555	-0.5141
  6 | -1.8845	-0.3324	1.5542	2.7901
  7 | -0.5233	-2.2836	2.0699	1.7801
  8 | 1.6323	-0.0473	-1.5845	-3.1928
  9 | 2.6754	0.8077	-2.0033	-4.8654
 10 | 0.6304	-0.0401	-1.5636	-4.4082
 11 | -0.0549	0.7124	-0.1761	0.5413
 12 | -0.4266	0.0246	-0.6581	-0.7382
 13 | 0.8557	1.4512	-2.4940	-1.4347
 14 | -0.0171	-0.4352	0.6203	-1.6252
 15 | -0.9959	0.9290	-0.3329	1.7076
 16 | -2.0722	-0.8817	2.2211	2.9998
 17 | -1.7186	1.7975	-0.1282	2.3517
 18 | -0.4030	-1.1166	0.5673	-0.7350
 19 | -0.6124	-1.0493	1.1091	0.3239
 20 | -0.6702	-1.9890	2.0309	4.8827
 21 | 3.7374	0.6900	-4.5156	-5.4249
 22 | 0.7593	-1.4717	2.1702	-2.6993
 23 | 0.5292	0.0101	-2.1892	-0.3359
 24 | 0.3970	-1.8412	0.8914	-0.4916
 25 | -0.9299	-0.8737	1.3707	0.3822
 26 | 1.1166	-0.9661	0.1240	-3.4790
 27 | -1.2555	0.4469	0.3784	0.2211
 28 | 1.4424	-0.3054	-1.0296	-3.4740
 29 | -1.1488	0.7690	0.2673	2.7539
 30 | 0.9678	1.0506	-0.6658	-1.1761
 31 | 0.3514	2.7608	-2.8240	0.0708
 32 | -1.3804	-0.2967	2.1990	1.2934
 33 | -1.0809	-0.9877	2.5134	2.4754
 34 | 1.4608	0.2750	-0.4643	-2.3781
 35 | -0.6966	-0.4893	1.9401	3.6462
 36 | -0.7881	-1.9041	3.4398	-1.0253
 37 | -2.1722	-0.1923	1.5797	2.2609
 38 | 1.8174	1.8073	-3.3697	-2.7750
 39 | -0.7475	-1.5030	2.7176	1.3412
 40 | 1.0173	-1.2902	-0.0663	-0.0069
 41 | -0.1615	1.9294	-4.0193	1.8541
 42 | -0.5748	-0.3202	1.3200	2.4133
 43 | -1.1685	-0.0768	2.5194	1.9970
 44 | -0.2126	-1.2685	2.2046	1.3999
 45 | -1.0464	0.3672	1.6161	0.1425
 46 | -2.3267	0.8607	1.0541	2.4690
 47 | -1.9539	0.9987	0.1051	1.2321
 48 | 3.6461	0.1582	-3.1530	-6.3531
 49 | -0.9065	0.4115	1.9341	0.8339
 50 | 2.1928	1.3224	-2.7755	-3.1842
 51 | 0.2386	1.6939	0.2476	0.1287
 52 | -0.6242	2.1098	-1.3863	1.0942
 53 | 0.5044	1.0454	-0.6192	-2.8114
 54 | 0.9365	-1.7828	-1.0134	-1.6601
 55 | -0.9296	-1.1985	-1.5116	2.4471
 56 | -1.0964	0.8336	1.5992	0.9111
 57 | -1.7580	0.8832	0.0317	2.3224
 58 | -0.6320	-1.7704	2.3145	-0.5251
 59 | 1.7320	0.5989	-2.1342	-0.2518
 60 | -2.7803	0.2246	2.8288	4.9774
 61 | 0.5977	0.3936	0.1141	-5.1668
 62 | 1.6267	0.5391	-2.6582	-0.9387
 63 | 0.2257	0.5744	-2.0453	-0.2799
 64 | -0.1244	-0.3079	0.6217	-2.8477
 65 | 0.4178	0.5938	-1.3026	0.6736
 66 | -2.4240	-0.1915	1.9394	1.6595
 67 | -0.3200	-0.5290	1.3608	0.1053
 68 | -0.2711	-0.2285	0.7589	2.3351
 69 | -2.0769	-2.0457	4.3621	-0.3176
 70 | 0.2448	0.1369	0.3841	-0.1960
 71 | 1.9563	1.9001	-1.7987	-4.6786
 72 | 0.5279	1.0052	-0.4629	-2.2633
 73 | -0.2974	-0.7097	2.4803	0.8162
 74 | -1.0234	1.2175	2.1856	-0.5048
 75 | 1.0905	-0.8068	0.0980	-2.3410
 76 | -0.0855	0.5519	-0.5142	0.8899
 77 | 2.4602	0.5366	-4.5404	-6.5170
 78 | 1.6912	-0.3711	-0.9148	-2.1933
 79 | -0.1867	0.2273	2.0432	-0.3138
 80 | 2.9617	1.0126	-1.7753	-6.2433
 81 | -1.7394	-0.0998	1.1763	1.8108
 82 | -1.6196	1.5710	0.6016	2.0248
 83 | 0.1636	-0.9657	0.2297	0.9335
 84 | -0.3530	-0.2258	0.5525	1.2017
 85 | 0.7028	2.3152	-2.2911	-3.7442
 86 | -0.3768	-0.3927	3.6198	1.3408
 87 | -0.3686	-0.4532	-1.1912	1.5279
 88 | -0.5629	-0.0435	2.6143	1.7727
 89 | 0.7314	-1.3178	-0.6782	0.0067
 90 | 1.1929	1.1898	-4.4034	-1.6804
 91 | -0.8873	-0.3301	1.5133	0.9344
 92 | -1.5190	-1.1777	2.9939	1.1257
 93 | 1.6624	-2.1171	0.8085	-1.7456
 94 | 0.4110	0.2126	1.3269	-0.4622
 95 | 1.0319	0.9566	-3.6901	-2.2194
 96 | -1.0043	1.8714	-0.2636	0.9089
 97 | 2.0059	0.6133	-0.7630	-3.2911
 98 | 0.4872	-0.3316	2.7334	-2.1955
 99 | 0.5883	1.7801	-1.9742	0.1135
100 | -1.4580	-0.0376	0.4683	1.7607
101 | -0.1916	-0.4198	1.8790	-0.8556
102 | -1.4837	1.8155	2.1336	2.8061
103 | -0.5337	0.9839	1.1293	-0.5282
104 | 1.6407	0.3349	-0.0267	-1.5050
105 | 0.6238	-1.8517	0.6203	0.1958
106 | -2.5333	2.1405	0.7495	3.0502
107 | -0.5257	-0.9685	1.8178	-0.0828
108 | 0.6999	-0.8113	-0.4740	1.2444
109 | 1.0557	1.1411	-1.4599	-4.1805
110 | -0.3433	-2.9020	4.7781	0.2236
111 | 0.5217	0.1654	-1.4771	1.6743
112 | 2.0238	-1.8289	-1.7135	-0.9162
113 | -2.2240	0.4801	1.2021	5.0573
114 | 1.1461	-0.4141	-1.0632	-1.2819
115 | 1.8664	0.4090	-2.7536	-0.7755
116 | -1.9743	0.7479	0.9804	3.3617
117 | -2.1489	0.9580	1.6971	2.4538
118 | 1.4355	-1.4944	1.4733	-1.1728
119 | 0.1738	-0.5645	-0.7992	-2.1144
120 | 0.0901	0.6463	-1.3093	0.6227
121 | -0.7281	0.1559	0.6058	1.4292
122 | 0.8046	-0.9338	-0.6133	-0.3955
123 | 2.3956	-1.2237	-1.3792	-2.8080
124 | 2.8278	0.6949	-5.1084	-3.0941
125 | 0.0938	-1.8694	1.0200	0.3269
126 | 1.8513	1.6712	-3.4822	-3.7860
127 | 0.1088	-0.2897	-0.4138	0.7781
128 | -0.1073	-0.0083	-0.8459	-0.0132
129 | 0.6670	-0.0755	-0.1446	0.1180
130 | 0.2086	1.2179	-0.3843	0.6610
131 | -0.9523	-0.0960	0.7736	2.4745
132 | -1.5776	-1.9706	2.1612	1.1536
133 | -0.9036	-0.9843	0.5070	2.6768
134 | 0.2362	-2.5126	4.0380	-0.9374
135 | -1.1661	0.0179	2.5292	0.6581
136 | 0.0743	1.3307	-0.7469	0.7069
137 | 0.7710	-0.3934	-0.8306	-1.6090
138 | -0.3029	-1.2925	-0.2811	1.4974
139 | 1.5642	0.5851	0.0480	-1.9128
140 | 0.2376	-1.1342	-0.7584	-1.9677
141 | 0.2356	0.3576	-1.6387	-0.3856
142 | 2.0256	2.3676	-4.0014	-1.6983
143 | 1.0638	-0.2230	1.4519	-1.7759
144 | 1.5696	-0.0213	-1.5929	-2.6401
145 | 1.5092	1.1245	-3.5357	-1.8973
146 | -0.8473	-0.5412	1.6849	2.5692
147 | 0.9661	-0.4296	-1.3711	-0.1204
148 | -1.0328	-0.0851	1.0845	2.7709
149 | -2.8313	1.8259	1.2051	5.5837
150 | -0.1831	-0.4562	1.5318	1.3124
151 | -1.0032	-2.4647	2.3802	4.2383
152 | -0.8411	-0.1665	-0.4396	1.4439
153 | 0.9924	0.3271	0.3042	-4.4135
154 | -2.0213	1.1423	1.0500	3.7076
155 | -0.0989	-0.4600	-0.0287	0.3529
156 | -1.4535	1.9188	-2.4567	1.3240
157 | -1.1204	-0.0499	0.4591	2.1006
158 | -0.1537	0.4462	-2.9080	0.3483
159 | 0.3714	-2.2912	0.9333	0.4463
160 | 1.3425	-2.6380	1.4324	0.4234
161 | 0.3575	0.1225	-0.1850	-1.7146
162 | 0.7206	1.8968	-1.3037	-1.3447
163 | 0.3865	-0.4463	1.6234	1.2099
164 | -1.0819	-0.4165	3.1390	1.7719
165 | -0.5861	0.7295	0.6409	-0.8569
166 | -2.4558	-0.7085	3.3759	3.5320
167 | -0.1128	1.8003	-0.0109	-2.8045
168 | 0.0800	1.7443	-1.4632	-2.7264
169 | -0.3858	-2.4176	2.8076	2.0060
170 | -1.1604	0.0195	1.3773	4.3832
171 | -0.8627	-0.1281	-1.3214	-0.9502
172 | 0.9266	-0.4145	-1.7691	-1.7310
173 | -1.7231	2.0692	0.2517	1.8568
174 | -2.3086	-0.4578	1.6574	2.9843
175 | -0.6486	1.4905	-0.0466	0.7442
176 | 0.5969	-1.2445	2.1217	2.6697
177 | -1.5879	0.9533	-0.0671	2.9362
178 | 2.6947	-0.0451	-1.4981	-5.3526
179 | 0.7474	1.4750	-2.2410	-0.1099
180 | 1.2673	1.7982	-2.8332	-1.0984
181 | 1.0167	-0.4659	-1.4477	-0.2601
182 | 0.8263	1.3368	-2.9995	-2.5377
183 | 0.1875	0.9879	-2.1974	1.7679
184 | -0.4536	0.9661	-0.0148	0.9418
185 | -0.1567	-0.1753	0.5911	0.9759
186 | 0.2399	-0.8817	1.5942	2.3870
187 | -0.4031	-0.1583	1.1970	1.9921
188 | -0.4596	1.1261	-0.6687	2.4065
189 | 0.2656	2.3007	-1.1115	-2.5974
190 | 1.4834	0.6500	-1.2544	-2.0055
191 | 1.1315	-0.8040	-1.7315	-1.3264
192 | -0.1856	1.4554	-2.8222	-0.3525
193 | -2.7191	-0.5089	3.2685	5.0877
194 | 1.4394	-0.3624	-3.3509	-3.7952
195 | 0.3257	-0.6707	3.0956	-1.5056
196 | 0.5568	-1.7177	-1.5716	1.9414
197 | 0.2370	-0.4311	0.7414	1.1741
198 | 2.4574	2.3876	-3.6998	-5.2536
199 | 0.1170	-0.5250	-1.4726	-0.6611
200 | -2.3979	-1.3714	2.0394	1.6436
201 | 1.1338	-0.0720	-1.2774	-0.0184
202 | -1.3767	1.3230	-0.7620	-0.0242
203 | -1.1361	3.6849	-2.4034	1.0340
204 | 2.1786	1.0071	-3.3056	-1.7772
205 | -0.5343	-1.1528	0.6364	-0.6077
206 | -1.9641	-1.0584	1.1450	1.7244
207 | 0.0700	-0.5360	-0.0691	-0.9412
208 | 0.3060	-0.8591	-0.5489	2.0720
209 | 1.7935	0.4778	-1.8380	-1.4346
210 | 0.2444	-0.0766	0.3870	-2.2446
211 | 3.9763	0.5331	-3.9668	-6.1428
212 | 1.1618	0.4152	-2.2597	-3.5332
213 | -0.8673	-3.1146	4.1059	2.2282
214 | 0.9415	-0.9396	0.4644	-0.7992
215 | 1.3708	0.9963	-2.3084	-0.2695
216 | 0.8514	-1.5102	0.9227	0.0140
217 | -0.6228	2.5899	-3.2144	-0.7179
218 | -0.1800	1.3901	-0.6488	0.1858
219 | 1.2328	-0.6689	0.5970	-0.0269
220 | -1.7251	2.5931	0.4002	4.4481
221 | -0.6810	-0.1881	0.4666	2.6144
222 | -0.5730	2.1918	-0.3723	1.7391
223 | -0.8952	-2.3713	2.9462	-2.1501
224 | -0.6120	-0.7797	0.1759	-0.1179
225 | 0.2928	0.7600	0.0061	0.2248
226 | 0.4955	-0.1316	-2.7636	-0.1957
227 | 0.7662	-1.0028	-0.4409	-1.9794
228 | -0.0624	0.8034	-0.6846	-1.7019
229 | -1.4535	1.5328	0.8868	0.8422
230 | -1.9072	0.5401	0.3414	0.8110
231 | 0.5327	0.3286	0.7527	-1.7560
232 | -0.6595	4.3424	0.1220	0.3916
233 | -0.5215	-0.9043	1.0217	0.1810
234 | 0.7258	-1.8901	0.8132	-2.0313
235 | 0.5154	-1.9842	0.9533	-1.3731
236 | 0.4045	0.7327	-1.1952	0.4754
237 | -3.1797	0.8949	1.9863	3.3509
238 | 1.0740	-0.8084	0.2763	-1.1935
239 | -1.7960	-0.0187	1.7740	0.6682
240 | 0.7441	-0.9647	0.9315	-0.1062
241 | 1.8131	0.8047	-3.3330	-3.1639
242 | -1.3795	-0.0029	0.6516	0.6998
243 | 1.8520	-0.1523	-0.9945	-4.1174
244 | -0.9588	-1.6728	3.1850	3.7717
245 | 1.2578	0.7965	-0.4046	-3.6951
246 | 2.6440	-0.9892	-1.0937	-0.9358
247 | 0.7264	0.4526	-0.6746	-0.3211
248 | 0.0359	-0.7785	1.1888	1.3371
249 | 1.6521	0.4801	-2.4243	-2.4316
250 | 1.0517	1.7430	-2.5435	-4.3184
251 | 0.9402	0.1955	0.6380	-0.4503
252 | -2.1345	2.2560	1.6121	2.6252
253 | 1.2691	-0.2979	-1.8756	0.3775
254 | -0.9723	0.1519	-0.1165	1.7808
255 | -0.7636	-1.9437	2.5902	0.4629
256 | 0.8594	0.6671	-2.9903	-1.1536
257 | -1.5447	-1.7721	2.7115	2.2037
258 | -0.4058	-0.1209	-1.5289	3.3357
259 | 1.0494	2.9380	-4.7786	-3.1036
260 | 0.4633	-4.2669	3.7000	-1.7105
261 | -0.0993	0.9984	-0.4197	1.2682
262 | 0.5996	2.3227	-3.1197	-0.3862
263 | -2.5564	-0.8718	2.6513	2.4441
264 | 0.2676	0.0187	-3.6161	0.0910
265 | 1.7030	0.9577	-2.9121	-1.5440
266 | 0.0844	1.7642	-1.3171	-1.3356
267 | -0.4432	-0.2331	1.6445	2.5670
268 | 0.1173	-2.0729	1.5214	0.3463
269 | -2.3268	1.6441	0.9693	1.4807
270 | 0.2442	0.5924	-0.3331	1.0727
271 | 0.3513	-1.6275	0.9091	-0.9964
272 | -1.4813	0.1498	0.0581	2.5020
273 | 2.3947	-0.8734	-1.1419	-3.7184
274 | 1.1624	0.8379	-1.1220	-1.9408
275 | 1.8596	-1.4381	1.1288	-2.7979
276 | 1.5988	1.3996	-1.4702	-1.9811
277 | -0.5039	-0.1993	0.4877	0.4607
278 | 0.4893	2.4756	-0.7496	-1.4381
279 | 1.8916	-0.1024	-2.0057	-0.3569
280 | -0.8170	0.3554	-0.0989	0.8559
281 | -0.4637	1.6717	-1.2414	1.0868
282 | -0.9791	-1.7058	1.9911	0.8143
283 | -0.8466	1.0339	-0.8416	3.6529
284 | -0.4185	-2.7288	3.3184	1.0349
285 | -2.1830	-1.4983	0.6337	3.0467
286 | -0.7861	-1.2050	1.8298	-1.1786
287 | -0.4931	0.3930	1.0190	-1.9413
288 | 2.3745	-1.2148	-2.2374	-2.0032
289 | -0.7766	0.3539	0.7056	3.3941
290 | 0.7520	1.1411	-3.5537	-2.8989
291 | 0.4115	0.3511	-0.6407	-2.9194
292 | 1.7353	-2.2867	-0.0580	-1.7502
293 | 0.4792	1.3989	-1.5811	-0.5186
294 | 0.2012	-2.3503	2.5158	1.1857
295 | -2.5446	-0.0227	3.0542	4.0142
296 | 1.4469	-0.8216	-0.0727	0.1570
297 | -2.9472	-0.0460	3.1429	3.3880
298 | 1.0161	-0.6344	0.8642	-2.5803
299 | -1.0139	-1.4754	4.7075	1.2065
300 | -0.4244	0.7052	-1.0493	-0.2121
301 | -2.3763	-3.1230	4.5055	3.4154
302 | 


--------------------------------------------------------------------------------
/data/linear_1.txt:
--------------------------------------------------------------------------------
   1 | X1	X2	X3	X4
   2 | -1.0900	0.7020	-1.0010	0.6305
   3 | 0.9753	-0.0074	1.0761	-2.3750
   4 | -0.0716	1.1252	0.1680	-0.7399
   5 | -1.2083	1.9245	-2.0682	0.2759
   6 | -0.1174	-0.1847	1.2259	-0.2650
   7 | 2.2218	-4.8443	3.4895	-0.8565
   8 | -0.2089	1.4192	0.3197	1.5023
   9 | 0.5006	-0.2772	2.0967	-1.9816
  10 | -1.2852	0.0731	-0.8476	1.6791
  11 | 1.8722	-2.4401	4.1977	-4.2063
  12 | 0.8941	-2.6381	1.4830	-0.0194
  13 | 0.0120	0.8654	-1.3861	0.7360
  14 | -0.2562	0.4400	-1.6554	0.0011
  15 | -1.3587	1.8398	-1.8499	1.1080
  16 | 2.2535	-2.3406	2.1120	-4.1602
  17 | 1.6085	-2.0604	-0.4677	4.5905
  18 | -1.8228	0.9803	-1.6191	-0.2597
  19 | -0.5865	2.0967	-0.7598	-1.2009
  20 | 0.9383	-0.6263	-0.2915	-1.1051
  21 | -0.8576	0.6174	-1.0390	3.1661
  22 | -1.5083	1.3886	-1.2546	4.3234
  23 | -0.5386	1.0624	-0.1146	1.5156
  24 | -0.7423	1.8258	0.8727	-0.4086
  25 | 1.3512	-1.4684	0.8017	-0.8902
  26 | -1.5792	0.8155	-2.2616	1.7818
  27 | -1.8223	0.8485	-1.0058	-0.2161
  28 | 0.2293	-1.0893	1.7045	-1.6349
  29 | 0.3030	-0.8952	-1.9097	1.2845
  30 | 2.5463	-3.6556	2.8598	-3.7812
  31 | 0.4202	-0.4327	-1.1161	0.5072
  32 | 0.7027	0.7484	-0.7606	2.6566
  33 | 1.0784	-1.5652	-0.6119	0.8388
  34 | 1.6851	-0.9671	2.2597	-2.4144
  35 | -2.1494	0.5791	1.5277	-2.2873
  36 | -1.4420	-0.0181	2.2233	-3.0601
  37 | 0.9623	-2.3638	3.3956	-1.1979
  38 | -1.1958	1.5628	-2.0653	3.9522
  39 | -2.0945	2.7584	-2.4518	3.4959
  40 | 2.4230	-3.8863	2.2600	0.0676
  41 | -3.1434	3.1654	-3.6987	2.6862
  42 | 1.1528	-1.3366	1.7751	-0.9773
  43 | 0.5044	-0.5288	-0.1883	4.7662
  44 | 0.1268	0.3990	-1.8133	-3.0767
  45 | 0.7961	1.0280	-1.6378	1.7308
  46 | 0.1113	-0.5718	1.8345	-1.2475
  47 | -2.9021	1.8964	-1.6401	2.5649
  48 | 0.2253	-0.8614	-0.8772	-0.6159
  49 | 2.4881	-3.2648	0.9078	-3.6011
  50 | -2.2131	2.5043	-1.1844	1.8573
  51 | -2.5469	4.3247	-2.9273	3.6801
  52 | -0.3303	0.2663	-1.4422	1.6375
  53 | 0.1301	-1.0919	-0.1882	1.2558
  54 | 0.5932	-0.3746	0.4301	1.3789
  55 | -0.4480	0.7237	-0.1688	-3.2781
  56 | 1.1805	-1.6336	-1.1342	0.1449
  57 | -5.7348	8.9318	-4.7774	3.2962
  58 | 0.9855	-0.4985	0.3980	0.3797
  59 | 2.6338	-3.3890	1.2142	-0.9318
  60 | 1.7410	-1.0574	1.3531	-0.3637
  61 | 0.5888	0.9060	-3.1398	1.3542
  62 | -0.7004	0.8317	0.1258	1.7372
  63 | -0.8239	1.3903	-1.8308	2.5732
  64 | -2.8089	4.0356	-4.0486	4.4886
  65 | -2.6094	4.1331	-3.1082	4.2127
  66 | -3.5301	3.7922	-1.2244	-0.0760
  67 | 2.3613	-1.9740	3.3404	-2.5997
  68 | -5.2289	6.0495	-5.4062	2.8838
  69 | 2.0040	-2.1515	3.5530	-1.3269
  70 | 0.6377	-0.5926	1.3743	-2.2304
  71 | 0.2704	-2.2372	1.4017	-2.4200
  72 | 2.2817	-3.3915	2.4688	0.6209
  73 | -0.3039	1.7541	0.2298	-2.2415
  74 | -2.6792	3.8673	-2.6817	1.2021
  75 | 0.0252	1.0187	0.0540	1.8806
  76 | -1.0506	1.4432	0.2670	-1.6632
  77 | -0.9783	1.7853	-0.8810	0.0840
  78 | 2.9202	-6.2215	5.0290	-4.7955
  79 | 0.4967	0.1130	-1.4306	4.5718
  80 | -2.9547	5.0248	-3.8556	1.2752
  81 | 0.0265	0.0224	-1.6073	-0.6677
  82 | -0.7528	3.2199	-2.1427	4.6341
  83 | 0.1364	-0.3022	0.2002	-1.1353
  84 | -1.1327	1.1132	-0.1359	1.7400
  85 | -2.1907	5.6550	-4.3916	4.8390
  86 | -0.7128	-1.0623	0.6621	-0.2906
  87 | -0.3692	1.4041	-3.3047	0.1088
  88 | -2.2932	3.8821	-2.6718	1.0170
  89 | -1.8851	0.2791	-1.4475	3.7933
  90 | 1.5718	-0.9038	0.9818	-0.3332
  91 | -1.0513	0.1418	0.1523	0.8604
  92 | -0.6382	-0.6193	1.3287	-3.1650
  93 | -1.4796	2.0304	-0.0091	-1.1158
  94 | -3.2332	5.1954	-5.1936	5.6137
  95 | 1.3012	-1.0980	1.3970	-0.0947
  96 | 0.0229	0.9881	-1.1116	1.9801
  97 | 2.3690	-1.1990	0.2022	0.2596
  98 | 0.9074	-2.0274	3.9905	-4.5246
  99 | -0.6015	0.4815	0.1291	0.3774
 100 | 1.2448	-1.7587	1.4784	-2.1623
 101 | -2.1992	2.3278	-0.4120	1.4942
 102 | 1.1530	-2.2928	2.4347	-0.9512
 103 | -0.6984	1.3583	-0.7819	1.9138
 104 | -1.4287	4.0516	-1.8757	1.1006
 105 | -1.4580	4.0475	-1.9301	2.0246
 106 | -1.0540	0.6494	-2.1668	0.5312
 107 | 0.8221	-3.0685	1.6854	-0.2097
 108 | 1.6921	-0.7993	-1.4755	-1.4381
 109 | -1.9909	2.3811	-2.7287	-0.7869
 110 | 2.0726	-2.7053	1.7090	-4.0177
 111 | -2.6480	4.3123	-2.8561	-0.1372
 112 | 0.5074	-0.5903	2.2619	0.3193
 113 | 1.6545	-3.5199	0.2476	-0.4944
 114 | -1.0355	0.8410	-2.1648	-1.2698
 115 | 2.5394	-3.4784	-0.1098	0.2000
 116 | 3.5382	-6.6119	4.9756	-4.6727
 117 | 3.7158	-6.2100	4.0908	-4.3217
 118 | 0.3725	-0.3199	-1.8884	1.3470
 119 | -1.2840	0.5753	-0.0107	0.0809
 120 | -1.2358	3.2912	-1.5626	2.0321
 121 | 0.2544	-0.5628	1.6012	1.6727
 122 | 1.3222	0.3004	-0.4623	0.9082
 123 | -3.4456	2.9455	-4.8205	2.9581
 124 | 0.4833	0.9948	0.8167	-0.1030
 125 | -0.4469	0.4463	2.0501	-0.8238
 126 | 0.7607	0.0655	-1.8798	2.5602
 127 | -2.4234	1.3072	-2.5409	0.4427
 128 | 2.9850	-5.2064	2.2033	0.3741
 129 | 1.0162	-0.9714	0.4169	1.0843
 130 | 0.2099	-0.2891	1.4305	2.0278
 131 | 0.1224	-1.7624	-0.8701	0.2907
 132 | -1.9964	5.3981	-2.2138	0.8448
 133 | 1.1217	-3.1691	2.5213	-3.1642
 134 | -3.0153	3.9632	-2.2729	2.3591
 135 | -1.8858	2.6231	0.1735	-1.3379
 136 | -2.4615	1.4408	-1.7808	3.5102
 137 | 1.0506	-0.9322	-0.1302	-2.9468
 138 | -3.5234	4.9808	-0.3089	0.0258
 139 | -0.2247	-1.6653	-0.5595	0.3912
 140 | -3.9930	4.8227	-2.5771	2.7147
 141 | -4.6587	5.8361	-3.4477	0.1261
 142 | 0.8946	-2.2407	0.6980	-1.0153
 143 | 0.9893	1.0781	-1.3372	2.1530
 144 | 1.7438	-1.2918	1.9945	-1.3344
 145 | -1.2155	3.6731	-3.7130	-0.4757
 146 | -2.3642	3.8972	-4.1603	1.9331
 147 | -1.9872	1.9445	-1.4156	-0.1221
 148 | -1.3008	3.5923	-3.5751	0.4944
 149 | 1.7242	-3.1833	1.3732	0.2472
 150 | 0.6183	-0.4379	0.3346	-0.1718
 151 | -0.5472	1.7678	-0.4433	-0.2038
 152 | 1.1722	-1.0002	1.0738	-0.8567
 153 | 2.2836	-1.0116	2.0051	-3.6734
 154 | 0.7720	0.1557	-0.6488	3.2384
 155 | 1.9198	-1.4280	-0.8870	2.4429
 156 | -1.4364	0.4043	1.1115	0.1074
 157 | -2.4727	5.3127	-2.2432	2.7069
 158 | -1.1611	2.6512	-0.0119	2.8549
 159 | -0.4212	0.3691	-1.0256	-1.7569
 160 | 0.2058	0.1710	0.0044	-0.2015
 161 | -2.1783	4.7534	-2.6275	1.6468
 162 | 6.7077	-8.5984	5.8192	-3.2625
 163 | 0.9011	-0.7036	1.1274	-1.6322
 164 | -1.9057	1.1766	0.9641	1.4560
 165 | 1.1679	-2.7600	1.4512	-2.2898
 166 | 1.7802	-2.2335	1.7346	-0.8743
 167 | -0.8994	0.6712	0.1166	-0.7219
 168 | 2.5067	-3.8387	3.2250	-5.0992
 169 | 0.2993	-1.2147	1.8962	-0.4666
 170 | 2.0035	-3.7196	3.8175	-1.2268
 171 | 0.4705	-1.0300	0.8779	-3.2260
 172 | 0.7338	1.9469	1.9910	-2.4116
 173 | 0.4932	-1.3459	1.3936	0.0645
 174 | 0.3452	-0.8638	1.0184	-0.6732
 175 | -1.1385	0.3247	-2.7951	1.2168
 176 | -2.2179	2.1718	0.3669	0.8148
 177 | 0.8757	1.1161	0.9324	-1.8629
 178 | 1.0861	-2.2711	0.5488	1.7941
 179 | 1.2754	0.4958	0.9060	-2.0120
 180 | 4.2121	-6.2745	6.5894	-1.4398
 181 | 1.6648	-1.5243	0.4118	-1.6482
 182 | -1.0071	0.2391	1.6285	-2.6830
 183 | 0.0481	-0.5188	0.2764	0.5032
 184 | 3.7995	-5.6557	2.7990	0.0031
 185 | -0.5356	1.3553	-1.4123	1.1974
 186 | -0.6964	0.7849	0.0793	-0.4092
 187 | -1.1570	-0.4206	0.2682	-0.4910
 188 | -0.5467	1.7940	-3.3012	1.7345
 189 | 0.6126	-0.1582	0.9827	-0.1947
 190 | 0.9807	-0.7914	0.9984	-1.9384
 191 | 2.0600	-2.7681	2.8354	1.1211
 192 | 1.5654	-2.7455	-0.4810	0.9567
 193 | -1.6577	-0.9398	3.0806	-1.5181
 194 | -1.5775	1.6468	-1.1509	0.1303
 195 | 0.0312	-0.6440	1.2859	-0.7424
 196 | -1.7438	2.9344	-5.2466	2.6752
 197 | 1.3552	0.0707	-1.0004	-0.2062
 198 | 2.3020	-2.8418	4.1448	-6.8893
 199 | -1.0886	2.2666	-1.2338	-1.1473
 200 | 0.1311	0.0016	-0.7682	0.9510
 201 | -4.7298	5.4501	-5.2314	3.8043
 202 | -1.4416	2.8645	-1.0849	1.2636
 203 | 2.4353	-6.6893	2.9965	-3.4684
 204 | 1.6311	-3.7167	4.5294	-4.6049
 205 | 0.7129	0.3790	-0.5915	-0.9539
 206 | 0.9853	-1.1985	-0.4103	0.1647
 207 | -0.2463	0.1348	0.3997	-1.8167
 208 | 2.4677	-4.1649	3.6247	-4.5539
 209 | -3.1433	2.2769	-1.4351	2.2472
 210 | -0.5997	0.7878	-0.7083	3.3493
 211 | -0.2219	2.9956	-3.2567	3.3879
 212 | 3.4457	-4.5597	4.4612	-2.6982
 213 | -0.9987	0.3857	-1.3589	0.8286
 214 | -2.3675	4.6713	-3.4630	2.4612
 215 | -0.3782	0.2420	2.8704	-1.0199
 216 | -1.7842	2.9929	-0.4335	0.1881
 217 | -3.5330	4.3402	-2.4082	-1.7555
 218 | 0.7279	-0.9461	0.2986	1.5253
 219 | -1.0857	4.0381	-1.1630	1.5600
 220 | 1.7275	-1.7774	-0.3628	-0.6869
 221 | 1.5493	-1.0240	-0.4974	-0.8631
 222 | 0.5943	1.0869	-0.9582	1.5274
 223 | 2.8690	-3.2563	3.3611	-1.4471
 224 | 2.9257	-3.0525	2.4868	-2.7332
 225 | 0.4027	-3.5227	3.5266	-0.8499
 226 | 3.3916	-4.9978	3.5416	-1.4827
 227 | -1.6987	3.0726	-1.3319	1.7633
 228 | -1.5557	3.4142	-2.8666	1.5640
 229 | -0.8027	-0.0695	-1.5131	-0.9153
 230 | 0.0736	-0.7860	1.5578	-0.9551
 231 | -0.4279	2.2720	-0.2011	-2.0304
 232 | 1.4023	-1.8293	1.3506	-0.4297
 233 | -2.7573	2.6795	-3.9001	4.2465
 234 | -0.4203	0.9734	-1.9729	-1.8064
 235 | -1.2864	1.6348	0.8188	-0.4216
 236 | -1.7385	2.0098	-0.9753	-0.0532
 237 | -2.2093	3.8695	-1.1137	1.4301
 238 | 0.8066	-1.2087	0.2463	1.3244
 239 | -1.2140	-0.2062	-1.0578	0.1600
 240 | -0.6960	0.7994	0.4188	-2.1940
 241 | 1.9200	-2.6634	3.0670	-3.0305
 242 | 2.0592	-4.0635	4.5978	-1.3770
 243 | 2.6652	-3.7128	3.3657	-1.5910
 244 | -1.6422	2.4859	-1.9821	4.0544
 245 | 1.1868	-1.3394	0.8355	1.0453
 246 | 0.6707	0.0650	-1.6489	-1.5324
 247 | 0.0346	1.7347	-2.8984	2.5162
 248 | -0.4212	0.0139	-0.0464	-1.7907
 249 | 2.0278	-2.7720	1.8203	-1.7754
 250 | -2.1878	2.7984	-3.7490	3.2679
 251 | 0.8070	-1.3033	0.0881	-1.8347
 252 | -0.1077	-1.9024	1.7961	0.5247
 253 | 2.1591	-4.9335	6.6325	-5.5053
 254 | -0.0300	-1.6648	1.8453	-2.5844
 255 | -3.3999	4.8242	-2.1158	1.7990
 256 | 0.1480	-1.5725	0.8437	-2.6698
 257 | 1.9823	-3.1753	1.5576	-1.1294
 258 | 2.6089	-4.1521	3.4486	1.7335
 259 | -5.2560	6.6287	-5.6363	7.8463
 260 | 0.3536	-0.5571	-0.9817	-1.2550
 261 | -0.8702	1.7194	0.8097	-1.0582
 262 | -3.6449	4.7141	-2.4439	-0.1028
 263 | 2.5143	-3.3446	1.2600	-4.8624
 264 | 1.2735	-2.2038	2.8952	-3.3995
 265 | -1.2572	-0.9776	-0.0843	0.8693
 266 | 3.8312	-5.7975	2.6337	-1.9688
 267 | 0.6265	-1.7849	2.2480	-2.5622
 268 | 0.6790	-1.1334	0.1967	-0.6159
 269 | 0.1081	1.3010	-3.5990	1.0454
 270 | 2.1146	-0.9540	2.0404	-1.6243
 271 | 0.0365	-0.6352	-0.7213	-2.6919
 272 | -0.4249	0.3460	0.9868	-0.4075
 273 | -0.2214	1.3200	-0.3962	-1.9658
 274 | -0.1918	-0.9431	1.4964	1.6336
 275 | 1.6507	-1.0985	0.5365	-1.1206
 276 | 2.1983	-3.1178	1.4616	-3.5599
 277 | -1.7563	3.2385	-3.6326	3.0152
 278 | -1.8454	1.1570	-0.7387	-0.3827
 279 | 1.3343	-2.6883	2.7234	-1.6175
 280 | 3.0179	-4.8692	2.9028	-5.2544
 281 | 0.2580	-1.1953	-0.9440	0.1418
 282 | 2.1201	-2.4369	-0.0939	-1.0381
 283 | -1.0192	1.7210	0.1855	-1.5238
 284 | 1.1887	-1.0719	0.7239	1.0624
 285 | 2.0584	-3.2305	0.9409	0.0083
 286 | -0.4827	0.0737	-0.5072	3.0439
 287 | 1.1285	-0.9235	1.3424	-2.1210
 288 | 0.9092	-1.0489	-0.6473	2.4011
 289 | -3.2417	2.5092	0.4515	1.4229
 290 | 2.4782	-5.4602	1.2755	-0.0098
 291 | -1.3435	3.4335	-3.9148	0.1571
 292 | -1.1343	3.5711	-0.3768	-2.2037
 293 | 2.0794	-3.1259	-0.0804	1.2884
 294 | 1.7978	-2.5039	2.7636	-4.1771
 295 | 2.2550	-3.7133	3.2286	-3.1313
 296 | 0.9811	-0.9379	1.8958	-2.1474
 297 | 2.6543	-2.8884	2.5257	2.8585
 298 | -0.8480	1.8336	-0.0115	3.5895
 299 | -4.2669	5.3205	-2.9371	3.5122
 300 | -0.5032	-1.2847	1.9429	-4.9289
 301 | -0.3978	-0.2867	-0.4268	-0.7667
 302 | 1.0185	-1.4342	-0.3521	3.9628
 303 | 1.4247	-2.8679	0.0886	-3.6574
 304 | 1.9571	-3.7417	2.4144	-4.1091
 305 | 3.4760	-5.0955	5.2131	-2.0376
 306 | 2.4234	-5.5613	4.6510	-1.8474
 307 | 0.7347	0.1590	1.4726	-1.6465
 308 | 0.8615	-1.4356	0.7517	-1.0305
 309 | -1.6648	0.6204	0.3582	-0.9059
 310 | -2.6102	3.9292	-5.3447	4.0920
 311 | 0.0467	1.3368	-2.4983	1.4298
 312 | 0.9549	-0.8607	1.1120	-1.1449
 313 | -0.9611	1.4355	-0.3609	1.5203
 314 | -0.0266	-0.6147	0.7583	0.6576
 315 | 2.2399	-2.7874	0.3019	0.1396
 316 | 0.6104	0.7339	-1.7352	0.4178
 317 | 1.2434	-0.7044	1.4070	0.3888
 318 | 1.0704	-2.3040	0.3654	1.5041
 319 | -0.4596	0.2533	-3.3432	1.1173
 320 | -0.0919	-1.0365	0.2518	0.4114
 321 | -0.5351	1.0634	-2.2042	5.0104
 322 | -2.5041	1.1629	2.5200	-0.6230
 323 | 0.1299	1.9460	-1.8787	1.6544
 324 | -1.2547	3.9004	-4.3475	2.1884
 325 | -1.3814	2.1247	-2.0662	0.2821
 326 | 1.5703	-1.2382	0.8177	-2.1443
 327 | 0.3177	-0.3730	0.1167	-1.8618
 328 | -0.7143	1.6336	-1.0752	1.2229
 329 | 1.1660	-3.6279	3.1018	-2.1935
 330 | -1.5572	3.5015	0.4779	-0.3391
 331 | 2.5459	-2.2746	2.1049	0.3450
 332 | 2.1769	-3.0118	3.2306	-2.0353
 333 | 2.2460	-3.6307	5.5391	-5.0131
 334 | -2.2455	1.0986	1.7277	0.8886
 335 | 0.6324	-0.9586	0.1012	2.9919
 336 | 1.0406	-1.5155	0.9363	0.2473
 337 | -2.8578	3.4910	-0.2807	2.5223
 338 | -1.0803	-0.2591	0.2334	-1.1981
 339 | 0.4759	1.0451	-0.8835	-1.3310
 340 | -0.4207	2.2075	-2.1733	-0.0340
 341 | 2.7382	-4.7871	2.8121	-3.6069
 342 | -3.5719	4.6522	-3.3314	1.8769
 343 | 1.4440	1.4395	0.6249	-0.5312
 344 | 1.0012	-2.3027	1.3425	0.5070
 345 | 1.2121	-1.9153	2.2605	-1.8846
 346 | -0.3512	0.4190	0.1697	0.3158
 347 | 2.9283	-2.3514	1.8289	-0.6127
 348 | 0.5468	-2.3691	1.2139	-1.7248
 349 | -2.7752	2.6966	-1.2113	3.3508
 350 | 1.3038	-1.0569	0.9502	-1.5312
 351 | -1.0035	1.5317	-4.9867	4.0461
 352 | 1.6253	-2.3069	1.6264	-1.9175
 353 | 1.0680	0.7962	-2.8005	2.5356
 354 | 0.3356	1.6983	-1.0563	3.5371
 355 | 1.3422	-2.2305	1.2191	0.2855
 356 | -0.3273	-1.9245	0.0748	1.8252
 357 | 0.1452	-0.6099	1.3791	-1.1909
 358 | -1.4478	3.0632	-1.8047	-0.5578
 359 | 0.8176	-0.8639	-2.1298	0.2753
 360 | -1.2815	0.0003	1.5293	-2.8635
 361 | 1.0604	-3.6932	3.7445	0.2880
 362 | 0.1834	-0.6681	1.2316	0.9439
 363 | -3.0338	4.2248	-3.3083	1.4648
 364 | 3.2925	-4.5650	3.4848	-3.1683
 365 | 2.4240	-0.7751	-0.1248	-2.0080
 366 | -0.9575	-0.8490	0.7004	0.6302
 367 | -0.7525	-0.8206	1.6034	-0.2371
 368 | 3.1474	-5.7806	3.8650	-1.6480
 369 | -1.1947	2.2771	-0.8035	-0.7070
 370 | -2.0065	2.3593	-0.0920	1.6741
 371 | 1.3797	-4.2628	3.6040	-0.3309
 372 | 0.6721	0.0390	-0.8996	1.9658
 373 | -1.6735	2.0734	-1.2047	-0.0968
 374 | 1.4036	-1.6025	0.7370	-2.4138
 375 | 0.3113	-0.0068	1.9862	-1.6741
 376 | -1.8215	2.5950	-0.0463	-3.0314
 377 | 0.9610	-0.1231	-0.0929	-2.2761
 378 | -0.4296	2.1091	-1.3728	-0.8612
 379 | -0.4915	-0.1205	-0.6505	0.4613
 380 | 1.7835	-3.3021	4.1038	-5.6244
 381 | -0.5010	-0.1385	-0.4778	1.0001
 382 | 2.3473	-4.5291	2.3209	-2.6532
 383 | 0.4503	-1.2951	1.6791	0.5772
 384 | -2.1868	2.4629	-1.0664	-0.7359
 385 | -2.1028	2.3250	-4.4700	3.5411
 386 | -2.7144	4.7650	-2.1897	2.7530
 387 | -0.0413	0.5473	-1.5077	3.2899
 388 | -0.5073	0.0286	-0.9097	1.0293
 389 | -0.3151	0.0564	1.5943	-3.5562
 390 | 1.9832	-4.3670	1.6846	-0.5051
 391 | -0.1265	-0.2920	0.4359	-2.3394
 392 | -1.6708	1.8447	-0.5476	-1.6043
 393 | 0.9820	-0.9190	-1.8713	4.3085
 394 | -0.4160	-0.2254	-1.6642	-0.2492
 395 | -0.3266	0.4575	0.8529	1.9110
 396 | -0.8633	1.1502	-3.5805	1.2594
 397 | 0.8169	-1.5419	1.7886	-1.6153
 398 | -1.8050	-0.4300	0.3783	-0.3982
 399 | -2.6035	3.1410	-1.1079	-1.8392
 400 | 1.3200	-1.5188	0.2214	2.6136
 401 | 0.5824	-1.0258	1.8195	-0.7269
 402 | -1.9800	2.8568	-2.5627	2.1322
 403 | 1.5593	-3.2141	3.9718	-2.3569
 404 | 0.6032	2.0693	-1.6617	-0.6860
 405 | -1.1488	-0.3849	-0.3694	-0.4872
 406 | 0.9376	-0.4751	-1.2248	1.8626
 407 | -1.5874	2.2718	0.1958	0.5979
 408 | -1.9156	3.3890	-1.0979	-2.1727
 409 | 2.4691	-4.2285	1.8238	-2.6738
 410 | 0.0166	-0.6289	-1.6618	1.8493
 411 | -0.8073	1.8931	-2.3469	-0.2570
 412 | 1.3514	-1.1593	0.6891	-0.5524
 413 | 1.1358	-2.2162	0.8506	-1.2774
 414 | 3.0605	-6.0286	3.9440	-1.4995
 415 | 0.9090	-0.4415	0.2407	1.7577
 416 | -0.6603	2.0587	-1.8735	3.0799
 417 | 0.9248	0.3771	1.8815	1.6127
 418 | -1.7751	4.0731	-1.4415	3.3666
 419 | 1.2626	-0.5517	-0.0148	-1.5493
 420 | 0.7294	-1.5001	5.3080	-4.0655
 421 | 1.5125	-1.4047	-1.5979	0.8999
 422 | -1.0162	0.4780	0.8544	-0.6338
 423 | 1.4069	-0.9963	0.5220	-1.0498
 424 | 0.0706	-0.7243	-1.2136	0.6513
 425 | 0.0118	1.7826	0.5564	-1.0101
 426 | -0.4757	-0.3423	-0.8140	-1.2068
 427 | -1.3822	0.2538	2.4522	-2.1863
 428 | 0.0792	0.4009	1.2876	0.2220
 429 | -3.3938	5.1413	-5.4668	2.1053
 430 | 1.1362	-0.1089	-0.2805	-1.0752
 431 | -0.9984	0.8605	-0.3897	0.7427
 432 | 0.4009	-1.2165	-1.6150	2.8729
 433 | -2.4979	3.0966	-1.1048	2.7158
 434 | -2.4306	4.7759	-2.5495	0.9799
 435 | 2.1501	-2.2842	2.1717	-2.1504
 436 | -1.1137	2.3072	-0.9840	2.4801
 437 | -1.0093	3.1891	-1.6972	1.8972
 438 | 1.0123	-1.2481	2.2432	-4.2394
 439 | 0.5678	-1.9080	0.4957	-1.9011
 440 | -1.1475	2.0122	-1.6535	0.1492
 441 | 1.6208	-2.1496	1.0100	-0.4237
 442 | 1.6926	-1.6242	-0.8967	1.3610
 443 | -0.8179	1.5342	-1.4107	2.6162
 444 | 0.9114	0.0543	0.9264	2.4302
 445 | -1.6727	2.8283	-1.4601	0.9702
 446 | 0.2734	-0.8439	2.1470	-0.6261
 447 | 0.0443	-0.3582	1.7375	-1.2375
 448 | -1.8790	4.2280	-3.4589	1.4625
 449 | 1.0886	-0.8534	-0.2343	-2.0556
 450 | -0.7961	-1.4788	-0.0393	-2.5669
 451 | 2.6049	-3.7579	2.8162	-1.7324
 452 | -0.9983	1.6051	-1.7941	0.2679
 453 | 1.8902	-2.1899	2.1966	-1.3463
 454 | -3.4214	3.6293	-2.6913	3.4523
 455 | 1.7781	-1.6748	1.2039	-0.9991
 456 | -2.9451	3.5319	-2.4987	-0.7302
 457 | 0.9390	-1.4322	1.8525	-2.8930
 458 | -0.1423	0.3619	2.1269	-3.7712
 459 | -0.9506	2.0603	-0.8798	0.8810
 460 | -0.6649	1.7907	-0.2783	2.7082
 461 | 0.8345	-1.4114	-1.5451	-1.1841
 462 | 0.8416	0.0118	-1.6991	2.5737
 463 | 0.2610	0.6620	1.5284	-0.4309
 464 | 0.6651	-3.4939	0.9922	-2.5448
 465 | 1.9326	-3.9649	2.3591	-1.5438
 466 | -0.4032	2.0720	-2.1272	0.6975
 467 | 1.2733	-2.4220	1.9593	-2.4888
 468 | -2.1227	2.7953	-1.4768	3.5187
 469 | 3.7303	-3.9749	1.8657	-0.3089
 470 | -0.2127	0.2082	1.1049	-0.7540
 471 | -0.1577	0.0742	1.4669	1.0705
 472 | -1.0820	2.6280	-0.5105	-1.4076
 473 | -0.3602	-0.9863	0.1732	-1.1650
 474 | 1.0607	-0.6782	-0.3550	-1.7433
 475 | 1.3560	-2.4044	4.0120	-3.8478
 476 | -3.3162	3.7079	0.1314	-0.7974
 477 | 0.8090	-0.6697	-1.3352	3.8430
 478 | 0.7376	0.2161	-1.0504	0.9077
 479 | -1.8278	2.4828	0.0569	1.9981
 480 | -0.8607	1.5036	0.5660	-1.6403
 481 | -1.0952	2.6776	-2.0192	-1.2558
 482 | 0.7885	-0.3211	0.7815	1.7303
 483 | -3.2768	5.5844	-4.4398	4.1887
 484 | 0.6617	-1.7350	0.6209	-1.0745
 485 | -2.2710	2.5003	-2.1394	1.5077
 486 | -0.4693	0.4201	0.4471	-1.5821
 487 | 0.7434	-2.5690	0.9093	-0.9086
 488 | -1.4229	2.9913	-1.4544	0.4889
 489 | -1.5150	1.8250	-3.4217	0.5995
 490 | 1.8356	-1.1636	0.2673	3.3280
 491 | -1.2275	1.7639	0.3961	0.8939
 492 | 3.3563	-4.1276	2.3028	-1.4136
 493 | 0.4958	0.3435	0.9711	-1.7145
 494 | 1.9937	-2.5598	0.3268	-0.7499
 495 | 1.5696	-3.0712	1.0593	-0.1477
 496 | 0.6775	1.9679	1.0086	1.7171
 497 | -1.3810	2.4189	-2.1483	-0.0203
 498 | 0.4674	-0.9928	-0.3510	0.9079
 499 | 1.9358	-3.3704	2.4630	0.0906
 500 | 3.4962	-4.9384	1.5484	-1.9419
 501 | -2.0586	3.9324	-5.3344	7.1554
 502 | -0.4168	1.1571	-2.9138	1.2333
 503 | 0.4311	0.3651	-0.0478	2.4457
 504 | -1.4001	1.6733	-1.3277	-0.6301
 505 | -0.5681	2.7337	-2.5014	1.1394
 506 | -3.2774	6.3466	-4.5821	0.9299
 507 | 1.4720	0.2139	-2.8939	1.5468
 508 | 0.9113	-1.4944	0.7225	0.0178
 509 | -2.6031	4.1277	-3.3743	3.1864
 510 | -1.8454	3.5137	-4.3429	2.2706
 511 | -2.4773	3.3929	-4.2474	3.8898
 512 | 0.8567	-2.0278	2.2026	-2.5945
 513 | 1.5364	-1.7663	1.9983	0.1438
 514 | 0.2370	-1.0952	1.0202	0.6644
 515 | -0.1614	0.5217	-2.7830	5.7433
 516 | 2.3362	-3.2806	0.1642	0.2210
 517 | -0.1898	-0.5339	-0.6074	0.0754
 518 | -0.9003	0.2863	0.5400	-0.1403
 519 | -0.0166	-1.1185	-0.3990	-1.3437
 520 | 1.2560	-3.3147	2.9521	-3.7248
 521 | 2.3244	-3.5451	0.7979	-0.2893
 522 | -0.8779	0.0251	1.9283	-1.9232
 523 | 1.9250	-2.1313	2.1332	-2.8456
 524 | 1.7201	-3.2695	2.9131	-2.6163
 525 | 0.7596	-0.2490	-1.2349	1.2033
 526 | -1.5992	3.1100	0.1082	-3.0093
 527 | -0.2541	0.9101	-3.9552	1.1286
 528 | 0.7130	-2.8651	1.5903	1.0326
 529 | 0.6766	-0.6547	-0.2474	0.3929
 530 | -1.6432	3.9385	-1.0241	-0.2330
 531 | -0.4408	-1.1395	2.6549	-1.7223
 532 | -0.1071	0.6903	-1.6576	-0.5475
 533 | -0.0114	-1.1852	0.9760	0.4618
 534 | -0.3380	-0.5095	-0.2835	1.8059
 535 | 0.8454	-1.1546	-0.4014	1.2588
 536 | -0.2374	0.7670	-0.7263	1.6838
 537 | 2.3567	-2.8675	1.4035	-0.0492
 538 | -1.2768	1.2499	0.7270	-3.9904
 539 | 3.3866	-4.4117	2.5137	1.5154
 540 | -0.6374	2.0809	0.6960	-0.1506
 541 | 2.1132	-2.8596	3.7121	0.6604
 542 | -0.1725	-1.5758	1.0722	-1.9899
 543 | -1.4375	1.3973	2.2079	-2.1502
 544 | -1.3858	1.3237	0.5400	-0.6116
 545 | -2.1444	2.9371	-2.8709	0.0533
 546 | -1.4075	2.0908	-1.2895	2.4425
 547 | 2.0539	-4.0151	4.4162	0.1400
 548 | -1.5983	2.8727	-1.9664	1.7177
 549 | 2.8714	-4.4406	2.2324	-5.6920
 550 | 0.6608	-1.2968	0.4926	-1.3594
 551 | 0.2265	1.2669	-2.7780	2.6726
 552 | 0.1477	0.3428	-0.8948	-0.8485
 553 | -2.4724	4.0512	-1.5994	1.7774
 554 | -0.2730	-1.0163	1.4474	-3.5532
 555 | 1.1559	-1.4453	0.5985	0.5235
 556 | 0.4427	0.5535	1.1643	-2.7164
 557 | 0.5666	-0.8211	1.0077	3.4879
 558 | -0.0231	0.8827	-1.0617	-0.3651
 559 | -0.7628	1.6556	-0.2797	-1.3479
 560 | -1.9997	1.8147	-1.1891	2.4071
 561 | -2.6363	3.6448	-3.3742	1.0443
 562 | -1.3767	0.4313	-1.6227	1.3824
 563 | 1.6429	-1.4162	-1.3247	-0.8525
 564 | -1.3132	-0.2357	0.6538	-0.2497
 565 | 0.4154	1.0370	-0.9801	3.5181
 566 | -0.2566	-0.7893	-0.2257	2.7240
 567 | -0.6877	1.4002	-2.9951	0.9035
 568 | -0.0231	-1.7146	1.6151	-2.7442
 569 | -1.0659	1.0261	-0.7140	-1.0691
 570 | 1.5397	-1.7437	2.5044	-3.0546
 571 | 4.2368	-4.9766	5.3573	-6.3826
 572 | -1.2585	0.2122	0.3837	-1.2266
 573 | 0.3982	-3.0785	2.3723	-3.2200
 574 | 2.1463	-3.2685	3.2932	-1.8343
 575 | -0.0647	-1.4213	-1.1823	0.9139
 576 | 2.6447	-4.3465	2.3848	-3.9587
 577 | -1.9526	4.9976	-1.6889	-0.5997
 578 | 0.1990	0.0961	1.6128	0.4050
 579 | 0.1764	-0.9440	0.1530	-2.0368
 580 | -3.4204	4.9875	-2.8102	0.9009
 581 | 1.9929	-4.4909	3.0770	-7.1560
 582 | -1.2281	1.9378	-0.5286	-1.7820
 583 | 2.2174	-3.8080	3.3064	-3.5737
 584 | 1.2011	-2.4105	2.6499	-3.4340
 585 | -0.8248	1.6551	-0.3054	0.5060
 586 | 1.2722	-1.7053	3.6538	-1.1343
 587 | -0.7326	1.1873	2.5334	-1.7431
 588 | -1.9787	1.8636	-1.9374	2.6812
 589 | -0.1082	-0.2865	1.3948	-0.8663
 590 | 2.8458	-2.3345	-0.5997	0.3648
 591 | -0.1704	-1.4838	0.2094	0.8450
 592 | 0.9409	-0.8251	2.1245	-2.3654
 593 | -3.5908	5.2481	-4.4655	3.2330
 594 | 0.0430	0.5639	1.1362	-0.6020
 595 | -0.6883	2.0468	-1.6201	4.7797
 596 | -1.1626	0.4387	-0.9056	0.7308
 597 | 1.0973	-1.2028	0.3617	-0.9746
 598 | -1.0538	4.0708	-4.3558	4.9951
 599 | -1.6591	3.2622	-0.9648	0.1864
 600 | 0.1235	-0.8777	2.9949	-0.7093
 601 | -0.9435	1.1575	-1.4956	0.9932
 602 | -0.3312	4.0587	-3.1710	3.1142
 603 | 1.0668	0.0938	-0.6088	0.8947
 604 | 1.2272	-0.2389	-0.9800	2.2638
 605 | 1.2629	-1.5627	0.1846	0.7614
 606 | 0.1628	-0.3513	0.2389	-2.0619
 607 | -1.1090	0.7156	-0.5224	-1.1571
 608 | 4.0992	-7.4618	4.6826	-7.0377
 609 | 0.6436	-1.5257	1.0065	2.4243
 610 | -0.2089	1.5767	0.8713	0.8575
 611 | -1.2635	1.8723	-3.8154	3.0404
 612 | 3.5878	-4.7729	2.3068	-1.0712
 613 | -0.2301	0.2900	-1.4258	2.4218
 614 | 1.1029	-1.9623	1.8677	-0.0401
 615 | -0.4229	-0.9332	1.0056	-3.3888
 616 | -0.0726	-0.5524	2.1742	-3.3476
 617 | 1.0923	-0.9266	0.6573	0.9386
 618 | 0.9944	1.1793	-0.6315	-1.6044
 619 | -0.3975	1.1411	-0.5557	-1.7210
 620 | -2.6711	2.2818	-2.9216	0.0625
 621 | 1.7141	-1.7526	2.1493	-0.3793
 622 | -0.1717	-0.1260	-3.4244	0.1543
 623 | 1.4601	-1.4186	0.5472	-1.2244
 624 | 3.1626	-4.3679	5.0693	-5.3153
 625 | 1.4400	-2.1011	1.3476	-2.4058
 626 | -0.2190	1.6387	-2.2434	5.9233
 627 | -2.1115	2.1260	-4.4432	1.1573
 628 | -4.1488	6.8225	-5.0869	5.0017
 629 | 1.4245	-0.8541	0.7167	0.5784
 630 | 4.8551	-6.1749	4.6590	-3.9562
 631 | -0.0708	1.7503	-2.3181	4.9543
 632 | 2.1805	-1.9256	2.7581	-1.9166
 633 | 3.2436	-2.6140	1.6178	-0.8281
 634 | -2.1353	3.1085	-1.3678	1.5000
 635 | 0.3014	-1.5068	-0.2148	1.0061
 636 | 0.4264	0.3321	1.8270	-2.9679
 637 | -0.3524	0.2858	0.6507	-0.0002
 638 | -0.2313	-0.8263	-0.6248	0.6938
 639 | 1.8945	-3.3462	4.6625	-2.2109
 640 | 0.5801	1.6233	-2.0298	4.1418
 641 | 1.0208	-0.8429	-1.4348	-0.8033
 642 | 0.1698	1.2046	-0.6420	2.6247
 643 | 1.1166	-0.5799	1.6047	-1.8165
 644 | -2.4276	1.6753	-2.2009	2.1769
 645 | -0.4621	-0.8289	1.3050	-1.1801
 646 | 1.1003	-0.7507	0.6983	3.8407
 647 | -2.9348	1.4070	0.9557	1.5990
 648 | -1.2595	2.5839	-0.0906	-1.4529
 649 | -1.4302	1.4269	-4.0040	-0.3571
 650 | 3.8791	-4.1095	3.8168	-6.2184
 651 | 0.1025	1.3120	-1.8457	2.8259
 652 | -0.7135	1.9147	-1.7530	1.4849
 653 | -0.8661	0.7347	0.0848	-0.3501
 654 | 2.0070	-1.9013	1.2305	-0.1666
 655 | 0.2362	0.6444	2.0550	-2.8106
 656 | -0.2277	0.3485	-0.3205	-0.4129
 657 | 0.3093	-0.7866	0.0744	0.3211
 658 | -1.2844	1.5033	0.7932	-0.2718
 659 | 0.2397	-2.4954	1.2031	-0.7917
 660 | 0.1087	0.2118	-0.9795	0.1218
 661 | -0.2526	1.9954	0.5358	1.5486
 662 | 0.6327	-0.7370	1.0742	-4.9349
 663 | -0.3905	0.3449	-0.6705	3.4781
 664 | 2.0921	-3.9816	3.1537	-2.6303
 665 | 1.9001	-2.6302	4.4552	-5.2211
 666 | -0.1103	-0.0216	0.1779	1.5178
 667 | -0.6161	3.4602	-3.7431	-0.4778
 668 | 1.7957	-2.3945	1.8503	-2.3394
 669 | -0.4459	-1.4958	2.4628	1.0894
 670 | 0.1516	1.6539	-3.4505	3.7447
 671 | -0.4750	1.6043	-3.2748	2.3154
 672 | -1.5244	3.2309	-0.8765	1.6157
 673 | 1.8608	-6.9307	5.8139	-6.6464
 674 | -0.0927	0.2326	-2.5053	1.1516
 675 | -1.4494	2.6426	-0.2491	2.3426
 676 | 3.5468	-4.4077	4.6819	-3.4005
 677 | 0.5225	0.0873	-0.2371	-2.7413
 678 | 1.7357	-2.3195	1.6259	-2.2460
 679 | 1.4716	-1.9525	-0.8040	-0.7493
 680 | 0.2971	-0.9877	0.3670	-1.2802
 681 | -1.9396	1.0106	-0.2404	-1.1892
 682 | 1.0997	1.0403	-2.3510	3.8877
 683 | -0.2247	-1.1363	0.3188	1.6240
 684 | 0.8247	-1.0204	-0.5899	1.7700
 685 | -1.8540	1.5840	-3.2960	0.1129
 686 | -1.4198	0.6306	-1.2670	0.8721
 687 | -1.7310	2.4145	-3.1544	2.2940
 688 | -0.8353	1.6364	-2.7729	2.6443
 689 | -0.2897	0.6140	-2.1460	-0.7876
 690 | 0.7914	-2.7810	1.4900	-1.1980
 691 | -4.1019	5.9892	-6.8134	4.2138
 692 | -0.5339	1.0234	0.1425	-0.5136
 693 | 1.3446	-1.8769	0.7677	-0.8951
 694 | -0.9499	3.1184	-0.7719	-1.2147
 695 | -1.1475	2.6028	-2.3317	1.1433
 696 | -0.2062	-1.1469	3.4937	-1.9062
 697 | 0.2772	0.6020	-2.6937	0.2347
 698 | 3.4986	-5.5072	4.3739	-1.6358
 699 | 0.2941	0.5346	0.4540	0.4593
 700 | -0.1242	-1.0397	-0.6652	-0.9404
 701 | 0.5710	-0.7745	-0.2705	1.0908
 702 | -0.4038	-1.0506	-0.0250	0.2840
 703 | 1.2326	-1.1179	0.6415	3.3723
 704 | 0.4547	1.6919	-1.9841	-0.7070
 705 | -0.1828	-1.7248	1.8417	-4.3951
 706 | -1.3410	2.7061	0.0560	0.3357
 707 | -0.7204	0.2881	-0.2452	1.7364
 708 | 0.1451	1.2196	-0.8318	0.3855
 709 | 1.2599	0.0647	0.0332	0.5144
 710 | -0.0635	1.6113	-1.4286	2.2698
 711 | -0.8989	0.7682	0.4676	0.0960
 712 | 0.2500	-0.7643	-0.0614	1.6907
 713 | 0.8116	-0.2115	-0.7260	0.0617
 714 | 2.0919	-3.6133	1.4912	-1.9217
 715 | 2.1941	-2.8912	1.5150	-0.9064
 716 | -1.8914	4.3030	-1.5844	3.2819
 717 | 1.5834	-2.3762	2.1190	-1.6414
 718 | -1.5385	3.1096	-3.1794	0.7403
 719 | 0.7907	-1.4693	-0.8390	1.8655
 720 | -2.5275	3.6909	0.0851	-0.9640
 721 | -0.6223	2.3442	-2.5934	5.9819
 722 | 0.1819	1.1218	-0.2446	0.4111
 723 | 1.8300	-3.6296	1.3749	-1.6477
 724 | 1.8891	-3.2785	2.3827	-0.3021
 725 | 2.9471	-4.5891	2.9364	2.8915
 726 | -0.2555	-0.7282	1.5609	-0.4774
 727 | -0.2466	-0.0108	-0.6169	1.0377
 728 | 0.5199	-0.2179	1.9092	-0.2896
 729 | -1.6583	2.0257	-3.6025	2.5196
 730 | 1.1440	-2.3990	1.5525	-1.4829
 731 | -0.3222	0.0137	-2.0799	3.7855
 732 | -0.2762	0.5465	0.0090	-0.5733
 733 | -0.9707	1.9340	-0.4506	0.8483
 734 | -1.7554	2.8878	-3.3775	2.6279
 735 | 1.0002	-1.9150	2.1717	-3.5622
 736 | 1.9198	-2.4457	1.8310	1.3853
 737 | -2.1114	4.0411	-2.9991	4.3427
 738 | 0.4696	0.1787	0.2097	0.5747
 739 | -1.0170	0.4186	0.2125	-1.2098
 740 | 0.2543	-1.8581	0.8080	-1.2704
 741 | -0.5188	1.4851	-0.1672	-0.0364
 742 | -0.2363	-1.4159	0.6137	-0.6576
 743 | -0.3346	0.9183	-0.4890	2.3744
 744 | 1.6403	-3.7174	3.1576	-3.6328
 745 | -0.7413	1.3192	0.2516	1.7977
 746 | 1.2935	-2.5978	1.8363	-2.0419
 747 | -0.5215	0.9413	0.1162	0.4492
 748 | -1.6242	2.3168	0.0903	-1.3101
 749 | -1.2568	0.8161	-2.0507	1.0183
 750 | 0.9187	-0.6627	0.7200	2.6387
 751 | 0.9864	-3.1636	0.9254	0.2961
 752 | 2.3889	-4.5698	3.2293	-2.7131
 753 | -1.7067	2.0460	-3.0723	1.1502
 754 | 1.1388	-1.9816	1.1526	-1.5554
 755 | -0.3920	2.4358	-0.6155	0.5625
 756 | -1.8825	2.5513	-0.4896	-3.1118
 757 | 1.6853	-4.0454	2.7298	0.4027
 758 | -2.0988	3.3934	-1.3767	0.9050
 759 | -1.2704	2.0068	-1.6652	-1.0216
 760 | -0.2885	-1.1837	-0.8939	-0.7224
 761 | 2.3683	-4.4616	4.0005	-1.3123
 762 | 1.7691	-0.2226	0.6268	1.0731
 763 | 0.5896	0.4490	3.1005	-3.1237
 764 | 0.4228	-1.7472	2.0891	0.4033
 765 | -1.7955	3.1510	-1.7674	2.0881
 766 | 2.4847	-3.5130	2.4446	-0.4069
 767 | -3.3482	2.5148	-1.5921	-2.9196
 768 | -3.4379	6.0661	-4.2876	1.9548
 769 | -0.5360	-0.3756	1.9567	-3.6211
 770 | -0.2472	-1.1594	0.8571	-2.5802
 771 | -2.0752	2.3663	-1.3541	0.2388
 772 | 1.5642	-2.2119	2.0732	-1.6247
 773 | 1.7296	-0.2041	1.1010	0.1398
 774 | 3.9610	-4.8667	4.4228	-1.5343
 775 | -2.0695	3.0284	-2.9496	3.0810
 776 | 1.5018	-2.2562	-0.5523	0.0616
 777 | -0.6183	0.7763	1.5869	-4.6849
 778 | -1.2221	0.2261	-3.3640	3.5412
 779 | 2.7101	-1.0966	1.1313	0.3147
 780 | -0.8781	2.2137	-3.8073	3.9269
 781 | 1.7141	-2.0729	0.5598	1.2045
 782 | 2.3888	-2.0931	3.9440	-3.7996
 783 | -1.0849	2.3981	-1.7999	3.0656
 784 | -0.4383	1.2743	-2.0390	-1.8611
 785 | 0.5260	-0.6056	-0.5337	-0.8356
 786 | -3.3395	7.5858	-7.1056	6.7210
 787 | -1.3720	2.5739	-2.0373	3.0435
 788 | -3.2173	4.5064	-5.5739	2.2760
 789 | -0.9211	0.6790	-0.7887	-0.4795
 790 | -3.4521	4.0135	-2.3831	-1.5525
 791 | 0.2334	0.0209	-1.4363	0.5307
 792 | 0.2051	0.2924	-2.0653	0.5229
 793 | -2.3372	1.9558	-1.9614	-0.7905
 794 | -0.5103	0.8747	1.6164	-5.2990
 795 | 1.4265	-1.4329	1.3139	-1.2606
 796 | 0.6899	-0.3550	0.8370	-0.6842
 797 | 1.4406	-3.3226	0.8486	2.7026
 798 | -0.3213	-0.2226	-1.4243	3.1334
 799 | -0.9383	0.8586	-0.4510	-0.6514
 800 | 1.0722	0.3533	-0.8133	2.3059
 801 | -0.4449	1.7347	-0.8885	2.5464
 802 | 1.2098	-1.0579	2.4587	-2.3556
 803 | -0.5972	1.7325	-1.2141	0.6929
 804 | 1.8557	-2.2163	-0.7773	-3.2109
 805 | -3.9633	7.0493	-4.0517	4.0580
 806 | 2.3499	-2.4360	-0.4699	0.1907
 807 | -2.2090	3.9579	-2.7447	2.5630
 808 | 2.0409	-1.3890	0.5305	-0.7100
 809 | -1.5530	1.4462	-0.8494	-0.0225
 810 | -0.8154	1.7089	-2.6047	0.7712
 811 | -1.5494	2.0046	-1.6449	-0.6655
 812 | 0.4328	-0.6720	-1.5493	-0.1024
 813 | 0.9040	-1.4732	0.4629	-1.4714
 814 | -0.5392	0.6420	-1.9468	0.3902
 815 | 1.9657	-4.8482	2.5054	-2.1197
 816 | -0.9150	-0.3956	-1.6931	-0.4444
 817 | 1.2451	-1.3795	1.7663	-3.2962
 818 | 1.6866	-2.5111	1.9434	-3.0946
 819 | 0.7229	0.4182	-1.3732	1.8016
 820 | 2.3166	-1.8348	1.6910	-0.2576
 821 | -1.1978	2.1864	-2.6629	3.2079
 822 | -2.9081	5.5592	-3.7433	4.0303
 823 | 0.1514	0.9284	-0.4192	1.3148
 824 | 0.8146	0.9973	1.2935	-0.1016
 825 | 0.3800	-0.9516	-0.7254	1.4185
 826 | 1.5295	-2.3837	3.3925	-1.6274
 827 | 0.3193	-1.1136	1.5844	-2.6091
 828 | -0.5814	-0.1342	-1.0138	0.4817
 829 | -0.5319	1.9003	-3.3557	-0.2620
 830 | 0.0595	-1.7778	1.1247	-1.1881
 831 | 2.1838	-2.5284	1.8484	1.0767
 832 | 1.1765	-2.7030	1.2177	-3.5466
 833 | 1.1729	-2.2183	1.5716	-2.1610
 834 | 1.4074	-2.3287	2.3727	-2.8695
 835 | -2.1570	5.4622	-3.6060	2.3635
 836 | -2.9056	3.1834	-4.0780	3.8333
 837 | 3.3327	-5.1715	4.4507	-3.4777
 838 | 0.2246	0.4826	-1.7699	3.5009
 839 | -1.6216	0.0275	-0.3002	-0.6462
 840 | -0.9997	1.4438	-2.5428	5.8892
 841 | 1.4724	-1.3622	-0.7678	1.6697
 842 | 0.3267	-0.9425	0.6459	-0.9690
 843 | -1.5665	3.1099	-2.8111	2.5340
 844 | -1.1159	1.4043	-0.0388	0.0484
 845 | -1.6853	1.8168	-1.7207	0.8520
 846 | -0.3045	1.8391	-1.9626	2.3557
 847 | -2.2312	3.9779	-3.4231	1.4446
 848 | -2.4957	2.7177	-2.1120	1.8291
 849 | -1.5454	1.6509	-2.1169	1.3858
 850 | -2.5767	5.8886	-3.7005	2.1089
 851 | -3.5095	5.2207	-3.0792	2.2176
 852 | 0.9174	-1.5576	-0.1363	-4.1269
 853 | -0.1040	-0.7111	2.1954	-1.6140
 854 | 1.1009	-0.1596	-0.6922	2.1744
 855 | 1.0937	-1.6498	3.0508	-2.9852
 856 | -0.8643	4.6597	-5.2543	3.5120
 857 | -0.0852	1.5620	-2.4315	2.4271
 858 | 3.4260	-6.5707	4.4279	-2.6850
 859 | 1.1534	-0.9416	-0.2435	-1.7676
 860 | -3.0078	4.0815	-4.6058	4.7613
 861 | -1.0728	2.3503	-0.8832	4.3604
 862 | -0.9355	-1.9271	0.5078	0.2688
 863 | -1.0609	-0.6423	0.4777	-0.7951
 864 | -0.0389	2.3210	-0.2672	0.5012
 865 | 0.1895	-3.4299	3.3487	-4.4104
 866 | 2.5491	-1.8714	-0.0514	-0.1542
 867 | -0.5800	0.8920	0.1340	-1.3382
 868 | -0.5285	-0.3792	-0.3480	2.1993
 869 | 0.8385	-2.4508	-0.2648	2.4220
 870 | -0.0739	-0.2533	1.9811	-5.0417
 871 | -4.7208	6.0891	-4.0244	3.1378
 872 | 2.1551	-4.7074	4.1099	-4.0267
 873 | -1.4624	2.4017	-1.4971	0.0732
 874 | 0.8731	-1.1784	-0.0538	0.5386
 875 | 1.3919	-1.2944	-0.8960	0.9090
 876 | 1.0433	-0.8126	0.2852	-2.4083
 877 | -1.0498	2.5705	-0.9064	-0.5148
 878 | 1.7455	-0.8369	-2.8313	1.3329
 879 | -0.9677	2.2147	-3.5659	2.6143
 880 | -1.9434	1.0051	0.4136	1.1005
 881 | 0.1472	0.3034	0.5597	2.1231
 882 | 2.0608	-2.7724	2.9494	2.2164
 883 | -0.1577	-0.4008	-0.4644	0.2242
 884 | -0.5515	2.1122	-1.2734	0.2451
 885 | 0.8898	0.0295	1.6357	-3.3726
 886 | -0.8623	4.5674	-2.5880	0.6151
 887 | 2.2424	-6.8449	2.2278	-1.4714
 888 | 1.1922	-2.9922	5.2063	-7.0552
 889 | 2.5713	-4.8439	2.9164	-3.4960
 890 | 1.8196	-2.3673	2.6014	-2.9728
 891 | 0.4280	0.1382	-1.7576	1.1610
 892 | 0.7388	0.0939	2.2428	-2.8571
 893 | -2.9329	3.6740	-1.3099	-0.3647
 894 | -0.2038	0.9021	0.5237	-2.0779
 895 | -1.2065	2.5882	-3.5814	2.1698
 896 | 3.4413	-4.1266	-0.0182	0.8868
 897 | 0.7141	-0.0004	-0.1035	0.7696
 898 | -1.7162	1.0006	-0.9179	-3.5358
 899 | -2.2039	2.3200	-1.6724	0.0514
 900 | 2.7340	-3.5528	1.8804	-1.0203
 901 | -0.4994	1.2852	-1.2943	2.0515
 902 | -2.5689	1.2279	-1.1733	0.8831
 903 | -0.4562	1.9039	-0.1184	2.8718
 904 | -0.0973	-1.0631	1.0433	-1.8119
 905 | -1.4423	3.3976	-0.7274	0.5250
 906 | -0.3972	1.2705	-3.3115	3.2310
 907 | 1.7093	0.0560	-0.1679	-1.6866
 908 | 0.3791	-2.6993	1.0324	-2.2579
 909 | -1.2452	2.5685	-4.1722	5.1294
 910 | 1.3545	-1.9676	0.6502	1.0037
 911 | -1.0581	2.0715	-2.9063	0.8582
 912 | -2.7012	4.1832	-2.3854	1.4059
 913 | 2.1239	-1.5530	1.0820	-0.1460
 914 | 0.6080	-0.3952	1.0802	-0.1689
 915 | -1.3927	2.4269	-2.2547	2.0877
 916 | 1.2666	-0.6127	0.6932	-1.5978
 917 | -1.2921	1.6469	-1.3241	3.4079
 918 | 0.8801	-2.7622	2.1419	-2.7264
 919 | -2.1474	5.4173	-1.8228	0.9176
 920 | -2.8582	3.9412	-3.0585	1.3601
 921 | 2.7681	-4.1379	1.5593	0.8439
 922 | 1.3447	-0.2916	-1.3644	3.5961
 923 | 0.4254	0.7426	-1.1264	2.9899
 924 | 1.2954	-2.2756	3.6319	-2.9951
 925 | -1.3143	0.2553	-0.9582	0.7555
 926 | 1.5075	-1.9301	1.5233	-1.3203
 927 | 0.4433	-0.8519	1.9387	-1.6657
 928 | -1.8945	1.8700	-2.9016	3.0011
 929 | 0.7809	0.0584	0.3304	0.4036
 930 | -0.7149	0.8361	-0.9331	0.3518
 931 | 1.0459	-2.2056	-0.6515	-1.6854
 932 | 1.1699	-0.7598	1.0981	-2.4104
 933 | 0.8734	-0.9978	0.1512	-2.1817
 934 | -1.9300	2.8939	-1.7897	1.4940
 935 | -0.6185	0.1926	2.5417	-0.4000
 936 | -0.5488	-0.2436	0.5878	1.1406
 937 | 0.4166	-1.8235	1.1957	-0.2927
 938 | -1.6611	2.1633	-0.2505	0.7485
 939 | 0.0914	0.7765	-2.8023	2.8577
 940 | 1.1448	-2.6539	0.5378	1.8889
 941 | -1.9650	1.7454	-1.7940	-2.4661
 942 | 3.1065	-4.7496	2.9677	-2.1307
 943 | 0.4019	-0.9636	0.1764	1.5424
 944 | -0.4860	1.1219	0.9786	-1.7279
 945 | 2.3860	-3.7293	2.2829	-2.4598
 946 | 3.6353	-3.8768	2.3513	-2.8779
 947 | -2.9467	2.8857	-0.4497	0.9294
 948 | -0.4677	0.3421	-1.0009	0.2309
 949 | 0.3372	-0.4736	-0.9242	-2.9794
 950 | 0.9720	-2.3608	1.4193	2.4428
 951 | -2.9585	4.7053	-5.2393	2.9978
 952 | 1.1438	-0.9526	1.7973	-1.0424
 953 | -1.0902	2.5361	-1.4610	-1.0395
 954 | -0.1426	-0.9968	1.5464	-4.5985
 955 | -1.9499	0.5039	-0.6940	2.1762
 956 | -3.4349	3.2793	-1.0720	-0.5750
 957 | -1.0521	0.8308	-0.1208	-1.0018
 958 | -0.1782	2.1182	-1.5318	-0.6670
 959 | -1.5844	0.9678	0.4949	-0.7587
 960 | 0.3264	0.4467	-0.5387	-0.3178
 961 | 1.2814	-1.5334	-0.7155	2.4770
 962 | -1.6018	1.1515	1.0733	-2.2780
 963 | -0.8348	2.6508	-1.3159	-0.8361
 964 | -1.1782	2.2640	-1.4300	3.9316
 965 | 0.6795	-0.8917	0.8928	0.7091
 966 | 5.2131	-6.1695	4.6219	-4.8163
 967 | 1.4737	-1.7050	0.9838	-0.8483
 968 | 0.5446	-0.0360	0.4342	-2.2048
 969 | 0.6494	-1.3413	2.9811	-1.4548
 970 | -2.4717	4.2516	-4.1279	2.6051
 971 | -0.7725	1.4424	-1.5611	1.2020
 972 | 2.6774	-2.6313	1.6314	-0.6541
 973 | -1.3634	1.0762	-1.4336	3.4863
 974 | 1.2870	-0.6134	0.9685	-0.2057
 975 | 0.0514	-0.0785	1.5413	1.3304
 976 | -1.6203	0.6220	-2.1104	-0.3684
 977 | -1.4634	1.8736	0.6978	-0.0384
 978 | -0.6193	2.0030	-0.4309	-0.0306
 979 | -0.4093	-0.1578	-0.6319	0.9247
 980 | -0.4354	0.6464	2.6831	1.8573
 981 | -2.9958	4.3398	-1.4766	-0.6262
 982 | 1.0059	-2.5382	3.6359	-3.3206
 983 | 0.7826	-1.9593	1.7679	-0.4976
 984 | 0.6347	-1.0327	2.1927	-5.7735
 985 | 0.3068	-0.4420	1.3557	0.7140
 986 | -0.0940	0.1703	0.9483	1.0319
 987 | -0.1446	0.0993	3.0105	-1.1109
 988 | 1.0615	-0.9156	1.3325	1.1579
 989 | 0.8891	1.2227	-2.6427	2.2665
 990 | 1.4013	-0.5896	-1.5443	-0.5556
 991 | 0.7773	-1.3005	-0.5529	3.7872
 992 | 3.4407	-4.1131	2.7247	0.5375
 993 | -3.3263	2.0598	-5.2521	3.3535
 994 | 1.2069	-1.0435	-2.0167	-1.2310
 995 | 0.6565	-0.0669	-1.1570	0.2013
 996 | 1.3436	-0.3213	-0.8895	1.4415
 997 | 3.5522	-4.1346	3.5319	-2.7047
 998 | 0.4108	-0.7597	1.9384	-3.1283
 999 | -1.4329	-0.3097	-0.0688	1.2975
1000 | -0.0549	-0.0765	1.0857	0.3450
1001 | 5.6242	-7.1046	3.8849	-3.0839
1002 | 


--------------------------------------------------------------------------------
/data/params_1.txt:
--------------------------------------------------------------------------------
   1 | X1	X2	X3	X4
   2 | 0.4221	0.4384	-1.3173	2.9460
   3 | 0.9492	1.4172	3.0107	-2.5591
   4 | -1.2589	-2.9390	-4.0365	3.1387
   5 | -0.1838	-0.0869	0.3865	1.0364
   6 | -0.0153	-0.7454	2.1462	-1.6822
   7 | -0.3087	-0.3780	-2.5973	3.2732
   8 | 1.4135	2.1229	2.2045	-1.9622
   9 | -0.3369	0.0961	-4.3773	3.5781
  10 | 1.3726	0.4430	3.3575	-3.1190
  11 | -0.5519	0.4889	-1.0742	1.0067
  12 | -0.3702	0.8806	-0.4347	1.6218
  13 | 0.1613	-0.3125	-1.9745	1.4639
  14 | -1.9433	-2.0454	-5.5510	4.9709
  15 | -0.2373	-0.0943	-1.8291	3.3212
  16 | 0.0960	-0.4582	0.2090	-1.6387
  17 | 1.5737	1.9769	1.3347	0.4191
  18 | -0.6177	0.4303	-3.8961	4.5672
  19 | -0.5416	-0.0257	-1.5083	2.2654
  20 | 1.3120	0.8179	0.5658	1.3635
  21 | -2.7114	-3.6563	-6.6238	5.2493
  22 | 2.2458	1.7482	0.7674	-0.8067
  23 | 0.1383	-0.0902	1.4498	-2.6829
  24 | 1.0011	3.1140	2.4010	1.7335
  25 | -0.5098	0.1656	-4.7299	3.8269
  26 | -1.2512	-2.4365	-3.6005	2.0945
  27 | 1.2103	2.2939	1.8404	-0.4667
  28 | 1.3678	1.0705	2.3198	0.6191
  29 | 0.8519	0.9737	2.8179	-3.0818
  30 | -0.6895	-1.5446	0.7317	-0.9051
  31 | 1.7776	3.2422	3.7977	-2.0273
  32 | -1.7405	1.9001	-4.4139	4.0717
  33 | 1.1029	0.1807	-0.0358	1.7188
  34 | 1.7817	0.2406	2.0504	-3.2231
  35 | -0.7134	-0.8464	-2.6561	4.0011
  36 | 1.2413	1.9334	2.4221	1.2244
  37 | 0.2386	0.6823	-1.1959	0.1787
  38 | -0.9218	-1.8805	-2.2121	1.8575
  39 | 0.0085	0.1856	1.2902	0.6128
  40 | 0.8860	2.3912	1.8825	-2.2596
  41 | -1.3470	-2.6017	-3.3230	1.4958
  42 | -2.3501	-0.2527	-4.6446	5.4920
  43 | 1.2622	1.1215	0.8703	-0.5787
  44 | -0.3280	0.7944	-3.2052	2.7608
  45 | -0.9986	-0.8495	-0.5365	-1.3153
  46 | -1.8836	-2.3289	0.6953	-1.3516
  47 | 0.7963	0.1409	1.0663	-1.5361
  48 | 1.8679	1.8098	4.5032	-2.7037
  49 | -0.8342	-1.9214	0.1954	-1.7231
  50 | -0.6599	0.0298	-2.0961	2.3547
  51 | 0.5265	-1.0956	0.6819	-0.8633
  52 | 0.7403	1.5281	6.2942	-5.4374
  53 | 2.0280	2.1030	3.2321	-1.7957
  54 | -0.5464	-0.2012	-1.3611	2.4479
  55 | -1.7944	-1.5835	-4.2611	3.7582
  56 | 1.5155	3.0680	5.4686	-5.0525
  57 | 0.1578	-0.5712	-3.5115	2.6895
  58 | 0.0269	-0.8508	-0.2057	1.7648
  59 | 0.0609	-1.1035	-1.1678	-0.0698
  60 | 0.4430	1.2429	0.0761	0.4405
  61 | -0.5597	-1.8779	-1.6392	0.5823
  62 | -0.7618	-1.1871	-1.9504	1.9863
  63 | -2.2828	-3.4836	-3.4350	4.0602
  64 | 2.6874	1.8042	4.3237	-2.9310
  65 | -1.4835	-3.0038	-2.8087	-1.3042
  66 | 1.0511	2.0064	-0.6945	-0.3868
  67 | -0.9530	-0.4949	-1.8805	0.9986
  68 | 3.2304	4.4726	6.7548	-4.6933
  69 | -1.4659	-1.2924	-1.3397	-0.1724
  70 | -0.0827	-0.7607	-0.9415	0.3493
  71 | 0.0107	-2.3775	0.3953	-3.5036
  72 | 0.4328	-0.7803	1.4881	-2.8410
  73 | -0.0568	-0.7892	-2.0522	1.9636
  74 | -0.4649	0.6341	2.1337	-1.9094
  75 | -0.5447	1.1631	-1.8098	3.7922
  76 | -0.5412	-1.1206	-0.4193	-1.1130
  77 | 2.1935	0.9406	2.4002	-1.6031
  78 | -0.2036	-1.8214	0.3701	-0.7954
  79 | -0.1302	0.9376	-1.1375	-1.0442
  80 | -0.8151	-2.0489	-3.1127	3.4073
  81 | 2.1216	2.9254	1.1789	0.9501
  82 | -0.8000	-1.8094	-3.0985	2.1389
  83 | -0.1136	0.2079	0.5581	0.0166
  84 | -1.5750	-0.8081	-4.5014	5.6083
  85 | -1.1694	-0.8229	-0.9731	-1.3999
  86 | -0.5363	-0.7507	-2.2879	3.4020
  87 | 0.0659	2.6693	-2.5252	0.6839
  88 | 1.2743	0.9704	2.8380	-5.8945
  89 | 0.3143	-1.4013	-1.1832	2.2993
  90 | 2.4719	1.0353	3.8212	-4.7810
  91 | 1.7280	3.1156	1.6403	1.8628
  92 | 0.3809	-2.4305	-0.4238	-0.4240
  93 | -0.2335	-1.1428	-0.2635	-0.8604
  94 | 0.3108	-0.8257	-1.2976	0.6161
  95 | -0.0816	0.0180	-1.2420	2.1012
  96 | 0.2342	1.0406	0.0705	-0.5182
  97 | 2.1600	3.5885	3.1074	-2.4208
  98 | -1.3978	0.4984	-4.2853	3.8048
  99 | 0.5205	1.5099	1.2366	-1.1065
 100 | 1.8619	1.5031	0.5421	-1.1230
 101 | 1.0042	1.3626	1.1262	-0.3403
 102 | 0.0533	3.5121	0.6921	1.0873
 103 | -1.0375	-2.4498	-4.8993	5.2073
 104 | 1.7036	0.9064	1.8648	-3.1294
 105 | 0.9415	1.3896	2.3639	-0.8299
 106 | 1.6802	2.7376	6.4177	-2.9759
 107 | -1.0406	-1.1874	-2.3030	2.8096
 108 | -0.0602	1.8655	0.7256	1.4306
 109 | 0.6997	-1.5696	-0.6425	0.8768
 110 | -0.8232	-0.5662	0.4193	0.3471
 111 | 1.0750	1.2896	0.4809	0.3900
 112 | -0.2770	0.2853	-3.1160	2.9963
 113 | 0.8744	-1.3777	1.1802	0.8666
 114 | 0.3229	-2.0220	-0.7336	0.8150
 115 | 0.3791	-0.5399	1.9064	0.3788
 116 | 1.9950	3.8203	0.2543	1.4392
 117 | -0.7438	1.1652	0.0391	-0.6343
 118 | -0.3964	-2.0365	-0.8261	-2.4984
 119 | 0.4931	2.1455	0.2163	1.7033
 120 | -0.8151	-1.2609	-1.6957	1.9154
 121 | 0.5680	-1.2519	-1.9496	1.6687
 122 | 1.5940	2.6880	0.5001	1.8136
 123 | -0.1798	-0.6030	-1.2748	-0.0474
 124 | -1.1356	-1.9288	-1.0715	1.7402
 125 | -0.3189	-1.7417	-3.0155	2.2012
 126 | 0.9236	-0.2126	1.1129	-2.1075
 127 | 1.5860	2.2490	0.9156	0.6870
 128 | -0.5742	1.2993	-0.5665	0.7481
 129 | 1.3007	1.5296	2.4215	-0.1881
 130 | -1.8416	-1.2974	-2.1990	1.9805
 131 | -0.8418	-0.8481	1.7427	-1.4174
 132 | 0.8017	-0.4446	1.7721	-0.8251
 133 | -1.3454	-2.2427	-0.8648	0.3529
 134 | 1.2588	1.1594	1.0904	0.9119
 135 | -1.3497	-1.3655	-2.8564	2.3510
 136 | 2.3817	2.8072	4.0609	-3.0936
 137 | 1.3820	1.6532	2.9098	-1.2292
 138 | 1.4827	3.0207	2.7008	-2.3162
 139 | 1.4449	-1.5429	3.9433	-2.9984
 140 | -1.6225	-1.3788	-1.1630	0.5102
 141 | 0.7046	0.6381	2.1051	-3.0108
 142 | 1.3322	0.1194	2.0138	-1.7477
 143 | -1.4934	1.5691	-3.7732	4.5560
 144 | -1.4324	-2.0244	-2.4805	1.4298
 145 | 1.2891	0.5035	4.1002	-6.2902
 146 | 0.2724	0.0563	0.8724	-0.5333
 147 | -0.1669	-1.0851	-0.9390	-0.8744
 148 | 0.8352	1.7432	0.3819	0.8269
 149 | 0.2182	-2.0789	0.2213	-1.5635
 150 | 1.2184	1.5160	1.3717	0.5089
 151 | 0.2872	2.1123	2.0826	0.2479
 152 | 0.7521	-0.4908	2.7687	-1.7748
 153 | 1.0511	1.8088	-0.2405	-1.3373
 154 | -0.6982	-2.3512	-0.8518	-0.1299
 155 | -1.8685	-1.2945	-6.1929	5.9108
 156 | 2.0928	2.5377	5.2196	-5.9488
 157 | 2.0260	1.6135	1.3948	-0.6602
 158 | -1.6393	-2.6317	-4.9696	0.9858
 159 | -2.6279	-2.6216	-5.4898	2.6160
 160 | 0.1795	1.5979	-0.8810	4.4242
 161 | 0.0662	0.8502	-1.3737	1.4543
 162 | 1.1938	0.7956	-1.3887	0.1524
 163 | 1.9644	1.2960	2.7610	-2.0831
 164 | -0.7438	-1.7077	-0.8291	-1.0895
 165 | -0.4597	-2.1041	-2.1065	0.7512
 166 | 1.3718	3.2860	5.0568	-3.5782
 167 | -3.2924	-2.9738	-9.2873	6.8004
 168 | 0.3266	-0.0157	-2.6747	3.1481
 169 | -1.1471	0.8667	-0.4318	2.8683
 170 | -0.5594	-1.0770	-2.6702	3.5538
 171 | -1.1435	0.8109	-3.0400	3.0015
 172 | 0.5848	-0.3361	-0.6288	2.5193
 173 | 0.6064	0.2134	3.8596	-2.6834
 174 | -0.4914	-2.7708	-0.6787	-0.6707
 175 | 2.1360	2.9496	5.5263	-4.4301
 176 | 1.1309	-0.7875	1.8785	-0.7299
 177 | -0.9808	0.8936	-0.9309	1.1030
 178 | 0.0944	-0.1684	-0.1508	-0.9904
 179 | -1.0203	-1.3748	0.8601	0.8602
 180 | 1.6617	0.5431	1.6265	-0.8985
 181 | -0.4051	1.9592	2.1060	-0.6222
 182 | -2.5894	-4.1678	-2.8560	1.0738
 183 | 0.3031	1.8596	1.7285	-2.8316
 184 | 0.9035	1.3588	0.9366	-0.7800
 185 | 2.1394	2.3134	3.4171	-1.3870
 186 | 0.5316	-0.8055	0.2680	-0.7528
 187 | 2.3502	3.5247	4.6712	-0.9047
 188 | -1.8994	-0.8916	-2.9110	3.2466
 189 | 0.5426	-0.7229	0.3876	-0.7971
 190 | -0.3920	0.3660	-2.2785	3.1365
 191 | 1.0449	0.9205	3.7890	-0.2354
 192 | 2.0753	1.1596	3.9070	-2.4280
 193 | 0.3357	-0.5130	-1.0780	-0.4683
 194 | -0.5928	0.0881	-0.1836	-0.9254
 195 | -1.2659	-0.9978	-1.0359	0.3054
 196 | 1.1711	0.7434	4.0947	-3.5762
 197 | -0.3725	-0.1824	1.6879	-2.0108
 198 | -0.3386	-0.0924	-1.7751	-0.0003
 199 | -1.3178	-3.8849	-5.4367	4.2559
 200 | 0.5460	-0.0285	1.9712	-1.9296
 201 | -1.4471	0.9032	-1.6257	2.2724
 202 | 2.3111	2.3026	6.5581	-7.5970
 203 | -1.7932	-2.0270	-5.5022	6.7413
 204 | -2.9694	-4.1483	-6.1015	3.0931
 205 | -0.6716	0.3793	1.3510	-0.5138
 206 | 1.5549	2.0291	2.8580	-0.3100
 207 | -0.3361	-1.0339	-0.0237	1.5034
 208 | -1.0818	-1.9339	-0.0445	0.5863
 209 | -0.8095	2.1480	1.9382	1.8058
 210 | -0.7383	1.1371	1.5550	-0.7095
 211 | -2.3481	-3.7457	-5.2956	0.0905
 212 | -0.7928	-0.0381	0.6234	-1.0773
 213 | 0.2111	1.4635	0.9228	0.4841
 214 | 2.1464	4.2999	4.3042	-2.4572
 215 | 0.5996	-0.5279	3.2525	-3.3798
 216 | -0.1402	2.3598	-1.2377	1.1719
 217 | -0.8706	-2.3439	-3.0613	1.8819
 218 | 1.0252	1.8943	1.8854	0.6542
 219 | -0.2315	-1.7033	-0.8078	-1.8235
 220 | 0.9203	1.7557	2.9017	-2.7575
 221 | 0.0720	0.2353	-0.6472	1.0341
 222 | 0.9023	-0.1701	0.3757	-0.8528
 223 | -1.5155	-0.1245	-2.8353	4.2380
 224 | 1.7210	1.4789	4.3153	-6.0321
 225 | -0.2678	-1.2289	-1.5351	1.2349
 226 | 1.0075	-1.2985	1.0202	-3.2551
 227 | -1.0951	-1.3614	-0.2926	1.0003
 228 | -0.5328	0.3670	-0.6750	0.2740
 229 | -0.2096	1.7322	-1.0528	1.2531
 230 | -0.1730	1.8005	0.1456	0.3775
 231 | 1.5614	0.6388	4.0117	-3.7534
 232 | 0.6454	1.6328	3.6341	-3.9130
 233 | 0.5907	-0.8215	-0.1281	1.5731
 234 | -1.4879	-3.8450	-4.1064	0.2378
 235 | 1.0088	1.6449	2.8611	-4.4131
 236 | 1.4601	0.1024	2.4678	-1.5117
 237 | 0.3695	1.2409	-0.5709	1.6225
 238 | -4.1015	-4.0449	-9.0040	8.0869
 239 | -0.1721	-2.1993	-2.2324	0.1576
 240 | 1.1400	1.2867	1.0537	0.2433
 241 | -1.0768	-0.3870	-1.8456	-0.8726
 242 | -2.5927	0.4117	-4.5035	2.5381
 243 | 0.1352	-0.0056	-0.9499	1.6577
 244 | -0.7668	-1.0976	0.3385	-1.0852
 245 | -0.2308	0.2340	2.0068	-2.3547
 246 | -0.5311	-1.8421	-3.1554	1.2833
 247 | 1.2256	1.2933	4.6867	-1.7969
 248 | 0.3557	-0.5998	1.0450	-0.8946
 249 | 3.4559	2.1941	6.9349	-5.8478
 250 | 0.4847	0.6631	2.2031	-1.7367
 251 | -1.4702	-1.9361	-0.2175	-3.0276
 252 | -0.0126	1.4828	-1.1065	1.7595
 253 | 0.7725	-1.6608	0.3436	0.0653
 254 | 1.3629	-0.9063	4.3995	-6.1864
 255 | 2.0368	1.4317	4.3147	-3.2661
 256 | 1.2608	1.0917	0.0254	1.9426
 257 | -0.4288	3.3123	1.7569	-0.1571
 258 | -0.5591	-1.8184	-1.4255	0.9952
 259 | 1.0064	0.3755	-0.2447	0.3557
 260 | -0.4902	0.8934	1.4711	-0.5725
 261 | 1.3334	-2.2710	3.5222	-4.3250
 262 | 0.3685	0.5561	0.6917	-0.7538
 263 | -0.2291	-1.0220	-1.3849	1.1744
 264 | -0.4519	-2.9717	-3.4148	1.7864
 265 | 1.6125	1.6404	0.7039	2.3613
 266 | -0.9058	-0.1002	2.7017	-2.3626
 267 | 0.5988	0.2731	1.4601	-0.2672
 268 | 1.3374	2.0414	1.3772	-0.4913
 269 | -0.4077	1.1350	-1.2892	1.8102
 270 | 1.2018	-1.5562	0.7782	-1.6808
 271 | -0.4459	-0.2122	-1.9862	2.9121
 272 | 0.9134	0.5364	5.0529	-4.3478
 273 | 0.8670	0.8845	0.8534	1.0234
 274 | 1.1584	1.5535	3.2380	-1.9452
 275 | -0.7084	-2.9439	-2.3624	2.4472
 276 | -0.5929	0.2061	-4.6020	3.9335
 277 | 2.7290	2.2243	5.4626	-6.0632
 278 | 1.0492	0.1157	0.9385	-1.8301
 279 | 2.6296	1.4288	6.5523	-6.6688
 280 | -1.4478	-2.7953	-5.5835	3.0066
 281 | -1.3150	-3.1975	-0.9487	1.1275
 282 | -0.2918	0.1629	2.7850	-1.8335
 283 | 0.7717	2.8904	2.3819	-0.4475
 284 | 0.1558	-0.3002	2.2535	-3.5183
 285 | -1.5040	-0.2251	-2.8013	1.1889
 286 | -0.2877	-0.1999	-1.7336	2.9412
 287 | 0.8268	2.3178	1.7893	0.0100
 288 | 0.9968	1.0185	-0.1383	1.7876
 289 | 0.6877	1.2983	2.5730	-3.5440
 290 | 1.5436	0.2673	1.6253	-3.6913
 291 | -0.0914	-0.3981	-2.0548	3.4705
 292 | -0.9880	-0.3287	-0.7854	0.4069
 293 | 1.4285	2.5875	1.2680	1.7061
 294 | -0.4086	0.2145	-0.4502	0.4815
 295 | 1.3865	1.7876	3.0702	-2.2037
 296 | -1.4396	-1.9437	-2.7500	1.4544
 297 | -0.4854	-1.1706	-1.9562	1.4765
 298 | 0.6932	0.7210	5.2635	-4.6271
 299 | 0.4473	-0.1053	-0.0610	-1.5039
 300 | 1.2486	0.3165	3.5894	-4.5874
 301 | -1.0020	-1.8378	-0.2352	1.7369
 302 | 1.0761	0.5849	2.0370	-1.7983
 303 | 0.8080	-0.3826	3.5695	-2.3067
 304 | -1.3195	-0.5294	-5.8050	7.1090
 305 | 1.2316	1.0195	3.5572	-1.6951
 306 | 0.7826	0.4403	1.2962	-0.9682
 307 | 1.1665	-0.2042	0.7832	0.1215
 308 | 0.7219	0.6794	-1.9772	1.5906
 309 | 1.0696	0.6326	1.7247	-0.3414
 310 | 0.3270	2.0521	1.6197	-1.7773
 311 | -0.3591	1.1746	2.0382	-1.0370
 312 | -0.0176	0.0498	-1.1415	0.6802
 313 | 0.1384	-0.5503	-1.9090	2.8729
 314 | -0.0398	-1.3852	-0.6622	0.2763
 315 | 0.2408	0.4574	-2.2373	3.1889
 316 | -2.5765	-3.7507	-4.5438	5.2000
 317 | 0.4908	-0.0332	2.1604	-1.9665
 318 | 1.0731	2.6972	1.4610	-0.7973
 319 | -0.8413	-1.4488	-0.9764	1.0266
 320 | -0.5542	-0.7063	-3.2696	4.7550
 321 | 1.0102	0.7882	4.2588	-3.9340
 322 | 0.1450	0.6975	1.8223	0.0678
 323 | 0.2828	0.7426	-0.6122	0.5385
 324 | 2.2403	1.4689	3.4380	-3.7422
 325 | -0.8625	-0.1129	-3.6903	2.8163
 326 | 0.8827	0.7347	2.9758	-1.5375
 327 | -0.8258	-2.8022	0.8067	-1.6966
 328 | 3.0356	3.4338	6.6386	-4.2144
 329 | -0.1238	0.3456	-1.8563	1.0319
 330 | -2.1536	-2.8786	-1.4978	-0.2480
 331 | 0.2414	-0.3007	-3.2513	3.0289
 332 | -1.1192	-0.9764	-0.9241	0.3775
 333 | -1.3837	-1.1293	-0.6887	0.8602
 334 | -2.1137	-3.0968	-4.9341	2.9998
 335 | -0.0979	0.1959	-0.3551	1.1983
 336 | 0.4240	0.2546	1.4607	-0.7983
 337 | -0.9771	-1.6813	-2.4644	2.8643
 338 | -0.0643	-0.2702	1.2848	-4.1266
 339 | -1.5268	-3.0281	-3.3209	0.5872
 340 | -0.5284	-2.2488	-4.4298	3.7614
 341 | -0.0429	-1.3719	-0.3469	-1.9798
 342 | 0.2387	-0.1271	0.7121	-0.6782
 343 | 1.0610	0.3634	0.3579	-2.4776
 344 | -2.1118	-1.3960	-2.1465	2.3440
 345 | 0.4140	-1.5741	0.8931	-0.1832
 346 | -0.5889	-1.8865	-2.4828	1.8725
 347 | -0.7008	-1.9102	0.2421	-0.3865
 348 | 1.4182	0.1309	1.0218	-0.9057
 349 | 0.4784	0.0289	1.4581	-1.9601
 350 | 1.3327	1.3803	3.7734	-3.0391
 351 | 1.3492	2.1318	1.6804	-2.0360
 352 | -0.8169	-0.3050	-2.6177	1.3214
 353 | 0.3106	-0.1786	-0.2707	0.6259
 354 | -0.0322	0.3086	1.7010	0.2549
 355 | 1.3485	1.7519	0.9032	-0.2329
 356 | 1.9703	1.0191	5.6907	-4.1068
 357 | -0.7059	-1.1646	-4.5834	5.1654
 358 | -1.3912	-0.6543	-0.4590	0.2121
 359 | 1.0457	1.2616	2.5750	0.6115
 360 | 1.5790	-0.6112	2.2807	-3.3287
 361 | 0.7463	-0.6071	2.3301	-2.7091
 362 | -0.8863	-1.2792	-3.3897	0.8131
 363 | -1.2480	-2.6815	-2.0513	1.1016
 364 | -1.2951	-1.5037	-3.0437	2.9696
 365 | 0.1988	-0.1523	-0.1351	1.2128
 366 | 1.7862	1.0209	2.3765	-1.0301
 367 | 0.0232	-0.2054	-1.2976	0.6003
 368 | 2.2411	-0.9455	2.9019	-4.4060
 369 | -0.6376	-0.7584	-1.1063	0.7693
 370 | 0.1973	-0.5247	-1.7270	2.6850
 371 | -0.5810	0.0675	1.6841	-3.6887
 372 | 1.3109	3.9982	5.7956	-4.4117
 373 | 1.2774	1.2307	4.2570	-3.9394
 374 | 0.8357	0.6900	2.6966	-4.5268
 375 | 0.1960	-0.3030	-1.8123	2.0318
 376 | 1.4537	2.9059	5.3114	-6.1683
 377 | 1.4870	1.9721	2.0162	-2.3447
 378 | 0.1487	-0.1423	2.0458	-3.4138
 379 | 2.4838	2.9584	4.8436	-3.1080
 380 | -1.7007	0.4949	-3.1421	3.0229
 381 | -0.0767	0.9124	0.6103	-2.3290
 382 | 1.3003	1.1504	4.1766	-3.4119
 383 | 2.4847	-0.8935	5.2028	-5.5396
 384 | 0.5247	0.4676	4.0276	-2.1602
 385 | 0.4765	0.8766	3.3361	-0.7136
 386 | 1.5709	0.5149	3.5040	-3.7556
 387 | 2.0771	0.4484	4.1284	-3.7246
 388 | -0.0891	0.6212	0.5538	0.2757
 389 | -0.3320	-1.1612	-3.7698	2.1168
 390 | 2.8789	2.0328	8.2193	-8.5263
 391 | -2.9083	-3.3313	-5.3299	5.0328
 392 | -0.9839	-0.0696	-0.0955	0.4527
 393 | -1.2441	1.9562	-2.0649	2.5998
 394 | 0.2834	2.2278	1.0234	0.2243
 395 | 0.8445	0.4794	-0.7517	0.7243
 396 | -0.4047	-0.4710	2.0105	-2.9939
 397 | 0.3239	-0.1109	-0.5258	0.6693
 398 | 0.2588	-1.0334	0.7332	-3.0833
 399 | 1.8482	1.4504	3.4422	-2.1724
 400 | -1.7409	-1.2615	-5.0336	3.7104
 401 | -0.4281	2.5417	-0.4135	2.6137
 402 | 1.1448	-0.7006	2.7636	-3.1788
 403 | 1.4227	4.4986	1.9905	1.8105
 404 | 0.1742	0.0261	-0.6839	-0.0361
 405 | -0.6525	-1.0191	-3.2400	2.2132
 406 | 0.2606	1.4683	-0.7828	1.5069
 407 | -0.2412	-1.3175	0.0373	-1.5513
 408 | -0.0175	1.3999	4.3298	-5.6834
 409 | 1.4820	2.8175	2.5687	-1.0200
 410 | 2.0134	0.1965	3.5009	-3.3929
 411 | -1.2145	-1.8609	1.4664	-4.2407
 412 | -0.4802	-1.0327	-0.5054	0.9732
 413 | -0.2647	1.3140	-0.8950	2.4167
 414 | -2.7675	-2.2948	-3.0091	1.9055
 415 | -0.2573	-0.3701	0.8630	0.3414
 416 | 0.2458	1.5357	0.9590	-2.0151
 417 | -0.6165	1.4784	2.6500	-3.6100
 418 | 0.4031	0.2714	2.9359	-1.8832
 419 | 0.5934	1.6299	2.1325	-0.9504
 420 | 0.9474	1.0787	0.9585	-3.3317
 421 | -0.4336	-2.2205	-2.6955	2.3728
 422 | 1.7193	2.1809	2.5452	-0.6334
 423 | 1.8018	1.5586	1.8424	1.0107
 424 | -2.1023	-1.8680	-5.3176	5.2661
 425 | -0.0040	0.8033	-1.8068	0.2447
 426 | -1.1871	-0.9583	-4.9276	2.5868
 427 | -0.0534	0.1875	0.1293	-0.6111
 428 | -1.7277	-2.1077	-1.5254	0.8533
 429 | 1.1112	2.0105	2.5280	-1.3788
 430 | 0.2168	-1.6762	1.7040	-3.3157
 431 | 1.1384	0.6374	1.6482	1.2901
 432 | -0.3773	0.4084	-4.0038	3.3591
 433 | -1.4849	-3.1382	-3.7851	3.1311
 434 | 2.2148	2.9897	3.3275	-0.1572
 435 | 1.0283	1.8381	5.6544	-5.1633
 436 | -0.3917	1.3397	0.0095	0.2976
 437 | 0.5030	1.2775	3.6297	-2.6396
 438 | 1.6763	1.0144	6.1336	-5.0702
 439 | -0.5492	-0.7054	2.6119	-3.1852
 440 | 0.3001	0.5844	-0.4320	1.4743
 441 | 1.9061	2.4351	2.3581	-1.5055
 442 | 0.7647	-0.7681	0.3428	-1.7734
 443 | -1.2509	0.5251	0.2771	-1.0364
 444 | -0.1489	-1.3473	1.0857	-0.1641
 445 | -0.2176	0.0417	0.6293	-0.3938
 446 | -1.0656	-1.5191	-0.0053	-1.6797
 447 | -1.4897	-2.0528	-4.0325	4.0726
 448 | -3.6290	-5.3014	-5.6506	4.6000
 449 | -0.8540	0.2747	-3.8989	4.6577
 450 | -1.5562	-1.3178	-3.6415	2.5800
 451 | -0.0357	1.9113	0.0393	2.4706
 452 | 1.1600	-0.0665	3.2032	-2.0242
 453 | 0.0074	-0.1853	-0.6150	2.8065
 454 | 1.6184	0.0356	2.6802	-0.8727
 455 | -0.3741	0.4066	0.2414	0.9678
 456 | -0.3044	0.5077	0.5705	0.4339
 457 | -0.5406	-0.9668	-0.2168	-1.0771
 458 | 1.0601	0.6901	2.5941	-2.8898
 459 | 0.2634	1.8413	-1.2870	2.5712
 460 | -2.4324	-2.4471	-4.3391	4.2879
 461 | -2.7327	-0.0412	-3.8631	1.0503
 462 | -1.0175	-2.2728	-0.1626	-1.5627
 463 | -1.1080	-1.0050	1.0603	-0.5066
 464 | -1.2206	-3.3028	-3.9826	3.6547
 465 | -0.0076	-2.5139	0.8435	-1.3532
 466 | 0.4005	-0.6428	0.5448	-1.0270
 467 | -1.1336	0.2474	-0.6572	1.2060
 468 | 1.7286	1.9731	3.5904	-3.3995
 469 | 0.1675	0.1514	-0.8637	3.4922
 470 | 0.3097	0.8796	-0.2108	-0.0779
 471 | -0.3254	-0.4969	-1.0881	1.9348
 472 | 0.0363	-0.9665	-0.0703	-0.4665
 473 | 0.5319	-1.4919	-2.2974	2.5919
 474 | 0.6288	0.7998	3.6209	-2.1737
 475 | -0.5335	2.4944	-2.8886	3.5566
 476 | 1.3921	2.7560	5.6088	-5.3341
 477 | -0.4104	-2.8793	1.6658	-2.6562
 478 | -0.0840	0.0132	0.8154	2.4806
 479 | 0.7330	-0.1490	-0.1950	-1.2075
 480 | 1.9442	2.2098	3.6322	-3.5461
 481 | 2.3104	2.0191	2.4832	-2.0771
 482 | 1.1945	-0.2601	1.8794	-2.4854
 483 | -0.0667	0.2148	1.3808	-0.1781
 484 | 1.5517	1.8335	5.2327	-3.6159
 485 | -1.1672	-0.5829	-4.0546	3.5922
 486 | 2.4052	4.8488	5.2471	-1.0166
 487 | -0.5882	0.2308	1.2214	-0.4744
 488 | 0.2314	0.6349	-0.1210	2.6659
 489 | 0.5457	-0.1376	0.4434	0.7594
 490 | 0.4623	-0.5657	2.4360	-1.6137
 491 | 0.0220	1.5290	-0.4958	0.7654
 492 | -0.8717	0.2540	0.8885	-1.7240
 493 | -1.1096	0.1498	-1.8292	1.5767
 494 | 0.2771	1.8464	2.5500	-0.9636
 495 | 0.7788	0.4695	2.6543	-0.2071
 496 | -1.2805	0.5941	0.3031	0.2070
 497 | -0.5894	-2.7659	2.1839	-1.7521
 498 | 0.6621	1.6978	-0.4947	2.3835
 499 | 0.1120	0.3543	0.0859	1.1393
 500 | -0.4318	0.4988	0.7392	-1.1712
 501 | 1.7640	2.2872	2.2433	0.1755
 502 | -1.0258	-0.1392	-0.5919	0.8601
 503 | 0.6705	-0.1807	-0.8380	-0.9691
 504 | 0.1467	-0.5993	-0.7674	-0.1996
 505 | -0.3711	-1.4255	-0.6464	1.1862
 506 | 1.4505	4.4049	-0.0964	2.3239
 507 | -2.5216	-1.7532	-6.6575	4.5629
 508 | -0.3691	0.8252	0.4696	0.6042
 509 | 0.7819	1.0549	1.5382	-2.7436
 510 | 1.8091	0.5833	5.8846	-5.2786
 511 | -0.9688	-1.8804	-1.8577	0.4901
 512 | 1.4828	0.1630	7.0501	-6.0849
 513 | 0.5272	0.2210	4.0813	-5.0069
 514 | 1.8930	1.3868	4.0628	-5.0543
 515 | 0.9389	-0.2721	2.3473	-2.0869
 516 | 1.1803	1.7784	2.4449	-0.1889
 517 | 1.0609	-0.7485	0.4142	-1.5863
 518 | -0.1359	1.6251	2.6516	-2.9342
 519 | 1.4142	1.0649	3.4620	-4.9002
 520 | 0.6008	-1.2809	1.9329	-2.6476
 521 | 0.6043	2.8750	1.8431	-0.4951
 522 | 0.5065	1.7988	1.0119	-0.6114
 523 | 0.8628	2.0477	0.8844	0.2036
 524 | 3.2462	2.9185	7.9731	-7.5870
 525 | -0.1379	-0.4886	-4.8918	4.0995
 526 | -1.3593	-0.4968	-1.0808	-1.1390
 527 | 2.7757	2.2563	3.7685	-1.5405
 528 | 1.1590	1.5534	2.7799	-0.0688
 529 | -0.1413	0.8298	1.6892	-1.0343
 530 | -0.8638	0.9030	-1.7259	4.5435
 531 | -0.5567	-0.2590	-0.8997	0.6125
 532 | -0.1543	2.3830	2.8560	-1.4861
 533 | 3.1945	3.0466	5.0699	-3.0448
 534 | 0.1866	-0.7855	0.4653	-0.5346
 535 | 1.3384	-1.1408	4.4893	-5.2114
 536 | 0.3941	-0.3620	-2.3235	1.6339
 537 | -0.8142	-1.8180	-2.2444	2.2256
 538 | -0.7526	0.3858	0.6852	0.6928
 539 | 0.5812	2.7461	4.0869	-2.0584
 540 | -1.6324	-1.7109	-7.8246	6.6612
 541 | -1.3821	-1.5081	-5.0492	5.2010
 542 | 1.9084	3.5973	4.2449	-4.0506
 543 | -1.1294	-2.3737	-1.8158	1.5849
 544 | -1.2417	-1.4748	-0.9370	0.8973
 545 | 0.4228	1.7431	0.2517	1.8793
 546 | 1.3096	2.3971	3.3020	-1.5678
 547 | 0.6783	1.0503	1.2364	-2.2278
 548 | 2.4131	-0.5640	3.9111	-4.5779
 549 | -2.0309	-3.8018	-2.9857	1.1926
 550 | 1.0318	1.9862	1.0901	-1.4298
 551 | 1.0278	0.7019	1.8038	-1.2205
 552 | 0.9475	-0.3721	3.3908	-2.6908
 553 | 0.4622	0.5492	0.2317	-1.0423
 554 | -1.3727	-1.9553	-1.4638	1.8602
 555 | 1.4251	2.2830	3.1546	-3.7820
 556 | 1.2113	2.1431	0.2968	1.2388
 557 | -1.2505	-0.1807	0.8611	-2.5957
 558 | 0.4768	-0.4560	0.3060	0.4227
 559 | -1.5786	-2.3952	-2.9030	3.7656
 560 | -0.4390	0.6961	0.0453	-0.8613
 561 | -0.1089	0.0583	0.5922	-1.5381
 562 | -2.1364	-1.2403	-7.1205	7.4554
 563 | 0.1300	-0.7509	0.0829	0.7459
 564 | 1.0827	1.6930	2.3512	0.4223
 565 | 1.2527	0.8023	0.4160	0.4510
 566 | -0.4434	0.3203	-0.5736	-0.8615
 567 | -1.7101	1.1834	-3.1879	3.3757
 568 | -0.9616	-0.6284	-0.8966	-0.4528
 569 | -1.5883	-1.6392	-3.3259	2.1540
 570 | -0.1931	1.0047	-1.6955	2.2410
 571 | 1.0905	2.9007	1.6767	-0.3381
 572 | 1.0968	1.8233	2.4394	-2.9024
 573 | 0.9667	2.1248	4.2196	-1.7983
 574 | -1.6148	0.4089	-3.5129	1.7873
 575 | 2.0176	4.0677	4.6033	-1.8887
 576 | -0.3824	-0.1504	-0.9108	-1.2141
 577 | 1.3798	0.3674	1.6223	-0.1609
 578 | 0.3617	-0.0634	1.5684	-0.9209
 579 | -0.7017	-0.0774	-0.5790	-0.8977
 580 | 0.6044	0.6246	1.7464	-1.0592
 581 | -0.3688	-2.1519	1.1904	-0.7954
 582 | -2.3101	-3.3738	-3.5312	3.4569
 583 | 1.1885	2.8202	3.4020	-2.8410
 584 | 0.0845	-0.1411	-0.2544	1.4883
 585 | -0.5307	0.6239	-0.0764	3.6316
 586 | -0.4763	0.4447	-0.5638	-1.1510
 587 | 1.4152	1.3564	1.7857	-1.8701
 588 | -1.5210	-0.4126	-2.4485	0.8362
 589 | -0.8487	-1.3262	-1.8305	0.6240
 590 | -0.8947	-0.5605	-0.4703	-0.3529
 591 | 0.7686	2.4885	1.1331	0.6781
 592 | 1.6384	2.5118	1.3864	0.1621
 593 | 1.0010	1.7451	-0.2762	0.2595
 594 | 0.4807	1.4548	4.9742	-3.2610
 595 | 1.0473	2.0668	4.3525	-3.3097
 596 | 0.0788	-1.4203	2.4255	-0.3301
 597 | -2.2306	-3.8870	-3.7001	1.9159
 598 | 0.5874	1.6003	-0.7438	1.6549
 599 | 1.4756	2.2393	4.0787	-3.8391
 600 | -0.5030	1.4913	0.2074	1.0861
 601 | -0.4347	0.6785	-2.6748	2.3082
 602 | -0.1111	-1.3967	-1.6404	1.2834
 603 | 1.5639	2.8363	2.5642	-2.9118
 604 | 1.2511	0.6893	4.1057	-4.2018
 605 | -0.4250	1.0096	1.4236	1.4049
 606 | 0.0815	-0.9773	1.0435	-2.9788
 607 | -0.1817	-0.8652	-2.8114	1.5907
 608 | 0.5952	1.0976	-1.1152	-1.3025
 609 | -1.3392	-0.3130	-4.6895	3.8328
 610 | -0.1405	-0.9766	-0.0223	2.0270
 611 | -0.1753	-0.5500	-1.7572	0.6174
 612 | 2.3826	1.6173	3.3825	-2.3766
 613 | 0.4081	0.2211	1.7949	-0.9556
 614 | 0.1571	-2.2358	1.2337	-2.0532
 615 | 0.5492	-0.4672	2.4981	-2.8609
 616 | -2.7580	-1.7945	-5.1297	2.6354
 617 | 0.1006	0.1469	0.9435	-1.3105
 618 | 0.2636	0.9543	0.2570	0.7055
 619 | 1.2427	2.5572	2.0227	0.5339
 620 | 0.0293	-0.2815	0.8742	-0.3877
 621 | -0.8928	2.0082	-4.2166	7.0338
 622 | 0.8227	-2.2286	0.9022	-1.9991
 623 | 0.2750	-2.3933	1.3408	-4.5404
 624 | 1.0314	0.0165	2.8261	-1.7506
 625 | 1.5891	-0.0366	6.2175	-3.1655
 626 | -1.0055	-2.9451	-1.2092	-0.8216
 627 | 0.6522	0.6545	0.2166	-0.7901
 628 | -0.7011	-0.8955	-2.6927	2.4811
 629 | 1.2141	1.6892	0.8590	1.8449
 630 | -1.0424	1.1561	-2.6228	2.1177
 631 | -0.6658	-0.0976	-0.8541	0.0506
 632 | -0.1820	1.7439	-0.7883	2.0911
 633 | 0.5704	1.7059	0.5362	0.0811
 634 | -1.7730	-3.8503	-0.6296	-3.0181
 635 | -1.0346	-0.0355	0.5912	-2.3518
 636 | 0.7074	1.6568	1.4173	0.3832
 637 | 0.2438	-0.8389	0.0342	1.1134
 638 | 0.4378	0.2198	-0.5559	2.7590
 639 | 0.3426	0.9553	-0.2672	-0.6559
 640 | 1.1168	2.2127	1.1917	1.4978
 641 | 1.7877	0.3554	2.3804	-3.6787
 642 | -0.1044	3.0831	1.1879	-0.2972
 643 | -1.4695	-1.7326	-1.1774	0.1953
 644 | 2.4817	3.4065	5.9234	-2.8419
 645 | 0.8637	-0.1261	2.8507	-2.9793
 646 | 1.9671	1.2499	2.9712	-4.2806
 647 | 0.4974	0.2890	-0.8741	1.6884
 648 | 1.1620	2.0488	3.8843	-3.9454
 649 | -2.2098	-3.5932	-3.7391	1.6634
 650 | -0.1332	-0.7305	2.6645	-1.6099
 651 | 0.4648	0.8003	0.4025	-2.1358
 652 | -0.1363	-0.0967	1.6756	-1.4968
 653 | -0.1277	0.7906	0.0377	-2.0824
 654 | 0.5539	1.9192	3.2564	-2.4236
 655 | -1.7684	-0.6146	-2.1915	2.5153
 656 | -0.5654	0.1659	-4.0975	4.2905
 657 | 1.4508	0.8496	2.4828	-2.1395
 658 | 1.7822	0.2653	3.6706	-4.7081
 659 | -0.2624	-2.2014	0.2433	-0.5328
 660 | 1.1261	2.9495	-0.5723	0.7239
 661 | -0.1907	-1.1867	0.9616	-1.6157
 662 | -0.8731	1.2671	-3.2853	3.8146
 663 | 0.0332	-2.5754	-1.2272	-1.0377
 664 | -1.5423	-0.4592	-0.5829	0.8995
 665 | -2.8951	-2.2287	-4.3907	2.8129
 666 | -0.0237	-0.7932	-2.1966	4.8650
 667 | -1.1942	-1.7105	-2.9147	1.6773
 668 | -0.5189	-0.4373	3.1877	-3.1881
 669 | 0.2745	-1.3961	1.2401	-2.8285
 670 | -0.1617	-1.2290	-2.4578	-0.1563
 671 | 0.6373	-0.4517	0.3370	0.6078
 672 | 0.3218	0.8918	4.7222	-5.6828
 673 | 1.3758	2.7275	2.1637	-0.7284
 674 | 1.6085	2.7398	3.1448	-3.4195
 675 | 1.6736	1.9384	5.0966	-2.4717
 676 | -1.3293	-3.2025	-4.4141	3.1804
 677 | 0.1278	0.3685	2.6931	-1.8363
 678 | 0.1585	1.0251	0.2425	-0.0684
 679 | -0.8808	-1.3826	0.7173	-1.1581
 680 | 1.6407	0.3166	5.7555	-5.7785
 681 | 1.8027	3.4724	3.2196	-2.1314
 682 | 1.2006	1.0765	1.7169	-2.1488
 683 | -0.5764	0.2289	-0.2922	1.4868
 684 | 1.4423	1.6906	1.6567	-1.1824
 685 | 1.7092	-0.0274	2.5530	-2.1152
 686 | 1.0716	2.2295	3.2452	-2.5768
 687 | -0.6006	-1.3288	-2.2388	2.8637
 688 | -0.7205	-0.6912	1.6515	-3.2910
 689 | -1.1837	0.3507	-1.6879	3.1121
 690 | 0.5626	2.8380	1.4699	-0.4932
 691 | -0.7537	-0.6953	-3.1658	3.0637
 692 | 1.2367	0.6409	0.9917	1.5116
 693 | -1.1035	-0.7161	-3.7742	2.4336
 694 | -1.8684	-0.4997	-4.0247	3.3118
 695 | 1.6296	2.2559	1.9531	-0.8001
 696 | 0.5641	2.1938	-0.2567	3.3194
 697 | 1.6163	-0.8917	1.4851	-0.5876
 698 | -1.5329	-1.6924	-0.8626	-0.0505
 699 | -0.1108	2.1406	0.7755	2.5766
 700 | 1.1528	2.4641	1.9131	-2.0588
 701 | -1.6771	-4.0750	-1.7141	0.7877
 702 | -0.3782	0.8156	-0.2093	0.8619
 703 | 2.0759	0.8934	2.1463	-0.1229
 704 | -2.1752	-1.2210	-4.4540	5.1064
 705 | -0.7154	-1.0728	-2.1205	1.2905
 706 | -1.1868	-1.1752	-0.7381	1.2352
 707 | 2.6860	3.6245	4.3923	-2.1751
 708 | 0.1989	-1.3788	-0.5605	-2.0883
 709 | 0.0528	0.4353	1.2900	-4.1841
 710 | -0.4220	0.3202	1.7995	-2.0235
 711 | -0.5720	0.3538	-2.5897	1.2366
 712 | -0.3566	-0.6282	3.0268	-2.7038
 713 | -0.9071	-1.9049	-2.3987	-0.8474
 714 | -1.0017	-0.1582	0.9731	-0.2732
 715 | -2.1240	-2.3114	-5.0146	4.0583
 716 | 0.4511	2.6216	0.5775	0.3030
 717 | -1.0954	-1.9547	-0.2099	-2.2556
 718 | 1.3981	0.3082	-0.3138	-0.4408
 719 | 0.5745	1.6630	1.5069	0.3801
 720 | 0.3224	0.1636	-0.1116	0.4408
 721 | -0.1363	0.2411	-4.3640	4.1182
 722 | 0.2307	-1.0134	-1.3896	1.6590
 723 | -1.6146	-0.6353	-3.6840	5.0874
 724 | -0.2182	-0.3006	-1.3621	2.7167
 725 | 0.9655	-0.0760	5.2645	-2.7839
 726 | 1.7344	-1.1806	4.6002	-4.5242
 727 | -1.7375	-3.8363	-1.8884	2.6531
 728 | -1.5359	-3.4614	-2.3717	-1.6653
 729 | 1.4541	-0.4962	4.9849	-4.5826
 730 | 0.9732	0.3811	3.5966	-3.2958
 731 | -0.4781	-1.0741	-1.7739	0.9003
 732 | 0.4542	0.9803	0.9116	0.6760
 733 | 0.6460	-1.3613	1.0015	-2.8363
 734 | -0.2928	0.5428	-0.1714	2.9715
 735 | 1.4964	1.3080	2.3591	-1.2514
 736 | 0.2136	0.7576	-1.1299	1.1749
 737 | 0.4673	1.0442	1.7568	-2.2547
 738 | 0.5142	-1.6821	-2.4375	3.4751
 739 | 0.9527	1.5655	1.8220	-1.6853
 740 | 0.2410	0.2732	0.1940	-0.3887
 741 | -0.3573	1.8085	-1.3991	2.5519
 742 | -0.1760	0.4221	1.1440	0.0856
 743 | 3.0036	2.7840	6.8599	-6.8364
 744 | 0.1090	1.0491	0.9933	2.0995
 745 | 0.2818	0.9315	0.8843	0.2420
 746 | 2.8380	2.2410	2.8134	-1.8016
 747 | 0.5023	3.1495	4.0731	-1.8039
 748 | -0.0582	-2.7374	-1.0129	-0.4615
 749 | -0.5505	-1.6343	-1.5596	3.2186
 750 | 1.0784	3.9231	1.0863	-1.5243
 751 | -1.2314	-3.0780	-1.6409	0.2469
 752 | 0.1335	0.4838	-3.9621	4.9386
 753 | 1.2333	2.0928	4.0071	-3.1075
 754 | -1.2693	-0.0084	-2.4141	1.6782
 755 | -1.9385	-3.4060	-4.0442	1.9451
 756 | -0.5854	-1.4130	-1.2278	2.3809
 757 | -0.2398	-1.7605	0.1230	1.1292
 758 | 0.2825	-0.8113	-1.5813	0.7049
 759 | -0.9477	-2.1846	0.4015	-0.8040
 760 | -0.1302	-0.4408	-0.1537	0.6034
 761 | 0.2546	0.2144	2.7379	-2.3807
 762 | -0.9835	-0.9002	-4.9966	3.1901
 763 | 0.5829	0.3994	2.1473	-1.7142
 764 | -3.1554	-2.0211	-6.5150	4.4761
 765 | -0.0377	-0.0528	3.3062	-3.6839
 766 | 1.5333	3.7894	1.7485	-0.7265
 767 | 2.0764	-0.6427	2.2172	-3.8340
 768 | 1.1776	1.7066	2.5069	-0.5581
 769 | 0.3302	-1.4003	-2.5360	4.2944
 770 | -1.2482	-0.1976	-2.0711	0.9456
 771 | -0.2406	-2.4457	-0.2400	-1.8886
 772 | -0.3726	-0.4929	-1.6038	1.0137
 773 | 0.0544	-0.5156	-0.3858	2.3670
 774 | -2.2220	-3.4974	-5.8398	3.5884
 775 | 1.1348	2.2434	2.9514	-0.1895
 776 | 0.0070	0.3971	0.5286	0.0357
 777 | 0.7752	-0.4956	0.1650	-0.7048
 778 | 0.1221	0.8675	2.5748	-2.9283
 779 | 0.7972	-1.8370	2.5939	-3.3404
 780 | -0.2612	-1.0567	1.2505	0.3564
 781 | 1.3166	0.9626	4.0171	-4.9185
 782 | -0.6494	-2.4589	-0.2840	0.6803
 783 | 1.1047	2.3211	5.3088	-0.5314
 784 | -1.8453	0.2950	-4.0475	4.7546
 785 | -1.0978	-1.8395	0.7786	-0.3847
 786 | -0.8782	-2.0656	-0.4668	0.2880
 787 | 0.2871	-0.0816	1.1756	-3.5576
 788 | 0.1089	-1.1181	0.7253	1.2728
 789 | 0.3108	-1.2102	2.3103	-3.5735
 790 | -0.1983	-1.3945	2.4447	-2.1784
 791 | -0.3916	0.4559	-1.2069	-0.4552
 792 | -1.3762	-2.9663	-4.9833	4.1377
 793 | 1.2871	2.4920	1.4206	0.0362
 794 | 0.7636	0.3324	1.9423	-0.4482
 795 | -0.5444	-3.4782	1.5397	-5.9865
 796 | -1.1021	-2.6265	-2.0601	1.0722
 797 | -0.3405	0.1923	-1.0233	0.3243
 798 | -0.3976	-0.7552	-0.8215	-0.9807
 799 | 2.4827	3.4896	8.4584	-5.1560
 800 | 0.1649	0.2971	-1.9113	0.4320
 801 | 1.0341	0.3985	0.3581	0.6171
 802 | -0.3598	-0.4640	0.6991	0.5921
 803 | 1.0401	-1.0886	3.5171	-4.5617
 804 | -0.4498	-2.0178	0.5046	-0.7718
 805 | -0.6825	-0.2963	-3.2908	2.4110
 806 | -0.3828	-1.2803	2.8865	-1.2187
 807 | 1.8802	1.6709	6.1067	-5.9179
 808 | 0.8295	1.7834	2.1371	-0.3955
 809 | 0.0102	3.0084	-0.5084	3.4905
 810 | 0.5776	0.3626	-0.9278	-2.0204
 811 | -0.8143	1.4269	-1.1079	1.3061
 812 | 1.4822	1.4707	5.5991	-2.7516
 813 | 0.4070	-0.7230	-0.2261	-1.3777
 814 | 4.7846	3.7717	7.3800	-6.2177
 815 | -0.2100	2.8019	-1.4262	0.7606
 816 | 0.5760	1.6616	3.5575	-2.3607
 817 | 2.3035	2.2732	4.2988	-3.4140
 818 | -0.9769	-1.6534	-3.3927	2.0202
 819 | -2.4994	-0.7589	-2.4763	3.0263
 820 | 1.0841	1.0333	2.1069	-1.3734
 821 | 0.0034	-0.3016	-3.8329	4.4283
 822 | 0.1927	2.6055	1.1588	0.8050
 823 | -0.9424	-0.1511	-1.6369	2.9666
 824 | 0.1256	0.6592	0.1015	-0.4799
 825 | 0.1968	0.1535	0.3561	0.0075
 826 | 0.4280	-0.7153	-1.4028	3.2275
 827 | 0.7786	-0.8761	1.1569	-2.4780
 828 | -0.1515	-1.8705	-0.8812	-0.1000
 829 | -1.2129	0.1701	-0.9798	2.3051
 830 | 1.0773	2.9089	1.7891	-1.8625
 831 | -1.9326	-3.0425	-2.9845	0.8451
 832 | -2.5948	-2.8116	-8.4860	7.3264
 833 | -0.5301	0.1297	0.3395	-0.1824
 834 | 0.0192	-2.3884	-0.5182	-0.3134
 835 | -0.0522	0.5292	3.8994	-5.9149
 836 | -2.6437	-4.9097	-4.2886	1.9631
 837 | 0.8417	-0.0547	1.9772	-1.2452
 838 | 1.3192	1.5192	2.4677	-0.9588
 839 | 2.7803	3.0402	5.4138	-3.1573
 840 | -1.8456	-0.3769	-2.8370	3.0724
 841 | -0.5356	0.0502	0.0274	-1.3851
 842 | -1.0116	-0.2560	-1.5152	1.8756
 843 | -1.2691	-1.8207	-2.8566	2.2257
 844 | -2.9592	-1.6625	-4.5308	2.7724
 845 | 1.3376	0.0780	0.6282	-2.0318
 846 | 1.6955	2.7780	3.2655	-1.2321
 847 | -0.4962	0.0688	-1.0017	2.2376
 848 | 0.5164	-0.5692	-0.5619	1.7152
 849 | -1.4864	-0.3974	-3.5628	2.1193
 850 | 0.6519	0.7522	-0.1924	-0.6601
 851 | -0.8696	-1.2542	1.2233	-2.7148
 852 | -1.3554	-2.4747	-2.8165	2.0809
 853 | -0.5958	-1.3723	-3.0388	2.2133
 854 | -0.2181	-0.3331	-2.4112	-0.3126
 855 | 1.3758	-0.0168	1.7395	-0.9770
 856 | 0.0204	-0.1737	0.7407	-2.0824
 857 | 1.0847	-0.0647	3.1116	-3.8508
 858 | 0.7748	0.8022	1.8025	-1.7415
 859 | -1.0252	-1.2644	-3.1217	3.6045
 860 | 0.1826	0.1773	-0.3842	0.5366
 861 | 1.4103	-0.3573	4.3991	-4.1621
 862 | -0.2224	1.2868	-0.3958	1.9198
 863 | 0.3426	0.3517	2.7783	-4.4088
 864 | 2.3729	3.4145	5.9708	-4.1185
 865 | 0.2591	0.5197	0.6004	-1.7345
 866 | -0.8681	-0.8067	-5.0768	3.9601
 867 | -0.6154	0.6562	-0.7971	1.1270
 868 | 0.3239	-1.7496	1.3340	-2.4100
 869 | -2.1064	-1.8042	-4.6845	3.7453
 870 | 0.6683	0.6338	0.5402	-1.2266
 871 | -2.6646	-1.8687	-4.5452	4.8848
 872 | -0.3647	-1.2198	-2.8048	1.8247
 873 | -0.6127	-0.3272	-1.2679	0.3454
 874 | -1.7400	-1.4406	-1.8326	0.9992
 875 | -0.1949	-0.9344	0.8785	-2.6007
 876 | -0.5906	0.8698	1.6671	-0.2432
 877 | -0.1016	1.3325	-0.1791	1.1254
 878 | -1.7227	-3.3169	-6.0545	2.1066
 879 | -1.1291	-1.1761	0.7185	-0.0358
 880 | -0.2963	-1.0722	-2.6762	2.1816
 881 | 0.0638	-0.5047	0.8469	-0.1959
 882 | 0.4864	0.5108	4.0873	-2.8461
 883 | 1.5949	2.8785	5.8924	-5.7475
 884 | 0.8358	0.3985	-0.0952	-1.0542
 885 | 0.4649	-0.2477	-2.4579	3.7152
 886 | 1.6585	3.3086	4.1332	-3.9437
 887 | -0.1360	-2.5494	-2.7867	2.2152
 888 | 0.4012	2.6478	0.3925	0.7472
 889 | 0.5966	-0.4979	2.0857	-1.0566
 890 | 2.7507	3.7337	7.5218	-5.4947
 891 | -0.4696	-2.0639	-0.5819	-0.7127
 892 | 0.0606	0.8769	1.4734	-2.7369
 893 | -0.4070	0.0100	0.8166	0.6752
 894 | 0.9719	-0.2078	-0.9551	1.1452
 895 | 1.9718	2.4406	4.9346	-2.7550
 896 | -1.1506	1.6626	-3.4655	1.0998
 897 | -0.2366	0.8708	-0.1483	0.3447
 898 | -0.4721	0.9020	-1.3401	1.9453
 899 | -0.6147	-1.4378	-0.2758	0.1698
 900 | 2.2717	0.7812	3.1275	-1.7342
 901 | 0.1132	0.7270	-1.3677	-0.4701
 902 | -0.5304	-0.2478	-1.4542	1.6716
 903 | -1.3161	-0.2612	-3.6551	1.6417
 904 | -1.2769	-0.9436	-3.3018	0.4782
 905 | -0.3208	-1.4066	-0.5900	-1.4112
 906 | 0.1059	1.8202	0.2379	-1.1848
 907 | -2.1978	-2.4442	-4.8365	2.3883
 908 | 0.1587	1.5477	0.7988	0.1191
 909 | 1.5613	3.8589	2.6686	-1.1137
 910 | 0.6241	0.3305	2.7025	-2.7390
 911 | -0.3806	-2.2565	-0.0469	0.8878
 912 | 1.7690	-0.2489	3.8450	-5.0639
 913 | -0.4449	0.2964	-4.3500	2.1049
 914 | 2.0994	2.7141	4.3622	-5.2659
 915 | 0.5318	1.2363	3.3073	-3.5220
 916 | 0.7683	-2.3456	0.0126	-1.2680
 917 | -2.3450	-4.2979	-4.3552	3.2049
 918 | 0.6160	3.0790	-0.1070	1.0240
 919 | -1.8849	-2.7989	-2.5195	-0.1890
 920 | 0.1586	0.9480	1.7823	-1.7179
 921 | 0.5691	1.8857	0.7091	-4.0504
 922 | -0.4613	-0.4608	-0.6497	-1.7062
 923 | 1.2753	3.0873	0.6291	-0.6398
 924 | 0.1073	-0.8329	1.1176	0.1849
 925 | -1.3496	-2.4360	-1.7843	0.5189
 926 | -0.8198	-1.4718	-2.6834	3.2494
 927 | 0.1722	0.6237	-0.6878	2.6488
 928 | 1.0178	1.6270	-0.4138	-0.3747
 929 | -0.1366	-1.6372	0.1285	-0.7308
 930 | 0.6704	2.1385	0.7335	0.8871
 931 | 0.7890	1.6467	3.2952	-2.5976
 932 | 3.6151	2.0056	7.8652	-8.1088
 933 | -1.5352	-0.0485	-3.8208	3.0523
 934 | -1.4060	-1.0717	-1.7603	-1.6007
 935 | -1.1863	-0.6363	-2.2183	1.6123
 936 | 1.5496	2.4745	2.1847	-1.3431
 937 | -1.8499	-0.6329	-0.1811	0.4338
 938 | 0.2072	-0.1804	0.4082	-1.7626
 939 | 0.3458	1.8013	3.0923	-1.4103
 940 | -0.0694	-3.3736	-1.4420	-0.2100
 941 | 1.5385	0.6984	4.2233	-3.2894
 942 | 0.6955	1.6870	0.3974	-0.1101
 943 | -0.6076	-1.5684	-3.4748	4.3326
 944 | -0.0365	-0.1675	1.5558	-1.3237
 945 | -0.1194	0.6756	1.3247	0.2663
 946 | -1.1577	-0.5517	-2.9294	1.6068
 947 | -0.8170	-2.5973	-1.3295	0.8809
 948 | 0.3804	1.5432	-0.3541	1.4189
 949 | -0.0824	-0.9253	-0.4567	0.5768
 950 | -0.1741	-0.1642	-2.1875	0.4246
 951 | -0.1718	1.1064	-0.6609	-1.6192
 952 | -0.9055	-0.4940	-2.4176	1.7905
 953 | -1.5150	-2.6009	-2.6577	1.4493
 954 | -0.1064	-1.1496	-0.7267	0.1980
 955 | -1.7595	-0.7345	-4.4818	3.2017
 956 | -0.2289	0.1311	-1.1109	-0.9558
 957 | 0.4064	2.0264	1.3587	-0.7615
 958 | -0.8551	-0.2973	-0.3452	-0.8025
 959 | 0.9702	1.5659	2.1626	-0.6366
 960 | 0.2939	1.2526	-0.1189	1.8658
 961 | -1.4682	-1.7908	-5.3585	2.6703
 962 | -0.9855	-0.2616	-2.2157	2.4479
 963 | 1.6280	1.3096	2.5282	-1.5845
 964 | 0.5126	0.4484	2.1478	-1.4552
 965 | -1.1912	-0.5212	-2.7978	0.7178
 966 | -1.1988	-0.3221	-1.5681	2.6952
 967 | 0.7929	1.0772	0.3456	0.2040
 968 | 1.1535	2.0657	2.9134	-2.1122
 969 | 0.6162	0.9338	1.4200	0.1007
 970 | -0.6909	-0.7126	-1.4572	2.0843
 971 | -1.2405	-2.5348	-1.2961	-0.3561
 972 | -0.4239	-0.6389	-1.7818	1.3040
 973 | 1.3915	0.3651	0.5989	0.9374
 974 | -2.0606	-0.2140	-2.2648	2.7552
 975 | -0.2142	-0.2045	0.2653	-0.9797
 976 | -0.1477	-0.8864	-0.4609	0.7602
 977 | -0.7074	-2.2578	0.3184	-2.6673
 978 | 1.0040	1.0383	2.7508	-4.6825
 979 | 0.4410	-0.0470	2.7774	-2.2094
 980 | -0.4109	-2.9471	-2.1369	0.9780
 981 | 0.3816	-0.2858	2.6062	-3.1575
 982 | 0.8521	1.4565	-0.0733	1.2292
 983 | -1.0888	-0.1359	1.1683	-2.6620
 984 | 0.3447	-0.6569	1.2974	-1.8227
 985 | -1.5570	-1.0419	-4.4403	2.1029
 986 | 0.4889	2.6463	1.4866	1.9629
 987 | -1.3828	-1.6130	-2.8327	-1.3808
 988 | 2.4356	0.5078	4.5393	-4.9270
 989 | 2.3195	3.0621	5.8867	-7.0965
 990 | -1.5778	-3.4421	-4.7022	5.3480
 991 | 0.2143	-0.2319	-0.8225	1.1643
 992 | 0.7414	-1.2725	1.2544	-1.2023
 993 | -0.1595	0.1827	-0.9906	1.8405
 994 | 1.7140	-0.0130	1.9959	-2.2336
 995 | -0.3711	-1.1818	0.0451	-1.5664
 996 | -0.3583	-1.1808	-1.6697	2.2321
 997 | 0.0775	0.5683	-1.6643	0.4994
 998 | 2.5427	2.0092	4.5448	-2.7661
 999 | 1.4372	3.2044	2.0283	0.8661
1000 | 0.9254	-0.1970	1.4643	-1.7150
1001 | 1.1724	4.2455	0.5621	0.5849
1002 | 


--------------------------------------------------------------------------------
/data/params_1_graph.txt:
--------------------------------------------------------------------------------
 1 | Graph Nodes:
 2 | X1,X2,X3,X4
 3 | 
 4 | Graph Edges:
 5 | 1. X1 --> X2 w =  1.0
 6 | 2. X1 --> X3 w =  2.0
 7 | 3. X2 --> X4 w =  0.5
 8 | 4. X3 --> X4 w = -1.0
 9 | 
10 | 


--------------------------------------------------------------------------------
/fges.py:
--------------------------------------------------------------------------------
  1 | import networkx as nx
  2 | import itertools
  3 | import graph_util
  4 | from sortedcontainers import SortedListWithKey
  5 | from meekrules import MeekRules
  6 | import numpy as np
  7 | import time
  8 | import dill
  9 | import os
 10 | from knowledge import Knowledge
 11 | 
 12 | 
 13 | class Arrow:
 14 |     __slots__ = ['a', 'b', 'na_y_x', 'h_or_t', 'bump', 'index']
 15 |     def __init__(self, a, b, na_y_x, hOrT, bump, arrow_index):
 16 |         self.a = a
 17 |         self.b = b
 18 |         self.na_y_x = na_y_x
 19 |         self.h_or_t = hOrT
 20 |         self.bump = bump
 21 |         self.index = arrow_index
 22 | 
 23 | 
 24 | class FGES:
 25 |     """
 26 |     Python FGES implementation, heavily inspired by tetrad
 27 |     https://github.com/cmu-phil/tetrad
 28 | 
 29 |     TODOs:
 30 | 
 31 |     - There is a way to set preset adjacencies in the tetrad algorithm,
 32 |     which constrains the edges that can actually be set. That's not
 33 |     implemented here.
 34 | 
 35 |     - Symmetric First Step unimplemented.
 36 | 
 37 |     """
 38 | 
 39 |     def __init__(self, variables, score, filename='', checkpoint_frequency=0,
 40 |                  save_name=None, knowledge=None, verbose=False):
 41 |         self.top_graphs = []
 42 |         self.last_checkpoint = time.time()
 43 |         # How often fges-py will save a checkpoint of the data
 44 |         self.checkpoint_frequency = checkpoint_frequency
 45 |         self.save_name = save_name
 46 |         # List of the nodes, in order
 47 |         self.variables = variables
 48 | 
 49 |         # Meant to be a map from the node to its column in the dataset,
 50 |         # but in this implementation, this should always be a map
 51 |         # from x -> x, i.e. {1:1, 2:2, ...}
 52 |         # self.node_dict = {}
 53 |         self.score = score
 54 |         self.sorted_arrows = SortedListWithKey(key=lambda val: -val.bump)
 55 |         self.arrow_dict = {}
 56 |         self.arrow_index = 0
 57 |         self.total_score = 0
 58 |         self.sparsity = score.penalty
 59 |         # Only needed for their `heuristic speedup`, it tells
 60 |         # you if two edges even have an effect on each other
 61 |         # the way we use this is effect_edges_graph[node] gives you
 62 |         # an iterable of nodes {w_1, w_2, w_3...} where node and
 63 |         # w_i have a non-zero total effect
 64 |         self.effect_edges_graph = {}
 65 |         self.cycle_bound = -1
 66 |         self.stored_neighbors = {}
 67 |         self.graph = None
 68 |         self.removed_edges = set()
 69 |         self.filename = filename
 70 |         self.in_bes = False
 71 |         self.knowledge = knowledge
 72 |         self.verbose = verbose
 73 | 
 74 |     def set_knowledge(self, knowledge):
 75 |         if not isinstance(knowledge, Knowledge):
 76 |             raise TypeError("knowledge must be of type Knowledge")
 77 |         else:
 78 |             self.knowledge = knowledge
 79 | 
 80 |     def get_dict(self):
 81 |         return {"graph": self.graph,
 82 |                 "sparsity": self.sparsity,
 83 |                 "filename": self.filename,
 84 |                 "nodes": len(self.variables),
 85 |                 "knowledge": self.knowledge}
 86 | 
 87 |     @classmethod
 88 |     def load_checkpoint(cls, filename):
 89 |         with open(filename, 'rb') as f:
 90 |             return dill.load(f)
 91 | 
 92 |     def search(self):
 93 |         """
 94 |         The main entry point into the algorithm.
 95 |         """
 96 |         # Create an empty directed graph
 97 |         if self.graph is None:
 98 |             self.graph = nx.DiGraph()
 99 |             self.graph.add_nodes_from(self.variables)
100 |             # print("Created Graph with nodes: ", self.graph.nodes())
101 | 
102 |             # for now faithfulness is assumed
103 |             self.add_required_edges()
104 | 
105 |             self.initialize_forward_edges_from_empty_graph()  # Adds all edges that have positive bump
106 | 
107 |         # Step 1: Run FES and BES with heuristic
108 |         # mode. The mode is used in reevaluate_forward
109 |         self.mode = "heuristic"
110 |         if not self.in_bes:
111 |             self.fes()
112 |             self.sorted_arrows = SortedListWithKey(key=lambda val: -val.bump)
113 |             self.arrow_dict = {}
114 |             self.stored_neighbors = {}
115 |             self.initialize_arrows_backwards()
116 |             self.in_bes = True
117 | 
118 |             if self.checkpoint_frequency > 0:
119 |                 self.create_checkpoint()
120 | 
121 |         self.bes()
122 | 
123 |         # Step 1: Run FES and BES with covernoncolliders
124 |         # mode. The mode is used in reevaluate_forward
125 | 
126 |         # self.mode = "covernoncolliders"
127 |         # self.fes()
128 |         # self.bes()
129 |         # print(self.graph.edges())
130 |         return self.get_dict()
131 | 
132 |     def fes(self):
133 |         """The basic workflow of FGES is to first consider add all edges with positive bump, as defined
134 |         by the SEMBicScore, to a sorted list (sorted by bump).
135 |         Edges are popped off this list and added to the graph, after which point the Meek rules are utilized to
136 |         orient edges in the graph that can be oriented. Then, all relevant bumps are recomputed and
137 |         the list is resorted. This process is repeated until there remain no edges to add with positive bump."""
138 |         # print("Running FES.`.")
139 |         # print("Length of sorted arrows", len(self.sorted_arrows))
140 |         # print(self.arrow_dict)
141 |         while len(self.sorted_arrows) > 0:
142 |             if self.checkpoint_frequency > 0 and (time.time() - self.last_checkpoint) > self.checkpoint_frequency:
143 |                 self.create_checkpoint()
144 |                 self.last_checkpoint = time.time()
145 |             max_bump_arrow = self.sorted_arrows.pop(0)  # Pops the highest bump edge off the sorted list
146 |             x = max_bump_arrow.a
147 |             y = max_bump_arrow.b
148 |             # print("Popped arrow: " + str(x) + " -> " + str(y))
149 | 
150 |             if graph_util.adjacent(self.graph, x, y):
151 |                 continue
152 | 
153 |             na_y_x = graph_util.get_na_y_x(self.graph, x, y)
154 | 
155 |             # TODO: max degree checks
156 |             # print(na_y_x)
157 | 
158 |             if max_bump_arrow.na_y_x != na_y_x:
159 |                 continue
160 | 
161 |             # print("Past crucial step")
162 | 
163 |             if not graph_util.get_t_neighbors(self.graph, x, y).issuperset(max_bump_arrow.h_or_t):
164 |                 continue
165 | 
166 |             if not self.valid_insert(x, y, max_bump_arrow.h_or_t, na_y_x):
167 |                 # print("Not valid insert")
168 |                 continue
169 | 
170 |             T = max_bump_arrow.h_or_t
171 |             bump = max_bump_arrow.bump
172 | 
173 |             # TODO: Insert should return a bool that we check here
174 |             inserted = self.insert(x, y, T, bump)  # Insert highest bump edge into the graph
175 |             if not inserted:
176 |                 continue
177 | 
178 |             self.total_score += bump
179 |             # print("Edge set before reapplying orientation: " + str(self.graph.edges()))
180 |             visited_nodes = self.reapply_orientation(x, y, None)  # Orient edges appropriately following insertion
181 |             # print("Edge set after reapplying orientation: " + str(self.graph.edges()))
182 |             to_process = set({})
183 | 
184 |             # check whether the (undirected) neighbors of each node in
185 |             # visited_nodes changed compared to stored neighbors
186 |             for node in visited_nodes:
187 |                 # gets undirected neighbors
188 |                 new_neighbors = graph_util.neighbors(self.graph, node)
189 |                 stored_neighbors = self.stored_neighbors.get(node)
190 |                 if stored_neighbors != new_neighbors:
191 |                     to_process.add(node)  # Reevaluate neighbor nodes
192 | 
193 |             to_process.add(x)  # Reevaluate edges relating to node x
194 |             to_process.add(y)  # Reevaluate edges relating to node y
195 | 
196 |             self.reevaluate_forward(to_process, max_bump_arrow)  # Do actual reevaluation
197 | 
198 |     def bes(self):
199 |         """BES removes edges from the graph generated by FGES, as added edges can now have negative bump in light
200 |         of the additions to the graph after those edges were added."""
201 | 
202 |         while len(self.sorted_arrows) > 0:
203 |             if self.checkpoint_frequency > 0 and (time.time() - self.last_checkpoint) > self.checkpoint_frequency:
204 |                 self.create_checkpoint()
205 |                 self.last_checkpoint = time.time()
206 | 
207 |             arrow = self.sorted_arrows.pop(0)
208 |             x = arrow.a
209 |             y = arrow.b
210 | 
211 |             if (not (arrow.na_y_x == graph_util.get_na_y_x(self.graph, x, y))) or \
212 |                     (not graph_util.adjacent(self.graph, x, y)) or (graph_util.has_dir_edge(self.graph, y, x)):
213 |                 continue
214 | 
215 |             if not self.valid_delete(x, y, arrow.h_or_t, arrow.na_y_x):
216 |                 continue
217 | 
218 |             H = arrow.h_or_t
219 |             bump = arrow.bump
220 | 
221 |             self.delete(x, y, H)
222 | 
223 |             meek_rules = MeekRules(knowledge=self.knowledge)
224 |             meek_rules.orient_implied_subset(self.graph, set([x, y]))
225 | 
226 |             self.total_score += bump
227 |             self.clear_arrow(x, y)
228 |             if self.verbose:
229 |                 print("BES: Removed arrow " + str(x) + " -> " + str(y) + " with bump -" + str(bump))
230 |             visited = self.reapply_orientation(x, y, H)
231 | 
232 |             to_process = set()
233 | 
234 |             for node in visited:
235 |                 neighbors = graph_util.neighbors(self.graph, node)
236 |                 str_neighbors = self.stored_neighbors[node]
237 | 
238 |                 if str_neighbors != neighbors:
239 |                     to_process.update([node])
240 | 
241 |             to_process.add(x)
242 |             to_process.add(y)
243 |             to_process.update(graph_util.get_common_adjacents(self.graph, x, y))
244 | 
245 |             # TODO: Store graph
246 |             self.reevaluate_backward(to_process)
247 | 
248 |     def initialize_arrows_backwards(self):
249 |         for (node_1, node_2) in self.graph.edges():
250 |             if self.knowledge is not None and not self.knowledge.no_edge_required(node_1, node_2):
251 |                 continue
252 |             self.clear_arrow(node_1, node_2)
253 |             self.clear_arrow(node_2, node_1)
254 | 
255 |             self.calculate_arrows_backward(node_1, node_2)
256 | 
257 |             self.stored_neighbors[node_1] = graph_util.neighbors(self.graph,
258 |                                                                  node_1)
259 |             self.stored_neighbors[node_2] = graph_util.neighbors(self.graph,
260 |                                                                  node_2)
261 | 
262 |     def calculate_arrows_backward(self, a, b):
263 |         """Finds all edges with negative bump"""
264 | 
265 |         if self.knowledge is not None and not self.knowledge.no_edge_required(a, b):
266 |             return
267 | 
268 |         na_y_x = graph_util.get_na_y_x(self.graph, a, b)
269 |         _na_y_x = list(na_y_x)
270 |         _depth = len(_na_y_x)
271 | 
272 |         for i in range(_depth + 1):
273 |             choices = itertools.combinations(range(0, _depth), i)
274 |             for choice in choices:
275 |                 diff = set([_na_y_x[k] for k in choice])
276 |                 h = set(_na_y_x)
277 |                 h = h - diff
278 | 
279 |                 if self.knowledge is not None and not self.valid_set_by_knowledge(b, h):
280 |                     continue
281 | 
282 |                 bump = self.delete_eval(a, b, diff, na_y_x)
283 | 
284 |                 if bump > 0:
285 |                     if self.verbose:
286 |                         print("Evaluated removal of an arrow " + str(
287 |                             a) + " -> " + str(b) + " with bump: " + str(bump))
288 |                     self.add_arrow(a, b, na_y_x, h, bump)
289 | 
290 |     def delete_eval(self, x, y, diff, na_y_x):
291 |         """Evaluates the bump of removing edge X-->Y"""
292 |         a = set(diff)
293 |         a.update(graph_util.get_parents(self.graph, y))
294 |         a = a - {x}
295 |         return -1 * self.score_graph_change(y, a, x)
296 | 
297 |     def reevaluate_forward(self, to_process, arrow):
298 |         # print("Re-evaluate forward with " + str(to_process) + " " + str(arrow))
299 |         for node in to_process:
300 |             if self.mode == "heuristic":
301 |                 nzero_effect_nodes = self.effect_edges_graph.get(node)
302 |                 # print("Re-evaluate forward. Currently on node: " + str(node))
303 |                 # print("nzero-effect-nodes: " + str(nzero_effect_nodes))
304 |             elif self.mode == "covernoncolliders":
305 |                 g = set()
306 |                 for n in graph_util.adjacent_nodes(self.graph, node):
307 |                     for m in graph_util.adjacent_nodes(self.graph, n):
308 |                         if graph_util.adjacent(self.graph, n, m):
309 |                             continue
310 | 
311 |                         if graph_util.is_def_collider(self.graph, m, n, node):
312 |                             continue
313 | 
314 |                         g.update(m)
315 | 
316 |                 nzero_effect_nodes = list(g)
317 |             if nzero_effect_nodes is not None:
318 |                 for w in nzero_effect_nodes:
319 |                     if w == node:
320 |                         continue
321 |                     if not graph_util.adjacent(self.graph, node, w):
322 |                         self.clear_arrow(w, node)
323 |                         self.calculate_arrows_forward(w, node)
324 | 
325 |     def reevaluate_backward(self, to_process):
326 |         for node in to_process:
327 |             self.stored_neighbors[node] = graph_util.neighbors(self.graph, node)
328 |             adjacent_nodes = graph_util.adjacent_nodes(self.graph, node)
329 | 
330 |             for adj_node in adjacent_nodes:
331 |                 if graph_util.has_dir_edge(self.graph, adj_node, node):
332 |                     self.clear_arrow(adj_node, node)
333 |                     self.clear_arrow(node, adj_node)
334 | 
335 |                     self.calculate_arrows_backward(adj_node, node)
336 |                 elif graph_util.has_undir_edge(self.graph, adj_node, node):
337 |                     self.clear_arrow(adj_node, node)
338 |                     self.clear_arrow(node, adj_node)
339 |                     self.calculate_arrows_backward(adj_node, node)
340 |                     self.calculate_arrows_backward(node, adj_node)
341 | 
342 |     def reapply_orientation(self, x, y, new_arrows):
343 |         to_process = {x, y}
344 |         if new_arrows is not None:
345 |             to_process.update(new_arrows)
346 | 
347 |         return self.meek_orient_restricted(to_process)
348 | 
349 |     def meek_orient_restricted(self, nodes):
350 |         # Runs meek rules on the changed adjacencies
351 |         meek_rules = MeekRules(undirect_unforced_edges=True,
352 |                                knowledge=self.knowledge)
353 |         meek_rules.orient_implied_subset(self.graph, nodes)
354 |         return meek_rules.get_visited()
355 | 
356 |     def valid_insert(self, x, y, T, na_y_x):
357 |         union = set(T)
358 | 
359 |         if self.knowledge is not None:
360 |             if self.knowledge.is_forbidden(x, y):
361 |                 return False
362 |             for node in union:
363 |                 if self.knowledge.is_forbidden(node, y):
364 |                     return False
365 | 
366 |         if na_y_x != set([]):
367 |             union.update(na_y_x)
368 |         return graph_util.is_clique(self.graph, union) and \
369 |                not graph_util.exists_unblocked_semi_directed_path(
370 |                    self.graph, y, x, union, self.cycle_bound)
371 | 
372 |     def valid_delete(self, x, y, H, na_y_x):
373 | 
374 |         if self.knowledge is not None:
375 |             for h in H:
376 |                 if self.knowledge.is_forbidden(x, h):
377 |                     return False
378 |                 if self.knowledge.is_forbidden(y, h):
379 |                     return False
380 | 
381 |         diff = set(na_y_x)
382 |         diff = diff - H
383 |         return graph_util.is_clique(self.graph, diff)
384 | 
385 |     def add_required_edges(self):
386 |         """Tetrad implementation is really confusing and seems to be
387 |         mostly checks to ensure required edges don't form a cycle"""
388 |         if self.knowledge is None:
389 |             return
390 | 
391 |         for edge in self.knowledge.required_edges:
392 |             # Make sure the required edges aren't a cycle
393 |             if not edge[0] in graph_util.get_ancestors(self.graph, edge[1]):
394 |                 graph_util.remove_dir_edge(self.graph, edge[1], edge[0])
395 |                 graph_util.add_dir_edge(self.graph, edge[0], edge[1])
396 |                 if self.verbose:
397 |                     print(f"Adding edge from knowledge: {edge[0]} -> {edge[1]}")
398 | 
399 |         for edge in self.knowledge.required_connections:
400 |             graph_util.add_undir_edge(self.graph, edge[1], edge[0])
401 | 
402 |     def initialize_two_step_edges(self, nodes):
403 |         for node in nodes:
404 | 
405 |             g = set()
406 | 
407 |             for n in graph_util.adjacent_nodes(self.graph, node):
408 |                 for m in graph_util.adjacent_nodes(self.graph, n):
409 | 
410 |                     if node == m:
411 |                         continue
412 | 
413 |                     if graph_util.adjacent(self.graph, node, m):
414 |                         continue
415 | 
416 |                     if graph_util.is_def_collider(self.graph, m, n, node):
417 |                         continue
418 | 
419 |                     g.update(m)
420 | 
421 |             for x in g:
422 |                 assert (x is not node)
423 |                 if self.knowledge is not None:
424 |                     if self.knowledge.is_forbidden(node, x) or self.knowledge.is_forbidden(x, node):
425 |                         continue
426 |                     # again, what's the point?
427 |                     if not self.valid_set_by_knowledge(node, set()):
428 |                         continue
429 | 
430 |                 # TODO: Adjacencies
431 | 
432 |                 if (x, node) in self.removed_edges:
433 |                     continue
434 | 
435 |                 self.calculate_arrows_forward(x, node)
436 | 
437 |     def initialize_forward_edges_from_empty_graph(self):
438 |         """
439 |         Initializes the state of the graph before executing fes()
440 |         This is called from search().
441 | 
442 |         TODO:
443 |         - This seems easily parallelizable
444 |         - There is a check for symmetricFirstStep here, which essentially
445 |         adds the bump between child <-> parent instead of just parent <-> child.
446 |         - This code also checks for boundGraph, which directly enforces
447 |         what kind of edges can be `bound`. In effect, this is a type of background knowledge.
448 | 
449 |         Unknowns:
450 |         - Confused by the same-reference emptySet() in the Java implementation for Arrow. Does that
451 |         mean that if one gets modified, all will?
452 |         """
453 |         for i in range(len(self.variables)):
454 |             self.stored_neighbors[self.variables[i]] = set()
455 |             for j in range(i + 1, len(self.variables)):
456 |                 if self.knowledge is not None:
457 |                     if self.knowledge.is_forbidden(self.variables[i], self.variables[j]) and self.knowledge.is_forbidden(self.variables[j], self.variables[i]):
458 |                         continue
459 |                     # literally don't know the point of these next 2 lines
460 |                     # because valid_set_by_knowledge on the empty set should
461 |                     # always return True, but it's in Tetrad...
462 |                     if not self.valid_set_by_knowledge(self.variables[i], set()):
463 |                         continue
464 |                 bump = self.score.local_score_diff(self.variables[j], self.variables[i])
465 |                 if self.verbose:
466 |                     print("Evaluated starting arrow " + str(self.variables[j]) + " -> " + str(
467 |                         self.variables[i]) + " with bump: " + str(bump))
468 |                 if bump > 0:
469 |                     self.mark_nonzero_effect(self.variables[i], self.variables[j])
470 |                     parent_node = self.variables[j]
471 |                     child_node = self.variables[i]
472 |                     self.add_arrow(parent_node, child_node, set(), set(), bump)
473 |                     self.add_arrow(child_node, parent_node, set(), set(), bump)
474 |         if self.verbose:
475 |             print("Initialized forward edges from empty graph")
476 | 
477 |     def mark_nonzero_effect(self, node_1, node_2):
478 |         """
479 |         Adds node_1 to the (instance-wide) effect edges list for node_2,
480 |         and vice versa.
481 |         """
482 |         if self.effect_edges_graph.get(node_1) is None:
483 |             self.effect_edges_graph[node_1] = [node_2]
484 |         else:
485 |             self.effect_edges_graph[node_1].append(node_2)
486 | 
487 |         if self.effect_edges_graph.get(node_2) is None:
488 |             self.effect_edges_graph[node_2] = [node_1]
489 |         else:
490 |             self.effect_edges_graph[node_2].append(node_1)
491 | 
492 |     def insert_eval(self, x, y, T, na_y_x):
493 |         """Evaluates bump for adding edge x->y given conditioning sets T and na_y_x"""
494 |         assert (x is not y)
495 |         _na_y_x = set(na_y_x)
496 |         _na_y_x.update(T)
497 |         _na_y_x.update(graph_util.get_parents(self.graph, y))
498 |         return self.score_graph_change(y, _na_y_x, x)
499 | 
500 |     def insert(self, x, y, T, bump):
501 |         """ T is a subset of the neighbors of Y that are not adjacent to
502 |         (connected by a directed or undirected edge) to X, this should
503 |         connect X -> Y and for t \in T, direct T -> Y if it's not already
504 |         directed
505 | 
506 |         Definition 12
507 | 
508 |         """
509 |         if self.verbose:
510 |             print("Doing an actual insertion with " + str(x) + " -> " + str(
511 |                 y) + " with T: " + str(T) + " and bump: " + str(bump))
512 | 
513 |         if graph_util.adjacent(self.graph, x, y):
514 |             return False
515 | 
516 |         # Adds directed edge
517 |         self.graph.add_edge(x, y)
518 | 
519 |         for node in T:
520 |             graph_util.undir_to_dir(self.graph, node, y)
521 | 
522 |         return True
523 | 
524 |     def delete(self, x, y, H):
525 |         # Remove any edge between x and y
526 |         graph_util.remove_dir_edge(self.graph, x, y)
527 |         graph_util.remove_dir_edge(self.graph, y, x)
528 | 
529 |         # H is the set of neighbors of y that are adjacent to x
530 |         for node in H:
531 |             if (graph_util.has_dir_edge(self.graph, node, y)
532 |                     or graph_util.has_dir_edge(self.graph, node, x)):
533 |                 continue
534 | 
535 |             # Direct the edge y --- node as y --> node
536 |             graph_util.undir_to_dir(self.graph, y, node)
537 | 
538 |             # If x --- node is undirected, direct it as x --> node
539 |             if graph_util.has_undir_edge(self.graph, x, node):
540 |                 graph_util.undir_to_dir(self.graph, x, node)
541 | 
542 |         self.removed_edges.add((x, y))
543 | 
544 |     def add_arrow(self, a, b, na_y_x, h_or_t, bump):
545 |         """Add arrow a->b with bump "bump" and conditioning sets na_y_x and h_or_t to sorted arrows list"""
546 |         # print("Added arrow: " + str(a) + " ->  " + str(b) + " with bump " + \
547 |         #  str(bump) + " and na_y_x " + str(na_y_x) + " and h_or_t " + str(h_or_t))
548 |         arrow = Arrow(a, b, na_y_x, h_or_t, bump, self.arrow_index)
549 |         self.sorted_arrows.add(arrow)
550 | 
551 |         pair = (a, b)
552 |         if self.arrow_dict.get(pair) is None:
553 |             self.arrow_dict[pair] = [arrow]
554 |         else:
555 |             self.arrow_dict[pair].append(arrow)
556 | 
557 |         self.arrow_index += 1
558 | 
559 |     def clear_arrow(self, a, b):
560 |         """Remove arrow a->b from sorted arrows list"""
561 |         pair = (a, b)
562 |         # print("Clearing arrow " + str(pair))
563 |         lookup_arrows = self.arrow_dict.get(pair)
564 |         # print(lookup_arrows)
565 |         if lookup_arrows is not None:
566 |             for arrow in lookup_arrows:
567 |                 # print("Removing " + str(arrow) + " from sorted_arrows")
568 |                 self.sorted_arrows.discard(arrow)
569 | 
570 |         self.arrow_dict[pair] = None
571 | 
572 |     def score_graph_change(self, y, parents, x):
573 |         """Evaluate change in score from adding x->y"""
574 |         assert (x is not y)
575 |         assert (y not in parents)
576 |         y_index = y
577 | 
578 |         parent_indices = list()
579 |         for parent_node in parents:
580 |             parent_indices.append(parent_node)
581 | 
582 |         return self.score.local_score_diff_parents(x, y_index, parent_indices)
583 | 
584 |     def calculate_arrows_forward(self, a, b):
585 |         # print("Calculate Arrows Forward: " + str(a) + " " + str(b))
586 |         if b not in self.effect_edges_graph[a] and self.mode == "heuristic":
587 |             print("Returning early...")
588 |             return
589 | 
590 |         if self.knowledge is not None and self.knowledge.is_forbidden(a, b):
591 |             return
592 | 
593 |         # print("Get neighbors for " + str(b) + " returns " + str(graph_util.neighbors(self.graph, b)))
594 | 
595 |         self.stored_neighbors[b] = graph_util.neighbors(self.graph, b)
596 | 
597 |         na_y_x = graph_util.get_na_y_x(self.graph, a, b)
598 |         _na_y_x = list(na_y_x)
599 | 
600 |         if not graph_util.is_clique(self.graph, na_y_x):
601 |             return
602 | 
603 |         t_neighbors = list(graph_util.get_t_neighbors(self.graph, a, b))
604 |         # print("tneighbors for " + str(a) + ", " + str(b) + " returns " + str(t_neighbors))
605 |         len_T = len(t_neighbors)
606 | 
607 |         def outer_loop():
608 |             previous_cliques = set()  # set of sets of nodes
609 |             previous_cliques.add(frozenset())
610 |             new_cliques = set()  # set of sets of nodes
611 |             for i in range(len_T + 1):
612 | 
613 |                 choices = itertools.combinations(range(len_T), i)
614 |                 choices2 = itertools.combinations(range(len_T), i)
615 |                 # print("All choices: ", list(choices2), " TNeighbors: ", t_neighbors)
616 |                 for choice in choices:
617 |                     T = frozenset([t_neighbors[k] for k in choice])
618 |                     # print("Choice:", T)
619 |                     union = set(na_y_x)
620 |                     union.update(T)
621 | 
622 |                     found_a_previous_clique = False
623 | 
624 |                     for clique in previous_cliques:
625 |                         # basically if clique is a subset of union
626 |                         if union >= clique:
627 |                             found_a_previous_clique = True
628 |                             break
629 | 
630 |                     if not found_a_previous_clique:
631 |                         # Break out of the outer for loop
632 |                         return
633 | 
634 |                     if not graph_util.is_clique(self.graph, union):
635 |                         continue
636 | 
637 |                     new_cliques.add(frozenset(union))
638 | 
639 |                     bump = self.insert_eval(a, b, T, na_y_x)
640 |                     # print("Evaluated arrow " + str(a) + " -> " + str(b) + " with T: " + str(T) + " and bump: " + str(bump));
641 | 
642 |                     if bump > 0:
643 |                         self.add_arrow(a, b, na_y_x, T, bump)
644 | 
645 |                 previous_cliques = new_cliques
646 |                 new_cliques = set()
647 | 
648 |         outer_loop()
649 | 
650 |     def valid_set_by_knowledge(self, x, subset):
651 |         """Use knowledge to decide if an insert of delete does not orient edges
652 |         in a forbidden way. If some orientation in the subset is forbidden,
653 |         the whole subset is forbidden"""
654 |         for node in subset:
655 |             if self.knowledge.is_forbidden(x, node):
656 |                 return False
657 |         return True
658 | 
659 |     def create_checkpoint(self):
660 |         with open(self.save_name + '-checkpoint.pkl', 'wb') as f:
661 |             dill.dump(self, f, dill.HIGHEST_PROTOCOL)
662 | 


--------------------------------------------------------------------------------
/graph_util.py:
--------------------------------------------------------------------------------
  1 | """
  2 | Graph Terminology
  3 | -----------------
  4 |  * DAG: Directed Acyclic Graph
  5 |  * PDAG: Partially Directed Acyclic Graph
  6 |  * Directed edge: x --> y
  7 |  * Undirected edge: x --- y is represented as the pair x --> y and y --> x
  8 |  * Parents(x): nodes y such that there is a directed edge y --> x
  9 |  * Neighbors(x): nodes y such that there is an undirected edge y --- x
 10 |  * Adjacents(x): nodes y such there is some edge between x and y
 11 |    (i.e. x --- y, x --> y, or x <-- y)
 12 |  * Directed path: A path of entirely directed edges in the same direction
 13 |  * Ancestors(x): nodes y such that there is a directed path y ~~> x
 14 |  * Unshielded collider: triple of vertices x, y, z with directed edges
 15 |    x --> y <-- z, and x and z are not adjacent
 16 |  * Semi-directed path: A path of directed and undirected edges, where no
 17 |    directed edge is going in the opposite direction
 18 | """
 19 | 
 20 | import queue
 21 | import networkx as nx
 22 | import itertools
 23 | 
 24 | def add_undir_edge(g, x, y):
 25 |     """Adds an undirected edge (x,y) to Graph g.
 26 |     Undirected edges are stores as pairs of directed edges (x,y) and (y,x)"""
 27 |     g.add_edge(x, y)
 28 |     g.add_edge(y, x)
 29 | 
 30 | def add_dir_edge(g, x, y):
 31 |     """Adds an directed edge (x,y) to Graph g."""
 32 |     g.add_edge(x, y)
 33 | 
 34 | def undir_to_dir(g, x, y):
 35 |     """ Keep only x --> y """
 36 |     if g.has_edge(y, x) and g.has_edge(x, y):
 37 |         # Current edge is x --- y
 38 |         g.remove_edge(y, x)
 39 |         # print("Directing " + str(x) + " -> " + str(y))
 40 |     elif g.has_edge(x, y):
 41 |         # Current edge is x --> y
 42 |         pass
 43 |         # print("No-op Directing " + str(x) + " -> " + str(y))
 44 |     elif g.has_edge(y, x):
 45 |         # Current edge is y --> x
 46 |         raise AssertionError("undir_to_dir: trying to reverse a directed edge")
 47 |     else:
 48 |         raise AssertionError("undir_to_dir: no such edge")
 49 | 
 50 | def get_parents(g, x):
 51 |     """Returns immediate parents of node x in graph g"""
 52 |     parents = []
 53 |     for node in adjacent_nodes(g, x):
 54 |         if has_dir_edge(g, node, x):
 55 |             parents.append(node)
 56 |     return parents
 57 | 
 58 | def get_ancestors(g, x, accum=None):
 59 |     """Returns all ancestors of a node x in graph g"""
 60 |     if accum is None:
 61 |         accum = set()
 62 |     if x in accum:
 63 |         return accum
 64 | 
 65 |     accum.add(x)
 66 |     parents = get_parents(g, x)
 67 |     for p in parents:
 68 |         accum = get_ancestors(g, p, accum)
 69 | 
 70 |     return accum
 71 | 
 72 | def has_undir_edge(g, x, y):
 73 |     """ Returns whether there is an undirected edge from x to y in Graph g """
 74 |     return g.has_edge(x, y) and g.has_edge(y, x)
 75 | 
 76 | 
 77 | def has_dir_edge(g, x, y):
 78 |     """Returns whether there is a directed edge from x to y in Graph g"""
 79 |     return g.has_edge(x, y) and not g.has_edge(y, x)
 80 | 
 81 | 
 82 | def is_unshielded_non_collider(g, node_a, node_b, node_c):
 83 |     """Returns whether nodes a,b,c form an unshielded non-coliding triple"""
 84 |     if (not adjacent(g, node_a, node_b)):
 85 |         return False
 86 |     
 87 |     if (not adjacent(g, node_c, node_b)):
 88 |         return False
 89 | 
 90 |     if (adjacent(g, node_a, node_c)):
 91 |         return False 
 92 | 
 93 |     if (is_ambiguous_triple(g, node_a, node_b, node_c)):
 94 |         return False 
 95 | 
 96 |     return not (has_dir_edge(g, node_a, node_b) and has_dir_edge(g, node_c, node_b))
 97 | 
 98 | def is_def_collider(g, node_1, node_2, node_3):
 99 |     """Returns whether nodes a,b,c form a collider a -> b <- c"""
100 |     return has_dir_edge(g, node_1, node_2) and has_dir_edge(g, node_3, node_2)
101 | 
102 | def is_unshielded_collider(g, node_1, node_2, node_3):
103 |     """Returns whether nodes a,b,c form an unshielded collider a -> b <- c"""
104 |     return has_dir_edge(g, node_1, node_2) and has_dir_edge(g, node_3, node_2) and not adjacent(g, node_1, node_3)
105 | 
106 | def check_for_colliders(g, n):
107 |     """Searches for an unshielded collider a -> n <- b"""
108 |     adj = [m for m in g.nodes() if has_dir_edge(g, m, n)]
109 |     new_colliders = set()
110 | 
111 |     for pair in itertools.combinations(adj, 2):
112 |         if is_unshielded_collider(g, pair[0], n, pair[1]):
113 |             new_colliders.add((pair[0], n, pair[1]))
114 | 
115 |     return new_colliders
116 | 
117 | def get_all_collider_triples(g):
118 |     """Returns set of all collider triples in a Graph g"""
119 |     colliders = [check_for_colliders(g, n) for n in g.nodes()]
120 |     return set.union(*colliders)
121 | 
122 | def is_ambiguous_triple(g, node_a, node_b, node_c): 
123 |     # TODO: Actually write this. I'm having a tough time finding
124 |     # where this logic is implemented, because it seems like
125 |     # ambiguous triples is not populated for an EdgeListGraph that is 
126 |     # populated with just a List<Node>s
127 |     return False 
128 | 
129 | def traverseSemiDirected(g, x, y):
130 |     """Returns y if there is a directed """
131 |     if has_undir_edge(g, x, y) or g.has_edge(x, y):
132 |         return y
133 |     return None
134 | 
135 | def adjacent(g, x, y):
136 |     """ Returns whether nodes x and y are adjacent """
137 |     return g.has_edge(x, y) or g.has_edge(y, x)
138 | 
139 | def undir_edge_neighbors(g, x, y):
140 |     """Alias for has_undir_edge"""
141 |     return has_undir_edge(g, x, y)
142 | 
143 | def adjacent_nodes(g, x):
144 |     """Returns all adjacent nodes to x in Graph g"""
145 |     return list(set(nx.all_neighbors(g, x)))
146 | 
147 | def neighbors(g, x):
148 |     """Returns all neighbors of x in Graph g.
149 |     A neighbor is an adjacent node that """
150 |     potentialNeighbors = nx.all_neighbors(g, x)
151 |     resulting_neighbors = set({})
152 |     for pNode in potentialNeighbors:
153 |         if undir_edge_neighbors(g, x, pNode):
154 |             resulting_neighbors.add(pNode)
155 | 
156 |     return resulting_neighbors
157 | 
158 | def get_na_y_x(g, x, y):
159 |     """Gets possible conditioning sets of nodes to consider for P(Y|X)"""
160 |     na_y_x = []
161 |     all_y_neighbors = set(nx.all_neighbors(g, y))
162 | 
163 |     for z in all_y_neighbors:
164 |         if has_undir_edge(g, z, y):
165 |             if adjacent(g, z, x):
166 |                 na_y_x.append(z)
167 | 
168 |     return set(na_y_x)
169 | 
170 | def is_clique(g, node_set):
171 |     """Checks to see if the nodes in node_set form a clique"""
172 |     for node in node_set:
173 |         for other_node in node_set:
174 |             if node != other_node and not adjacent(g, node, other_node):
175 |                 return False 
176 |     return True
177 | 
178 | def get_t_neighbors(g, x, y):
179 |     """Returns possible members of conditioning set for x---y edge consideration"""
180 |     t = set([])
181 |     all_y_neighbors = set(nx.all_neighbors(g, y))
182 | 
183 |     for z in all_y_neighbors:
184 |         if has_undir_edge(g, z, y):
185 |             if adjacent(g, z, x):
186 |                 continue
187 |             t.add(z)
188 | 
189 |     return t
190 | 
191 | def is_kite(g, a, d, b, c):
192 |     """
193 |     Returns if nodes a,b,c, and d form a kite
194 |     D --- B, D --- A, D --- C, B --> A <-- C
195 |     See Meek (1995) Rule 3
196 |     """
197 |     return has_undir_edge(g, d, a) and \
198 |            has_undir_edge(g, d, b) and \
199 |            has_undir_edge(g, d, c) and \
200 |            has_dir_edge(g, b, a) and \
201 |            has_dir_edge(g, c, a)
202 | 
203 | def get_common_adjacents(g, x, y):
204 |     """Get the nodes that are adjacent to both x and y"""
205 |     return set(adjacent_nodes(g, x)).intersection(set(adjacent_nodes(g, y)))
206 | 
207 | def remove_dir_edge(g, x, y):
208 |     """Removes the directed edge x --> y"""
209 |     if g.has_edge(x, y):
210 |         g.remove_edge(x, y)
211 | 
212 | def exists_unblocked_semi_directed_path(g, origin, dest, cond_set, bound):
213 |     """Checks if there exists a unblocked semi directed path (that is, there could be a possible path) from
214 |     origin to dest, while conditioning on cond_set"""
215 |     if bound == -1:
216 |         bound = 1000
217 | 
218 |     q = queue.Queue()
219 |     v = set()
220 |     q.put(origin)
221 |     v.add(origin)
222 | 
223 |     e = None 
224 |     distance = 0
225 | 
226 |     while not q.empty():
227 |         t = q.get()
228 |         if t == dest:
229 |             return True 
230 | 
231 |         if e == t:
232 |             e = None 
233 |             distance += 1
234 |             if distance > bound:
235 |                 return False 
236 | 
237 |         for u in set(nx.all_neighbors(g, t)):
238 |             c = traverseSemiDirected(g, t, u)
239 |             if c is None:
240 |                 continue 
241 | 
242 |             if c in cond_set:
243 |                 continue 
244 | 
245 |             if c == dest:
246 |                 return True 
247 | 
248 |             if not c in v:
249 |                 v.add(c)
250 |                 q.put(c)
251 | 
252 |                 if e == None: 
253 |                     e = c 
254 |     return False
255 | 
256 | def detect_cycle_at_node(graph, node):
257 |     '''Detect a cycle involving a specific node'''
258 |     q = queue.Queue()
259 |     visited = set()
260 |     q.put(node)
261 | 
262 |     while not q.empty():
263 |         t = q.get()
264 |         for child in graph.neighbors(t):
265 |             if has_dir_edge(graph, t, child):
266 |                 if child == node:
267 |                     return True
268 |                 elif child not in visited:
269 |                     q.put(child)
270 |         visited.add(t)
271 | 
272 |     return False
273 | 
274 | def detect_cycle(graph):
275 |     '''Detect a cycle by finding directed loop.'''
276 |     for n in graph.nodes():
277 |         if detect_cycle_at_node(graph, n):
278 |             return True
279 |     return False
280 | 


--------------------------------------------------------------------------------
/knowledge.py:
--------------------------------------------------------------------------------
 1 | """
 2 | knowledge.py
 3 | 
 4 | Description from Tetrad
 5 | 
 6 | Stores information about required and forbidden edges and common causes for
 7 | use in algorithm. This information can be set edge by edge or else globally
 8 | via temporal tiers. When setting temporal tiers, all edges from later tiers
 9 | to earlier tiers are forbidden.
10 | 
11 | For this class, all variable names are referenced by name only. This is
12 | because the same Knowledge object is intended to plug into different graphs
13 | with MyNodes that possibly have the same names. Thus, if the Knowledge object
14 | forbids the edge X --> Y, then it forbids any edge which connects a MyNode
15 | named "X" to a MyNode named "Y", even if the underlying MyNodes themselves
16 | named "X" and "Y", respectively, are not the same.
17 | """
18 | import graph_util
19 | 
20 | class Knowledge:
21 |     def __init__(self):
22 |         self.required_edges = set()
23 |         self.forbidden_edges = set()
24 |         self.required_connections = set()
25 |         self.tier_map = {}
26 |         self.forbidden_within_tiers = {}
27 | 
28 |     def set_forbidden(self, x, y):
29 |         self.forbidden_edges.add((x, y))
30 | 
31 |     def remove_forbidden(self, x, y):
32 |         self.forbidden_edges -= {(x, y)}
33 | 
34 |     def set_required(self, x, y):
35 |         self.required_edges.add((x, y))
36 | 
37 |     def remove_required(self, x, y):
38 |         self.required_edges -= {(x, y)}
39 | 
40 |     def set_required_connection(self, x, y):
41 |         self.required_connections.add((x, y))
42 | 
43 |     def remove_required_connection(self, x, y):
44 |         self.required_connections -= {(x, y)}
45 | 
46 |     def set_tier(self, node, tier):
47 |         self.tier_map[node] = tier
48 | 
49 |     def is_forbidden_by_tiers(self, x, y):
50 |         if not x in self.tier_map.keys() or not y in self.tier_map.keys():
51 |             return False
52 |         if self.tier_map[x] == self.tier_map[y]:
53 |             return self.forbidden_within_tiers[x] == self.forbidden_within_tiers[y]
54 |         return self.tier_map[x] > self.tier_map[y]
55 | 
56 |     def set_tier_forbidden_within(self, tier, forbidden):
57 |         self.forbidden_within_tiers[tier] = forbidden
58 | 
59 |     def is_forbidden(self, x, y):
60 |         if self.is_forbidden_by_tiers(x, y):
61 |             return True
62 |         else:
63 |             return (x, y) in self.forbidden_edges
64 | 
65 |     def no_edge_required(self, x, y):
66 |         return not (self.is_required(x, y) or self.is_required(y, x) or
67 |                     (x, y) in self.required_connections or
68 |                     (y, x) in self.required_connections)
69 | 
70 |     def is_required(self, x, y):
71 |         return (x, y) in self.required_edges
72 | 
73 |     def is_violated_by(self, graph):
74 |         for edge in self.required_edges:
75 |             if not graph_util.has_dir_edge(graph, edge[0], edge[1]):
76 |                 return True
77 | 
78 |         for edge in graph.edges:
79 |             if graph_util.has_undir_edge(graph, edge[0], edge[1]):
80 |                 continue
81 | 
82 |             if self.is_forbidden(edge[0], edge[1]):
83 |                 return True
84 | 
85 |         return False


--------------------------------------------------------------------------------
/meekrules.py:
--------------------------------------------------------------------------------
  1 | import graph_util
  2 | import itertools
  3 | 
  4 | 
  5 | class MeekRules:
  6 |     __slots__ = ['undirect_unforced_edges', 'init_nodes', 'node_subset',
  7 |                  'visited', 'direct_stack', 'oriented', 'knowledge']
  8 | 
  9 |     def __init__(self, undirect_unforced_edges=True, knowledge=None):
 10 |         # Unforced parents should be undirected before orienting
 11 |         self.undirect_unforced_edges = undirect_unforced_edges
 12 |         self.init_nodes = []
 13 |         self.node_subset = {}
 14 |         self.visited = set()
 15 |         self.direct_stack = []
 16 |         self.oriented = set()
 17 |         self.knowledge = knowledge
 18 | 
 19 |     def orient_implied_subset(self, graph, node_subset):
 20 |         self.node_subset = node_subset
 21 |         self.visited.update(node_subset)
 22 |         self.orient_using_meek_rules_locally(graph)
 23 | 
 24 |     def orient_implied(self, graph):
 25 |         self.orient_implied_subset(graph, graph.nodes())
 26 | 
 27 |     def orient_using_meek_rules_locally(self, graph):
 28 |         """Orient graph using the four Meek rules"""
 29 |         if self.undirect_unforced_edges:
 30 |             for node in self.node_subset:
 31 |                 self.undirect_unforced_edges_func(node, graph)
 32 |                 self.direct_stack.extend(
 33 |                     graph_util.adjacent_nodes(graph, node))
 34 | 
 35 |         # TODO: Combine loops
 36 |         for node in self.node_subset:
 37 |             self.run_meek_rules(node, graph)
 38 |         if self.direct_stack != []:
 39 |             last_node = self.direct_stack.pop()
 40 |         else:
 41 |             last_node = None
 42 | 
 43 |         while last_node is not None:
 44 |             # print(last_node)
 45 |             if self.undirect_unforced_edges:
 46 |                 self.undirect_unforced_edges_func(last_node, graph)
 47 | 
 48 |             self.run_meek_rules(last_node, graph)
 49 |             # print("past run_meek_rules")
 50 |             if len(self.direct_stack) > 0:
 51 |                 last_node = self.direct_stack.pop()
 52 |             else:
 53 |                 last_node = None
 54 | 
 55 |     def undirect_unforced_edges_func(self, node, graph):
 56 |         """Removes directed edges that are not forced by an unshielded collider about node"""
 57 |         node_parents = graph_util.get_parents(graph, node)
 58 |         parents_to_undirect = set(node_parents)
 59 | 
 60 |         # Find any unshielded colliders in node_parents, and orient them
 61 |         for (p1, p2) in itertools.combinations(node_parents, 2):
 62 |             if not graph_util.adjacent(graph, p1, p2):
 63 |                 # Have an unshielded collider p1 -> node <- p2, which forces orientation
 64 |                 self.oriented.update([(p1, node), (p2, node)])
 65 |                 parents_to_undirect.difference_update([p1, p2])
 66 | 
 67 |         did_unorient = False
 68 | 
 69 |         for parent in parents_to_undirect:
 70 |             if self.knowledge is not None:
 71 |                 must_orient = self.knowledge.is_required(parent, node) or \
 72 |                               self.knowledge.is_forbidden(node, parent)
 73 |             else:
 74 |                 must_orient = False
 75 |             if not (parent, node) in self.oriented and not must_orient:
 76 |                 # Undirect parent -> node
 77 |                 graph_util.remove_dir_edge(graph, parent, node)
 78 |                 graph_util.add_undir_edge(graph, parent, node)
 79 |                 self.visited.add(node)
 80 |                 self.visited.add(parent)
 81 |                 # print(f"unorienting {parent} -> {node}")
 82 |                 did_unorient = True
 83 | 
 84 |         if did_unorient:
 85 |             for adjacent in graph_util.adjacent_nodes(graph, node):
 86 |                 self.direct_stack.append(adjacent)
 87 | 
 88 |             self.direct_stack.append(node)
 89 | 
 90 |     def run_meek_rules(self, node, graph):
 91 |         self.run_meek_rule_one(node, graph)
 92 |         self.run_meek_rule_two(node, graph)
 93 |         self.run_meek_rule_three(node, graph)
 94 |         self.run_meek_rule_four(node, graph)
 95 | 
 96 |     def run_meek_rule_one(self, node, graph):
 97 |         """
 98 |                 Meek's rule R1: if a-->b, b---c, and a not adj to c, then a-->c
 99 |                 """
100 |         # print("Running meek rule one", node)
101 |         adjacencies = graph_util.adjacent_nodes(graph, node)
102 |         if len(adjacencies) < 2:
103 |             return
104 |         all_combinations = itertools.combinations(
105 |             range(0, len(adjacencies)), 2)
106 |         for (index_one, index_two) in all_combinations:
107 |             node_a = adjacencies[index_one]
108 |             node_c = adjacencies[index_two]
109 | 
110 |             # TODO: Parallelize these flipped versions?
111 |             self.r1_helper(node_a, node, node_c, graph)
112 |             self.r1_helper(node_c, node, node_a, graph)
113 | 
114 |     def r1_helper(self, node_a, node_b, node_c, graph):
115 |         if ((not graph_util.adjacent(graph, node_a, node_c)) and
116 |                 (graph_util.has_dir_edge(graph, node_a, node_b) or (node_a, node_b) in self.oriented) and
117 |                 graph_util.has_undir_edge(graph, node_b, node_c)):
118 |             if not graph_util.is_unshielded_non_collider(graph, node_a, node_b, node_c):
119 |                 return
120 | 
121 |             if self.is_arrowpoint_allowed(node_b, node_c):
122 |                 # print("R1: " + str(node_b) + " " + str(node_c))
123 |                 if (node_a, node_c) not in self.oriented and (node_c, node_a) not in self.oriented and \
124 |                         (node_b, node_c) not in self.oriented and (node_c, node_b) not in self.oriented:
125 |                     self.direct(node_b, node_c, graph)
126 | 
127 |     def direct(self, node_1, node_2, graph):
128 |         # print("Int Directing " + str(node_1) + " " + str(node_2))
129 |         if self.knowledge is not None:
130 |             if self.knowledge.is_forbidden(node_1, node_2):
131 |                 return
132 | 
133 |         graph_util.remove_dir_edge(graph, node_1, node_2)
134 |         graph_util.remove_dir_edge(graph, node_2, node_1)
135 |         graph_util.add_dir_edge(graph, node_1, node_2)
136 |         self.visited.update([node_1, node_2])
137 |         # node_1 -> node_2 edge
138 |         if (node_1, node_2) not in self.oriented and \
139 |                 (node_2, node_1) not in self.oriented:
140 |             self.oriented.add((node_1, node_2))
141 |             self.direct_stack.append(node_2)
142 | 
143 |     def run_meek_rule_two(self, node_b, graph):
144 |         # print("Running meek rule two", node_b)
145 |         adjacencies = graph_util.adjacent_nodes(graph, node_b)
146 |         if len(adjacencies) < 2:
147 |             return
148 |         all_combinations = itertools.combinations(
149 |             range(0, len(adjacencies)), 2)
150 |         for (index_one, index_two) in all_combinations:
151 |             node_a = adjacencies[index_one]
152 |             node_c = adjacencies[index_two]
153 |             self.r2_helper(node_a, node_b, node_c, graph)
154 |             self.r2_helper(node_b, node_a, node_c, graph)
155 |             self.r2_helper(node_a, node_c, node_b, graph)
156 |             self.r2_helper(node_c, node_a, node_b, graph)
157 | 
158 |     def r2_helper(self, a, b, c, graph):
159 |         if graph_util.has_dir_edge(graph, a, b) and \
160 |                 graph_util.has_dir_edge(graph, b, c) and \
161 |                 graph_util.has_undir_edge(graph, a, c):
162 |             if self.is_arrowpoint_allowed(a, c):
163 |                 self.direct(a, c, graph)
164 | 
165 |     def run_meek_rule_three(self, node, graph):
166 |         """
167 |         A --- B, A --- X, A --- C, B --> X <-- C, B -/- C => A --> X
168 |         The parameter node = X
169 |         """
170 |         # print("Running meek rule three", node)
171 |         adjacencies = graph_util.adjacent_nodes(graph, node)
172 | 
173 |         if len(adjacencies) < 3:
174 |             return
175 | 
176 |         for node_a in adjacencies:
177 |             if graph_util.has_undir_edge(graph, node, node_a):
178 |                 copy_adjacencies = [a for a in adjacencies if a != node_a]
179 |                 all_combinations = itertools.combinations(copy_adjacencies, 2)
180 | 
181 |                 for node_b, node_c in all_combinations:
182 |                     if graph_util.is_kite(graph, node, node_a, node_b, node_c) and \
183 |                             self.is_arrowpoint_allowed(node_a, node) and \
184 |                             graph_util.is_unshielded_non_collider(graph, node_c, node_a, node_b):
185 |                         # print("R3: " + str(node_a) + " " + str(node))
186 |                         self.direct(node_a, node, graph)
187 | 
188 |     def run_meek_rule_four(self, a, graph):
189 |         if self.knowledge is None:
190 |             return
191 | 
192 |         adjacent_nodes = graph_util.adjacent_nodes(graph, a)
193 | 
194 |         for (b, c, d) in itertools.permutations(adjacent_nodes, 3):
195 |             if (graph_util.has_undir_edge(graph, a, b) and
196 |                     graph_util.has_dir_edge(graph, b, c) and
197 |                     graph_util.has_dir_edge(graph, c, d) and
198 |                     graph_util.has_undir_edge(graph, d, a) and
199 |                     self.is_arrowpoint_allowed(a, d)):
200 |                 self.direct(a, d, graph)
201 | 
202 |     def is_arrowpoint_allowed(self, from_node, to_node):
203 |         if self.knowledge is None:
204 |             return True
205 | 
206 |         return not self.knowledge.is_required(to_node, from_node) and \
207 |                not self.knowledge.is_forbidden(from_node, to_node)
208 | 
209 |     def get_visited(self):
210 |         """ This is what FGES actually uses """
211 |         return self.visited
212 | 


--------------------------------------------------------------------------------
/runner.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | from SEMScore import *
 3 | from fges import *
 4 | import time
 5 | import sys
 6 | 
 7 | import pickle
 8 | import argparse
 9 | 
10 | parser = argparse.ArgumentParser(description="Run FGES.")
11 | parser.add_argument("dataset", type=str,
12 |                     help="File to load data from (text file with a " \
13 |                          "row for each datapoint and a column for each variable. \
14 |                          If name of file ends in -checkpoint, this is assumed to be  \
15 |                          a saved checkpoint instead")
16 | parser.add_argument("save_name", type=str, help="File to save output to.")
17 | 
18 | parser.add_argument("sparsity", type=float, help="Sparsity penalty to use.")
19 | 
20 | parser.add_argument("-c", "--checkpoint", action="store_true",
21 |                     help="dataset is a FGES pickled checkpoint.")
22 | parser.add_argument("--checkpoint_frequency", type=int, default=0,
23 |                     help="Frequency to checkpoint work (in seconds). \
24 |                           Defaults to 0 to turn off checkpointing.")
25 | 
26 | def load_file(data_file):
27 |     return np.loadtxt(data_file, skiprows = 1)
28 | 
29 | def main():
30 |     args = parser.parse_args()
31 |     if args.dataset[-15:] == "-checkpoint.pkl":
32 |         start_time = time.time()
33 |         fges = FGES.load_checkpoint(args.dataset)
34 |         fges.last_checkpoint = time.time()
35 |         result = fges.search(checkpoint=True)
36 |     else:
37 |         dataset = load_file(args.dataset)
38 |         score = SEMBicScore(args.sparsity, dataset=dataset) # Initialize SEMBic Object
39 |         variables = list(range(len(dataset[0])))
40 |         print("Running FGES on graph with " + str(len(variables)) + " nodes.")
41 |         fges = FGES(variables, score,
42 |                     filename=args.dataset,
43 |                     checkpoint_frequency=args.checkpoint_frequency,
44 |                     save_name=args.save_name)
45 |         start_time = time.time()
46 |         result = fges.search()
47 | 
48 |     print("--- %s seconds ---" % (time.time() - start_time))
49 |     with open(args.save_name + '.pkl', 'wb') as f:
50 |         pickle.dump(result, f, pickle.HIGHEST_PROTOCOL)
51 | 
52 | if __name__ == "__main__":
53 |     main()
54 | 


--------------------------------------------------------------------------------
/search_util.py:
--------------------------------------------------------------------------------
  1 | 
  2 | import networkx as nx
  3 | 
  4 | from meekrules import MeekRules
  5 | from graph_util import *
  6 | import numpy as np
  7 | import queue
  8 | 
  9 | def get_undir_edge(g):
 10 |     '''Find an undirected edge in Graph g, or None if none exist'''
 11 |     for (x, y) in g.edges():
 12 |         if has_undir_edge(g, x, y):
 13 |             return (x, y)
 14 |     return None
 15 | 
 16 | def dagFromPattern(graph):
 17 |     '''
 18 |     Construct a specific graph from an equivalence class
 19 |     :param graph: Equivalence class (i.e. DAG with unoriented edges)
 20 |     :return: Candidate dag, or None if unsuccessful
 21 |     '''
 22 | 
 23 |     dag = graph.copy()
 24 |     graph_colliders = get_all_collider_triples(graph)
 25 |     rules = MeekRules(undirect_unforced_edges=False)
 26 | 
 27 |     if detect_cycle(dag):
 28 |         return None
 29 | 
 30 |     def check_graph(dag, node):
 31 |         '''
 32 |         Check if a dag is okay.
 33 |         :param dag: dag to check
 34 |         :param node: node to check for cycles
 35 |         :return: dag with implied edges if valid, else None
 36 |         '''
 37 |         rules.orient_implied(dag)
 38 |         new_colliders = get_all_collider_triples(dag)
 39 |         if new_colliders == graph_colliders and not detect_cycle_at_node(dag, node):
 40 |             return dag
 41 |         else:
 42 |             return None
 43 | 
 44 |     def try_to_solve(pattern):
 45 |         '''
 46 |         Try to find a fully oriented dag from a pattern using a DFS
 47 |         :param pattern: the pattern to try
 48 |         :return: dag if successful, else None
 49 |         '''
 50 |         if pattern is None:
 51 |             return None
 52 | 
 53 |         edge = get_undir_edge(pattern)
 54 | 
 55 |         if edge is None:
 56 |             # No more undirected edges
 57 |             return pattern
 58 | 
 59 |         (node1, node2) = edge
 60 |         new_g = pattern.copy()
 61 |         if node2 not in get_ancestors(new_g, node1):
 62 |             # Orient edge node1 -> node2
 63 |             new_g.remove_edge(node2, node1)
 64 |             result = try_to_solve(check_graph(new_g, node1))
 65 |             if result is not None:
 66 |                 return result
 67 | 
 68 |         new_g = pattern.copy()
 69 |         if node1 not in get_ancestors(new_g, node2):
 70 |             # Orient edge node2 -> node1
 71 |             new_g.remove_edge(node1, node2)
 72 |             result = try_to_solve(check_graph(new_g, node2))
 73 |             if result is not None:
 74 |                 return result
 75 | 
 76 |         return None
 77 | 
 78 |     return try_to_solve(graph)
 79 | 
 80 | #TODO: use smarter penalty function than simply a count
 81 | def dagFromPatternWithColliders(graph):
 82 |     '''
 83 |     Construct a DAG from the pattern graph that minimizes the number of new colliders added.
 84 |     :param graph: The pattern to use
 85 |     :return: DAG
 86 |     '''
 87 |     pattern = graph.copy()
 88 | 
 89 |     assert not detect_cycle(pattern), "Pattern must be acyclic to start"
 90 | 
 91 |     optimal_graph = None
 92 |     optimal_penalty = np.inf
 93 | 
 94 |     # Stack of (colliders before messing with the edge,
 95 |     #           penalty before messing with the edge,
 96 |     #           edge to mess with,
 97 |     #           status)
 98 |     history = queue.LifoQueue(maxsize=len(pattern.edges()))
 99 |     history.put((get_all_collider_triples(pattern), 0, get_undir_edge(pattern), 0))
100 | 
101 |     while not history.empty():
102 |         c, p, edge, status = history.get()
103 | 
104 |         if edge is None:
105 |             if p < optimal_penalty:
106 |                 optimal_penalty = p
107 |                 optimal_graph = pattern.copy()
108 |             continue
109 | 
110 |         (x, y) = edge
111 | 
112 |         if status == 0:
113 |             # Orient x -> y
114 |             pattern.remove_edge(y, x)
115 |             c1 = check_for_colliders(pattern, y)
116 |             p1 = p + len(c1 - c)  # set difference
117 |             history.put((c, p, edge, 1))
118 | 
119 |             if not detect_cycle_at_node(pattern, x) and p1 < optimal_penalty:
120 |                 history.put((c.union(c1), p1, get_undir_edge(pattern), 0))
121 | 
122 |         elif status == 1:
123 |             # Orient y -> x
124 |             pattern.add_edge(y, x)
125 |             pattern.remove_edge(x, y)
126 |             c1 = check_for_colliders(pattern, x)
127 |             p1 = p + len(c1 - c)
128 |             history.put((c, p, edge, 2))
129 | 
130 |             if not detect_cycle_at_node(pattern, y) and p1 < optimal_penalty:
131 |                 history.put((c.union(c1), p1, get_undir_edge(pattern), 0))
132 | 
133 |         elif status == 2:
134 |             pattern.add_edge(x, y)
135 | 
136 |     assert optimal_graph is not None
137 | 
138 |     return (optimal_graph, optimal_penalty)
139 | 
140 | 
141 | def mean_shift_data(data):
142 |     '''Shift all variables in a dataset to have mean zero'''
143 |     return data - np.mean(data, axis=0)
144 | 
145 | def estimate_parameters(dag, data):
146 |     '''
147 |     Estimate the parameters of a DAG to fit the data.
148 |     :return: matrix of edge coefficients, and diagonal matrix of residuals
149 |     For the parameters matrix, p[i, j] is the weight of edge i -> j
150 |     '''
151 | 
152 |     assert get_undir_edge(dag) is None
153 | 
154 |     data = mean_shift_data(data)
155 |     num_nodes = len(dag.nodes())
156 | 
157 |     edge_parameters = np.zeros((num_nodes, num_nodes))
158 |     residuals = np.zeros((num_nodes, num_nodes))
159 | 
160 |     for j in range(num_nodes):
161 |         inbound_nodes = [i for i in range(num_nodes) if has_dir_edge(dag, i, j)]
162 | 
163 |         if len(inbound_nodes) == 0:
164 |             residuals[j, j] = np.var(data[:, j])
165 |             continue
166 | 
167 |         assert j not in inbound_nodes
168 | 
169 |         a = data[:, inbound_nodes]
170 |         b = data[:, j]
171 | 
172 |         params, r, _, _ = np.linalg.lstsq(a, b)
173 | 
174 |         residuals[j, j] = r / (data.shape[0] - 1)
175 | 
176 |         for i in range(len(inbound_nodes)):
177 |             edge_parameters[inbound_nodes[i], j] = params[i]
178 |             # v = edge_parameters * v + e
179 | 
180 |     return np.array(edge_parameters), np.array(residuals)
181 | 
182 | def get_covariance_matrix(params, resids):
183 |     '''
184 |     Get the covariance matrix from edge parameters
185 |      (representing a DAG) and the residuals.
186 | 
187 |     For the equation, see "Causal Mapping of Emotion Networks in the Human Brain" (p. 15)
188 |     The params matrix is taken with orientation p[i, j] is the weight for edge i -> j
189 |     '''
190 |     id = np.identity(params.shape[0])
191 |     a = np.linalg.inv(id - params.transpose())
192 | 
193 |     return np.matmul(np.matmul(a, resids), np.transpose(a))


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/tests/__init__.py:
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https://raw.githubusercontent.com/eberharf/fges-py/961188a48b8689ae451861a7232262adffb46d45/tests/__init__.py


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/tests/fges_tests.py:
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  1 | from SEMScore import *
  2 | from fges import *
  3 | from tests.test_util import *
  4 | import unittest
  5 | import random
  6 | 
  7 | def run_fges_file(data_file, **kwargs):
  8 |     '''
  9 |     Run FGES on a data file, returning the resulting graph
 10 |     :param data_file: the data file to use
 11 |     :return: DiGraph from fges.search()
 12 |     '''
 13 |     return run_fges_array(np.loadtxt(data_file, skiprows = 1), **kwargs)
 14 | 
 15 | def run_fges_array(dataset, **kwargs):
 16 |     '''
 17 |     Run FGES on a loaded array, with a row for each datapoint and a column for each variable.
 18 |     :param dataset: numpy array
 19 |     :return: DiGraph from fges.search()
 20 |     '''
 21 |     score = SEMBicScore(dataset, 2)  # Initialize SEMBic Object
 22 |     variables = list(range(len(dataset[0])))
 23 |     print("Running FGES on graph with " + str(len(variables)) + " nodes.")
 24 |     fges = FGES(variables, score, **kwargs)
 25 |     return fges.search()
 26 | 
 27 | def assert_unoriented_edge(edges, e):
 28 |     assert (e in edges) and (e[::-1] in edges)
 29 | 
 30 | def assert_oriented_edge(edges, e):
 31 |     assert (e in edges) and not (e[::-1] in edges)
 32 | 
 33 | class SimpleTests(unittest.TestCase):
 34 | 
 35 |     def test_collider_1(self):
 36 |         '''
 37 |         Test a simple collider X1 -> X3 <- X2
 38 |         FGES should obtain the exact graph
 39 |         '''
 40 |         result = run_fges_file("../data/collider_1.txt")
 41 |         edges = result['graph'].edges()
 42 | 
 43 |         assert_oriented_edge(edges, (0, 2))
 44 |         assert_oriented_edge(edges, (1, 2))
 45 | 
 46 |     def test_collider_2(self):
 47 |         '''
 48 |         Test a collider with common cause
 49 |          X1 -> X2 -> X3
 50 |          X1 -> X4 -> X3
 51 |         FGES should resolve collider at X3, and connection between other nodes
 52 |         '''
 53 |         result = run_fges_file("../data/collider_2.txt")
 54 |         edges = result['graph'].edges()
 55 | 
 56 |         assert_oriented_edge(edges, (1, 2))
 57 |         assert_oriented_edge(edges, (3, 2))
 58 |         assert_unoriented_edge(edges, (0, 1))
 59 |         assert_unoriented_edge(edges, (0, 3))
 60 | 
 61 |     def test_collider_3(self):
 62 |         '''
 63 |         Graph Edges:
 64 |           {X0, X1} --> X2 --> {X3, X4} --> X5
 65 | 
 66 |         FGES should orient all edges
 67 |         '''
 68 |         result = run_fges_file("../data/collider_3.txt")
 69 |         edges = result['graph'].edges()
 70 | 
 71 |         print("Computed Edges:", edges)
 72 | 
 73 |         expected = [(0, 2), (1, 2), (2, 3), (2, 4), (3, 5), (4, 5)]
 74 |         all_correct = True
 75 | 
 76 |         for e in expected:
 77 |             if e not in edges:
 78 |                 all_correct = False
 79 |                 print("Missing edge", e, "({} -> {})".format(*e))
 80 | 
 81 |         for e in edges:
 82 |             if e not in expected:
 83 |                 all_correct = False
 84 |                 print("Extra edge", e, "({} -> {})".format(*e))
 85 | 
 86 |         assert all_correct
 87 | 
 88 |     def test_collider_4(self):
 89 |         '''
 90 |         Graph Edges:
 91 |           {X1, X2} --> X3 --> X4 --> X5
 92 | 
 93 |         FGES should orient all edges
 94 |         '''
 95 |         result = run_fges_file("../data/collider_4.txt")
 96 |         edges = result['graph'].edges()
 97 | 
 98 |         expected = [(0, 2), (1, 2), (2, 3), (3, 4)]
 99 | 
100 |         for e in expected:
101 |             assert_oriented_edge(edges, e)
102 | 
103 |         assert(len(edges) == len(expected))
104 | 
105 |     def test_collider_5(self):
106 |         '''
107 |         Graph Edges:
108 |           {X1, X2} --> X3; X1 --> X4
109 | 
110 |         FGES should orient all edges
111 |         '''
112 |         result = run_fges_file("../data/collider_5.txt")
113 |         edges = result['graph'].edges()
114 | 
115 |         assert_oriented_edge(edges, (0, 2))
116 |         assert_oriented_edge(edges, (1, 2))
117 |         assert_unoriented_edge(edges, (0, 3))
118 | 
119 |         assert(len(edges) == 4)
120 | 
121 |     def test_linear_1(self):
122 |         '''
123 |         X1 --> X2 --> X3 --> X4
124 | 
125 |         FGES should not be able to orient any edges
126 |         '''
127 |         result = run_fges_file("../data/linear_1.txt")
128 |         edges = result['graph'].edges()
129 | 
130 |         assert_unoriented_edge(edges, (0, 1))
131 |         assert_unoriented_edge(edges, (1, 2))
132 |         assert_unoriented_edge(edges, (2, 3))
133 | 
134 |     def test_single_edge_1(self):
135 |         '''
136 |         Graph with 10 variables and a single edge.
137 |         '''
138 |         result = run_fges_file("../data/single_edge_1.txt")
139 |         edges = result['graph'].edges()
140 | 
141 |         assert len(edges) == 2
142 |         assert_unoriented_edge(edges, (0, 1))
143 | 
144 |     def test_single_edge_2(self):
145 |         '''
146 |         Graph with 50 variables and a single edge.
147 |         '''
148 |         result = run_fges_file("../data/single_edge_2.txt")
149 |         edges = result['graph'].edges()
150 | 
151 |         assert len(edges) == 2
152 |         assert_unoriented_edge(edges, (0, 1))
153 | 
154 |     def test_single_edge_3(self):
155 |         '''
156 |         Graph with 100 variables and a single edge.
157 |         '''
158 |         result = run_fges_file("../data/single_edge_3.txt")
159 |         edges = result['graph'].edges()
160 | 
161 |         print(edges)
162 |         assert len(edges) == 2
163 |         assert_unoriented_edge(edges, (36, 58))
164 | 
165 |     def test_fifty_edges(self):
166 |         result = run_fges_file("../data/50_edges.txt")
167 |         edges = result['graph'].edges()
168 | 
169 |         dirs = [e for e in edges if e[::-1] not in edges]
170 |         undirs = [e for e in edges if e[0] < e[1] and e[::-1] in edges]
171 |         assert len(dirs) + len(undirs) == 50
172 | 
173 | 
174 | class TestCheckpoints(unittest.TestCase):
175 | 
176 |     def checkpoint_verify(self, data_file):
177 |         result = run_fges_file(data_file, checkpoint_frequency=1, save_name='test_tmp')
178 |         result2 = FGES.load_checkpoint('test_tmp-checkpoint.pkl').search()
179 |         os.remove("test_tmp-checkpoint.pkl")
180 |         assert set(result['graph'].edges()) == set(result2['graph'].edges())
181 | 
182 |     def test_checkpoints(self):
183 |         for i in range(1, 6):
184 |             self.checkpoint_verify("../data/collider_{}.txt".format(i))
185 | 
186 | class RandomFGESTests(unittest.TestCase):
187 |     def test_v_structure(self):
188 |         '''
189 |         Graph Edges:
190 |           X0 --- X1 --> X2 <-- X3
191 |         '''
192 |         g = np.zeros((4, 4))
193 |         g[0, 1] = 1
194 |         g[1, 2] = 1
195 |         g[3, 2] = 1
196 | 
197 |         d = generate_data(g, [0, 1, 3, 2], 1000)
198 | 
199 |         result = run_fges_array(d)
200 |         edges = result['graph'].edges()
201 | 
202 |         assert_unoriented_edge(edges, (0, 1))
203 |         assert_oriented_edge(edges, (1, 2))
204 |         assert_oriented_edge(edges, (3, 2))
205 |         assert len(edges) == 4
206 | 
207 |     def test_y_structure(self):
208 |         '''
209 |         Graph Edges:
210 |           X0 --> X1 <-- X2
211 |           X1 --> X3
212 |         '''
213 |         g = np.zeros((4, 4))
214 |         g[0, 1] = 1
215 |         g[2, 1] = -1
216 |         g[1, 3] = 2
217 | 
218 |         d = generate_data(g, [0, 2, 1, 3], 1000)
219 | 
220 |         result = run_fges_array(d)
221 |         edges = result['graph'].edges()
222 | 
223 |         print(edges)
224 | 
225 |         assert_oriented_edge(edges, (0, 1))
226 |         assert_oriented_edge(edges, (2, 1))
227 |         assert_oriented_edge(edges, (1, 3))
228 |         assert len(edges) == 3
229 | 
230 |     def test_diamond(self):
231 |         '''
232 |         Graph Edges:
233 |           {X0, X1} --> X2 --> {X3, X4} --> X5 <-- X6
234 |         FGES should orient all edges
235 |         '''
236 |         g = np.zeros((7, 7))
237 |         g[0, 2] = 1
238 |         g[1, 2] = 1
239 |         g[2, 3] = 1
240 |         g[2, 4] = 1
241 |         g[3, 5] = 1
242 |         g[4, 5] = 1
243 |         g[6, 5] = 1
244 | 
245 |         g *= np.random.uniform(0.5, 10, g.shape)
246 |         g *= np.random.choice([-1, 1], g.shape)
247 | 
248 |         d = generate_data(g, [0, 1, 2, 3, 4, 6, 5], 100000)
249 | 
250 |         result = run_fges_array(d)
251 |         edges = result['graph'].edges()
252 | 
253 |         assert_oriented_edge(edges, (0, 2))
254 |         assert_oriented_edge(edges, (1, 2))
255 |         assert_oriented_edge(edges, (2, 3))
256 |         assert_oriented_edge(edges, (2, 4))
257 |         assert_oriented_edge(edges, (3, 5))
258 |         assert_oriented_edge(edges, (4, 5))
259 |         assert_oriented_edge(edges, (6, 5))
260 |         assert len(edges) == 7
261 | 
262 | class TestKnowledge(unittest.TestCase):
263 |     def test_simple_forbidden(self):
264 |         """forbids all edges in case of simple_linear_test"""
265 |         wisdom = Knowledge()
266 |         for i in range(4):
267 |             for j in range(i):
268 |                 wisdom.set_forbidden(i, j)
269 |                 wisdom.set_forbidden(j, i)
270 |         result = run_fges("../data/linear_1.txt", knowledge=wisdom)
271 |         assert len(result['graph'].edges) == 0
272 | 
273 |     def test_random_required(self):
274 |         """requires an edge in a graph that would normally have no edges"""
275 |         result = run_fges("../data/40_random.txt")
276 |         assert len(result['graph'].edges) == 0
277 | 
278 |         wisdom = Knowledge()
279 |         x = random.randint(0, 39)
280 |         y = random.randint(0, 39)
281 |         while y == x:
282 |             y = random.randint(0, 39)
283 |         wisdom.set_required(x, y)
284 |         result = run_fges("../data/40_random.txt", knowledge=wisdom)
285 |         print(x, y)
286 |         print(result['graph'].edges)
287 |         assert not wisdom.is_violated_by(result['graph'])
288 | 
289 |     def test_random_forbidden(self):
290 |         """
291 |         generates graph, then forbids a random edge and regenerates, checking
292 |         for absence of edge
293 |         """
294 |         result = run_fges("../data/50_fully_connected.txt")
295 |         edges = list(result['graph'].edges)
296 |         edge = random.choice(edges)
297 |         wisdom = Knowledge()
298 |         wisdom.set_forbidden(edge[0], edge[1])
299 |         wisdom.set_forbidden(edge[1], edge[0])
300 |         knowledge_result = run_fges("../data/50_fully_connected.txt", knowledge=wisdom)
301 |         assert not graph_util.adjacent(knowledge_result['graph'], edge[0], edge[1])
302 | 
303 |     def test_tiers(self):
304 |         '''
305 |         X1 --> X2 --> X3 --> X4
306 | 
307 |         FGES should be able to orient all edges with knowledge
308 |         '''
309 |         wisdom = Knowledge()
310 |         for i in range(4):
311 |             wisdom.set_tier(i, i)
312 |         result = run_fges("../data/linear_1.txt", knowledge=wisdom)
313 |         edges = result['graph'].edges()
314 |         assert_oriented_edge(edges, (0, 1))
315 |         assert_oriented_edge(edges, (1, 2))
316 |         assert_oriented_edge(edges, (2, 3))
317 | 
318 |     def test_required_connections(self):
319 | 
320 |         wisdom = Knowledge()
321 |         wisdom.set_required_connection(0, 3)
322 | 
323 |         result = run_fges("../data/linear_1.txt", knowledge=wisdom)
324 |         edges = result['graph'].edges()
325 |         print(edges)
326 |         assert (0, 3) in edges or (3, 0) in edges
327 | 
328 | 
329 | if __name__ == "__main__":
330 |     unittest.main()
331 | 


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/tests/test_graph_util.py:
--------------------------------------------------------------------------------
 1 | from graph_util import *
 2 | import networkx as nx
 3 | import unittest
 4 | 
 5 | class TestAncestors(unittest.TestCase):
 6 | 
 7 |     def test_simple_graph(self):
 8 |         '''
 9 |         Test a simple graph X0 -> X1 -> X2 -> X3
10 |         '''
11 |         graph = nx.DiGraph()
12 |         graph.add_nodes_from([0, 1, 2, 3])
13 |         for i in [0, 1, 2]:
14 |             graph.add_edge(i, i + 1)
15 | 
16 |         for i in range(4):
17 |             assert get_ancestors(graph, i) == set(range(i + 1))
18 | 
19 |     def test_cyclic_graph(self):
20 |         '''
21 |         X0 -> {X1, X2} -> X3
22 |         '''
23 |         graph = nx.DiGraph()
24 |         graph.add_nodes_from([0, 1, 2, 3])
25 |         graph.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
26 | 
27 |         assert get_ancestors(graph, 0) == set([0])
28 |         assert get_ancestors(graph, 1) == set([0, 1])
29 |         assert get_ancestors(graph, 2) == set([0, 2])
30 |         assert get_ancestors(graph, 3) == set([0, 1, 2, 3])
31 | 
32 |     def test_undirected_edges(self):
33 |         '''
34 |         Ancestors should only consider directed edges
35 |         X0 -> X1 -> X2 -- X3 --> X4
36 |         '''
37 |         graph = nx.DiGraph()
38 |         graph.add_nodes_from([0, 1, 2, 3, 4])
39 |         graph.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 2), (3, 4)])
40 | 
41 |         assert get_ancestors(graph, 0) == set([0])
42 |         assert get_ancestors(graph, 1) == set([0, 1])
43 |         assert get_ancestors(graph, 2) == set([0, 1, 2])
44 |         assert get_ancestors(graph, 3) == set([3])
45 |         assert get_ancestors(graph, 4) == set([3, 4])
46 | 
47 | if __name__ == "__main__":
48 |     unittest.main()


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/tests/test_meek_rules.py:
--------------------------------------------------------------------------------
  1 | import unittest
  2 | import networkx as nx
  3 | 
  4 | from meekrules import MeekRules
  5 | from graph_util import *
  6 | from knowledge import Knowledge
  7 | 
  8 | def make_graph(num_vertices, edges):
  9 |     graph = nx.DiGraph()
 10 |     graph.add_nodes_from(list(range(num_vertices)))
 11 |     graph.add_edges_from(edges)
 12 |     return graph
 13 | 
 14 | def group_edges(edges):
 15 |     undirs = []
 16 |     dirs = []
 17 |     for e in edges:
 18 |         if e[::-1] in dirs:
 19 |             dirs.remove(e[::-1])
 20 |             undirs.append(e)
 21 |         else:
 22 |             dirs.append(e)
 23 |     return undirs, dirs
 24 | 
 25 | class SingleRuleTests(unittest.TestCase):
 26 | 
 27 |     def test_rule_1(self):
 28 |         # 0 --> 1 --- 2  =>  0 --> 1 --> 2
 29 |         g = make_graph(3, [(0, 1), (1, 2), (2, 1)])
 30 |         meek = MeekRules(undirect_unforced_edges=False)
 31 |         meek.orient_implied(g)
 32 | 
 33 |         assert len(g.edges()) == 2
 34 |         assert has_dir_edge(g, 0, 1)
 35 |         assert has_dir_edge(g, 1, 2)
 36 | 
 37 |         # 0 --- 1 --> 2  =>  nothing
 38 |         g = make_graph(3, [(0, 1), (1, 0), (1, 2)])
 39 |         meek = MeekRules(undirect_unforced_edges=False)
 40 |         meek.orient_implied(g)
 41 | 
 42 |         assert len(g.edges()) == 3
 43 |         assert has_undir_edge(g, 0, 1)
 44 |         assert has_dir_edge(g, 1, 2)
 45 | 
 46 |         # 0 --> 1 --- 2 and 0 -- 2  =>  nothing
 47 |         g = make_graph(3, [(0, 1), (1, 2), (2, 1), (0, 2), (2, 0)])
 48 |         meek = MeekRules(undirect_unforced_edges=False)
 49 |         meek.orient_implied(g)
 50 | 
 51 |         assert len(g.edges()) == 5
 52 |         assert has_dir_edge(g, 0, 1)
 53 |         assert has_undir_edge(g, 0, 2)
 54 |         assert has_undir_edge(g, 1, 2)
 55 | 
 56 |     def test_rule_2(self):
 57 |         # 0 --> 1 --> 2 and 0 --- 2  => 0 --> 2
 58 |         g = make_graph(3, [(0, 1), (1, 2), (0, 2), (2, 0)])
 59 |         meek = MeekRules(undirect_unforced_edges=False)
 60 |         meek.orient_implied(g)
 61 | 
 62 |         assert len(g.edges()) == 3
 63 |         assert has_dir_edge(g, 0, 1)
 64 |         assert has_dir_edge(g, 0, 2)
 65 |         assert has_dir_edge(g, 1, 2)
 66 | 
 67 |     def test_rule_3(self):
 68 |         '''
 69 |         0 --- 1, 0 --- 2, 0 --- 3, 1 --> 2 <-- 3  => 0 --> 2
 70 |         '''
 71 |         g = make_graph(4, [(0, 1), (1, 0), (0, 2), (2, 0), (0, 3), (3, 0),
 72 |                            (1, 2), (3, 2)])
 73 | 
 74 |         assert is_kite(g, 2, 0, 1, 3)
 75 |         assert is_unshielded_non_collider(g, 3, 0, 1)
 76 | 
 77 |         meek = MeekRules(undirect_unforced_edges=False)
 78 |         meek.orient_implied(g)
 79 | 
 80 |         assert len(g.edges()) == 7
 81 |         assert has_undir_edge(g, 0, 1)
 82 |         assert has_undir_edge(g, 0, 3)
 83 |         assert has_dir_edge(g, 0, 2)
 84 |         assert has_dir_edge(g, 1, 2)
 85 |         assert has_dir_edge(g, 3, 2)
 86 | 
 87 |         g = make_graph(4, [(0, 1), (1, 0), (0, 2), (2, 0), (0, 3), (3, 0),
 88 |                            (1, 2), (3, 2), (1, 3)])
 89 | 
 90 |         assert is_kite(g, 2, 0, 1, 3)
 91 |         assert not is_unshielded_non_collider(g, 3, 0, 1)
 92 | 
 93 |         meek = MeekRules(undirect_unforced_edges=False)
 94 |         meek.orient_implied(g)
 95 | 
 96 |         assert len(g.edges()) == 9
 97 |         assert has_undir_edge(g, 0, 1)
 98 |         assert has_undir_edge(g, 0, 2)
 99 |         assert has_undir_edge(g, 0, 3)
100 |         assert has_dir_edge(g, 1, 2)
101 |         assert has_dir_edge(g, 3, 2)
102 |         assert has_dir_edge(g, 1, 3)
103 | 
104 |     def test_rule_4(self):
105 |         g = make_graph(4, [(0, 1), (1, 0),
106 |                            (0, 2), (2, 0),
107 |                            (0, 3), (3, 0),
108 |                            (1, 2),
109 |                            (2, 3)])
110 |         k = Knowledge()
111 |         k.set_forbidden(1, 3)
112 | 
113 |         meek = MeekRules(undirect_unforced_edges=False, knowledge=k)
114 |         meek.orient_implied_subset(g, [0])
115 | 
116 |         assert len(g.edges()) == 7
117 |         assert has_dir_edge(g, 1, 2)
118 |         assert has_dir_edge(g, 2, 3)
119 |         assert has_dir_edge(g, 0, 3)
120 |         assert has_undir_edge(g, 0, 1)
121 |         assert has_undir_edge(g, 0, 2)
122 | 
123 | 
124 | class LargeGraphTests(unittest.TestCase):
125 | 
126 |     def test_meek_graph_1a(self):
127 |         g = make_graph(10, [
128 |             (0, 3), (3, 0),
129 |             (3, 6),
130 |             (4, 6),
131 |             (1, 4), (4, 1),
132 |             (1, 2),
133 |             (6, 7), (7, 6),
134 |             (5, 7), (7, 5),
135 |             (7, 8), (8, 7),
136 |             (5, 8), (8, 5),
137 |             (5, 2),
138 |             (2, 9),
139 |             (8, 9),
140 |             (5, 9), (9, 5)
141 |         ])
142 | 
143 |         meek = MeekRules(undirect_unforced_edges=False)
144 |         meek.orient_implied(g)
145 | 
146 |         expected_undir_edges = [
147 |             (0, 3),
148 |             (1, 4),
149 |             (5, 8),
150 |         ]
151 | 
152 |         expected_dir_edges = [
153 |             (3, 6),
154 |             (4, 6),
155 |             (1, 2),
156 |             (6, 7),
157 |             (7, 5),
158 |             (7, 8),
159 |             (5, 2),
160 |             (2, 9),
161 |             (8, 9),
162 |             (5, 9),
163 |         ]
164 | 
165 |         for e in expected_undir_edges:
166 |             assert has_undir_edge(g, *e)
167 |         for e in expected_dir_edges:
168 |             assert has_dir_edge(g, *e)
169 |         assert len(g.edges()) == len(expected_dir_edges) + 2 * len(expected_undir_edges)
170 | 
171 |     def test_meek_graph_1b(self):
172 |         '''
173 |         Add extra oriented edges, that should be unoriented
174 |         '''
175 |         g = make_graph(10, [
176 |             (3, 0), #
177 |             (3, 6),
178 |             (4, 6),
179 |             (1, 4), #
180 |             (1, 2),
181 |             (6, 7), (7, 6),
182 |             (5, 7), (7, 5),
183 |             (7, 8), (8, 7),
184 |             (5, 8), #
185 |             (5, 2),
186 |             (2, 9),
187 |             (8, 9),
188 |             (5, 9), (9, 5)
189 |         ])
190 | 
191 |         meek = MeekRules(undirect_unforced_edges=True)
192 |         meek.orient_implied(g)
193 | 
194 |         expected_undir_edges = [
195 |             (0, 3),
196 |             (1, 4),
197 |             (5, 8),
198 |         ]
199 | 
200 |         expected_dir_edges = [
201 |             (3, 6),
202 |             (4, 6),
203 |             (1, 2),
204 |             (6, 7),
205 |             (7, 5),
206 |             (7, 8),
207 |             (5, 2),
208 |             (2, 9),
209 |             (8, 9),
210 |             (5, 9),
211 |         ]
212 | 
213 |         for e in expected_undir_edges:
214 |             assert has_undir_edge(g, *e)
215 |         for e in expected_dir_edges:
216 |             assert has_dir_edge(g, *e)
217 |         assert len(g.edges()) == len(expected_dir_edges) + 2 * len(expected_undir_edges)
218 | 
219 |     def test_undirect_edges_1(self):
220 |         g = make_graph(10, [
221 |             (3, 0),  #
222 |             (3, 6),
223 |             (4, 6),
224 |             (1, 4),  #
225 |             (1, 2),
226 |             (6, 7), (7, 6),
227 |             (5, 7), (7, 5),
228 |             (7, 8), (8, 7),
229 |             (5, 8),  #
230 |             (5, 2),
231 |             (2, 9),
232 |             (8, 9),
233 |             (5, 9), (9, 5)
234 |         ])
235 | 
236 |         meek = MeekRules()
237 | 
238 |         meek.undirect_unforced_edges_func(0, g)
239 |         assert has_undir_edge(g, 0, 3)
240 |         assert has_dir_edge(g, 3, 6)
241 | 
242 |         meek.undirect_unforced_edges_func(4, g)
243 |         assert has_undir_edge(g, 4, 1)
244 |         assert has_dir_edge(g, 4, 6)
245 | 
246 |         meek.undirect_unforced_edges_func(8, g)
247 |         assert has_dir_edge(g, 8, 9)
248 |         assert has_undir_edge(g, 8, 7)
249 |         assert has_undir_edge(g, 8, 5)
250 | 
251 | if __name__ == "__main__":
252 |     unittest.main()


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/tests/test_search_util.py:
--------------------------------------------------------------------------------
  1 | from search_util import *
  2 | from graph_util import *
  3 | import networkx as nx
  4 | import unittest
  5 | from SemEstimator import SemEstimator
  6 | 
  7 | class TestDagFromPattern(unittest.TestCase):
  8 | 
  9 |     def test_triple(self):
 10 |         '''
 11 |         X0 -- X1 -- X2
 12 |         Resulting graph shouldn't have X1 be a collider
 13 |         '''
 14 |         graph = nx.DiGraph()
 15 |         graph.add_nodes_from([0, 1, 2])
 16 |         graph.add_edges_from([(0, 1), (1, 0), (1, 2), (2, 1)])
 17 | 
 18 |         dag = dagFromPattern(graph)
 19 | 
 20 |         assert get_undir_edge(dag) is None
 21 |         assert not is_def_collider(dag, 0, 1, 2)
 22 | 
 23 |     def test_cross(self):
 24 |         '''X0 -- X1 -- X2 and X3 -- X1 -- X4'''
 25 |         graph = nx.DiGraph()
 26 |         graph.add_nodes_from([0, 1, 2, 3, 4])
 27 |         graph.add_edges_from([(0, 1), (1, 0),
 28 |                               (1, 2), (2, 1),
 29 |                               (3, 1), (1, 3),
 30 |                               (1, 4), (4, 1)])
 31 | 
 32 |         dag = dagFromPattern(graph)
 33 | 
 34 |         assert get_undir_edge(dag) is None
 35 |         for i in [0, 2, 3, 4]:
 36 |             for j in [0, 2, 3, 4]:
 37 |                 if i != j:
 38 |                     assert not is_def_collider(dag, i, 1, j)
 39 | 
 40 |     def test_undo(self):
 41 |         '''
 42 |         X0 --- X1 <-- X2
 43 |         The algorithm will first try X0 --> X1, then have to
 44 |           retry since this creates a collider.
 45 |         '''
 46 |         graph = nx.DiGraph()
 47 |         graph.add_nodes_from([0, 1, 2])
 48 |         graph.add_edges_from([(0, 1), (1, 0), (2, 1)])
 49 | 
 50 |         dag = dagFromPattern(graph)
 51 | 
 52 |         assert get_undir_edge(dag) is None
 53 |         assert not is_def_collider(dag, 0, 1, 2)
 54 |         assert has_dir_edge(dag, 1, 0)
 55 | 
 56 |     def test_several(self):
 57 |         '''
 58 |         X0 --- X1 --> X2 <-- X3 --- X4
 59 |         '''
 60 |         graph = nx.DiGraph()
 61 |         graph.add_nodes_from([0, 1, 2, 3, 4])
 62 |         graph.add_edges_from([(0, 1), (1, 0),
 63 |                               (1, 2),
 64 |                               (3, 2),
 65 |                               (3, 4), (4, 3)])
 66 | 
 67 |         dag = dagFromPattern(graph)
 68 | 
 69 |         assert get_undir_edge(dag) is None
 70 |         assert not is_def_collider(dag, 0, 1, 2)
 71 |         assert is_def_collider(dag, 1, 2, 3)
 72 |         assert not is_def_collider(dag, 2, 3, 4)
 73 | 
 74 |     def test_cycle(self):
 75 |         '''
 76 |         X0 -- X1 -- X2 -- X3 -- X0
 77 |         '''
 78 |         graph = nx.DiGraph()
 79 |         graph.add_nodes_from([0, 1, 2, 3])
 80 |         graph.add_edges_from([(0, 1), (1, 0),
 81 |                               (1, 2), (2, 1),
 82 |                               (2, 3), (3, 2),
 83 |                               (3, 0), (0, 3)])
 84 |         dag = dagFromPattern(graph)
 85 |         assert dag is None
 86 | 
 87 | class TestDagFromPatternWithColliders(unittest.TestCase):
 88 | 
 89 |     def test_triple(self):
 90 |         '''
 91 |         X0 -- X1 -- X2
 92 |         Resulting graph shouldn't have X1 be a collider
 93 |         '''
 94 |         graph = nx.DiGraph()
 95 |         graph.add_nodes_from([0, 1, 2])
 96 |         graph.add_edges_from([(0, 1), (1, 0), (1, 2), (2, 1)])
 97 | 
 98 |         dag, penalty = dagFromPatternWithColliders(graph)
 99 | 
100 |         assert dag is not None
101 |         assert penalty == 0
102 |         assert get_undir_edge(dag) is None
103 |         assert not is_def_collider(dag, 0, 1, 2)
104 | 
105 |     def test_cross(self):
106 |         '''X0 -- X1 -- X2 and X3 -- X1 -- X4'''
107 |         graph = nx.DiGraph()
108 |         graph.add_nodes_from([0, 1, 2, 3, 4])
109 |         graph.add_edges_from([(0, 1), (1, 0),
110 |                               (1, 2), (2, 1),
111 |                               (3, 1), (1, 3),
112 |                               (1, 4), (4, 1)])
113 | 
114 |         dag, penalty = dagFromPatternWithColliders(graph)
115 | 
116 |         assert dag is not None
117 |         assert penalty == 0
118 | 
119 |         assert get_undir_edge(dag) is None
120 |         for i in [0, 2, 3, 4]:
121 |             for j in [0, 2, 3, 4]:
122 |                 if i != j:
123 |                     assert not is_def_collider(dag, i, 1, j)
124 | 
125 |     def test_undo(self):
126 |         '''
127 |         X0 --- X1 <-- X2
128 |         The algorithm will first try X0 --> X1, then have to
129 |           retry since this creates a collider.
130 |         '''
131 |         graph = nx.DiGraph()
132 |         graph.add_nodes_from([0, 1, 2])
133 |         graph.add_edges_from([(0, 1), (1, 0), (2, 1)])
134 | 
135 |         dag, penalty = dagFromPatternWithColliders(graph)
136 | 
137 |         assert dag is not None
138 |         assert penalty == 0
139 | 
140 |         assert get_undir_edge(dag) is None
141 |         assert not is_def_collider(dag, 0, 1, 2)
142 |         assert has_dir_edge(dag, 1, 0)
143 | 
144 |     def test_several(self):
145 |         '''
146 |         X0 --- X1 --> X2 <-- X3 --- X4
147 |         '''
148 |         graph = nx.DiGraph()
149 |         graph.add_nodes_from([0, 1, 2, 3, 4])
150 |         graph.add_edges_from([(0, 1), (1, 0),
151 |                               (1, 2),
152 |                               (3, 2),
153 |                               (3, 4), (4, 3)])
154 | 
155 |         dag, penalty = dagFromPatternWithColliders(graph)
156 | 
157 |         assert dag is not None
158 |         assert penalty == 0
159 | 
160 |         assert get_undir_edge(dag) is None
161 |         assert not is_def_collider(dag, 0, 1, 2)
162 |         assert is_def_collider(dag, 1, 2, 3)
163 |         assert not is_def_collider(dag, 2, 3, 4)
164 | 
165 |     def test_cycle(self):
166 |         '''
167 |         X0 -- X1 -- X2 -- X3 -- X0
168 |         '''
169 |         graph = nx.DiGraph()
170 |         graph.add_nodes_from([0, 1, 2, 3])
171 |         graph.add_edges_from([(0, 1), (1, 0),
172 |                               (1, 2), (2, 1),
173 |                               (2, 3), (3, 2),
174 |                               (3, 0), (0, 3)])
175 |         dag, penalty = dagFromPatternWithColliders(graph)
176 | 
177 |         assert dag is not None
178 |         assert penalty == 1
179 |         assert not detect_cycle(dag)
180 | 
181 | class TestEstimateParameters(unittest.TestCase):
182 | 
183 |     def test_params_1(self):
184 |         '''
185 |         Graph Edges:
186 |             1. X1 --> X2 w =  1.0
187 |             2. X1 --> X3 w =  2.0
188 |             3. X2 --> X4 w =  0.5
189 |             4. X3 --> X4 w = -1.0
190 |         '''
191 |         dataset = np.loadtxt("../data/params_1.txt", skiprows=1)
192 | 
193 |         estimator = SemEstimator(dataset)
194 |         estimator.estimate()
195 | 
196 |         print(dataset.shape)
197 | 
198 |         true_params = np.array([[0, 1, 2, 0],
199 |                                 [0, 0, 0, 0.5],
200 |                                 [0, 0, 0, -1],
201 |                                 [0, 0, 0, 0]])
202 | 
203 |         true_pred = np.matmul(dataset, true_params)
204 |         true_errors = true_pred - dataset
205 |         true_variances = np.var(true_errors, axis=0)
206 | 
207 |         print("Estimated Parameters:\n", estimator.params)
208 |         print("True Parameters:\n", true_params)
209 | 
210 |         print("Graph Error Variances:\n", estimator.residuals.diagonal())
211 |         print("True Error Variances:\n", true_variances)
212 | 
213 |         print("Graph Covariance:\n", estimator.graph_cov)
214 |         print("True Covariance:\n", estimator.true_cov)
215 | 
216 |     def test_cycle(self):
217 |         '''Test cycle X0 --- X1 --- X2 --- X3 --- X0'''
218 |         graph = nx.DiGraph()
219 |         graph.add_nodes_from([0, 1, 2, 3])
220 |         graph.add_edges_from([(0, 1), (1, 0),
221 |                               (1, 2), (2, 1),
222 |                               (2, 3), (3, 2),
223 |                               (3, 0), (0, 3)])
224 |         assert dagFromPattern(graph) is None
225 | 
226 |         graph.remove_edge(0, 1)
227 |         graph.remove_edge(0, 3)
228 |         new_dag = dagFromPattern(graph)
229 |         assert new_dag is not None
230 |         assert set(new_dag.edges()) == set([(1, 0), (1, 2), (2, 3), (3, 0)])
231 | 
232 | if __name__ == "__main__":
233 |     unittest.main()


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/tests/test_util.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | 
 3 | def generate_graph(num_variables, sparsity=0.1, edge_weight_range=(0.5, 1.5)):
 4 |     '''
 5 |     Generate a random DAG (with edge weights), represented as a matrix.
 6 |     :param num_variables: the number of variables in the graph
 7 |     :param sparsity: the sparsity of the edges (i.e. the percentage of edges present compared to a complete DAG)
 8 |     :param edge_weight_range: range to sample uniformly to generate edge weights
 9 |     :return: the matrix of edge weights, and a topological ordering of the vertices
10 |     '''
11 |     edge_weights = np.random.uniform(edge_weight_range[0], edge_weight_range[1], (num_variables, num_variables))
12 |     # Edge weights are uniformly distributed over +/- edge_weight_range
13 |     edge_weights *= np.random.choice([1, -1], (num_variables, num_variables))
14 |     # Apply sparsity filter
15 |     edge_weights *= (np.random.random((num_variables, num_variables)) < sparsity)
16 |     # Make a DAG
17 |     edge_weights = np.triu(edge_weights, 1)
18 | 
19 |     # Shuffle vertices
20 |     vertex_shuffle = np.random.permutation(num_variables)
21 |     edge_weights = edge_weights[vertex_shuffle, :]
22 |     edge_weights = edge_weights[:, vertex_shuffle]
23 | 
24 |     return edge_weights, vertex_shuffle
25 | 
26 | def generate_data(graph, vertex_order, num_data_points, variable_noise=1):
27 |     num_vertices = graph.shape[0]
28 | 
29 |     data = np.zeros((num_data_points, num_vertices))
30 | 
31 |     data[:, vertex_order[0]] = np.random.normal(0, variable_noise, num_data_points)
32 | 
33 |     for i in range(1, num_vertices):
34 |         data[:, vertex_order[i]] = np.matmul(data[:, vertex_order[:i]], graph[vertex_order[:i], vertex_order[i]])
35 |         data[:, vertex_order[i]] += np.random.normal(0, variable_noise, num_data_points)
36 |     return data


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