├── .gitignore ├── .travis.yml ├── README.md ├── example ├── dataset.json ├── dataset.png └── result.png ├── requirements.txt ├── setup.py └── tdamapper ├── __init__.py ├── clusterfunctions ├── __init__.py ├── abstractClusterFunction.py └── vietorisRipsClustering.py ├── combinatoricalHelper.py ├── mapper.py ├── oneNerve.py ├── referenceMap.py └── tests ├── __init__.py ├── test_cluster_functions.py ├── test_combinatorical_helper.py ├── test_one_nerve.py └── test_reference_map.py /.gitignore: -------------------------------------------------------------------------------- 1 | # 2 | datasets/createDataSet.py 3 | 4 | # Byte-compiled / optimized / DLL files 5 | __pycache__/ 6 | *.py[cod] 7 | 8 | # C extensions 9 | *.so 10 | 11 | # Distribution / packaging 12 | .Python 13 | env/ 14 | build/ 15 | develop-eggs/ 16 | dist/ 17 | downloads/ 18 | eggs/ 19 | .eggs/ 20 | lib/ 21 | lib64/ 22 | parts/ 23 | sdist/ 24 | var/ 25 | *.egg-info/ 26 | .installed.cfg 27 | *.egg 28 | 29 | # PyInstaller 30 | # Usually these files are written by a python script from a template 31 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 32 | *.manifest 33 | *.spec 34 | 35 | # Installer logs 36 | pip-log.txt 37 | pip-delete-this-directory.txt 38 | 39 | # Unit test / coverage reports 40 | htmlcov/ 41 | .tox/ 42 | .coverage 43 | .cache 44 | nosetests.xml 45 | coverage.xml 46 | 47 | # Translations 48 | *.mo 49 | *.pot 50 | 51 | # Django stuff: 52 | *.log 53 | 54 | # Sphinx documentation 55 | docs/_build/ 56 | 57 | # PyBuilder 58 | target/ -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: python 2 | python: 3 | - "2.7" 4 | # command to install dependencies 5 | install: "pip install -r requirements.txt" 6 | # command to run tests 7 | script: py.test -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # TDA-Mapper-py 2 | 3 | [![Build Status](https://travis-ci.org/mirkoklukas/tda-mapper-py.svg?branch=master)](https://travis-ci.org/mirkoklukas/tda-mapper-py) 4 | 5 | A straightforward implementation of the mapper construction by Carlsson-Memoli-Singh. I wrote a little blog post about it at http://blog.mirkoklukas.com/ 6 | 7 | ## Example 8 | 9 | 10 | ``` python 11 | from tdamapper.clusterfunctions import VietorisRipsClustering 12 | from tdamapper import mapper 13 | from tdamapper.referenceMap import create_functional_cover, coordinate_projection 14 | import json 15 | 16 | # Example data set 17 | with open("./example/dataset.json") as f: 18 | data = json.load(f); 19 | data = [ tuple(p) for p in data ] 20 | 21 | # Gather the mapper input 22 | VR = VietorisRipsClustering(epsilon = 0.6) 23 | zAxis = coordinate_projection(axis=2, domain=data) 24 | funcCover = create_functional_cover(endpoints=range(-12,12), overlap=0.5) 25 | 26 | # Run the alogrithm 27 | result = mapper(VR, zAxis, funcCover) 28 | 29 | ``` 30 | 31 | Below you see a visualization of the mapper result. The graph is colored by the values of ```zAxis```, the projection on the z-axis. The size of the nodes 32 | reflects the size of the associated clusters. 33 | 34 | The take away should be that there are actually two separate branches growing out of a bigger cluster. 35 | You shouldn't focus too much on the fact that the two branches cross each other. Although it reflects the reality of the situation pretty well, it is rather a bi-product of the fact that the data set lives in so few dimensions. 36 | 37 | ![The result of the mapper construction](https://github.com/mirkoklukas/tda-mapper-py/blob/master/example/result.png "The result of the mapper construction") 38 | 39 | And indeed (what a terrible example it would have been if that was not the case) looking at a 3d plot of the original dataset we see that this reflects the shape pretty well. 40 | 41 | ![An example data set](https://github.com/mirkoklukas/tda-mapper-py/blob/master/example/dataset.png "An example data set") -------------------------------------------------------------------------------- /example/dataset.json: -------------------------------------------------------------------------------- 1 | [[1.0634506712615583, 0.05454245623723517, -10.041141156149942], [1.053674334149039, -0.013296697386472437, -9.946525335861764], [0.9504595173260679, 0.01541790319034966, 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-0.021768833856053126, 10.04820282949919]] -------------------------------------------------------------------------------- /example/dataset.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mirkoklukas/tda-mapper-py/7014d8f9eb4b216c181ce38e71043ee8cb5cc129/example/dataset.png -------------------------------------------------------------------------------- /example/result.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mirkoklukas/tda-mapper-py/7014d8f9eb4b216c181ce38e71043ee8cb5cc129/example/result.png -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | pytest>=2.6.0 -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from setuptools import setup 2 | 3 | setup(name='tdamapper', 4 | version='0.1', 5 | description='A straight-forward implementation of the mapper construction by Carlsson--Memoli--Singh.', 6 | url='https://github.com/mirkoklukas/tda-mapper-py', 7 | author='Mirko Klukas', 8 | author_email='mirko.klukas@gmail.com', 9 | license='MIT', 10 | packages=['tdamapper'], 11 | zip_safe=False) -------------------------------------------------------------------------------- /tdamapper/__init__.py: -------------------------------------------------------------------------------- 1 | from tdamapper.mapper import mapper 2 | from tdamapper.clusterfunctions.abstractClusterFunction import AbstractClusterFunction -------------------------------------------------------------------------------- /tdamapper/clusterfunctions/__init__.py: -------------------------------------------------------------------------------- 1 | from tdamapper.clusterfunctions.vietorisRipsClustering import VietorisRipsClustering 2 | from tdamapper.clusterfunctions.abstractClusterFunction import AbstractClusterFunction 3 | -------------------------------------------------------------------------------- /tdamapper/clusterfunctions/abstractClusterFunction.py: -------------------------------------------------------------------------------- 1 | # ------------------------------------------------------ 2 | # An abstract base class for a cluster function. 3 | # ------------------------------------------------------ 4 | 5 | import operator 6 | 7 | def extendIndex(i, Us): 8 | return [ ((i,j),U) for j,U in enumerate(Us)] 9 | 10 | class AbstractClusterFunction(object): 11 | def __call__(self, data): 12 | """ 13 | Implements the default behaviour for clustering the empty list, and 14 | passes along the data to the cluster function. 15 | """ 16 | if len(data) == 0: 17 | return [] 18 | else: 19 | return self.cluster(data) 20 | 21 | def cluster(self, data): 22 | """ 23 | Given a list of data points it returns a list of clusters, 24 | where a cluster is list of data points. 25 | 26 | Args: 27 | data: A list of data points, e.g. tuples in R**n or unique identifiers. 28 | Returns: 29 | A list of clusters, where a cluster is a list of data points. 30 | """ 31 | raise NotImplementedError("Should have implemented this") 32 | 33 | def push_forward(self, cover): 34 | """ 35 | Takes a cover and applies the cluster function to each element, 36 | and collects the clusters to form a new cover. 37 | 38 | Args: 39 | cover: A dictionary whose values are lists of elements. 40 | Returns: 41 | Another cover, where the new sets are clusters. 42 | """ 43 | listOfIndexedClusters = [ extendIndex(i,self(U)) for i,U in cover.iteritems()] 44 | return dict(reduce(operator.add , listOfIndexedClusters, [])) 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | -------------------------------------------------------------------------------- /tdamapper/clusterfunctions/vietorisRipsClustering.py: -------------------------------------------------------------------------------- 1 | # ------------------------------------------------------ 2 | # A super simple cluster algorithm. 3 | # ------------------------------------------------------ 4 | from abstractClusterFunction import AbstractClusterFunction 5 | from ..combinatoricalHelper import extract_unordered_pairs 6 | import math 7 | 8 | # ------------------------------------------------------ 9 | # Some Helper. 10 | # ------------------------------------------------------ 11 | def euclidianDistance(xs,ys): 12 | return math.sqrt(sum(map(lambda (x,y): (x-y)**2,zip(xs,ys)))) 13 | 14 | def getConnectedComponent(x, G): 15 | if x not in G: 16 | raise LookupError("This is NOT a vertex of the complex!") 17 | 18 | visited = set([x]) 19 | targets = G[x][:] 20 | 21 | while len(targets)>0: 22 | y = targets.pop() 23 | if y not in visited: 24 | visited.add(y) 25 | targets.extend(G[y]) 26 | 27 | return visited 28 | 29 | def getAllConnectedComponents(G): 30 | keys = set(G.keys()) 31 | components = [] 32 | 33 | while len(keys) > 0: 34 | x = keys.pop() 35 | component = getConnectedComponent(x,G) 36 | keys = keys - component 37 | components.append(component) 38 | 39 | return components 40 | 41 | # ------------------------------------------------------ 42 | # The cluster class. 43 | # ------------------------------------------------------ 44 | class VietorisRipsClustering(AbstractClusterFunction): 45 | def __init__(self, epsilon, distance = euclidianDistance): 46 | self.epsilon = epsilon 47 | self.distance = distance 48 | 49 | def cluster(self, data): 50 | G = dict([(x, []) for x in data]) 51 | pairs = extract_unordered_pairs(data) 52 | 53 | for (p,q) in pairs: 54 | if(self.distance(p, q) <= self.epsilon): 55 | G[p].append(q) 56 | G[q].append(p) 57 | 58 | return getAllConnectedComponents(G) 59 | 60 | 61 | 62 | -------------------------------------------------------------------------------- /tdamapper/combinatoricalHelper.py: -------------------------------------------------------------------------------- 1 | # ------------------------------------------------------ 2 | # Some Helper. 3 | # ------------------------------------------------------ 4 | 5 | def extract_unordered_pairs(ids): 6 | """Given a list of n ids it returns a list of all n-over-2 unordered pairs.""" 7 | pairs = [] 8 | for i in range(len(ids)): 9 | for j in range(i+1, len(ids)): 10 | pairs.append((ids[i],ids[j])) 11 | return pairs 12 | 13 | # ------------------------------------------------------ 14 | 15 | def get_horizontal_paths(listOfLists): 16 | """Given a list of lists it returns a list of tuples whose k'th entry is in the k'th list.""" 17 | if len(listOfLists) == 0: 18 | return [] 19 | if len(listOfLists) == 1: 20 | return [ (x,) for x in listOfLists[0]] 21 | else: 22 | shortTuples = get_horizontal_paths(listOfLists[1:]) 23 | return [ (x,) + shortTuple for x in listOfLists[0] for shortTuple in shortTuples] 24 | 25 | # ------------------------------------------------------ -------------------------------------------------------------------------------- /tdamapper/mapper.py: -------------------------------------------------------------------------------- 1 | # ------------------------------------------------------ 2 | # A straightforward implementation of the mapper construction by Carlsson--Memoli--Singh. 3 | # (I wrote a little blog post about it at http://mapsfunctionsandarrows.blogspot.de) 4 | # ------------------------------------------------------ 5 | 6 | from tdamapper.oneNerve import compute_one_nerve 7 | from tdamapper.clusterfunctions.abstractClusterFunction import AbstractClusterFunction 8 | from tdamapper.referenceMap import ReferenceMap 9 | 10 | 11 | def mapper(clusterFct, referenceFct, funcCover): 12 | """Mapper is a construction that uses a given cluster-algorithm to 13 | associate a simplicial complex to a reference map on a given data set. 14 | 15 | Args: 16 | clusterFct: A class that inherits from AbstractClusterFunction. 17 | referenceFct: A ReferenceFunction class. A callable class that can be called with elements form the dataset. 18 | funcCover: A dict of boolean functions (characteristic functions), 19 | that are defined on the target space of the given filter. 20 | Returns: 21 | A simplicial complex given in terms of a pair (U, S), where 22 | U is the covering whose nerve is constructed, and 23 | S is the set/list of 1-simplices 24 | """ 25 | if not isinstance(clusterFct, AbstractClusterFunction) or not isinstance(referenceFct, ReferenceMap): 26 | raise TypeError("Please take look at the function signature....") 27 | 28 | indexedClusterCover = clusterFct.push_forward(referenceFct.pull_back(funcCover)) 29 | oneNerve = compute_one_nerve(indexedClusterCover) 30 | 31 | return oneNerve 32 | 33 | 34 | -------------------------------------------------------------------------------- /tdamapper/oneNerve.py: -------------------------------------------------------------------------------- 1 | # ------------------------------------------------------ 2 | # Computing the 1-nerve of a cover. 3 | # ------------------------------------------------------ 4 | 5 | from tdamapper.combinatoricalHelper import extract_unordered_pairs 6 | 7 | # ------------------------------------------------------ 8 | 9 | def hasNonEmptyIntersection (A, B): 10 | """Given two iterables it checks wether they have a common element.""" 11 | return len(set(A)&set(B)) > 0 12 | 13 | # ------------------------------------------------------ 14 | 15 | class Graph(tuple, object): 16 | def __init__(self, *args): 17 | super(tuple, self).__init__(*args) 18 | self.node = self[0] 19 | self.links = self[1] 20 | 21 | def nodes(self): 22 | return self(0) 23 | 24 | def links(self): 25 | return self(1) 26 | 27 | def cast_to_d3js(self): 28 | cover = self[0] 29 | simplicies = self[1] 30 | keys = cover.keys() 31 | lookup = dict(zip(keys, range(len(keys)))) 32 | d3jsGraph = { 33 | "nodes": [ 34 | { 35 | "name": key, 36 | "group": key[0], 37 | "size": len(cover[key]) 38 | } 39 | for key in keys], 40 | "links": [ 41 | { 42 | "source": lookup[i], 43 | "target": lookup[j], 44 | "size": len(set(cover[i])&set(cover[j])), 45 | "value": 1 46 | } 47 | for (i, j) in simplicies] 48 | } 49 | 50 | return d3jsGraph 51 | 52 | 53 | def compute_one_nerve(covering, simplexCondition = hasNonEmptyIntersection): 54 | """ 55 | Given a covering it computes the associated 1-nerve. 56 | 57 | Args: 58 | covering: A dict of iterables. 59 | simplexCondition(A, B): A boolean function that returns true iff 60 | a 1-simplex between the two iterables A,B should be added. 61 | Returns: 62 | A tuple (C,S), where C is the given covering, and S is 63 | a list of 2-tuples (i,j), with i 0: 16 | dict.__init__(self, values) 17 | self.domain = self.keys() 18 | else: 19 | self.domain = domain 20 | 21 | self.func = functionExpression 22 | 23 | def __call__(self, x): 24 | """ 25 | Given a data point x it returns the associated value. 26 | """ 27 | if self.has_key(x): 28 | return self[x] 29 | elif self.func is not None: 30 | y = self.func(x) 31 | self[x] = y 32 | return y 33 | else: 34 | msg = "There is no function expression defined " \ 35 | "nor does an entry with that key exist..." 36 | raise LookupError(msg) 37 | 38 | def set_domain(self, data): 39 | self.domain = data 40 | return self 41 | 42 | def pre_image(self, condition): 43 | return [ x for x in self.domain if condition(self(x))] 44 | 45 | def pull_back(self, functionalCover): 46 | """ 47 | Given a dictionary whose values are characteristic functions 48 | it returns a covering of the domain. 49 | """ 50 | entries = [ (i, self.pre_image(condition)) for i,condition in functionalCover.iteritems()] 51 | return dict(entries) 52 | 53 | # ------------------------------------------------------ 54 | # Some reference maps and factories 55 | # ------------------------------------------------------ 56 | 57 | def coordinate_projection(axis, domain): 58 | """ 59 | Creates a ReferenceMap that corresponds to the projection to the specified 60 | coordinate axis. 61 | """ 62 | return ReferenceMap(functionExpression=lambda v: v[axis], domain=domain) 63 | 64 | # ------------------------------------------------------ 65 | # Helper to create filter conditions. 66 | # ------------------------------------------------------ 67 | 68 | def turn_interval_into_function(I): 69 | """ 70 | Given an interval, i.e. a list with two entries [a,b], 71 | it returns its characteristic function. 72 | """ 73 | def f_I(x): 74 | return I[0] <= x and x <= I[1] 75 | return f_I 76 | 77 | 78 | def create_intervals(endpoints, overlap): 79 | """ 80 | Creates a list of overlapping intervals, where the endpoints are 81 | chosen near the entries in a list of values. 82 | """ 83 | endpoints = sorted(endpoints) 84 | delta = overlap/2 85 | intervals = [] 86 | for i in range(len(endpoints) - 1): 87 | intervals.append([endpoints[i] - delta, endpoints[i+1] + delta]) 88 | 89 | return intervals 90 | 91 | 92 | def create_functional_cover(endpoints, overlap): 93 | """ 94 | Creates a dict of characteristic functions corresponding to overlapping intervals, 95 | whose endpoints are chosen near the entries in a list of values. 96 | """ 97 | intervals = create_intervals(endpoints, overlap) 98 | fcts = map(turn_interval_into_function, intervals) 99 | funcCover = dict(zip(range(len(fcts)), fcts)) 100 | return funcCover 101 | 102 | 103 | def cond_and(*conditions): 104 | return lambda x: reduce(lambda b,f: b and f(x),conditions, True) 105 | 106 | 107 | 108 | 109 | 110 | -------------------------------------------------------------------------------- /tdamapper/tests/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/mirkoklukas/tda-mapper-py/7014d8f9eb4b216c181ce38e71043ee8cb5cc129/tdamapper/tests/__init__.py -------------------------------------------------------------------------------- /tdamapper/tests/test_cluster_functions.py: -------------------------------------------------------------------------------- 1 | from tdamapper.clusterfunctions.abstractClusterFunction import AbstractClusterFunction 2 | from tdamapper.clusterfunctions.vietorisRipsClustering import euclidianDistance, VietorisRipsClustering, getConnectedComponent, getAllConnectedComponents 3 | import math 4 | 5 | # ------------------------------------------------------ 6 | 7 | def test_abstract_cluster_function(): 8 | class StupidClustering(AbstractClusterFunction): 9 | def cluster(self, data): 10 | return [data[:len(data)/2], data[len(data)/2:]] 11 | 12 | clusterer = StupidClustering() 13 | 14 | cover = { 15 | 1: [1, 2, 3, 4], 16 | "two": [2, 3, {5: 5}, 6] 17 | } 18 | expectedPushForward = { 19 | (1, 0): [1, 2], 20 | (1, 1): [3, 4], 21 | ("two", 0): [2, 3], 22 | ("two", 1): [{5: 5}, 6] 23 | } 24 | 25 | assert [] == clusterer([]) 26 | assert expectedPushForward == clusterer.push_forward(cover) 27 | assert {} == clusterer.push_forward({}) 28 | 29 | # ------------------------------------------------------ 30 | 31 | def test_vietoris_rips_clustering_with_given_distance(): 32 | VR = VietorisRipsClustering(epsilon=2.0, distance=lambda a,b: abs(a-b)) 33 | 34 | clusters = VR([1,2,3,4,5,10,12,20]) 35 | expected = [ 36 | set([1,2,3,4,5]), 37 | set([10,12]), 38 | set([20]) 39 | ] 40 | 41 | assert [] == VR([]) 42 | 43 | for c in clusters: 44 | assert c in expected 45 | for c in expected: 46 | assert c in clusters 47 | 48 | 49 | # ------------------------------------------------------ 50 | 51 | def test_vietoris_rips_clustering_with_default_distance(): 52 | VR = VietorisRipsClustering(epsilon=1.6) 53 | 54 | clusters = VR([ 55 | (0,0), 56 | (1,0), 57 | (1,1), 58 | (4,0), 59 | (4,.1), 60 | (3.5,0.4) 61 | ]) 62 | expected = [ 63 | set([(0,0), (1,0), (1,1)]), 64 | set([(4,0), (3.5,0.4), (4,0.1)]) 65 | ] 66 | 67 | assert [] == VR([]) 68 | 69 | for c in clusters: 70 | assert c in expected 71 | for c in expected: 72 | assert c in clusters 73 | 74 | # ------------------------------------------------------ 75 | 76 | def test_graph_functions(): 77 | G = { 78 | 1:[2,3], 79 | 2:[1,3], 80 | 3:[1,2], 81 | 4:[5], 82 | 5:[4], 83 | 6:[] 84 | } 85 | 86 | assert set([1,2,3]) == getConnectedComponent(1,G) 87 | 88 | components = getAllConnectedComponents(G) 89 | expected = [set([1,2,3]), set([4,5]), set([6])] 90 | 91 | for c in components: 92 | assert c in expected 93 | for c in expected: 94 | assert c in components 95 | 96 | 97 | # ------------------------------------------------------ 98 | 99 | def test_euclidian_distance(): 100 | assert math.sqrt(2) == euclidianDistance((1,0,0),(0,1,0)) 101 | assert math.sqrt(2) == euclidianDistance([1,0,0],[0,0,1]) 102 | 103 | # ------------------------------------------------------ 104 | 105 | 106 | 107 | 108 | 109 | -------------------------------------------------------------------------------- /tdamapper/tests/test_combinatorical_helper.py: -------------------------------------------------------------------------------- 1 | from tdamapper.combinatoricalHelper import * 2 | 3 | # ------------------------------------------------------ 4 | 5 | def test_extract_unordered_pairs(): 6 | assert [] == extract_unordered_pairs([]) 7 | assert [(1,"two"),(1,(3,3)),("two",(3,3))] == extract_unordered_pairs([1,"two",(3,3)]) 8 | 9 | # ------------------------------------------------------ 10 | 11 | def test_get_horizontal_paths(): 12 | assert [] == get_horizontal_paths([]) 13 | assert [] == get_horizontal_paths([[],[]]) 14 | assert [(1, 2, {"three":3}), (1, "two", {"three":3})] == get_horizontal_paths([[1], [2,"two"], [{"three":3}]]) 15 | 16 | # ------------------------------------------------------ -------------------------------------------------------------------------------- /tdamapper/tests/test_one_nerve.py: -------------------------------------------------------------------------------- 1 | from tdamapper.oneNerve import * 2 | 3 | # ------------------------------------------------------ 4 | 5 | def test_non_empty_intersection(): 6 | assert hasNonEmptyIntersection(set([1,2]), set([2,"two"])) == True 7 | assert hasNonEmptyIntersection(set([1,2]), set(["one","two"])) == False 8 | 9 | # ------------------------------------------------------ 10 | 11 | def test_one_nerve(): 12 | covering = { 13 | 1: [1,2,3], 14 | 2: [3,4,5], 15 | 3: [5,6,1] 16 | } 17 | assert ({},[]) == compute_one_nerve({}) 18 | 19 | nerve = compute_one_nerve(covering) 20 | simplices = [(1,2),(2,3),(1,3)] 21 | assert nerve[0] == covering 22 | 23 | for s in nerve[1]: 24 | assert s in simplices 25 | for s in simplices: 26 | assert s in nerve[1] 27 | 28 | # ------------------------------------------------------ 29 | 30 | 31 | 32 | -------------------------------------------------------------------------------- /tdamapper/tests/test_reference_map.py: -------------------------------------------------------------------------------- 1 | from tdamapper.referenceMap import ReferenceMap 2 | import pytest 3 | 4 | 5 | # ------------------------------------------------------ 6 | 7 | def test_reference_map_with_values(): 8 | values = [ 9 | (1,0), 10 | (2,0), 11 | (3,0), 12 | (4,1), 13 | (5,1), 14 | (6,1) 15 | ] 16 | refmap = ReferenceMap(values) 17 | 18 | with pytest.raises(LookupError): 19 | refmap(100) 20 | 21 | assert refmap(1) == 0 22 | assert refmap(5) == 1 23 | 24 | # ------------------------------------------------------ 25 | 26 | 27 | def test_reference_map_with_function(): 28 | def f(x): 29 | return x*2; 30 | 31 | refmap = ReferenceMap(functionExpression=f, domain=range(100)) 32 | 33 | assert refmap(1) == 2 34 | assert refmap(5) == 10 35 | 36 | # ------------------------------------------------------ 37 | 38 | def test_reference_map_methods(): 39 | 40 | refmap = ReferenceMap(functionExpression=lambda x: x*0.5, domain=range(100)) 41 | funcCover = { 42 | "lower": lambda x: x < 10, 43 | "higher": lambda x: x > 10 44 | } 45 | 46 | assert refmap.pre_image(lambda x: False) == [] 47 | assert refmap.pre_image(lambda x: 0<= x and x < 10) == range(20) 48 | assert refmap.pull_back(funcCover) == { 49 | "lower": range(20), 50 | "higher": range(21,100) 51 | } 52 | 53 | # ------------------------------------------------------ 54 | 55 | # ------------------------------------------------------ 56 | 57 | # ------------------------------------------------------ 58 | 59 | # ------------------------------------------------------ 60 | 61 | # ------------------------------------------------------ 62 | 63 | 64 | 65 | 66 | 67 | --------------------------------------------------------------------------------