def set_up_competition(self, best_fit):
#The competition takes place in the oldest generation.
#competitors will consist of unions of pairs of lists contained
#in the output of self.coalescent().
coalescent = self.coalescent()
#A space is allocated in the memory to store the different competitors.
coalescence_hypothesis = list()
#The following loop makes the union of the first generation associated
#with taxon t with the first generations associated with the taxa r in
#best_fit[t].
for t in range(len(coalescent)):
#The following ensures that if best_fit[t] is empty, then the first
#generation of the phylogenesis of t is given.
common_ancestor = _image_of_partition(coalescent[t])
#The following loop add the first generations of the friend of the
#taxon t to the 'common ancestors.
for r in best_fit[t]:
common_ancestor = _image_of_partition(common_ancestor +
coalescent[r])
#The list 'common_ancestor' to only give one representative to the
#union it represents.
common_ancestor.sort()
coalescence_hypothesis.append(common_ancestor)
#The list of competitors is returned, where each competitor is indexed
#by the integer of the taxon it is supposed to represent.
return coalescence_hypothesis
def _join_preimages_of_partitions(preimage1, preimage2, speed_mode):
#Spaces are allocated in the memory so that the lists saved at the addresses
#of the variables 'preimage1' and 'preimage2' are not modified.
tmp1 = list()
tmp2 = list()
#In addition, repetitions that may occur in each internal list of the
#two inputs are eliminated: e.g. [7,1,3,4,7] --> [7,1,3,4]
for i in range(len(preimage1)):
tmp1.append(_image_of_partition(preimage1[i]))
for i in range(len(preimage2)):
tmp2.append(_image_of_partition(preimage2[i]))
#Reads preimage1;
for i1 in range(len(tmp1)):
#Reads in the i1-th internal lists of preimage1;
for j1 in range(len(tmp1[i1])):
#Reads preimage2;
for i2 in range(len(tmp2)):
#The variable flag indicates whether the value tmp1[i1][j1]
#has been found in one of the internal lists of preimage2;
flag = False
#Reads in the i2-th internal lists of preimage2.
for j2 in range(len(tmp2[i2])):
#The j1-th element of the i1-th internal list of preimage1
#is found in preimage2, specifically at position j2
#of the i2-th internal list.
if tmp1[i1][j1] == tmp2[i2][j2]:
#The i2-th internal lists of preimage2 is appended
#to the i1-th internal lists of preimage1.
tmp1[i1].extend(tmp2[i2])
#The i2-th internal lists of preimage2 is emptied.
tmp2[i2] = []
#Repeated elements occuring in the union of the two internal
#lists, in preimage1, are eliminated.
tmp1[i1] = _image_of_partition(tmp1[i1])
#the variable flag indicates whether the j1-th element of
#the i1-th internal list of preimage1 was found in preimage2.
flag = True
break
#tmp1[i1][j1] no longer needs to be searched in preimage2.
if speed_mode == FAST and flag == True:
break
#On the one hand, the union of the first internal list of preimage1
#with all the other internal lists of preimage2 that intersect
#it is appended to preimage2.
tmp2.append(tmp1[i1])
#On the other hand, this union is emptied in preimage1.
tmp1[i1] = []
#A space is allocated for the output of the procedure.
the_join = list()
#Only includes the non-empty lists of preimage2 in the output.
for i in range(len(tmp2)):
if tmp2[i] != []:
the_join.append(tmp2[i])
#The output contains the non-empty lists of preimage2.
return the_join
def make_friends(self, taxon):
#The friendships are essentially formed at the level of the oldest
#generation. Friendships will consist of unions of pairs of lists contained
#in the output of self.coalescent().
coalescent = self.coalescent()
#Allocates two spaces in the memory to store the output of the function:
#- 'friends' will contain indices (i.e. the taxa that can be
# related to the input taxon).
#- 'coalescence_hypothesis' that contains the unions of the oldest
# generation of 'taxon' with the oldest generation associated with an
# individual in 'firends'.
friends = list()
coalescence_hypothesis = list()
#The following loop fills in the lists 'friends'
#and 'coalescence_hypothesis'. The list 'friends' contains all those
#of the phylogeny that are not in coalescent[taxon]. The list
#'coalescence_hypothesis' contains the union of coalescent[taxon] and
#coalescent[r] for every index r in the list 'friends'.
for r in range(len(coalescent)):
if not (r in coalescent[taxon]):
friends.append(r)
#The union of coalescent[taxon] and coalescent[r] is computed through
#_image_of_partition and then sorted in order to give a unique
#representative to the union (e.g. [0,1]U[2,5] should be the same
#as [2,5]U[0,1].
common_ancestor = _image_of_partition(coalescent[taxon] +
coalescent[r])
common_ancestor.sort()
coalescence_hypothesis.append(common_ancestor)
#the procedure returns the list of friends for the input taxon and the
#associated common ancestors stored in the list 'coalescence_hypothesis'.
return (friends, coalescence_hypothesis)
def __init__(self,source,target,*args):
if len(source) == len(target):
#Relabeling the source and target by using _epi_factorize_partition
#will allow us to quickly know whether there is an arrow from the source
#and the target (see below).
self.source = _epi_factorize_partition(source)
self.target = _epi_factorize_partition(target)
#The following line computes the binary relation that is supposed to
#encode the function from the codomain of the underlying
#epimorphism encoding the source partition to the codomain of the
#epimorphsim encoding the target partition.
self.arrow = _image_of_partition(zip(self.source,self.target))
#The following loop checks if the binary relation contained
#in self.arrow is a function.
for i in range(len(self.arrow)):
#Checking the following condition is equivalent to checking
#whether the label i in self.source is mapped to a unique element in
#self.target, namely the value contained in self.arrow[i][1].
#Note that: the mapping might not be unique when the indexing of
#the labels of the source partition is not compatible with that
#of the target partition.
if self.arrow[i][0]==i:
#We are only interested in the image (not the graph) of the function.
self.arrow[i] = self.arrow[i][1]
else:
if len(args) > 0 and args[0] == False:
exit()
else:
print("Error: in MorphismOfPartitions.__init__: source and target are not compatible.")
exit()
def _epi_factorize_partition(partition):
#The relabeling depends on the cardinal of the image of the partition.
#Computing the cardinal of the image is roughly the same as computing
#the image itself.
the_image = _image_of_partition(partition)
#A space is allocated to contain the relabeled list.
epimorphism = list()
#If the i-th element of the list is the j-th element of the image
#then this element is relabelled by the integer j.
for i in range(len(partition)):
for j in range(len(the_image)):
if partition[i] == the_image[j]:
epimorphism.append(j)
break
#Returns the relabeled list.
return epimorphism
def _preimage_of_partition(partition):
#A space is allocated in the memory to contain the preimage of the input list.
the_preimage = list()
#The number of fibers contained by the preimage is equal to the number
#of elements in the image of the partition.
for i in _image_of_partition(partition):
#Allocates (empty) pointers in order to store the fibers of the partition.
the_preimage.append([])
#The relabeled list of 'partition' gives the desired indexing
#of the fibers contained in the preimage of partition.
epimorphism = _epi_factorize_partition(partition)
for i in range(len(epimorphism)):
#The following line adds the integer i to the epimorphism[i]-th
#fiber of the preimage.
the_preimage[epimorphism[i]].append(i)
#After the loop, all the fibers are filled and the preimage is returned
return the_preimage
def score(self, partitions, friendship_network):
#The following function will allow us to check if there exists a morphism
#of partitions between two given lists (seen as partitions).
def homset(partition1, partition2):
try:
MorphismOfPartitions(partition1, partition2, False)
return True
except:
return False
#The following function returns a Boolean value indicating whether two
#lists are equal or disjoint. If this is not the case, False is returned.
def exact_condition(list1, list2):
intersection = list()
for k in list1:
if k in list2:
intersection.append(k)
#Either the two lists are disjoint.
if intersection == []:
return True
#Or they are equal, which means that they are both equal to
#their intersection.
else:
#The following lines check that list1 is included in the intersection.
for k in list1:
if not (k in intersection):
return False
#The following lines check that list2 is included in the intersection.
for k in list2:
if not (k in intersection):
return False
return True
#STEP 1:
#The variable 'score_matrix' will encode a tensor of dimension 3,
#which means a list of lists of lists. Its coefficients, of the from
#score_matrix[i][t][r] are defined for
#- an index i indexing a partition in the list 'partitions'
#- an index t indexing a list in friendship_network
#- an index r indexing a taxon in friendship_network[0][t]
#and they each contain a pair (flag,label) where
# - 'label' is an integer representing the list stored in
#friendship_network[1][t][r] (i.e. a hypothetical ancestor) labeled with
#respect to all the other lists of friendship_network[1][t] up to
#list equality, which means that if the list friendship_network[1][t][r]
#is equal to the list friendship_network[1][s][r], then
#score_matrix[i][t][r] and score_matrix[i][t][s] receive the same label.
#- 'flag' is a Boolean value indicating whether the partitions indexed
#by i in 'partitions' satisfies the exactness condition for the
#hypothetical ancestor friendship_network[1][s][r].
score_matrix = list()
#For convenience, the list of lists of lists friendship_network[1] is
#renamed as 'hypotheses'.
hypotheses = friendship_network[1]
#The following loop gives labels to the different lists (i.e. the
#hypothetical ancestors) in hypotheses in order to recognize them up
#to list equality.
labeling = list()
for t in range(len(hypotheses)):
labeling.append(_epi_factorize_partition(hypotheses[t]))
#The following loop fills the coefficients of 'score_matrix' in.
for i in range(len(partitions)):
#The variable score_row will contain the rows of the matrix.
score_row = list()
#The following loop runs over the set of indices representing
#each taxon 't' of the phylogeny.
for t in range(len(hypotheses)):
#The variable 'score_coalescence' will be used to compute
#the component 'flag' of score_matrix[i][t][r]' while
#the variable 'score_labeling' will be used to compute
#the component 'label' of score_matrix[i][t][r]'
score_coalescence = list()
score_labeling = list()
#The following loop runs over the set of indices representing the
#taxa 'r' of the phylogeny that may possibly coalesce with 't'.
for r in range(len(hypotheses[t])):
#The variable 'x' contains the obvious partition of the set of taxa
#whose only non-trivial part is the list of indices
#representing the hypothetical ancestor 'hypotheses[t][r]'.
x = EquivalenceRelation([hypotheses[t][r]],
len(self.phylogeneses) - 1)
#The following lines check whether there is a morphism of partitions
#form 'x' to the partition partitions[i]. This condition will
#later be referred to as the 'large score condition'.
#i.e. x --> P(partitions[i])
if homset(x.quotient(), partitions[i]):
#If the condition is satisfied, then the hypothetical ancestor
#hypotheses[t][r] is stored in 'score_coalescence[r]' and
#its label is stored in 'score_labeling[r]'.
score_coalescence.append(hypotheses[t][r])
score_labeling.append(labeling[t][r])
#The following lines now construct the coefficients of the list
#score_matrix[i][t]
score_coeff = list()
#By construction, the following loop runs over the set of indices
#representing the taxa 'r' of the phylogeny that satisfy the
#'large score condition' (see above). The goal is now to determine
#which of these taxa also satisfy the 'exact score condition'.
for r in range(len(score_coalescence)):
#The variable 'flag' is the Boolean condition meant to be
#stored in the pair score_matrix[i][t][r] and is meant to
#indicate whether the 'exact score condition' is satisfied.
flag = True
#The following lines check whether 'r' satisfies the 'exact
#score condition', which must be checked with respect to all
#the other taxa 's' satisfying the 'large score condition'.
for s in range(len(score_coalescence)):
if s != r:
flag = flag and exact_condition(\
score_coalescence[r],\
score_coalescence[s])
#As described above, the coefficient score_matrix[i][t][r]
#is constructed as a pair (flag,label).
score_coeff.append((flag, score_labeling[r]))
#The list score_coeff corresponds to what is called the 'support
#functor' in the mathematical version of the present work.
#Also, since the images of the support functor are sets, we need to
#consider the output of the procedure _image_of_partition(score_coeff)
#instead of the list score_coeff itself since it may contain several
#times the same list.
#Use if needed:
#print("[DEBUG] Support functor("+str((t,i))+"): " \
#+ str(_image_of_partition(score_coeff)))
score_row.append(_image_of_partition(score_coeff))
score_matrix.append(score_row)
#STEP 2:
#The following lines integrate the tensor score_matrix[i][t][r] over
#the indices i, namely the indices indexing the partitions
#of 'partitions'. More specifically, the following lines count the number
#of segments making the large and exact scores for a given ancestor
#represented by a certain label 'l'.
#Below, the variable 'score_cardinality' is meant to contain a matrix
#that contains the large and exact score.
score_cardinality = list()
#The following loops initialize the matrix 'score_cardinality'
#with null scores.
for t in range(len(labeling)):
row = list()
#Note that the following loop runs over the image of labeling[t],
#which means that only the representative of the hypothetical
#ancestors is important and not the taxa 'r' they may be associated with.
for l in range(len(_image_of_partition(labeling[t]))):
#The first and second integer are the initial values for the large
#and exact scores, respectively.
row.append([0, 0])
score_cardinality.append(row)
#The matrix 'score_cardinality' is now updated by counting the flags that
#were set to False and True in the 3-dimensional tensor 'score_matrix'.
for i in range(len(score_matrix)):
for t in range(len(score_matrix[i])):
for (f, l) in score_matrix[i][t]:
if f == True:
score_cardinality[t][l][
1] = score_cardinality[t][l][1] + 1
score_cardinality[t][l][
0] = score_cardinality[t][l][0] + 1
else:
score_cardinality[t][l][
0] = score_cardinality[t][l][0] + 1
#STEP 3:
#The following lines are a copy of STEP 2 but where one produces a matrix
#indexed by the 'friends' of the given taxon t instead of producing a
#matrix indexed by the labels of the representative of the common
#ancestors. Note that STEP 2 was essential for the count of the large and
#exact scores, which are meant to be computed with respect to the
#hypothetical ancestors and not the 'friends' of taxon t.
friendships = friendship_network[0]
score_cardinality_adjusted = list()
for t in range(len(labeling)):
row = list()
#This time, the following line is not computed with respect to the
#image of labeling[t].
for r in range(len(labeling[t])):
row.append(())
score_cardinality_adjusted.append(row)
for t in range(len(labeling)):
for r in range(len(labeling[t])):
score_cardinality_adjusted[t][r] = (
friendships[t][r], score_cardinality[t][labeling[t][r]][0],
score_cardinality[t][labeling[t][r]][1])
#The procedure returns a triple (r,large,exact) where r runs over the
#elements of friendships[t] where 'large' is the large score of the
#possible ancestor hypotheses[t][r] and where 'exact' is the exact score
#of the possible ancestor hypotheses[t][r].
return score_cardinality_adjusted
def extend(self, extension):
#The variable indicates whether if the extension of the phylogeny
#is 'complete', in the sense that all the lists l in 'extension' have
#already been added in previous generations, which, in fact,
#should also be the first ones.
flag = False
#The following loop checks all the lists l of 'extension' are already
#appreaing in the first generations.
for t in range(len(self.phylogeneses)):
for i in range(len(extension)):
#Checks if the list 'extension' requires to add a new generation
#to the taxa t. Then the next 'if' tests whether the generation
#is actually a new generation, adding new taxa to the phylogeny.
if extension[i][0] == t:
#The extension will provide a valid phylogeny if all the lists l
#contains the first generation associated with the history of the
#taxon t with which they are coupled. The following lines check
#that this is the case.
for j in self.phylogeneses[t].history[
len(self.phylogeneses[t].history) - 1]:
if not (j in extension[i][1]):
print(
"Error: in Phylogeny.extend: the extension is not compatible with the phylogenesis of taxon "
+ str(t))
exit()
#The following lines check whether the extension is actually adding
#a new individual to the history of the taxon t. If this is not
#the case for all the taxa of the extension, then the phylogeny
#is considered to be already complete, so that the variable flag
#is never changed to the value True.
for j in extension[i][1]:
#The following lines check if new individuals appear in
#extension[i][1] in addition of those already in
#self.phylogeneses[t].history.
if not (j in self.phylogeneses[t].history[
len(self.phylogeneses[t].history) - 1]):
#A new generation has been detected, the phylogeny is therefore
#not complete and 'flag' is set to True.
flag = True
#The following condition holds whenever there is at least one phylogenesis
#that is not complete.
if flag == True:
#The following lines add the new generation l of a pair
#(t,l) in 'extension' to the taxa t. Otherwise, the first
#generation of a taxa that do not appear in 'extension'
#is repeated in its phylogenesis.
for t in range(len(self.phylogeneses)):
#The variable found_flag indicates whether the taxa t appears in
#the first components of the pairs of the list 'extension' or not.
found_flag = False
for i in range(len(extension)):
if extension[i][0] == t:
#The procedure _image_of_partition is used to eliminate the
#repetitions of integers that can occur in extension[i][1].
self.phylogeneses[t].history.append(\
_image_of_partition(extension[i][1]))
found_flag = True
break
#The taxa was not associated with any list l in 'extension'.
if found_flag == False:
#The first generation is repeated (there is no repetition of
#integer in this list).
self.phylogeneses[t].history.append(
self.phylogeneses[t].history[
len(self.phylogeneses[t].history) - 1])
#The following output indicates that the phylogeny was not complete,
#and another run is necessary to determine if the phylogeny is now
#completed.
return True
else:
##The following output indicates that the phylogeny is now complete.
return False