From a8632fec39da71de2ec1d8ef56260fa47c4d5d7e Mon Sep 17 00:00:00 2001
From: Oceane <oceane.fourquet@outlook.fr>
Date: Thu, 29 Sep 2022 11:12:50 +0200
Subject: [PATCH] first commit with modules in python

---
 .DS_Store                                     | Bin 0 -> 6148 bytes
 Module/.DS_Store                              | Bin 0 -> 6148 bytes
 .../cost_matrix_uncertainty.cpython-38.pyc    | Bin 0 -> 3695 bytes
 .../cost_matrix_uncertainty.cpython-39.pyc    | Bin 0 -> 3810 bytes
 .../cost_matrix_uncertainty_v2.cpython-39.pyc | Bin 0 -> 5009 bytes
 Module/__pycache__/measures.cpython-38.pyc    | Bin 0 -> 2405 bytes
 Module/__pycache__/measures.cpython-39.pyc    | Bin 0 -> 2412 bytes
 ...monotonic_regression_4cases.cpython-39.pyc | Bin 0 -> 11382 bytes
 ...onic_regression_uncertainty.cpython-38.pyc | Bin 0 -> 12575 bytes
 ...onic_regression_uncertainty.cpython-39.pyc | Bin 0 -> 12799 bytes
 ..._regression_uncertainty_bis.cpython-39.pyc | Bin 0 -> 9497 bytes
 ...c_regression_uncertainty_v1.cpython-39.pyc | Bin 0 -> 10211 bytes
 ...c_regression_uncertainty_v2.cpython-39.pyc | Bin 0 -> 9859 bytes
 .../optimal_k_aggregations.cpython-38.pyc     | Bin 0 -> 4224 bytes
 .../optimal_k_aggregations.cpython-39.pyc     | Bin 0 -> 4315 bytes
 .../optimal_k_aggregations_v2.cpython-39.pyc  | Bin 0 -> 3608 bytes
 .../__pycache__/preselection.cpython-39.pyc   | Bin 0 -> 2415 bytes
 .../selection_algorithm.cpython-38.pyc        | Bin 0 -> 5225 bytes
 .../selection_algorithm.cpython-39.pyc        | Bin 0 -> 5173 bytes
 .../selection_algorithm_v2.cpython-39.pyc     | Bin 0 -> 6027 bytes
 .../__pycache__/show_results.cpython-38.pyc   | Bin 0 -> 5683 bytes
 .../__pycache__/show_results.cpython-39.pyc   | Bin 0 -> 5682 bytes
 .../show_results_4cases.cpython-38.pyc        | Bin 0 -> 5378 bytes
 .../show_results_4cases.cpython-39.pyc        | Bin 0 -> 8079 bytes
 Module/__pycache__/stages.cpython-38.pyc      | Bin 0 -> 2100 bytes
 Module/__pycache__/stages.cpython-39.pyc      | Bin 0 -> 2390 bytes
 Module/__pycache__/tools.cpython-38.pyc       | Bin 0 -> 3593 bytes
 Module/__pycache__/tools.cpython-39.pyc       | Bin 0 -> 4329 bytes
 Module/cost_matrix_uncertainty.py             | 150 ++++
 Module/measures.py                            | 131 +++
 Module/monotonic_regression_uncertainty.py    | 778 ++++++++++++++++++
 Module/optimal_k_aggregations.py              | 151 ++++
 Module/preselection.py                        |  59 ++
 Module/selection_algorithm.py                 | 161 ++++
 Module/show_results_4cases.py                 | 498 +++++++++++
 Module/stages.py                              |  82 ++
 Module/tools.py                               | 186 +++++
 37 files changed, 2196 insertions(+)
 create mode 100644 .DS_Store
 create mode 100755 Module/.DS_Store
 create mode 100755 Module/__pycache__/cost_matrix_uncertainty.cpython-38.pyc
 create mode 100644 Module/__pycache__/cost_matrix_uncertainty.cpython-39.pyc
 create mode 100755 Module/__pycache__/cost_matrix_uncertainty_v2.cpython-39.pyc
 create mode 100755 Module/__pycache__/measures.cpython-38.pyc
 create mode 100644 Module/__pycache__/measures.cpython-39.pyc
 create mode 100755 Module/__pycache__/monotonic_regression_4cases.cpython-39.pyc
 create mode 100755 Module/__pycache__/monotonic_regression_uncertainty.cpython-38.pyc
 create mode 100644 Module/__pycache__/monotonic_regression_uncertainty.cpython-39.pyc
 create mode 100755 Module/__pycache__/monotonic_regression_uncertainty_bis.cpython-39.pyc
 create mode 100755 Module/__pycache__/monotonic_regression_uncertainty_v1.cpython-39.pyc
 create mode 100755 Module/__pycache__/monotonic_regression_uncertainty_v2.cpython-39.pyc
 create mode 100755 Module/__pycache__/optimal_k_aggregations.cpython-38.pyc
 create mode 100644 Module/__pycache__/optimal_k_aggregations.cpython-39.pyc
 create mode 100755 Module/__pycache__/optimal_k_aggregations_v2.cpython-39.pyc
 create mode 100644 Module/__pycache__/preselection.cpython-39.pyc
 create mode 100755 Module/__pycache__/selection_algorithm.cpython-38.pyc
 create mode 100644 Module/__pycache__/selection_algorithm.cpython-39.pyc
 create mode 100755 Module/__pycache__/selection_algorithm_v2.cpython-39.pyc
 create mode 100755 Module/__pycache__/show_results.cpython-38.pyc
 create mode 100644 Module/__pycache__/show_results.cpython-39.pyc
 create mode 100755 Module/__pycache__/show_results_4cases.cpython-38.pyc
 create mode 100644 Module/__pycache__/show_results_4cases.cpython-39.pyc
 create mode 100755 Module/__pycache__/stages.cpython-38.pyc
 create mode 100644 Module/__pycache__/stages.cpython-39.pyc
 create mode 100755 Module/__pycache__/tools.cpython-38.pyc
 create mode 100644 Module/__pycache__/tools.cpython-39.pyc
 create mode 100755 Module/cost_matrix_uncertainty.py
 create mode 100755 Module/measures.py
 create mode 100755 Module/monotonic_regression_uncertainty.py
 create mode 100755 Module/optimal_k_aggregations.py
 create mode 100644 Module/preselection.py
 create mode 100755 Module/selection_algorithm.py
 create mode 100755 Module/show_results_4cases.py
 create mode 100755 Module/stages.py
 create mode 100755 Module/tools.py

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diff --git a/Module/cost_matrix_uncertainty.py b/Module/cost_matrix_uncertainty.py
new file mode 100755
index 0000000..9ef4090
--- /dev/null
+++ b/Module/cost_matrix_uncertainty.py
@@ -0,0 +1,150 @@
+from Module import monotonic_regression_uncertainty as mru
+from Module import tools
+
+
+import numpy as np
+import pandas as pd
+import os
+import time
+from itertools import chain
+import copy
+
+
+import multiprocessing as mp
+
+
+### Useful functions for parallele
+
+def vals_mp(pairs, df_2, out, funct):
+    vals = list()
+    for p in pairs:
+        vals.append((p, df_2, out, funct))
+    return vals
+
+
+#### ERROR MATRIX ######
+
+
+def single_error(p, df_2, out, funct):
+
+    p1, p2, key = p.split('/')
+    key = int(key)
+    rev, up = tools.equiv_key_case(key)
+
+    diag = df_2['target'].values.tolist()
+
+    tr1, tr2 = df_2[p1].values.tolist(), df_2[p2].values.tolist()
+
+    data = [((tr1[n], tr2[n] ), 1, diag[n]) for n in range(len(diag))]
+    out_p = (out[p1], out[p2])
+    X, models = mru.compute_recursion(data, (rev, up, key))
+
+    reg_err, bpr, bpb, r_p, b_p = models[key]
+    pred = funct(out_p, bpr, bpb, rev, up)
+
+    if pred == -1:
+        return (p, -1) #if uncertain, we keep it like this
+    else:
+        return (p, abs(1-int(pred == out['target']))) #int(True) = 1 so if the pred is equal to real label, error is equal to 0
+
+
+def error_matrix(df_, pairs, nbcpus, funct):
+    try:
+        nbcpus = int (os.getenv('OMP_NUM_THREADS') )
+    except:
+        pass
+    pool = mp.Pool(nbcpus)
+
+
+    df = copy.deepcopy(df_)
+
+    index = list()
+
+    mat_err = pd.DataFrame(columns = pairs + ['target']) #Dataframe with possible classifiers as columns
+
+    for j in range(len(df)):# For each patient j, we add a line to the dataframe contaning whereas the patient was misclassified or not (1 if misclassified, 0 otherwise)
+        out = df.iloc[j, :]
+        df_2 = df.drop([j])#classifiers are constructed according to the set of patients without patient j
+        df_2.reset_index(drop=True, inplace=True)
+
+        vals = vals_mp(pairs, df_2, out, funct)
+
+        res = pool.starmap(single_error, vals, max(1,len(vals)//nbcpus)) #res is an array (size = nb of pairs) that the name of the classifier and whereas the poatient was misclassified or not
+
+        dico_err = {r[0] : r[1] for r in res}
+        dico_err['target'] = out['target']
+        dico_err_s = pd.Series(dico_err)
+        dico_err_s.name = 'P'+str(j+1)
+        mat_err = pd.concat((mat_err, dico_err_s.to_frame().T), axis=0)
+        del df_2
+
+
+
+
+    unc = {col: mat_err[col].to_list().count(-1) for col in pairs}
+    unc['target'] = np.nan
+    unc_s = pd.Series(unc)
+    unc_s.name = 'uncertain'
+
+    mat_err_unc = pd.concat((mat_err,unc_s.to_frame().T), axis=0)
+
+
+
+    cols = list(mat_err_unc.columns)
+    cols.remove('target')
+    rem = list()
+    for col in cols:
+        val = mat_err_unc.at['uncertain', col]
+        if val > len(df)/3:
+            rem.append(col)
+    mat_err.drop(rem, axis=1, inplace=True)
+    mat_err_unc.drop(rem, axis=1, inplace=True)
+
+    err = {col: mat_err[col].to_list().count(1)/(mat_err[col].to_list().count(1) + mat_err[col].to_list().count(0)) for col in pairs if col not in rem}
+    err['target'] = np.nan
+    err_s = pd.Series(err)
+    err_s.name = 'error'
+
+    mat_err_final = pd.concat((mat_err_unc,err_s.to_frame().T), axis=0)
+
+
+    mat_err_final.sort_values(axis = 1, by=['error', 'uncertain'], inplace=True)
+
+    del df
+    return mat_err_final
+
+
+
+
+#### GOING error matrix to prediction matrix
+def error_to_prediction(matrix, df):
+    diags = df['target'].values.tolist()
+
+    prediction_mat = {}
+    for cls in matrix.keys():
+        if cls != 'target':
+            errors = matrix[cls]
+            pred = list()
+            for i in range(len(errors)):
+                if errors[i] == 0:
+                    pred.append(diags[i])
+                elif errors[i] == 1:
+                    pred.append(int(abs(1-diags[i])))
+                elif errors[i] == -1:
+                    pred.append(-1)
+            prediction_mat[cls] = pred
+
+    return prediction_mat
+
+
+
+
+
+### Get dict relating classifiers with error score
+
+
+def cost_classifiers(ndf):
+    cols = list(ndf.columns)
+    cols.remove('target')
+    cost = {cols[i] : ndf[cols[i]].loc[['error']][0] for i in range(len(cols))}
+    return cost
diff --git a/Module/measures.py b/Module/measures.py
new file mode 100755
index 0000000..1ea5533
--- /dev/null
+++ b/Module/measures.py
@@ -0,0 +1,131 @@
+import math
+
+
+#cls = classifier
+# boolean prediction : 0 if the prediction is correct, 1 if it's wrong
+#pred_xi : array of the boolean prediction of xi over the M classifiers
+#set (size MxN) is a list of the boolean prediction of the M classifiers over the N patients
+
+def m_xi(pred_xi):
+    #number of classifiers producing error for the input sample xi
+    #pred_xi is the boolean prediction of xi over the M classifiers
+    return sum(pred_xi)
+
+def error_rate_clj(pred_clj):
+    # error rate of jth classifier
+    #pred_clj is the boolean prediction of the N patients by classifier j
+    return sum(pred_clj)/len(pred_clj)
+
+def ensemble_mean_error_rate(set):
+    #average error rate over the M classifiers
+    #set (size MxN) is a list of the boolean prediction of the M classifiers over the N patients
+    M = len(set)
+    e = 0
+    for i in range(M):
+        e += error_rate_clj(set[i])
+    return e/M
+
+
+
+def yi_MV_1(pred_xi):
+    #pred_xi is the boolean prediction of xi over the M classifiers
+    #majority boolean prediction error in favor of the wrong pred 1
+    M = len(pred_xi)
+    if m_xi(pred_xi) >= M/2:
+        #if the nb of misclassification is greater than or equal to the nb of classifiers
+        #then the preditcion made with majority voting is wrong
+        return 1
+    else:
+        return 0
+
+def yi_MV_0(pred_xi):
+    #pred_xi is the boolean prediction of xi over the M classifiers
+    #majority boolean prediction error in favor of correct pred 0
+    M = len(pred_xi)
+    if m_xi(pred_xi) > M/2:
+        #if the nb of misclassification is greater than the nb of classifiers
+        #then the preditcion made with majority voting is wrong
+        return 1
+    else:
+        return 0
+
+def MVE(set, meth = yi_MV_1):
+    #majority voting error rate
+    M = len(set) #Nb of classifiers
+    N = len(set[0]) #Nb of patients
+    mve = 0
+    for i in range(N): #For each patient i
+        #construction of pred_xi
+        pred_xi = list()
+        for j in range(M):#For each classifier j
+            pred_xi.append(set[j][i]) #We add the misclassification error of patient i for the classifier j
+
+        yi_mv = meth(pred_xi) #Whereas the patient i was misclassified or not according to the ensemble
+
+        mve += yi_mv
+    return mve/N
+
+
+
+def D2_ij(pred1, pred2):
+    #disagreement measure for 2 pairs
+    #pred1 and pred2 (size N) are the output of classifiers for the N patients
+    N = len(pred1)
+    D2 = 0
+    for i in range(N):
+        if pred1[i] != pred2[i]:
+            D2 += 1
+    return D2/N
+
+def D2(set):
+    #average disagreement measure over all pairs of a set
+    #set (size MxN) is a list of the boolean prediction of the M classifiers over the N patients
+    M = len(set)
+    D2 = 0
+    for i in range(M):
+        for j in range(i+1, M):
+            if i != j:
+                D2 += D2_ij(set[i], set[j])
+
+    return (2*D2)/(M*(M-1))
+
+
+def F2_ij(pred1, pred2):
+    #double fault measure
+    #pred1 and pred2 (size N) are the output of classifiers for the N patients
+    N = len(pred1)
+    N11 = 0
+    for i in range(N):
+        if pred1[i] == 1 and pred2[i] == 1:
+            #double fault
+            N11 +=1
+    return N11/N
+
+def F2(set):
+    #average double fault measure over all pairs of a set
+    #set (size MxN) is a list of the boolean prediction of the M classifiers over the N patients
+    M = len(set)
+    F2 = 0
+    for i in range(M):
+        for j in range(i+1, M):
+            if i != j:
+                F2 += F2_ij(set[i], set[j])
+    return (2*F2)/(M*(M-1))
+
+def entropy(set):
+    #set (size MxN) is a list of the boolean prediction of the M classifiers over the N patients
+    #The entropy measure reaches its maximum (EN 1⁄4 1) for the highest disagreement, which is the case of observing M/2 votes with identical value (0 or 1) and
+    #M M/2 with the alternative value. The lowest entropy (EN 1⁄4 0) is observed if all classifier outputs are
+    #identical.
+    M = len(set)
+    N = len(set[0])
+
+    EN = 0
+    for i in range(N):
+        #construction of pred_xi
+        pred_xi = list()
+        for j in range(M):
+            pred_xi.append(set[j][i])
+
+        EN += min(m_xi(pred_xi), M-m_xi(pred_xi)) / (M-math.ceil(M/2))
+    return EN/N
diff --git a/Module/monotonic_regression_uncertainty.py b/Module/monotonic_regression_uncertainty.py
new file mode 100755
index 0000000..48cb10f
--- /dev/null
+++ b/Module/monotonic_regression_uncertainty.py
@@ -0,0 +1,778 @@
+from Module import tools
+
+import numpy as np
+from math import ceil, log, pow
+import pandas as pd
+import os
+import multiprocessing as mp
+import copy
+import time
+
+
+
+#Useful functions
+
+def err(v, w, z): #error function defined in the paper
+    return w*abs(v-z)
+
+next_ = lambda x: int( pow(2, ceil(log(x, 2))))
+
+def index_leaves(A, k):
+    #As we use a balanced binary tree, leaves can be at at most two levels. This function constructs
+    #a dictionary linking each leaf index to the index of the corresponding node in the tree
+    #A is an array contaning all the values of the nodes
+    #k is the number of leaves in the tree
+    p_lev = next_(k) - k
+    lev = k - p_lev
+    ind_leaves = {}
+    for i in range(1, lev+1):
+        ind_leaves[i] = (len(A)-lev) + i
+    for i in range(1, p_lev+1):
+        ind_leaves[lev+i ] = (len(A)-k) + i
+    return ind_leaves
+
+def is_leaf(ind_leaves, num):
+    #confirms or not whether the node under study is a leaf
+    if num in ind_leaves.values():
+        return True
+    else:
+        return False
+
+def find_leaves(ind_leaves, num, L):
+    #return a list with all the leaves below the node num
+    #ind_leaves is the dictionary with leaf index as key and node index as values
+    #num is the the node we are studying
+    #L is the list we are updating with the leaves
+
+    if not is_leaf(ind_leaves, num):
+        find_leaves(ind_leaves, 2*num, L)
+        find_leaves(ind_leaves, 2*num +1, L)
+    else:
+        L.append(num)
+
+def Z_(H, A, ind_leaves):
+    #Show Z : this one won't appear in the final programm. It's just to check the tree for the moment
+    Z = list()
+    for i in range(1,len(H)+1):
+        v_i = ind_leaves[i]
+        Z.append(int(compute_Z(A,v_i)))
+    print('Z', Z)
+    return Z
+
+def is_A_balanced(A):
+    flag = True
+    for i in range(1, len(A), 2):
+        if A[i] != 0 and A[i+1] != 0:
+            flag = False
+    return flag
+
+########Initialize A
+def initialization(data, rev):
+    #rev enable us to test increasing and decreasing isotonicity
+    #X is an array with sorted data
+    #H is a soretd list of all column values
+    #A is the array initialised at zero
+    #ind_leaves is the dictionnary linking each leaf index to the index of the corresponding node in the tree
+    X = sorted(data, reverse = rev)
+    H = sorted(list(set([X[i][0][1] for i in range(len(X))])))
+    A = np.zeros(2*len(H)+1)
+    H.append(float('inf'))
+    ind_leaves = index_leaves(A, len(H))
+    return X, H, A, ind_leaves
+
+
+#####STEP 1 : compute Z and Z(g,c_g)
+def compute_Z(A,v):
+    #compute Z by going up the tree from leaf v to the root (Z(g,h) = sum of z_v on the path to the root)
+    Z = A[v-1]
+    while True:
+        if v == 1:
+            break
+        v = v//2
+        Z += A[v-1]
+    return Z
+
+#These two functions help for updating the tree when Z(g,c_g) is computed (it can change a lot in the path to the root)
+def degenerate_interval(A, v, ind_leaves):
+    p = v //2
+    mod = v%2
+    while True:
+        if p == 1:
+            break
+        if A[p-1] != 0:
+            add_value(A, p, v, ind_leaves)
+            A[p-1] = 0
+        p = p//2
+        mod = p%2
+
+
+
+def add_value(A, p, v, ind_leaves):
+    L = list()
+    find_leaves(ind_leaves, p, L)
+    for l in L:
+        if l != v:
+            A[l-1] += A[p-1]
+
+
+def rebalance(A,v, ind_leaves):
+    if v != 0:
+        p = v//2
+        mod = v%2
+        w = 2*p+(1-mod)
+        if A[v-1] != 0 and A[w-1] !=0:
+            delta = min(A[v-1], A[w-1])
+            A[p-1] += delta
+            A[v-1] -= delta
+            A[w-1] -= delta
+    else:
+        mini = float('inf')
+        for i in ind_leaves.values():
+            Z = compute_Z(A,i)
+            if Z < mini:
+                mini = Z
+        A[0] = mini
+
+
+
+
+def step1(ind_cg, A, nb_leaves, ind_leaves, err1, S, H):
+    #t0 = time.process_time()
+    mini = float('inf')
+    h = 0
+    c = 1 #not sure of this
+    for i in range(ind_cg, nb_leaves+1):
+        v_i = ind_leaves[i]
+        Z = compute_Z(A,v_i)
+
+        if Z < mini:
+            mini = Z
+            ind = i
+            c = 1
+            h = H[i-1]
+        elif Z == mini:
+            c+=1
+    if c>1:
+        while compute_Z(A,ind_leaves[ind]) == mini and ind < nb_leaves:
+            ind+=1
+        if ind == nb_leaves:
+            h = H[ind-1]  #value of the leaves that give minimum Z(g,h)
+        else:
+            h = H[ind-2]
+    if len(S) ==0:
+        h=H[0]
+    S.append(h)
+
+
+
+    deg = compute_Z(A,ind_leaves[ind_cg]) - A[ind_leaves[ind_cg]-1] #sum of z_v on the path from c_g to the root, but minus the leaf c_g
+
+    #if the new value of Z(g,c_g) minus deg is greater or equal to 0, then the value in A for leaf c_g is equal to the difference
+    # however, in the other case, it means that we have to change the path to make it correspond
+
+
+    if deg <= mini + err1:
+        A[ind_leaves[ind_cg]-1] = mini + err1 - deg
+    else:
+        A[ind_leaves[ind_cg]-1] = mini + err1
+        degenerate_interval(A, ind_leaves[ind_cg], ind_leaves)
+    #print('Step1', time.process_time() - t0)
+
+
+
+
+
+
+#######STEP 2 : update right and left
+
+#Update right c_g
+def v_has_right(v, A):
+    #indicates whether the node v has a right child branch
+    if 2*v+1 <= len(A):
+        return True
+    else:
+        return False
+
+def update_right(v, A, val):
+    #update right child branch by adding val
+    A[2*v] += val
+
+def update_all_right(v, A, err0):
+    p = v//2
+    while True:
+        if v_has_right(p, A) and 2*p+1 !=v:
+            update_right(p, A, err0)
+
+        if p == 1: #end when root has been updated
+            break
+        v = p
+        p = p//2
+
+
+
+#Update left c_g
+def v_has_left(v, A):
+    #indicates whether the node v has a left child branch
+    if 2*v <= len(A):
+        return True
+    else:
+        return False
+
+def update_left(v, A, val):
+    #update left child branch by adding val
+    A[2*v-1] += val
+
+
+
+def update_all_left(v, A, err1):
+    p = v//2
+    while True:
+        if v_has_left(p, A) and 2*p != v:
+            update_left(p, A, err1)
+
+        if p == 1: #end when root has been updated
+            break
+        v = p
+        p = p//2
+
+
+def step2(A, v, err0, err1):
+    #t0 = time.process_time()
+    #add the error in left and right intervals
+    update_all_right(v, A, err0)
+    update_all_left(v, A, err1)
+    #print('Step2', time.process_time() - t0)
+
+
+
+
+
+########RECURSION
+
+def recursion(A, H, c_g, ind_leaves, err0, err1, nb_leaves, S):
+    ind_cg = H.index(c_g) + 1
+    v_cg = ind_leaves[ind_cg]
+
+    step1(ind_cg, A, nb_leaves, ind_leaves, err1, S, H)
+
+    step2(A, v_cg, err0, err1)
+
+
+
+#######TRACEBACK
+def find_h_Z_min(A, ind_leaves):
+    p = 1
+    while True:
+        v = 2*p
+        w = 2*p +1
+        if A[v-1] == 0:
+            p = v
+        else:
+            p = w
+
+        if is_leaf(ind_leaves,p):
+            return p
+    return None
+
+def search_key(dico, val):
+    l = [c for c,v in dico.items() if v==val]
+    if len(l) != 0:
+        return l[0]
+    else:
+        return -1
+
+
+def find_highest_point(X, hh):
+    #find the point with highest rows
+    for x in X:
+        if x[0][1] == hh:
+            return x
+
+def find_index_point(X, xy):
+    for x in X:
+        if xy in x:
+            return X.index(x)
+    return None
+
+def traceback(A, X, H, ind_leaves, S, up):
+    #By going up in the steps, we can determine the breaking point that construct the regression
+    b = search_key(ind_leaves,find_h_Z_min(A, ind_leaves)) #We look for leaf with minimal Z value as it is the first point
+    h = H[b-1]
+    breakpoint = list()
+    for i in range(len(X)-1, -1, -1):
+        x = X[i] #ie point by decreasing order of the sorted array
+        xy, w, lab = x
+        cg = xy[1] #column
+        if h == cg:#h is a breaking point
+            h = S[i] #we take the h from the previous step
+            breakpoint.append(xy)
+
+    if X[0][2] == int(up) and X[0][0][1] == H[-2]: #To avoid forgetting the first point if it's the highest in column
+        breakpoint.append(X[0][0])
+
+    hx = find_highest_point(X, H[-2]) #To avoid forgetting the last point if the highest
+    id_hx = X.index(hx)
+    if len(breakpoint)!=0:
+        id_hbp = find_index_point(X, breakpoint[0])
+        if hx[2] == int(up) and id_hx < id_hbp:
+            breakpoint.append(hx[0])
+
+    return breakpoint
+
+
+def labels_point(X, bpr, rev, up):
+    r_p = list()
+    b_p = list()
+
+    reg_err = 0
+    for x in X:
+        lab = x[2]
+        x = x[0]
+
+        if up and x in bpr:
+            r_p.append(x)
+            if lab == 0:
+                reg_err +=1
+
+        elif not up and x in bpr:
+            b_p.append(x)
+            if lab == 1:
+                reg_err +=1
+
+        else:
+            if not rev and up: #CASE 1
+                flag = 0
+                for br in bpr:
+                    if x[0] >= br[0] and x[1] >= br[1]:
+                        flag = 1
+                if flag == 0:
+                    b_p.append(x)
+                    if lab == 1:
+                        reg_err +=1
+                else:
+                    r_p.append(x)
+                    if lab == 0:
+                        reg_err +=1
+
+            if rev and up: #CASE 2
+                flag = 0 #consider as blue by default
+                for br in bpr:
+                    if x[0] <= br[0] and x[1] >= br[1]:
+                        flag = 1
+                if flag == 0:
+                    b_p.append(x)
+                    if lab == 1:
+                        reg_err +=1
+                else:
+                    r_p.append(x)
+                    if lab == 0:
+                        reg_err +=1
+
+            if not rev and not up: #CASE 3
+                flag = 1 #consider as red by default
+                for br in bpr:
+                    if x[0] >= br[0] and x[1] >= br[1]:
+                        flag = 0
+                if flag == 0:
+                    b_p.append(x)
+                    if lab == 1:
+                        reg_err +=1
+                else:
+                    r_p.append(x)
+                    if lab == 0:
+                        reg_err +=1
+
+            if rev and not up: #CASE 4
+                flag = 1 #consider as red by default
+                for br in bpr:
+                    if  x[0] <= br[0] and x[1] >= br[1]:
+                        flag =0
+                if flag == 0:
+                    b_p.append(x)
+                    if lab == 1:
+                        reg_err +=1
+                else:
+                    r_p.append(x)
+                    if lab == 0:
+                        reg_err +=1
+
+
+    return r_p, b_p, reg_err
+
+
+
+
+#previous functions give us the data labelled as 0 and 1. But if we want
+#to predict new points, we must know the official separation. As we prefer
+#false positive rather than false negative, we draw the lines closest
+#to "blue" points
+
+def breakpoint_b(X, b_p, rev, up):
+    bpb = list()
+    b_ps = sorted(b_p)
+    if not rev and up: #CASE 1
+        while len(b_ps) != 0:
+            maxi = b_ps[-1]
+            x, y = maxi
+            bpb.append(maxi)
+            b_ps = [pt for pt in b_ps if pt[1] > y]
+            b_ps = sorted(b_ps)
+
+
+    elif rev and up: #CASE 2
+        while len(b_ps) != 0:
+            maxi = b_ps[0]
+            x, y = maxi
+            bpb.append(maxi)
+            b_ps = [pt for pt in b_ps if pt[1] > y]
+            b_ps = sorted(b_ps)
+
+    elif not rev and not up: #CASE 3
+        while len(b_ps) != 0:
+            maxi = b_ps[0]
+            x, y = maxi
+            bpb.append(maxi)
+            b_ps = [pt for pt in b_ps if pt[0] > x]
+            b_ps = sorted(b_ps)
+
+    elif rev and not up: #CASE 4
+        while len(b_ps) != 0:
+            maxi = b_ps[-1]
+            x, y = maxi
+            bpb.append(maxi)
+            b_ps = [pt for pt in b_ps if pt[0] < x]
+            b_ps = sorted(b_ps)
+    return bpb
+
+
+#Clean the list of border points
+
+def clean_blue(bpr, rev, up):
+    bpr = sorted(bpr)
+    nbpr = list()
+
+    if rev and not up:
+        for bp in bpr:
+            itv = bpr[bpr.index(bp)+1:]
+            flag = True
+            for it in itv:
+                if it[1] <= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    elif rev and up:
+        for bp in bpr:
+            itv = bpr[:bpr.index(bp)]
+            flag = True
+            for it in itv:
+                if it[1] >= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    elif not rev and not up:
+
+        for bp in bpr:
+            itv = bpr[:bpr.index(bp)]
+            flag = True
+            for it in itv:
+                if it[1] <= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    elif not rev and up:
+
+        for bp in bpr:
+            itv = bpr[bpr.index(bp)+1:]
+            flag = True
+            for it in itv:
+                if it[1] >= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    assert len(nbpr) <= len(bpr)
+    return nbpr
+
+
+def clean_red(bpr, rev, up):
+    bpr = sorted(bpr)
+    nbpr = list()
+
+    if rev and up:
+
+        for bp in bpr:
+            itv = bpr[bpr.index(bp)+1:]
+            flag = True
+            for it in itv:
+                if it[1] <= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    elif rev and not up:
+
+        for bp in bpr:
+            itv = bpr[:bpr.index(bp)]
+            flag = True
+            for it in itv:
+                if it[1] >= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    elif not rev and up:
+
+        for bp in bpr:
+            itv = bpr[:bpr.index(bp)]
+            flag = True
+            for it in itv:
+                if it[1] <= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    elif not rev and not up:
+
+        for bp in bpr:
+            itv = bpr[bpr.index(bp)+1:]
+            flag = True
+            for it in itv:
+                if it[1] >= bp[1]:
+                    flag=False
+                    break
+            if flag:
+                nbpr.append(bp)
+
+    assert len(nbpr) <= len(bpr)
+    return nbpr
+
+
+
+#####MAIN FUNCTION
+
+def compute_recursion(data, case = None):
+        #return X : sorted data
+        # labels : labelisation of each points
+        # bpb : points creating the delimitation of blue area
+        # bpr : points creating the delimitation of red area
+
+    models = {}
+    if case is None:
+
+        for rev in [True, False]:
+            for up in [True, False]:
+
+                X, H, A, ind_leaves = initialization(data, rev)
+
+                S = list()
+                labs = [x[2] for x in X]
+                nb_leaves = len(H)
+
+                for i in range(len(X)): #((r,c), w, label)
+                    x = X[i]
+                    xy, w, lab = x
+                    cg = xy[1]
+                    err0, err1 = err(lab, w, abs(1-int(up))), err(lab, w, int(up))
+
+                    recursion(A, H, cg, ind_leaves, err0, err1, nb_leaves, S)
+
+                while not is_A_balanced(A):
+                    for v in range(len(A), -1, -1):
+                        rebalance(A,v, ind_leaves)
+
+                if up:
+                    bpr = traceback(A, X, H, ind_leaves, S, up)
+                    r_p, b_p, reg_err = labels_point(X, bpr, rev, up)
+
+                    bpb = breakpoint_b(X, b_p, rev, up)
+
+                else:
+                    bpb = traceback(A, X, H, ind_leaves, S, up)
+
+                    r_p, b_p, reg_err = labels_point(X, bpb, rev, up)
+                    bpr = breakpoint_b(X, r_p, rev, up)
+
+                bpr = clean_red(bpr, rev, up)
+                bpb = clean_blue(bpb, rev, up)
+
+                if rev and up:
+                    models[2] = (reg_err, bpr, bpb, r_p, b_p)
+                elif not rev and up:
+                    models[1] = (reg_err, bpr, bpb, r_p, b_p)
+                elif not rev and not up:
+                    models[3] = (reg_err, bpr, bpb, r_p, b_p)
+                else:
+                    models[4] = (reg_err, bpr, bpb, r_p, b_p)
+
+    else:
+        #print('case {}'.format(case))
+        rev, up = case[0], case[1]
+        X, H, A, ind_leaves = initialization(data, rev)
+        S = list()
+        labs = [x[2] for x in X]
+        nb_leaves = len(H)
+        #print(X)
+        for i in range(len(X)): #((r,c), w, label)
+            x = X[i]
+            xy, w, lab = x
+            cg = xy[1]
+            err0, err1 = err(lab, w, abs(1-int(up))), err(lab, w, int(up))
+
+            recursion(A, H, cg, ind_leaves, err0, err1, nb_leaves, S)
+
+        while not is_A_balanced(A):
+            for v in range(len(A), -1, -1):
+                rebalance(A,v, ind_leaves)
+
+        if up:
+            bpr = traceback(A, X, H, ind_leaves, S, up)
+            r_p, b_p, reg_err = labels_point(X, bpr, rev, up)
+
+            bpb = breakpoint_b(X, b_p, rev, up)
+
+        else:
+            bpb = traceback(A, X, H, ind_leaves, S, up)
+            r_p, b_p, reg_err = labels_point(X, bpb, rev, up)
+            bpr = breakpoint_b(X, r_p, rev, up)
+
+        bpr = clean_red(bpr, rev, up)
+        bpb = clean_blue(bpb, rev, up)
+
+        models[case[2]] = (reg_err, bpr, bpb, r_p, b_p)
+
+    return X, models
+
+
+#### PREDICTION For diff case
+
+def predict_uncertainty(p, bpr, bpb, rev, up):
+    flag = -1
+    if not rev and up: #CASE 1
+        for b in bpr:
+            if p[0] >= b[0] and p[1] >= b[1]:
+                flag = 1
+
+        for b in bpb:
+            if p[0] <= b[0] and p[1] <= b[1]:
+                flag = 0
+
+
+    elif rev and up: #CASE 2
+        for b in bpr:
+            if p[0] <= b[0] and p[1] >= b[1]:
+                flag = 1
+
+        for b in bpb:
+            if p[0] >= b[0] and p[1] <= b[1]:
+                flag = 0
+
+    elif not rev and not up: #CASE 3
+        for b in bpr:
+            if p[0] <= b[0] and p[1] <= b[1]:
+                flag = 1
+
+        for b in bpb:
+            if p[0] >= b[0] and p[1] >= b[1]:
+                flag = 0
+
+
+    elif rev and not up: #CASE 4
+        for b in bpr:
+            if p[0] >= b[0] and p[1] <= b[1]:
+                flag = 1
+
+        for b in bpb:
+            if p[0] <= b[0] and p[1] >= b[1]:
+                flag = 0
+    assert flag in [1, 0, -1], "Problem with prediction of the point, label is not 0, 1 or -1"
+
+    return flag
+
+
+
+def predict_severe(p, bpr, bpb, rev, up):
+    # points in grey area are automatically labelled in red area
+    flag = predict_uncertainty(p, bpr, bpb, rev, up)
+    if flag == -1:
+        flag = 1
+
+    assert flag in [1, 0], "Problem with prediction of the point, label is not 0 or 1"
+
+
+    return flag
+
+
+def predict_non_severe(p, bpr, bpb, rev, up):
+    # points in grey area are automatically labelled in blue area
+    flag = predict_uncertainty(p, bpr, bpb, rev, up)
+    if flag == -1:
+        flag = 0
+
+    assert flag in [1, 0], "Problem with prediction of the point, label is not 0 or 1"
+
+    return flag
+
+
+
+#def predict_severe(p, bpr, bpb, rev, up):
+    # points in grey area are automatically labelled in red area
+#    flag = 1
+#    if not rev and up: #CASE 1
+#        for b in bpb:
+#            if p[0] <= b[0] and p[1] <= b[1]:
+#                flag = 0
+
+
+#    elif rev and up: #CASE 2
+#        for b in bpb:
+#            if p[0] >= b[0] and p[1] <= b[1]:
+#                flag = 0
+
+#    elif not rev and not up: #CASE 3
+#        for b in bpb:
+#            if p[0] >= b[0] and p[1] >= b[1]:
+#                flag = 0
+
+
+#    elif rev and not up: #CASE 4
+#        for b in bpb:
+#            if p[0] <= b[0] and p[1] >= b[1]:
+#                flag = 0
+#    return flag
+
+
+#def predict_non_severe(p, bpr, bpb, rev, up):
+    # points in grey area are automatically labelled in blue area
+#    flag = 0
+#    if not rev and up: #CASE 1
+#        for b in bpr:
+#            if p[0] >= b[0] and p[1] >= b[1]:
+#                flag = 1
+
+
+#    elif rev and up: #CASE 2
+#        for b in bpr:
+#            if p[0] <= b[0] and p[1] >= b[1]:
+#                flag = 1
+
+#    elif not rev and not up: #CASE 3
+#        for b in bpr:
+#            if p[0] <= b[0] and p[1] <= b[1]:
+#                flag = 1
+
+#    elif rev and not up: #CASE 4
+#        for b in bpr:
+#            if p[0] >= b[0] and p[1] <= b[1]:
+#                flag = 1
+
+#    return flag
diff --git a/Module/optimal_k_aggregations.py b/Module/optimal_k_aggregations.py
new file mode 100755
index 0000000..fe0c450
--- /dev/null
+++ b/Module/optimal_k_aggregations.py
@@ -0,0 +1,151 @@
+from Module import cost_matrix_uncertainty as cmu
+from Module import monotonic_regression_uncertainty as mru
+from Module import selection_algorithm as sa
+from Module import tools
+
+
+
+import time
+import pandas as pd
+import multiprocessing as mp
+import copy
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+
+def find_k_metamodel(df, ndf, cost, k, nbcpus, strat):
+    l = list()
+    mini = 1
+    for s in strat:
+        p, mve = s(df, ndf, cost, k, nbcpus)
+        if mve<mini:
+            mini = mve
+        l.append((mve, p, s.__name__))
+    potential = [L for L in l if L[0] == mini]
+    potential.sort(key=lambda x:x[2], reverse = True)
+    return potential[0]
+
+
+#Functions that given some classifiers, construct the associated ensemble model and predict the output for a single patient
+
+def prediction_pairs(df, out, pair, funct):
+    p1, p2, key = pair.split('/')
+    key = int(key)
+    rev, up = tools.equiv_key_case(key)
+
+    tr1, tr2 = df[p1].values.tolist(), df[p2].values.tolist()
+    diag = df['target'].values.tolist()
+
+    data = [((tr1[n], tr2[n] ), 1, diag[n]) for n in range(len(diag))]
+    out_p = (out[p1], out[p2])
+
+    X, models = mru.compute_recursion(data, (rev, up, key))
+    reg_err, bpr, bpb, r_p, b_p = models[key]
+    pred = funct(out_p, bpr, bpb, rev, up) #
+    return pred
+
+
+def create_and_predict_metamodel(df_, out, pairs, nbcpus, funct):
+    #Return the majority vote prediction (pred_metamodel) and the probability of the being severe (nb of severe/total nb)
+    pool = mp.Pool(nbcpus)
+    df = copy.deepcopy(df_)
+
+    vals = [(df, out, p, funct) for p in pairs]
+
+    preds = pool.starmap(prediction_pairs, vals, max(1,len(vals)//nbcpus)) #Get all the predictions made by the different pairs for a single patient
+
+    del df
+    return tools.pred_metamodel(preds), tools.proba_metamodel(preds)
+
+
+
+##Big loop to compute the average error for ensemble contaning k classifiers
+
+
+def k_missclassification(df, cls, nbcpus, funct, strat, min_k, max_k, log):
+    print('k misclassification : {}\n'.format(funct))
+
+    k_mis = {k : list() for k in range(3, max_k)} #Store for each value of k, whereas patients were misclassified or not with an ensemble of k classifiers
+
+    #pairs_err = {cl : list() for cl in cls} #For each classifiers we are going to store the average misclassification error (computed with LOOCV) made with each patients
+
+
+    for j in range(len(df)):
+        t1 = time.time()
+        f = open(log, 'a')
+        f.write('Patient {} \n'.format(j))
+        f.close()
+        out = df.iloc[j, :]
+        df_2 = df.drop([j])
+        df_2.reset_index(drop=True, inplace=True)
+
+        ndf_err = cmu.error_matrix(df_2, cls, nbcpus,funct)
+
+
+        f = open(log, 'a')
+        f.write('cost matrix computed \n')
+        f.close()
+
+
+        cost = cmu.cost_classifiers(ndf_err)
+
+
+        if min_k == 1:
+        #k = 1 : As a first pair, we take one with the lowest error
+            temp = min(cost.values())
+            res = [key for key in cost.keys() if cost[key] == temp] #Many classifiers can have the lowest error
+            pair = [res[0]] #We take one arbitrary
+
+
+            pred, proba = create_and_predict_metamodel(df_2, out, pair, nbcpus, funct)
+            if proba != -1:
+                k_mis[1].append(abs(out['target']-pred))
+            else:  #case of proba = -1 means that all the classifiers in the metamodel predicted the point as uncertain
+                print('case of unknown point in oka')
+
+            min_k +=1
+
+        #k > 1: ensemble classifiers
+        for k in range(min_k, max_k):
+            t0 = time.time()
+            mve, pairs, algo = find_k_metamodel(df_2, ndf_err, cost, k, nbcpus, strat)
+            pred, proba = create_and_predict_metamodel(df_2, out, pairs, nbcpus, funct)
+
+            if proba != -1:
+                k_mis[k].append(abs(out['target']-pred))
+            else:  #case of proba = -1 means that all the classifiers in the metamodel predicted the point as uncertain
+                print('case of unknown point in oka')
+
+            f = open(log, 'a')
+            f.write('Creation metamodel for k = {} in {}s \n'.format(k, time.time()-t0))
+            f.close()
+
+        f = open(log, 'a')
+        f.write('End patient in {}s \n'.format(time.time() - t1))
+        f.close()
+
+
+    k_error = {k : np.mean(k_mis[k]) for k in range(min_k, max_k)}
+
+    return k_error
+
+
+
+def optimal_k(k_error):
+    mini = min(k_error.values())
+    keys = [k for k in k_error.keys() if k_error[k] == mini]
+    return min(keys), mini
+
+
+def print_k_error(k_error, file):
+    x, y = k_error.keys(), k_error.values()
+    plt.figure()
+    plt.plot(x,y)
+    plt.title('Average error for ensembles of classifiers')
+    plt.xlabel('Nb of classifiers')
+    plt.ylabel('Average error')
+    if file:
+        plt.savefig(file)
+    else:
+        plt.show()
diff --git a/Module/preselection.py b/Module/preselection.py
new file mode 100644
index 0000000..caffa4d
--- /dev/null
+++ b/Module/preselection.py
@@ -0,0 +1,59 @@
+from Module import cost_matrix_uncertainty as cmu
+from Module import optimal_k_aggregations as oka
+from Module import monotonic_regression_uncertainty as mru
+from Module import tools
+from Module import selection_algorithm as sa
+
+import multiprocessing as mp
+
+import pandas as pd
+import matplotlib.pyplot as plt
+import os
+
+
+def all_configurations(df):
+    transcripts = list(df.columns)
+    transcripts.remove('target')
+
+    configurations = list()
+    for i in range(len(transcripts)):
+        for j in range(i+1, len(transcripts)):
+            for key in range(1,5):
+                configurations.append('/'.join([transcripts[i], transcripts[j], str(key)]))
+    return configurations
+
+
+def single_score(cl, df):
+    p1, p2, key = cl.split('/')
+    key = int(key)
+    rev, up = tools.equiv_key_case(key)
+
+    diag = df['target'].to_list()
+    tr1, tr2 = df[p1].to_list(), df[p2].to_list()
+    data = [((tr1[i], tr2[i]), 1, diag[i]) for i in range(len(diag))]
+
+
+    X, m = mru.compute_recursion(data, (rev, up, key))
+    reg_err, bpr, bpb, r_p, b_p = m[key]
+
+    return (cl, reg_err)
+
+def regression_error_score(df, cls, nbcpus):
+    pool = mp.Pool(nbcpus)
+
+    vals = [(cl, df) for cl in cls]
+    res = pool.starmap(single_score, vals, max(1, len(vals)//nbcpus))
+
+    dico = {r[0] : r[1] for r in res}
+    s = pd.Series(dico)
+    s.name = 'regression error'
+    return s
+
+def regression_error_matrix(df, nbcpus):
+    config = all_configurations(df)
+    reg = regression_error_score(df, config, nbcpus)
+    return reg
+
+
+def preselection_reg_err(reg_err_mat, threshold):
+    return reg_err_mat[reg_err_mat<threshold]
diff --git a/Module/selection_algorithm.py b/Module/selection_algorithm.py
new file mode 100755
index 0000000..8471605
--- /dev/null
+++ b/Module/selection_algorithm.py
@@ -0,0 +1,161 @@
+from Module import cost_matrix_uncertainty as cmu
+from Module import measures as ms
+
+import copy
+import multiprocessing as mp
+import time
+
+
+#Filter the matrix: eliminate redundant transcripts
+
+def filter_pairs_greedy(pairs):
+    used_trans = list()
+    delete_col = list()
+    for i in range(len(pairs)):
+        p1, p2, key = pairs[i].split("/")
+        if p1 in used_trans or p2 in used_trans:
+            delete_col.append(pairs[i])
+        else:
+            used_trans.append(p1)
+            used_trans.append(p2)
+    for x in delete_col:
+        pairs.remove(x)
+    return pairs
+
+
+
+def filter_pairs_adapt(pairs, cl):
+    delete_pairs = list()
+    idx = pairs.index(cl)
+    for i in range(idx, len(pairs)):
+        p1, p2, key = pairs[i].split("/")
+        if p1 in cl or p2 in cl:
+            delete_pairs.append(pairs[i])
+    for x in delete_pairs:
+        pairs.remove(x)
+    return pairs
+
+
+#########N-best
+
+
+
+def NB(df, ndf_, cost, k, nbcpus, mes = ms.MVE):
+
+    ndf = copy.deepcopy(ndf_)
+    ndf.drop(['uncertain', 'error'], inplace=True)
+
+    pairs = sorted(cost.items(), key=lambda t: t[1])
+    pairs = [pairs[i][0] for i in range(len(pairs))]
+    pairs = filter_pairs_greedy(pairs)
+    pairs = pairs[0:k]
+
+    set = [ndf[p].values.tolist() for p in pairs]
+
+    return pairs, ms.MVE(set)
+
+
+##### Forward search
+
+
+def test_candidate_FS(cand_pairs, cls, ndf, mes, i):
+    cp = cand_pairs[i]
+
+    candidate_set_pairs = [ndf[cl].values.tolist() for cl in cls]
+    candidate_set_pairs.append(ndf[cp].values.tolist())
+    cp_ms = mes(candidate_set_pairs)
+
+    return (i, cp, cp_ms)
+
+
+
+def FS(df, ndf_, cost, k, nbcpus, mes = ms.MVE, jump = 30):
+    pool = mp.Pool(nbcpus)
+
+    ndf = copy.deepcopy(ndf_)
+    ndf.drop(['uncertain', 'error'], inplace=True)
+
+    temp = min(cost.values())
+    res = [key for key in cost.keys() if cost[key] == temp] #Many classifiers can have the lowest error
+    cl = res[0] #We take one arbitrary
+    cls = [cl] #We start with an ensemble of k=1 classifiers
+
+    pairs = sorted(cost.items(), key=lambda t: t[1])
+    pairs = [pairs[i][0] for i in range(len(pairs))]
+
+    ind = 1
+    tot_ind = ind
+
+    while len(cls) < k: #We add classifiers until we reach k
+        #Condition if we reach the end of the list of classifiers, we start again from the begining by eliminating the already used cls
+        if tot_ind + jump > len(pairs):
+            pairs = [pairs[p] for p in range(len(pairs)) if pairs[p] not in cls]
+            ind = 1
+            tot_ind = ind
+
+        cand_pairs = pairs[ind:ind+jump]
+
+        vals = [(cand_pairs, cls, ndf, mes, i) for i in range(len(cand_pairs))]
+
+        res = pool.starmap(test_candidate_FS, vals, max(1,len(vals)//nbcpus))
+        res.sort(key=lambda x:x[2])
+
+        i, cp, cp_ms = res[0]
+        best_cp_ms = cp_ms
+        best_cand = cp
+        ind = tot_ind + i +1
+        tot_ind = ind
+
+
+        cls.append(best_cand)
+
+        pairs = filter_pairs_adapt(pairs, best_cand)
+
+
+    set = [ndf[p].values.tolist() for p in cls]
+
+    return cls, ms.MVE(set)
+
+
+#### Backward Search
+
+
+def test_candidate_BS(cand_pairs, cls, ndf, mes, i):
+    cp = cand_pairs[i]
+
+    candidate_set_pairs = [ndf[cl].values.tolist() for cl in cls if cl != cp]
+
+    cp_ms = mes(candidate_set_pairs)
+
+    return (i, cp, cp_ms)
+
+
+def BS(df, ndf_, cost, k, nbcpus, mes = ms.F2, end = 30):
+
+    pool = mp.Pool(nbcpus)
+    ndf = copy.deepcopy(ndf_)
+    ndf.drop(['uncertain', 'error'], inplace=True)
+
+
+    pairs = sorted(cost.items(), key=lambda t: t[1])
+    pairs = [pairs[i][0] for i in range(len(pairs))]
+    pairs = filter_pairs_greedy(pairs)
+    cls = pairs[:end]
+
+    while len(cls) > k:
+
+        cand_pairs = cls.copy()
+
+        vals = [(cand_pairs, cls, ndf, mes, i) for i in range(len(cand_pairs))]
+
+        res = pool.starmap(test_candidate_BS, vals, max(1,len(vals)//nbcpus))
+
+        res.sort(key=lambda x:x[2])
+
+        i, cp, cp_ms = res[0]
+        cls.remove(cp)
+
+
+    set = [ndf[p].values.tolist() for p in cls]
+
+    return cls, ms.MVE(set)
diff --git a/Module/show_results_4cases.py b/Module/show_results_4cases.py
new file mode 100755
index 0000000..f83fc86
--- /dev/null
+++ b/Module/show_results_4cases.py
@@ -0,0 +1,498 @@
+from Module import monotonic_regression_uncertainty as mru
+from Module import tools
+
+import multiprocessing as mp
+
+import matplotlib.pyplot as plt
+from matplotlib import patches
+import colorsys
+import random
+
+from math import log
+
+
+
+
+def cr_models(p, df):
+    p1, p2, key = p.split('/')
+    key = int(key)
+    rev, up = tools.equiv_key_case(key)
+    tr1 = df[p1].values.tolist()
+    tr2 = df[p2].values.tolist()
+    diag = df['target'].values.tolist()
+    data = [((tr1[n], tr2[n] ), 1, diag[n]) for n in range(len(diag))]
+
+    X, models = mru.compute_recursion(data, (rev, up, key))
+
+    return p1, p2, models, data
+
+
+def print_model(data, models, p1, p2, df1, pathname = None, cm=None):
+    #print the monotonic space with the 3 areas
+
+    if '.1.1' in p1:
+        p1 = p1[:-2]
+    if '.1.1' in p2:
+        p2 = p2[:-2]
+
+    try:
+        g1 = df1[df1['Probeset_ID'] == p1]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g1 = p1
+    try:
+        g2 = df1[df1['Probeset_ID'] == p2]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g2 = p2
+
+    for key in models.keys():
+        key = int(key)
+        #print('Key', key)
+        plt.figure(figsize=(3,3))
+        ax = plt.axes()
+        ax.set_facecolor("lightgray")
+
+        x_r = list()
+        y_r = list()
+        x_b = list()
+        y_b = list()
+        for i in range(len(data)):
+            xy, w, lab = data[i]
+            x, y = xy
+            if lab == 0: #blue
+                x_r.append(x)
+                y_r.append(y)
+            else: #red
+                x_b.append(x)
+                y_b.append(y)
+
+        reg_err, bpr, bpb, r_p, b_p = models[key]
+
+
+        min_x = min(min(x_r), min(x_b))-0.05
+        min_y = min(min(y_r), min(y_b))-0.05
+        max_x = max(max(x_r), max(x_b))+0.05
+        max_y = max(max(y_r), max(y_b))+0.05
+
+        for bp in bpb:
+            x, y = bp
+            if key == 1:
+                ax.add_artist(patches.Rectangle((min_x, min_y), abs(x-min_x), abs(y-min_y), facecolor = 'lightskyblue', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((x, min_y), max_x+abs(x), abs(y-min_y), facecolor = 'lightskyblue', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((x, y), max_x+abs(x), max_y+abs(y), facecolor = 'lightskyblue', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((min_x, y ), abs(x-min_x), max_y+abs(y), facecolor = 'lightskyblue', zorder = 1))
+
+
+        for bp in bpr:
+            x, y = bp
+
+
+            if key == 1:
+                ax.add_artist(patches.Rectangle((x, y), max_x+abs(x), max_y+abs(y), facecolor ='lightcoral', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((min_x, y ), abs(x-min_x), max_y+abs(y), facecolor = 'lightcoral', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((min_x, min_y), abs(x-min_x), abs(y-min_y), facecolor = 'lightcoral', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((x, min_y), max_x+abs(x), abs(y-min_y), facecolor = 'lightcoral', zorder = 1))
+
+
+        #plt.scatter(x_r, y_r, c = 'blue', marker='.', zorder = 2)
+        #plt.scatter(x_b, y_b, c = 'red', marker='.', zorder = 2)
+
+        random.shuffle(data)
+
+        for d in data:
+            if d[2] == 0:
+                plt.scatter(d[0][0], d[0][1], c = 'blue', marker='.', zorder = 2)
+            elif d[2] == 1:
+                plt.scatter(d[0][0], d[0][1], c = 'red', marker='.', zorder = 2)
+        plt.xlabel(g1)
+        plt.ylabel(g2)
+
+        if cm is not None:
+            pair = '/'.join([p1, p2, str(key)])
+            error = cm.at['error', pair]
+            plt.title('LOOCV Error {}'.format(error))
+
+        if pathname is not None:
+            plt.savefig(pathname + g1 + '_' + g2  + '.png')
+
+            f = open(pathname + 'gene.txt', 'a')
+            f.write('{} : {}\n'.format(g1, p1))
+            f.write('{} : {}\n'.format(g2, p2))
+            f.close()
+        else:
+            plt.show()
+
+
+
+def print_model_log(data, models, p1, p2, df1, pathname = None):
+    #print the monotonic space with the 3 areas
+
+    data = [((log(d[0][0]), log([0][1])), d[1], d[2]) for d in data]
+
+    if '.1.1' in p1:
+        p1 = p1[:-2]
+    if '.1.1' in p2:
+        p2 = p2[:-2]
+
+    try:
+        g1 = df1[df1['Probeset_ID'] == p1]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g1 = p1
+    try:
+        g2 = df1[df1['Probeset_ID'] == p2]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g2 = p2
+
+    for key in models.keys():
+        key = int(key)
+        #print('Key', key)
+        plt.figure(figsize=(3,3))
+        ax = plt.axes()
+        ax.set_facecolor("lightgray")
+
+        x_r = list()
+        y_r = list()
+        x_b = list()
+        y_b = list()
+        for i in range(len(data)):
+            xy, w, lab = data[i]
+            x, y = xy
+            if lab == 0: #blue
+                x_r.append(x)
+                y_r.append(y)
+            else: #red
+                x_b.append(x)
+                y_b.append(y)
+
+        reg_err, bpr, bpb, r_p, b_p = models[key]
+
+        for bp in bpb:
+            x, y = bp
+            if key == 1:
+                ax.add_artist(patches.Rectangle((0.0, 0.0), x, y, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((x, 0), 1000, y, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((x, y), 1000, 1000, facecolor = 'lightskyblue', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((0, y ), x, 1000, facecolor = 'lightskyblue', zorder = 1))
+
+
+        for bp in bpr:
+            x, y = bp
+
+
+            if key == 1:
+                ax.add_artist(patches.Rectangle((x, y), 1000, 1000, facecolor ='lightcoral', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((0, y ), x, 1000, facecolor = 'lightcoral', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((0.0, 0.0), x, y, facecolor = 'lightcoral', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((x, 0), 1000, y, facecolor = 'lightcoral', zorder = 1))
+
+
+        #plt.scatter(x_r, y_r, c = 'blue', marker='.', zorder = 2)
+        #plt.scatter(x_b, y_b, c = 'red', marker='.', zorder = 2)
+
+        random.shuffle(data)
+
+        for d in data:
+            if d[2] == 0:
+                plt.scatter(d[0][0], d[0][1], c = 'blue', marker='.', zorder = 2)
+            elif d[2] == 1:
+                plt.scatter(d[0][0], d[0][1], c = 'red', marker='.', zorder = 2)
+        plt.xlabel(g1)
+        plt.ylabel(g2)
+
+        if pathname is not None:
+            plt.savefig(pathname + g1 + '_' + g2  + '.png')
+
+            f = open(pathname + 'gene.txt', 'a')
+            f.write('{} : {}\n'.format(g1, p1))
+            f.write('{} : {}\n'.format(g2, p2))
+            f.close()
+        else:
+            plt.show()
+
+
+
+def print_model_out(data, out, models, p1, p2, df1, pathname = None):
+    #print the monotonic space with the 3 areas
+
+    if '.1.1' in p1:
+        p1 = p1[:-2]
+    if '.1.1' in p2:
+        p2 = p2[:-2]
+
+    try:
+        g1 = df1[df1['Probeset_ID'] == p1]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g1 = p1
+    try:
+        g2 = df1[df1['Probeset_ID'] == p2]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g2 = p2
+
+    for key in models.keys():
+        key = int(key)
+        print('Key', key)
+        plt.figure(figsize=(5,5))
+        ax = plt.axes()
+        ax.set_facecolor("lightgray")
+
+        x_r = list()
+        y_r = list()
+        x_b = list()
+        y_b = list()
+        for i in range(len(data)):
+            xy, w, lab = data[i]
+            x, y = xy
+            if lab == 0: #blue
+                x_r.append(x)
+                y_r.append(y)
+            else: #red
+                x_b.append(x)
+                y_b.append(y)
+
+        reg_err, bpr, bpb, r_p, b_p = models[key]
+
+        for bp in bpb:
+            x, y = bp
+            if key == 1:
+                ax.add_artist(patches.Rectangle((0.0, 0.0), x, y, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((x, 0), 1000, y, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((x, y), 1000, 1000, facecolor = 'lightskyblue', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((0, y ), x, 1000, facecolor = 'lightskyblue', zorder = 1))
+
+
+        for bp in bpr:
+            x, y = bp
+
+
+            if key == 1:
+                ax.add_artist(patches.Rectangle((x, y), 1000, 1000, facecolor ='lightcoral', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((0, y ), x, 1000, facecolor = 'lightcoral', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((0.0, 0.0), x, y, facecolor = 'lightcoral', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((x, 0), 1000, y, facecolor = 'lightcoral', zorder = 1))
+
+
+        #plt.scatter(x_r, y_r, c = 'blue', zorder = 2)
+        #plt.scatter(x_b, y_b, c = 'red', zorder = 2)
+
+        random.shuffle(data)
+
+        for d in data:
+            if d[2] == 0:
+                plt.scatter(d[0][0], d[0][1], c = 'blue', marker='.', zorder = 2)
+            elif d[2] == 1:
+                plt.scatter(d[0][0], d[0][1], c = 'red', marker='.', zorder = 2)
+        plt.scatter(out[0], out[1], c = 'g', zorder = 2)
+        plt.xlabel(g1)
+        plt.ylabel(g2)
+
+        if pathname is not None:
+            plt.savefig(pathname + g1 + '_' + g2  + '.png')
+
+            f = open(pathname + 'gene.txt', 'a')
+            f.write('{} : {}\n'.format(g1, p1))
+            f.write('{} : {}\n'.format(g2, p2))
+            f.close()
+        else:
+            plt.show()
+
+
+
+def rank_h(x, D, rev):
+    h = [d[0] for d in D]
+    h = sorted(h, reverse=rev)
+    r = h.index(x)
+
+    if rev:
+        return len(D) - r + 1
+    else:
+        return r+1
+
+def rank_v(x, D, up):
+    h = [d[1] for d in D]
+    h.sort()
+    r = h.index(x)
+    #if up:
+    return r+1
+    #else:
+    #    return len(D) - r + 1
+
+
+
+
+
+
+
+def print_model_RS(data, models, p1, p2, df1, pathname = None, cm=None):
+    D_hat = [x[0] for x in data]
+
+
+    plt.figure(figsize=(3,3))
+    ax = plt.axes()
+    ax.set_facecolor("lightgray")
+    plt.title('Ranking Space')
+    plt.xlabel(p1)
+    plt.ylabel(p2)
+
+    for key in models.keys():
+        key = int(key)
+
+        rev, up = tools.equiv_key_case(key)
+
+        reg, bpr, bpb, rps, bps = models[key]
+
+
+
+        for bp in bpb:
+            x, y = bp
+            rxd = rank_h(x, D_hat, rev)
+            ryd = rank_v(y, D_hat, up)
+
+            if key == 1:
+                ax.add_artist(patches.Rectangle((0.0, 0.0), rxd, ryd, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((rxd, 0), 1000, ryd, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((rxd, ryd), 1000, 1000, facecolor = 'lightskyblue', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((0, ryd ), rxd, 1000, facecolor = 'lightskyblue', zorder = 1))
+
+
+        for bp in bpr:
+            x, y = bp
+            rxd = rank_h(x, D_hat, rev)
+            ryd = rank_v(y, D_hat, up)
+
+            if key == 1:
+                ax.add_artist(patches.Rectangle((rxd, ryd), 1000, 1000, facecolor ='lightcoral', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((0, ryd ), rxd, 1000, facecolor = 'lightcoral', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((0.0, 0.0), rxd, ryd, facecolor = 'lightcoral', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((rxd, 0), 1000, ryd, facecolor = 'lightcoral', zorder = 1))
+
+        random.shuffle(data)
+        for d in data:
+            rxd = rank_h(d[0][0], D_hat, rev)
+            ryd = rank_v(d[0][1], D_hat, up)
+            if d[2] == 1:
+                plt.scatter(rxd, ryd, c='red', marker='.', zorder=2)
+            elif d[2] == 0:
+                plt.scatter(rxd, ryd, c='blue', marker='.', zorder=2)
+
+        plt.show()
+
+def print_severe(data, models, p1, p2, df1, pathname = None):
+    #print the monotonic space with the 3 areas
+
+    if '.1.1' in p1:
+        p1 = p1[:-2]
+    if '.1.1' in p2:
+        p2 = p2[:-2]
+
+    try:
+        g1 = df1[df1['Probeset_ID'] == p1]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g1 = p1
+    try:
+        g2 = df1[df1['Probeset_ID'] == p2]['Gene.Symbol'].values.tolist()[0]
+    except:
+        g2 = p2
+
+    for key in models.keys():
+        key = int(key)
+        print('Key', key)
+        plt.figure(figsize=(5,5))
+        ax = plt.axes()
+        ax.set_facecolor("lightcoral")
+
+        x_r = list()
+        y_r = list()
+        x_b = list()
+        y_b = list()
+        for i in range(len(data)):
+            xy, w, lab = data[i]
+            x, y = xy
+            if lab == 0: #blue
+                x_r.append(x)
+                y_r.append(y)
+            else: #red
+                x_b.append(x)
+                y_b.append(y)
+
+        reg_err, bpr, bpb, r_p, b_p = models[key]
+
+        for bp in bpb:
+            x, y = bp
+            if key == 1:
+                ax.add_artist(patches.Rectangle((0.0, 0.0), x, y, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 2:
+                ax.add_artist(patches.Rectangle((x, 0), 1000, y, facecolor = 'lightskyblue', zorder = 1))
+            elif key == 3:
+                ax.add_artist(patches.Rectangle((x, y), 1000, 1000, facecolor = 'lightskyblue', zorder = 1))
+            else:
+                ax.add_artist(patches.Rectangle((0, y ), x, 1000, facecolor = 'lightskyblue', zorder = 1))
+
+
+        #for bp in bpr:
+        #    x, y = bp
+
+
+        #    if key == 1:
+        #        ax.add_artist(patches.Rectangle((x, y), 1000, 1000, facecolor ='lightcoral', zorder = 1))
+        #    elif key == 2:
+        #        ax.add_artist(patches.Rectangle((0, y ), x, 1000, facecolor = 'lightcoral', zorder = 1))
+        #    elif key == 3:
+        #        ax.add_artist(patches.Rectangle((0.0, 0.0), x, y, facecolor = 'lightcoral', zorder = 1))
+        #    else:
+        #        ax.add_artist(patches.Rectangle((x, 0), 1000, y, facecolor = 'lightcoral', zorder = 1))
+
+
+        random.shuffle(data)
+
+        for d in data:
+            if d[2] == 0:
+                plt.scatter(d[0][0], d[0][1], c = 'blue', marker='.', zorder = 2)
+            elif d[2] == 1:
+                plt.scatter(d[0][0], d[0][1], c = 'red', marker='.', zorder = 2)
+        plt.xlabel(g1)
+        plt.ylabel(g2)
+
+        if pathname is not None:
+            plt.savefig(pathname + g1 + '_' + g2  + '.png')
+
+            f = open(pathname + 'gene.txt', 'a')
+            f.write('{} : {}\n'.format(g1, p1))
+            f.write('{} : {}\n'.format(g2, p2))
+            f.close()
+        else:
+            plt.show()
+
+
+
+def show_results(df, probs_df, pairs, nbcpus, pathname, cm):
+    pool = mp.Pool(nbcpus)
+    vals = [(p, df) for p in pairs]
+
+    res = pool.starmap(cr_models, vals, max(1,len(vals)//nbcpus) )
+
+    for r in res:
+        p1, p2, models, data = r
+        print_model(data, models, p1, p2, probs_df, pathname, cm)
diff --git a/Module/stages.py b/Module/stages.py
new file mode 100755
index 0000000..24ab16b
--- /dev/null
+++ b/Module/stages.py
@@ -0,0 +1,82 @@
+from Module import cost_matrix_uncertainty as cmu
+from Module import optimal_k_aggregations as oka
+from Module import monotonic_regression_uncertainty as mru
+from Module import tools
+from Module import selection_algorithm as sa
+from Module import preselection as psl
+
+import pandas as pd
+import matplotlib.pyplot as plt
+import os
+
+
+from sklearn.metrics import roc_auc_score, confusion_matrix, matthews_corrcoef
+
+
+def stage0(df, nbcpus, threshold):
+    reg = psl.regression_error_matrix(df, nbcpus)
+    if threshold is not None:
+        reg = psl.preselection_reg_err(reg, threshold)
+    return reg
+
+
+
+
+def stage_1(df, cls, min_k, max_k, nbcpus, strat, funct, log):
+    k_error = oka.k_missclassification(df, cls, nbcpus, funct, strat, min_k, max_k, log)
+    k_opt, err_k = oka.optimal_k(k_error)
+    return k_opt, k_error
+
+
+
+def stage_2(df, cls, k_opt, auc_file, conf_mat_file, nbcpus, funct, strat, logs):
+    errors, y_true, y_pred, y_proba = list(), list(), list(), list()
+
+    for i in range(len(df)):
+        out = df.iloc[i, :]
+        df_2 = df.drop([i])
+        df_2.reset_index(drop=True, inplace=True)
+        f = open(logs, 'a')
+        f.write('Patient {} \n'.format(i))
+        f.close()
+
+        ndf_err = cmu.error_matrix(df_2, cls, nbcpus,funct)
+        cost = cmu.cost_classifiers(ndf_err)
+
+        f = open(logs, 'a')
+        f.write('Matrix computed \n')
+        f.close()
+
+        mve, pairs, algo = oka.find_k_metamodel(df_2, ndf_err, cost, k_opt, nbcpus, strat)
+        pred, proba = oka.create_and_predict_metamodel(df_2, out, pairs, nbcpus, funct)
+
+        f = open(logs, 'a')
+        f.write('Pred={}, Proba={} \n'.format(pred, proba))
+        f.close()
+
+        errors.append(abs(out['target']-pred))
+        y_proba.append(proba)
+        y_true.append(out['target'])
+        y_pred.append(pred)
+
+
+    acc = errors.count(0)/len(errors)
+    auc = tools.auc_score(y_proba, y_true, auc_file)
+    auc2 = roc_auc_score(y_true, y_proba)
+    CI = tools.confidence_interval(auc, y_true)
+    conf_mat = confusion_matrix(y_true, y_pred)
+    mcc = matthews_corrcoef(y_true, y_pred)
+
+    f = open(logs, 'a')
+    f.write('acc={}, auc={}, CI = {}, aucsk = {}, confusion_matrix = {}, mcc = {} \n'.format(acc, auc, CI, auc2, conf_mat, mcc))
+    f.close()
+
+    labels, probas, uncertain_pts = tools.unclassified_points(y_true, y_proba)
+    return acc, auc, CI, conf_mat
+
+def stage_3(df, cls, k_opt, nbcpus, funct, strat):
+    ndf_err = cmu.error_matrix(df, cls, nbcpus,funct)
+    ndf_err.to_csv('cm_st3.csv')
+    cost = cmu.cost_classifiers(ndf_err)
+    mve, pairs, algo = oka.find_k_metamodel(df, ndf_err, cost, k_opt, nbcpus, strat)
+    return pairs, mve
diff --git a/Module/tools.py b/Module/tools.py
new file mode 100755
index 0000000..273b80d
--- /dev/null
+++ b/Module/tools.py
@@ -0,0 +1,186 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from copy import deepcopy
+import seaborn as sn
+
+
+def equiv_key_case(i):
+    equiv = {1 : (False, True), 2: (True, True), 3:(False, False), 4:(True, False)}
+    return equiv[i]
+
+
+
+
+def equiv_case_key(rev):
+    equiv = {(False, True):1, (True, True):2, (False, False):3, (True, False):4}
+    return equiv[rev]
+
+
+#PREDICTION FROM A METAMODEL
+def pred_metamodel(preds):
+    #preds is an array with all the predicted labels from the classifiers belongig to the meta model
+    a = preds.count(1)
+    b = preds.count(0)
+    c = preds.count(-1)
+    assert a + b +c == len(preds), "Problem in the error predictions for a patient"
+    if c == len(preds): #In the case where all the predictions are equal to -1, we predict the patient as 1
+        return 1
+    if a < b:# If less 1 than 0, predict as 0
+        return 0
+    else: #If more or same nb of 1 as nb of 0, predict as 1
+        return 1
+
+
+# Prediction probability of being severe
+def proba_metamodel(preds):
+    #preds is an array with all the predicted labels from the classifiers belongig to the meta model
+    a = preds.count(1)
+    b = preds.count(0)
+    c = preds.count(-1)
+    assert a + b +c == len(preds), "Problem in the probabilities for a patient"
+    if a+b != 0:
+        return a/(a+b)
+    else:
+        return -1
+
+
+def get_index_positions(list_of_elems, element):
+    index_pos_list = []
+    index_pos = 0
+    while True:
+        try:
+            index_pos = list_of_elems.index(element, index_pos)
+            # Add the index position in list
+            index_pos_list.append(index_pos)
+            index_pos += 1
+        except ValueError as e:
+            break
+    return index_pos_list
+
+def unclassified_points(labels, probas):
+    #print('probas {}'.format(probas))
+    un_pts = get_index_positions(probas, -1)
+    #print('unclassified_points {}'.format(un_pts))
+    new_labels = deepcopy(labels)
+    new_probas = deepcopy(probas)
+    for i in range(len(probas)):
+        if i not in un_pts:
+            new_labels.append(labels[i])
+            new_probas.append(probas[i])
+    return new_labels, new_probas, un_pts
+
+
+
+
+
+####AUC score
+def perf_metrics(y_actual, y_hat,threshold):
+    tp = 0
+    fp = 0
+    tn = 0
+    fn = 0
+
+    for i in range(len(y_hat)):
+        if(y_hat[i] >= threshold):
+            if(y_actual[i] == 1):
+                tp += 1
+            else:
+                fp += 1
+        elif(y_hat[i] < threshold):
+            if(y_actual[i] == 0):
+                tn += 1
+            else:
+                fn += 1
+    tpr = tp/(tp+fn)
+    fpr = fp/(tn+fp)
+
+    return [fpr,tpr]
+
+
+
+
+def auc_score(probas, labels, auc_file=None):
+    thresholds = np.arange(0.0, 1.01, 0.001)
+
+    roc_points = []
+    for threshold in thresholds:
+        rates = perf_metrics(labels, probas, threshold)
+        roc_points.append(rates)
+
+    fpr_array = []
+    tpr_array = []
+    for i in range(len(roc_points)-1):
+        point1 = roc_points[i];
+        point2 = roc_points[i+1]
+        tpr_array.append([point1[0], point2[0]])
+        fpr_array.append([point1[1], point2[1]])
+
+    auc3 = sum(np.trapz(tpr_array,fpr_array))+1
+    assert auc3 <= 1 and auc3 >= 0, "AUC score is not in [0,1]"
+    print('Area under curve={}'.format(auc3))
+
+    CI = confidence_interval(auc3, labels)
+
+    if auc_file is not None:
+        plt.plot(tpr_array, fpr_array, linestyle='--', color='darkorange', lw = 2, label='ROC curve', clip_on=False)
+        plt.plot([0, 1], [0, 1], color='navy', linestyle='--')
+        plt.xlim([0.0, 1.0])
+        plt.ylim([0.0, 1.0])
+        plt.xlabel('False Positive Rate')
+        plt.ylabel('True Positive Rate')
+        plt.title('AUC={}, CI=[{};{}] '.format(round(auc3,3), CI[0], CI[1]))
+        plt.legend(loc="lower right")
+        plt.savefig(auc_file)
+    return auc3
+
+
+def confidence_interval(auc, labels):
+    labels = list(labels)
+    N1 = labels.count(1)
+    N2 = labels.count(0)
+    Q1 = auc/(2-auc)
+    Q2 = (2*(auc**2))/(1+auc)
+    SE = np.sqrt((auc*(1-auc)+(N1-1)*(Q1-auc**2)+(N2-1)*(Q2-auc**2))/(N1*N2))
+    low_b = auc - 1.96*SE
+    high_b = auc + 1.96*SE
+    if low_b < 0:
+        low_b = 0
+    if high_b > 1:
+        high_b = 1
+    return [round(low_b, 3), round(high_b,3)]
+
+
+
+def confusion_matrix(y_real, y_pred, conf_mat_file):
+    tp = 0
+    fp = 0
+    tn = 0
+    fn = 0
+
+    for i in range(len(y_real)):
+        if y_real[i] == 1:
+            if y_pred[i] == 1:
+                tp += 1
+            else:
+                fn += 1
+        elif y_real[i] == 0:
+            if y_pred[i] == 0:
+                tn += 1
+            else:
+                fp += 1
+
+    conf_mat = [[tn, fn], [fp, tp]]
+
+    if conf_mat_file is not None:
+        df_cm = pd.DataFrame(array, range(6), range(6))
+        plt.figure(figsize=(5,5))
+        sn.set(font_scale=1.4)
+        sn.heatmap(df_cm, annot=True, annot_kws={"size": 16})
+        plt.xlabel('True labels')
+        plt.ylabel('Output labels')
+        plt.title('Confusion matrix')
+        plt.legend()
+        plt.savefig(conf_mat_file)
+
+
+    return conf_mat
-- 
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