.. _2020profilerst:

================
Tech - profiling
================


.. only:: html

    **Links:** :download:`notebook <2020_profile.ipynb>`, :downloadlink:`html <2020_profile2html.html>`, :download:`python <2020_profile.py>`, :downloadlink:`slides <2020_profile.slides.html>`, :githublink:`GitHub|_doc/notebooks/td1a_home/2020_profile.ipynb|*`


Le `profilage de
code <https://fr.wikipedia.org/wiki/Profilage_de_code>`__ ou *profiling*
en anglais signifie qu’on mesure le temps passé dans chaque partie d’un
programme pour en découvrir les parties les plus coûteuses et les
améliorer. On souhaite toujours accélérer un programme trop lent, le
profiling permet de savoir sur quelles parties se concentrer.

.. code:: ipython3

    from jyquickhelper import add_notebook_menu
    add_notebook_menu()






.. contents::
    :local:





Autre lecture : `Exemple de
profiling <http://www.xavierdupre.fr/app/ensae_teaching_cs/helpsphinx/notebooks/profiling_example.html#profilingexamplerst>`__.

Enoncé
------

On applique le profiling au code suivant pour découvrir laquelle de ces
fonctions est la plus lente. Vous pouvez changer ce code pour un de ceux
que vous avez écrits précédemment.

.. code:: ipython3

    def _gini_sort(Y):
        return list(sorted(Y))
    
    
    def _gini_init(Y):
        return [[1, y] for y in Y]
    
    
    def _gini_cumsum(couples):
        for i in range(1, len(couples)):
            couples[i][0] += couples[i-1][0]
            couples[i][1] += couples[i-1][1]
        for i in range(0, len(couples)):
            couples[i][0] /= couples[-1][0]
            couples[i][1] /= couples[-1][1]
        return couples
    
        
    def _gini_final(couples):
        g = couples[0][0] * couples[0][1]
        n = len(couples)
    
        for i in range(1, n):
            dx = couples[i][0] - couples[i-1][0]
            y = couples[i-1][1] + couples[i][1]
            g += dx * y
    
        return 1. - g / 2
    
    
    def gini(Y):
        Y = _gini_sort(Y)
        couples = _gini_init(Y)
        couples = _gini_cumsum(couples)
        return _gini_final(couples)
    
    
    gini([1, 1, 1, 1, 1]), gini([0, 0, 0, 0, 100000])




.. parsed-literal::
    (0.5, 0.9)



Pour ces deux exemples caractéristiques, on retrouve bien des valeurs
attendues.

Exercice 1 : profiler le code précédent
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Le langage python dispose d’un module qui mesure le temps passé dans
chaque fonction
`profile <https://docs.python.org/3/library/profile.html>`__. Il faut
l’utiliser.


Exercice 2 : changer la fonction \_gini_final si possible en plus rapide
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Exercice 3 : vous améliorez la fonction \_gini_final, profilez pour savoir de combien ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Exercice 4 : utiliser d’autres modules de profiling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Si c’est possible, comme
`pyinstrument <https://github.com/joerick/pyinstrument>`__ ou
`py-spy <https://github.com/benfred/py-spy>`__. Il y a deux façons de
faire du profiling :


-  **déterministe :** on mesure le temps passé dans chaque fonction, à
   chaque appel, ce type de profilage n’est souvent possible que pour
   des langages interprétés,
-  **statistique :** tous les centièmes de secondes, on regarde quelle
   ligne de quelle fonction le programme exécute. On compte ensuite
   combien de fois la ligne exécutée était dans une fonction pour
   déterminer le temps passé dans chaque fonction.

Les deux modules proposés sont statistiques, le premier est
déterministe. Bien évidemment, le fait de mesurer le temps passé prend
du temps également, plus on s’arrête souvant, plus l’exécution est
ralentie.


Exercice 5 : la fonction \_gini_cumsum contient deux boucles. Quelle est la plus rapide ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Réponses
--------

Exercice 1 : profiler le code précédent
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

On reprend un des exemples de cette page `The Python
Profilers <https://docs.python.org/3/library/profile.html#module-cProfile>`__.

.. code:: ipython3

    import cProfile, pstats, io
    from pstats import SortKey
    pr = cProfile.Profile()
    pr.enable()
    
    gini([1, 1, 1, 1, 1])
    
    pr.disable()
    s = io.StringIO()
    sortby = SortKey.CUMULATIVE
    ps = pstats.Stats(pr, stream=s).sort_stats(sortby)
    ps.print_stats()
    print(s.getvalue())


.. parsed-literal::
             55 function calls in 0.000 seconds
       Ordered by: cumulative time
       ncalls  tottime  percall  cumtime  percall filename:lineno(function)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\interactiveshell.py:3400(run_code)
            2    0.000    0.000    0.000    0.000 {built-in method builtins.exec}
            1    0.000    0.000    0.000    0.000 <ipython-input-3-405f7b24fbdc>:8(<module>)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\codeop.py:142(__call__)
            2    0.000    0.000    0.000    0.000 {built-in method builtins.compile}
            1    0.000    0.000    0.000    0.000 <ipython-input-3-405f7b24fbdc>:6(<module>)
            1    0.000    0.000    0.000    0.000 <ipython-input-2-6d8b3d4c048c>:31(gini)
            1    0.000    0.000    0.000    0.000 <ipython-input-2-6d8b3d4c048c>:9(_gini_cumsum)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:242(helper)
            4    0.000    0.000    0.000    0.000 {built-in method builtins.next}
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:86(__init__)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:112(__enter__)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:121(__exit__)
            1    0.000    0.000    0.000    0.000 <ipython-input-2-6d8b3d4c048c>:19(_gini_final)
            4    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\compilerop.py:166(extra_flags)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\hooks.py:103(__call__)
            1    0.000    0.000    0.000    0.000 <ipython-input-2-6d8b3d4c048c>:1(_gini_sort)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\traitlets\traitlets.py:564(__get__)
            1    0.000    0.000    0.000    0.000 <ipython-input-2-6d8b3d4c048c>:5(_gini_init)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\interactiveshell.py:3338(compare)
            4    0.000    0.000    0.000    0.000 {built-in method builtins.getattr}
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\traitlets\traitlets.py:533(get)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\utils\ipstruct.py:125(__getattr__)
            1    0.000    0.000    0.000    0.000 {built-in method builtins.sorted}
            1    0.000    0.000    0.000    0.000 <ipython-input-2-6d8b3d4c048c>:6(<listcomp>)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\interactiveshell.py:1278(user_global_ns)
            1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
            3    0.000    0.000    0.000    0.000 {built-in method builtins.len}
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\hooks.py:168(pre_run_code_hook)
    
    
    


Tous les temps sont nuls. Le code est trop rapide. Il faut soit exécuter
le code plusieurs fois, soit prendre un tableau plus grand.

.. code:: ipython3

    import cProfile, pstats, io
    from pstats import SortKey
    pr = cProfile.Profile()
    pr.enable()
    
    for i in range(1000):
        gini([1 for i in range(1000)])
    
    pr.disable()
    s = io.StringIO()
    sortby = SortKey.CUMULATIVE
    ps = pstats.Stats(pr, stream=s).sort_stats(sortby)
    ps.print_stats()
    print(s.getvalue())


.. parsed-literal::
             11045 function calls in 1.352 seconds
       Ordered by: cumulative time
       ncalls  tottime  percall  cumtime  percall filename:lineno(function)
            2    0.000    0.000    1.352    0.676 c:\python395_x64\lib\site-packages\IPython\core\interactiveshell.py:3400(run_code)
            2    0.000    0.000    1.352    0.676 {built-in method builtins.exec}
            1    0.040    0.040    1.352    1.352 <ipython-input-4-b1075e275d99>:6(<module>)
         1000    0.003    0.000    1.266    0.001 <ipython-input-2-6d8b3d4c048c>:31(gini)
         1000    0.706    0.001    0.707    0.001 <ipython-input-2-6d8b3d4c048c>:9(_gini_cumsum)
         1000    0.357    0.000    0.357    0.000 <ipython-input-2-6d8b3d4c048c>:19(_gini_final)
         1000    0.001    0.000    0.185    0.000 <ipython-input-2-6d8b3d4c048c>:5(_gini_init)
         1000    0.184    0.000    0.184    0.000 <ipython-input-2-6d8b3d4c048c>:6(<listcomp>)
         1000    0.047    0.000    0.047    0.000 <ipython-input-4-b1075e275d99>:7(<listcomp>)
         1000    0.005    0.000    0.013    0.000 <ipython-input-2-6d8b3d4c048c>:1(_gini_sort)
         1000    0.008    0.000    0.008    0.000 {built-in method builtins.sorted}
         3000    0.001    0.000    0.001    0.000 {built-in method builtins.len}
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\codeop.py:142(__call__)
            2    0.000    0.000    0.000    0.000 {built-in method builtins.compile}
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:242(helper)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:86(__init__)
            4    0.000    0.000    0.000    0.000 {built-in method builtins.next}
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:121(__exit__)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\contextlib.py:112(__enter__)
            4    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\compilerop.py:166(extra_flags)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\hooks.py:103(__call__)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\traitlets\traitlets.py:564(__get__)
            1    0.000    0.000    0.000    0.000 <ipython-input-4-b1075e275d99>:9(<module>)
            4    0.000    0.000    0.000    0.000 {built-in method builtins.getattr}
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\interactiveshell.py:3338(compare)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\utils\ipstruct.py:125(__getattr__)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\traitlets\traitlets.py:533(get)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\interactiveshell.py:1278(user_global_ns)
            2    0.000    0.000    0.000    0.000 c:\python395_x64\lib\site-packages\IPython\core\hooks.py:168(pre_run_code_hook)
            1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
    
    
    


C’est un peu illisible. On filtre.

.. code:: ipython3

    def filtre(text):
        lines = text.split("\n")
        return "\n".join(filter(lambda t: "gini" in t, lines))
    
    print(filtre(s.getvalue()))


.. parsed-literal::
         1000    0.003    0.000    1.266    0.001 <ipython-input-2-6d8b3d4c048c>:31(gini)
         1000    0.706    0.001    0.707    0.001 <ipython-input-2-6d8b3d4c048c>:9(_gini_cumsum)
         1000    0.357    0.000    0.357    0.000 <ipython-input-2-6d8b3d4c048c>:19(_gini_final)
         1000    0.001    0.000    0.185    0.000 <ipython-input-2-6d8b3d4c048c>:5(_gini_init)
         1000    0.005    0.000    0.013    0.000 <ipython-input-2-6d8b3d4c048c>:1(_gini_sort)


Exercice 2 : changer la fonction \_gini_final si possible en plus rapide
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code:: ipython3

    def _gini_final_faster(couples):
        g = couples[0][0] * couples[0][1]
        n = len(couples)
    
        # par construction, tous les dx sont identiques, cela fait des calculs en moins
        # le code suivant est plus rapide mais peut encore être optimisé
        dx = couples[0][0]
        sy = couples[0][0]
        for i in range(1, n):        
            sy = couples[i-1][1] + couples[i][1]
            g += dx * sy
    
        return 1. - g / 2
    
    
    def gini_faster(Y):
        Y = _gini_sort(Y)
        couples = _gini_init(Y)
        couples = _gini_cumsum(couples)
        return _gini_final_faster(couples)
    
    
    (gini_faster([0, 0, 0, 0, 5000]), gini_faster([1, 1, 1, 1, 1]),
     gini([0, 0, 0, 0, 5000]), gini([1, 1, 1, 1, 1]))




.. parsed-literal::
    (0.9, 0.5, 0.9, 0.5)



Exercice 3 : vous améliorez la fonction \_gini_final, profilez pour savoir de combien ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

On appelle les deux fonctions pour pouvoir comparer.

.. code:: ipython3

    import cProfile, pstats, io
    from pstats import SortKey
    pr = cProfile.Profile()
    pr.enable()
    
    for i in range(1000):
        gini([1 for i in range(1000)])
        gini_faster([1 for i in range(1000)])
    
    pr.disable()
    s = io.StringIO()
    sortby = SortKey.CUMULATIVE
    ps = pstats.Stats(pr, stream=s).sort_stats(sortby)
    ps.print_stats()
    print(filtre(s.getvalue()))


.. parsed-literal::
         2000    1.085    0.001    1.086    0.001 <ipython-input-2-6d8b3d4c048c>:9(_gini_cumsum)
         1000    0.003    0.000    0.999    0.001 <ipython-input-2-6d8b3d4c048c>:31(gini)
         1000    0.003    0.000    0.882    0.001 <ipython-input-6-a3c3cc48873e>:16(gini_faster)
         2000    0.002    0.000    0.315    0.000 <ipython-input-2-6d8b3d4c048c>:5(_gini_init)
         1000    0.275    0.000    0.275    0.000 <ipython-input-2-6d8b3d4c048c>:19(_gini_final)
         1000    0.174    0.000    0.175    0.000 <ipython-input-6-a3c3cc48873e>:1(_gini_final_faster)
         2000    0.009    0.000    0.024    0.000 <ipython-input-2-6d8b3d4c048c>:1(_gini_sort)


La seconde version est plus rapide.

Exercice 4 : utiliser d’autres modules de profiling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`pyinstrument <https://github.com/joerick/pyinstrument>`__ n’est pas
peut-être pas installé. Il fonctionne de la même façon.

.. code:: ipython3

    from pyinstrument import Profiler
    from IPython.display import HTML
    
    profiler = Profiler()
    profiler.start()
    
    for i in range(1000):
        gini([1 for i in range(1000)])
        gini_faster([1 for i in range(1000)])
    
    profiler.stop()
    
    HTML(profiler.output_html())






.. raw:: html

    <!DOCTYPE html>
                <html>
                <head>
                    <meta charset="utf-8">
                </head>
                <body>
                    <div id="app"></div>
                    <script>
                        window.profileSession = {"start_time": 1631962284.086769,"duration": 1.969397,"sample_count": 1653,"program": "c:\\python395_x64\\lib\\site-packages\\ipykernel_launcher.py -f C:\\Users\\xavie\\AppData\\Roaming\\jupyter\\runtime\\kernel-1eed0371-646e-46ff-bc54-443160574996.json","cpu_time": 1.968750,"root_frame": {"function": "run_ast_nodes","file_path_short": "IPython\\core\\interactiveshell.py","file_path": "c:\\python395_x64\\lib\\site-packages\\IPython\\core\\interactiveshell.py","line_no": 3249,"time": 1.982246,"is_application_code": false,"children": [{"function": "run_code","file_path_short": "IPython\\core\\interactiveshell.py","file_path": "c:\\python395_x64\\lib\\site-packages\\IPython\\core\\interactiveshell.py","line_no": 3400,"time": 1.981233,"is_application_code": false,"children": [{"function": "<module>","file_path_short": "<ipython-input-8-0eda72fe16d7>","file_path": "<ipython-input-8-0eda72fe16d7>","line_no": 7,"time": 1.981233,"is_application_code": true,"children": [{"function": "gini","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 31,"time": 0.967679,"is_application_code": true,"children": [{"function": "_gini_cumsum","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 9,"time": 0.528089,"is_application_code": true,"children": []},{"function": "_gini_final","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 19,"time": 0.253923,"is_application_code": true,"children": []},{"function": "_gini_init","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 5,"time": 0.178671,"is_application_code": true,"children": [{"function": "<listcomp>","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 6,"time": 0.178671,"is_application_code": true,"children": []}]}]},{"function": "gini_faster","file_path_short": "<ipython-input-6-a3c3cc48873e>","file_path": "<ipython-input-6-a3c3cc48873e>","line_no": 16,"time": 0.878102,"is_application_code": true,"children": [{"function": "_gini_cumsum","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 9,"time": 0.553157,"is_application_code": true,"children": []},{"function": "_gini_init","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 5,"time": 0.167072,"is_application_code": true,"children": [{"function": "<listcomp>","file_path_short": "<ipython-input-2-6d8b3d4c048c>","file_path": "<ipython-input-2-6d8b3d4c048c>","line_no": 6,"time": 0.166071,"is_application_code": true,"children": []}]},{"function": "_gini_final_faster","file_path_short": "<ipython-input-6-a3c3cc48873e>","file_path": "<ipython-input-6-a3c3cc48873e>","line_no": 1,"time": 0.148854,"is_application_code": true,"children": []}]},{"function": "<listcomp>","file_path_short": "<ipython-input-8-0eda72fe16d7>","file_path": "<ipython-input-8-0eda72fe16d7>","line_no": 9,"time": 0.082162,"is_application_code": true,"children": []},{"function": "[self]","file_path_short": "","file_path": "<ipython-input-8-0eda72fe16d7>","line_no": 7,"time": 0.040959,"is_application_code": false,"children": []}]}]}]}}

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C’est plus facile à lire.

Exercice 5 : la fonction \_gini_cumsum contient deux boucles. Quelle est la plus rapide ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Pour ce faire, on découpe la fonction en deux.

.. code:: ipython3

    def _gini_cumsum2a(couples):
        for i in range(1, len(couples)):
            couples[i][0] += couples[i-1][0]
            couples[i][1] += couples[i-1][1]
        return couples
    
    
    def _gini_cumsum2b(couples):
        for i in range(0, len(couples)):
            couples[i][0] /= couples[-1][0]
            couples[i][1] /= couples[-1][1]
        return couples
    
    
    def _gini_cumsum2(couples):
        _gini_cumsum2a(couples)
        _gini_cumsum2b(couples)
        return couples
    
    
    def gini2(Y):
        Y = _gini_sort(Y)
        couples = _gini_init(Y)
        couples = _gini_cumsum2(couples)
        return _gini_final(couples)
    
    
    gini2([1, 1, 1, 1, 1]), gini2([0, 0, 0, 0, 100000])




.. parsed-literal::
    (0.5, 0.9)



.. code:: ipython3

    import cProfile, pstats, io
    from pstats import SortKey
    pr = cProfile.Profile()
    pr.enable()
    
    for i in range(1000):
        gini2([1 for i in range(1000)])
        gini_faster([1 for i in range(1000)])
    
    pr.disable()
    s = io.StringIO()
    sortby = SortKey.CUMULATIVE
    ps = pstats.Stats(pr, stream=s).sort_stats(sortby)
    ps.print_stats()
    print(filtre(s.getvalue()))


.. parsed-literal::
         1000    0.003    0.000    1.144    0.001 <ipython-input-9-2fd5204eb0f7>:21(gini2)
         1000    0.003    0.000    1.038    0.001 <ipython-input-6-a3c3cc48873e>:16(gini_faster)
         1000    0.001    0.000    0.641    0.001 <ipython-input-9-2fd5204eb0f7>:15(_gini_cumsum2)
         1000    0.637    0.001    0.638    0.001 <ipython-input-2-6d8b3d4c048c>:9(_gini_cumsum)
         2000    0.002    0.000    0.341    0.000 <ipython-input-2-6d8b3d4c048c>:5(_gini_init)
         1000    0.332    0.000    0.332    0.000 <ipython-input-2-6d8b3d4c048c>:19(_gini_final)
         1000    0.326    0.000    0.326    0.000 <ipython-input-9-2fd5204eb0f7>:1(_gini_cumsum2a)
         1000    0.314    0.000    0.314    0.000 <ipython-input-9-2fd5204eb0f7>:8(_gini_cumsum2b)
         1000    0.200    0.000    0.200    0.000 <ipython-input-6-a3c3cc48873e>:1(_gini_final_faster)
         2000    0.009    0.000    0.024    0.000 <ipython-input-2-6d8b3d4c048c>:1(_gini_sort)


Elles sont aussi rapides l’une que l’autre. On peut néanmoins en
accélérer une puisqu’on divise tous les éléments d’un tableau par une
même valeur. On peut la stocker dans une variable plutôt que d’aller la
chercher à chaque fois dans le tableau.

.. code:: ipython3

    def _gini_cumsum3b(couples):
        total0 = couples[-1][0]
        total1 = couples[-1][1]
        for i in range(0, len(couples)):
            couples[i][0] /= total0
            couples[i][1] /= total1
        return couples
    
    
    def _gini_cumsum3(couples):
        _gini_cumsum2a(couples)
        _gini_cumsum3b(couples)
        return couples
    
    
    def gini3(Y):
        Y = _gini_sort(Y)
        couples = _gini_init(Y)
        couples = _gini_cumsum3(couples)
        return _gini_final(couples)
    
    
    gini2([1, 1, 1, 1, 1]), gini2([0, 0, 0, 0, 100000])




.. parsed-literal::
    (0.5, 0.9)



.. code:: ipython3

    import cProfile, pstats, io
    from pstats import SortKey
    pr = cProfile.Profile()
    pr.enable()
    
    for i in range(1000):
        gini2([1 for i in range(1000)])
        gini3([1 for i in range(1000)])
    
    pr.disable()
    s = io.StringIO()
    sortby = SortKey.CUMULATIVE
    ps = pstats.Stats(pr, stream=s).sort_stats(sortby)
    ps.print_stats()
    print(filtre(s.getvalue()))


.. parsed-literal::
         1000    0.002    0.000    1.002    0.001 <ipython-input-9-2fd5204eb0f7>:21(gini2)
         1000    0.002    0.000    0.935    0.001 <ipython-input-11-492a2c865fd9>:16(gini3)
         2000    0.568    0.000    0.568    0.000 <ipython-input-2-6d8b3d4c048c>:19(_gini_final)
         2000    0.567    0.000    0.567    0.000 <ipython-input-9-2fd5204eb0f7>:1(_gini_cumsum2a)
         1000    0.001    0.000    0.561    0.001 <ipython-input-9-2fd5204eb0f7>:15(_gini_cumsum2)
         1000    0.001    0.000    0.496    0.000 <ipython-input-11-492a2c865fd9>:10(_gini_cumsum3)
         2000    0.002    0.000    0.285    0.000 <ipython-input-2-6d8b3d4c048c>:5(_gini_init)
         1000    0.275    0.000    0.275    0.000 <ipython-input-9-2fd5204eb0f7>:8(_gini_cumsum2b)
         1000    0.213    0.000    0.213    0.000 <ipython-input-11-492a2c865fd9>:1(_gini_cumsum3b)
         2000    0.008    0.000    0.022    0.000 <ipython-input-2-6d8b3d4c048c>:1(_gini_sort)


C’est mieux même si l’amélioration ne paraît pas nécessairement
significative par rapport au temps total, le résultat l’est si on
regarde le temps fonction par fonction.