Abelfunctions Performance Profile

gistfile1.txt

Performance profile on the following Python script:

  from sage.all_cmdline import *   # import sage library
  _sage_const_3 = Integer(3); _sage_const_2 = Integer(2); _sage_const_7 = Integer(7)

  from abelfunctions import *
  R = QQ['x, y']; (x, y,) = R._first_ngens(2)
  X = RiemannSurface(y**_sage_const_3  + _sage_const_2 *x**_sage_const_3 *y - x**_sage_const_7 )

  X.riemann_matrix()   
  
Run using:

  $ python -m cProfile -o output.profile ./riemann_matrix_perf_test.sage.py
  $ python -m pstats ./output.profile
  % sort cumulative
  % stats 30
  % sort time
  % stats 30

========== Cumulative Time ==========
Tue Aug 23 09:59:26 2022    ./output.profile

         209829119 function calls (209215439 primitive calls) in 170.681 seconds

   Ordered by: cumulative time
   List reduced from 10338 to 30 due to restriction <30>

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
   2445/1    0.017    0.000  170.687  170.687 {built-in method builtins.exec}
        1    0.001    0.001  170.684  170.684 riemann_matrix_perf_test.sage.py:4(<module>)
        1    0.001    0.001  166.831  166.831 riemann_surface.py:412(riemann_matrix)
        1    0.000    0.000  166.375  166.375 riemann_surface.py:367(period_matrix)
        1    0.000    0.000  165.341  165.341 riemann_surface.py:78(differentials)
        1    0.000    0.000  165.341  165.341 riemann_surface.py:260(holomorphic_differentials)
        1    0.000    0.000  165.341  165.341 differentials.py:225(differentials)
        1    0.003    0.003  165.335  165.335 differentials.py:148(differentials_numerators)
        7    0.032    0.005  164.374   23.482 differentials.py:55(mnuk_conditions)
123334/1120    1.277    0.000  162.012    0.145 unique_factorization_domains.py:128(_gcd_univariate_polynomial)
122214/4336    5.546    0.000  160.404    0.037 {method 'gcd' of 'sage.rings.polynomial.multi_polynomial.MPolynomial' objects}
493693/492517    3.114    0.000  105.133    0.000 rings.py:929(__getitem__)
504838/503338    4.037    0.000  101.327    0.000 polynomial_ring_constructor.py:51(PolynomialRing)
      125    0.048    0.000   89.680    0.717 multi_polynomial_element.py:100(__call__)
   504853    9.234    0.000   86.499    0.000 {built-in method sage.structure.category_object.normalize_names}
  3141745    9.521    0.000   77.308    0.000 multi_polynomial_element.py:427(_repr_)
  3141745   16.859    0.000   61.487    0.000 {method 'poly_repr' of 'sage.rings.polynomial.polydict.PolyDict' objects}
    92108    1.037    0.000   27.379    0.000 multi_polynomial_element.py:1585(_floordiv_)
  3141067    2.711    0.000   26.793    0.000 qqbar.py:3833(_neg_)
  3746425    1.797    0.000   25.459    0.000 qqbar.py:4722(__init__)
  3866050    7.548    0.000   24.742    0.000 qqbar.py:3592(__init__)
      477    0.019    0.000   21.416    0.045 multi_polynomial_element.py:160(<listcomp>)
       36    0.004    0.000   14.537    0.404 fraction_field.py:323(wrapper)
641591/641073    5.123    0.000   14.507    0.000 multi_polynomial_ring.py:176(__call__)
     2129    0.105    0.000   13.869    0.007 qqbar_decorators.py:37(wrapper)
  3748256    4.822    0.000   12.462    0.000 qqbar.py:6414(_interval_fast)
 13622259    7.739    0.000   12.278    0.000 qqbar.py:4746(_richcmp_)
      477    0.009    0.000   11.731    0.025 {sage.misc.misc_c.prod}
  3342466    4.182    0.000    8.029    0.000 term_order.py:997(sortkey_degrevlex)
   242379    1.240    0.000    6.815    0.000 polynomial_ring_constructor.py:754(_multi_variate)
   
   
   
========== Time ==========
Tue Aug 23 09:59:26 2022    ./output.profile

         209829119 function calls (209215439 primitive calls) in 170.681 seconds

   Ordered by: internal time
   List reduced from 10338 to 30 due to restriction <30>

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
  3141745   16.859    0.000   61.487    0.000 {method 'poly_repr' of 'sage.rings.polynomial.polydict.PolyDict' objects}
  3141745    9.521    0.000   77.308    0.000 multi_polynomial_element.py:427(_repr_)
   504853    9.234    0.000   86.499    0.000 {built-in method sage.structure.category_object.normalize_names}
 13622259    7.739    0.000   12.278    0.000 qqbar.py:4746(_richcmp_)
  3866050    7.548    0.000   24.742    0.000 qqbar.py:3592(__init__)
 44196401    6.505    0.000    6.507    0.000 {built-in method builtins.isinstance}
  3984860    6.408    0.000    6.408    0.000 sets_cat.py:990(_element_constructor_from_element_class)
122214/4336    5.546    0.000  160.404    0.037 {method 'gcd' of 'sage.rings.polynomial.multi_polynomial.MPolynomial' objects}
641591/641073    5.123    0.000   14.507    0.000 multi_polynomial_ring.py:176(__call__)
  3748256    4.822    0.000   12.462    0.000 qqbar.py:6414(_interval_fast)
  3342466    4.182    0.000    8.029    0.000 term_order.py:997(sortkey_degrevlex)
504838/503338    4.037    0.000  101.327    0.000 polynomial_ring_constructor.py:51(PolynomialRing)
1014399/1014398    3.114    0.000    4.985    0.000 multi_polynomial_element.py:383(__init__)
493693/492517    3.114    0.000  105.133    0.000 rings.py:929(__getitem__)
  3726542    2.827    0.000    3.411    0.000 qqbar.py:6346(__init__)
  3141067    2.711    0.000   26.793    0.000 qqbar.py:3833(_neg_)
 10364054    2.340    0.000    2.340    0.000 {built-in method sage.structure.richcmp.richcmp}
   242905    1.979    0.000    3.982    0.000 term_order.py:570(__init__)
  3141067    1.944    0.000    4.791    0.000 qqbar.py:6485(neg)
3047899/3017486    1.866    0.000    2.284    0.000 multi_polynomial_element.py:1554(__eq__)
  3746425    1.797    0.000   25.459    0.000 qqbar.py:4722(__init__)
  3787420    1.643    0.000    1.643    0.000 {built-in method sage.rings.real_mpfi.RealIntervalField}
  3325365    1.560    0.000    2.778    0.000 term_order.py:885(sortkey)
3433818/3432726    1.299    0.000    1.351    0.000 {built-in method builtins.getattr}
 11426729    1.294    0.000    1.294    0.000 {method 'parent' of 'sage.structure.element.Element' objects}
123334/1120    1.277    0.000  162.012    0.145 unique_factorization_domains.py:128(_gcd_univariate_polynomial)
    51827    1.255    0.000    1.255    0.000 {built-in method select.select}
645587/645574    1.240    0.000    2.465    0.000 {method '_coerce_' of 'sage.structure.parent_old.Parent' objects}
   242379    1.240    0.000    6.815    0.000 polynomial_ring_constructor.py:754(_multi_variate)
   153813    1.177    0.000    1.787    0.000 {method '_mpoly_dict_recursive' of 'sage.rings.polynomial.polynomial_element.Polynomial' objects}

A ton of time is spent doing arithmetic in QQbar and/or polynomial arithmetic. From what I remember a long while ago, the contents of differentials.py was a major performance choke point for the package. To clarify the timings, running

from abelfunctions import *
R.<x,y> = QQ[]
X = RiemannSurface(y**3 + 2*x**3*y - x**7)
X.holomorphic_differentials()

takes about 100s or about 60% of the Riemann matrix calculation time. Granted, this is half of requirements for computing the Riemann matrix but both analytic continuation and subsequent integration along the paths use the remaining 40% of time.