Pure Sage Riemann Matrix Timings

test.profile

Thu Jan  7 14:06:54 2016    test.profile

         7206599 function calls (7193937 primitive calls) in 67.121 seconds

   Ordered by: internal time
   List reduced from 1682 to 20 due to restriction <20>

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
   107328   29.405    0.000   31.848    0.000 analytic_continuation_smale.py:44(newton)
   321984   19.540    0.000   21.290    0.000 analytic_continuation_smale.py:79(smale_beta)
   107328    7.152    0.000    7.854    0.000 analytic_continuation_smale.py:103(smale_gamma)
583634/583326    4.116    0.000    4.946    0.000 complex_field.py:353(_element_constructor_)
    34816    1.049    0.000    1.151    0.000 differentials.py:287(eval)
    36224    0.964    0.000   62.267    0.002 analytic_continuation_smale.py:196(analytically_continue)
  2651628    0.651    0.000    0.651    0.000 {isinstance}
72375/72371    0.230    0.000    0.230    0.000 {numpy.core.multiarray.array}
    34816    0.207    0.000   61.988    0.002 function_base.py:1869(_vectorize_call)
   360884    0.179    0.000    0.179    0.000 {range}
    34816    0.156    0.000   61.510    0.002 analytic_continuation_smale.py:280(omega_gamma)
   107328    0.141    0.000   15.335    0.000 analytic_continuation_smale.py:135(smale_alpha)
   583634    0.131    0.000    0.131    0.000 complex_field.py:43(late_import)
   583326    0.120    0.000    0.120    0.000 complex_field.py:283(_real_field)
    26848    0.118    0.000    0.118    0.000 riemann_surface_path.py:619(get_x)
     2864    0.096    0.000   62.156    0.022 quadrature.py:111(vfunc)
    34904    0.096    0.000    0.123    0.000 riemann_surface_path.py:251(_nearest_checkpoint_index)
8952/8918    0.086    0.000    0.098    0.000 complex_interval_field.py:364(__call__)
6326/6085    0.082    0.000    0.211    0.000 multi_polynomial_ring.py:184(__call__)
    34904    0.080    0.000   60.166    0.002 riemann_surface_path.py:371(get_y)

This is from a pure Sage (no Cython) version of Abelfunctions. The numerics is really really slow compared to the older Cython version. For example, on my machine the above runs in 67s whereas before a Riemann matrix could be calculated in 4s.

Eventual Cythonization is preferred but at the time of this writing compiling Abelfunction Cython code from Sage doesn't really work.

Now here's something interesting: I use Numpy data types everywhere because reasons. Well, changing all instances of

fast_callable(foo, vars=[x,y])

to

fast_callable(foo, vars=[x,y], domain=numpy.complex)

resulted in the following awesome speedup:

Thu Jan  7 14:54:03 2016    test.profile

         3126477 function calls (3113809 primitive calls) in 12.873 seconds

   Ordered by: internal time
   List reduced from 1682 to 20 due to restriction <20>

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
   107328    3.676    0.000    3.676    0.000 analytic_continuation_smale.py:46(newton)
   107328    2.612    0.000    2.664    0.000 analytic_continuation_smale.py:107(smale_gamma)
   321984    2.005    0.000    2.005    0.000 analytic_continuation_smale.py:83(smale_beta)
    36224    0.718    0.000    9.308    0.000 analytic_continuation_smale.py:200(analytically_continue)
72375/72371    0.192    0.000    0.192    0.000 {numpy.core.multiarray.array}
    34816    0.169    0.000   10.072    0.000 function_base.py:1869(_vectorize_call)
    34816    0.151    0.000    0.151    0.000 differentials.py:289(eval)
   360884    0.140    0.000    0.140    0.000 {range}
    34816    0.127    0.000    9.675    0.000 analytic_continuation_smale.py:284(omega_gamma)
    26848    0.113    0.000    0.113    0.000 riemann_surface_path.py:619(get_x)
   107328    0.109    0.000    3.496    0.000 analytic_continuation_smale.py:139(smale_alpha)
    34904    0.092    0.000    0.114    0.000 riemann_surface_path.py:251(_nearest_checkpoint_index)
   319766    0.087    0.000    0.087    0.000 {isinstance}
8952/8918    0.081    0.000    0.092    0.000 complex_interval_field.py:364(__call__)
6326/6085    0.078    0.000    0.209    0.000 multi_polynomial_ring.py:184(__call__)
     2864    0.075    0.000   10.208    0.004 quadrature.py:111(vfunc)
    34904    0.074    0.000    9.240    0.000 riemann_surface_path.py:371(get_y)
     9300    0.068    0.000    0.193    0.000 polynomial_ring.py:318(_element_constructor_)
    12608    0.064    0.000    0.064    0.000 riemann_surface_path.py:623(get_dxdt)
    26473    0.064    0.000    0.412    0.000 qqbar.py:3151(__init__)