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)

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__)