Mv.dual is very slow

Hi,

I was trying this version of galgebra and I found Mv.dual method is very slow for low dimension geometric algebras. I hoped the issue was fixed there (This issue is reproducible with brombo version).

A short snippet :

from galgebra.ga import Ga

GA = Ga('e*1|2|3')
a = GA.mv('a', 'vector')
b = GA.mv('b', 'vector')
c = GA.mv('c', 'vector')

def cross(x, y):
    return (x ^ y).dual()

I only profile : xx = cross(a, cross(b, c))

cProfile reports :

         16807237 function calls (15373382 primitive calls) in 5.316 seconds

   Ordered by: cumulative time

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        2    0.000    0.000    5.316    2.658 /home/sylvain/Documents/pygae/tests/test_dual.py:41(cross)
63300/1661    0.047    0.000    5.200    0.003 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/cache.py:91(wrapper)
        2    0.000    0.000    5.106    2.553 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:1050(dual)
        2    0.000    0.000    5.039    2.520 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:506(__mul__)
5864/5592    0.037    0.000    4.517    0.001 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/operations.py:28(__new__)
1789/1582    0.001    0.000    3.483    0.002 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/decorators.py:84(__sympifyit_wrapper)
1602/1579    0.001    0.000    3.481    0.002 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/decorators.py:122(binary_op_wrapper)
       62    0.003    0.000    3.371    0.054 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/ga.py:103(nc_subs)
       22    0.000    0.000    3.136    0.143 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/ga.py:1137(base_to_blade_rep)
      927    0.001    0.000    3.058    0.003 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/expr.py:117(__add__)
     1045    0.130    0.000    3.054    0.003 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/add.py:78(flatten)
       10    0.000    0.000    2.956    0.296 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:383(blade_rep)
     5787    0.053    0.000    2.443    0.000 {method 'sort' of 'list' objects}
507395/196716    0.766    0.000    2.390    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/basic.py:170(compare)
     1046    0.000    0.000    2.091    0.002 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/add.py:19(_addsort)
       82    0.000    0.000    1.722    0.021 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/function.py:1982(expand)
       33    0.001    0.000    1.721    0.052 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/expr.py:3071(expand)
246474/297    0.329    0.000    1.720    0.006 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/expr.py:3041(_expand_hint)
        6    0.000    0.000    1.464    0.244 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:287(__init__)
        6    0.000    0.000    1.464    0.244 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:124(characterise_Mv)
     8886    0.025    0.000    1.146    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:854(_eval_expand_mul)
4744/4487    0.126    0.000    1.083    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:97(flatten)
   262792    0.194    0.000    1.050    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/symbol.py:250(_hashable_content)
   262792    0.363    0.000    0.633    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/symbol.py:254(assumptions0)
    77094    0.037    0.000    0.621    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/operations.py:68(_new_rawargs)
    84366    0.154    0.000    0.600    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/operations.py:54(_from_args)
        4    0.000    0.000    0.502    0.125 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/ga.py:66(update_and_substitute)
604605/508233    0.121    0.000    0.444    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/assumptions.py:242(getit)
  662/646    0.001    0.000    0.421    0.001 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/expr.py:137(__mul__)
        2    0.000    0.000    0.418    0.209 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/ga.py:1170(mul)
    72928    0.117    0.000    0.382    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/logic.py:112(fuzzy_and)
    71594    0.058    0.000    0.374    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:768(as_coeff_Mul)
  211/133    0.000    0.000    0.365    0.003 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:835(_expandsums)
        8    0.001    0.000    0.360    0.045 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/metric.py:42(linear_expand)
     4737    0.002    0.000    0.354    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:32(_mulsort)
17861/654    0.051    0.000    0.342    0.001 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/assumptions.py:254(_ask)
     5796    0.104    0.000    0.303    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/basic.py:1695(_exec_constructor_postprocessors)
       39    0.001    0.000    0.273    0.007 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:850(<listcomp>)
   648176    0.188    0.000    0.269    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/core.py:73(__cmp__)
  2338243    0.261    0.000    0.261    0.000 {built-in method builtins.isinstance}
  1732062    0.251    0.000    0.251    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/symbol.py:256(<genexpr>)
     8886    0.038    0.000    0.250    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/simplify/radsimp.py:930(fraction)
1018718/360300    0.130    0.000    0.238    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/basic.py:121(__hash__)
       28    0.000    0.000    0.231    0.008 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/ga.py:1145(blade_to_base_rep)
        4    0.000    0.000    0.228    0.057 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:375(base_rep)
   324088    0.081    0.000    0.224    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/core.py:101(__gt__)
     9486    0.073    0.000    0.212    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:380(_gather)
        2    0.000    0.000    0.210    0.105 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:769(__xor__)
   262825    0.205    0.000    0.205    0.000 {built-in method builtins.sorted}
 1052/902    0.001    0.000    0.200    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/mul.py:1160(_eval_is_integer)
   324088    0.073    0.000    0.199    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/core.py:96(__lt__)
   647160    0.105    0.000    0.179    0.000 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/sympy/core/operations.py:64(<genexpr>)
        4    0.000    0.000    0.167    0.042 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/mv.py:922(is_scalar)
        4    0.000    0.000    0.167    0.042 /home/sylvain/Documents/pygae/venv/lib/python3.6/site-packages/galgebra/ga.py:1333(grades)
    15832    0.052    0.000    0.159    0.000 /usr/lib/python3.6/random.py:263(shuffle)

Regards

[ghost]

Are you sure you wanted to calculate it for a completely general metric and not g=[1,1,1] and use GA = Ga(‘e*1|2|3’,g=[1,1,1]).

[utensil]

Sorry for the late reply, I finally get to do a profiling at https://nbviewer.jupyter.org/github/utensil/julia-playground/blob/master/py/profile_mv_dual.ipynb with reproducible steps if you’re also on a Mac.

I think the reason is irrelevant to the normalized I since I also tried set norm=False explicitly and when I tried to set norm=True the error of !!!!Basis normalization only implemented for orthogonal basis!!!! reminded me further that this is not the case.

As shown in the call graph, most of the time is spent on constructing 1k of SymPy objects in base_to_blade_rep. And I need to investigate this further for the root cause.