I've done some profiling of my code and it seems that my main slowdowns are
coming from multiplication and addition of free algebra elements. Is there
anyway I can make it go faster? I would like to do some more complicated
computations but currently my code has been running for half an hour and
still hasn't produced any results. I plan on parallelizing it in a few
places, but was wondering if I could do anything about this as well. I
tried compiling phi_ext_sk down to c with cython and added type hints in a
few places but it didn't help.
Specifically, here is what I get.
307 """
308 phi_b_ext returns
phi_b_ext(a_ij)
309 """
310
311 32 37956 1186.1 0.2 e =
self.phi_ext_sk(self.w[0], a)
312
313 416 431 1.0 0.0 for i in
self.w[1:]:
314 384 229 0.6 0.0 new_e = 0
315 10152 11593 1.1 0.1 for k, v in
e._FreeAlgebraElement__monomial_coefficients.iteritems():
316 9768 14406 1.5 0.1 new_g = 1
317 58800 158459 2.7 0.7 for g, p
in k:
318 49032 6465240 131.9 30.0 g1 =
self.phi_ext_sk(i, g)
319 49032 7820633 159.5 36.3 new_g
= new_g*g1
320 49032 47335 1.0 0.2 if p
!= 1:
321
print "POW!!!!"
322 9768 2818386 288.5 13.1 new_g =
v*new_g
323 9768 4146233 424.5 19.3 new_e =
new_e + new_g
324 384 6524 17.0 0.0 e = new_e
325
326 32 16 0.5 0.0 return e
Function: phi_ext_sk at line 253
[4/681]
Total time: 6.70627 s
Line # Hits Time Per Hit % Time Line Contents
==============================================================
253 @profile
254 def phi_ext_sk(self,
k, a):
255 """
256 phi_ext_sk returns
phi^ext_sigma_z(a_xy)
257 """
258
259 49064 3622876 73.8 54.0 i, j =
self.gdicta[a]
260
261 49064 46425 0.9 0.7 if k > 0:
262
263 49064 34162 0.7 0.5 if i == k + 1:
264 12004 8191 0.7 0.1 if j != k
and j != k + 1:
265 8460 8997 1.1 0.1 return
self.astar[k, j]
266 else:
267 3544 3904 1.1 0.1 return
self.astar[k, k+1]
268 37060 23978 0.6 0.4 elif j == k +
1:
269 12004 8038 0.7 0.1 if i != k
and i != k + 1:
270 8460 9035 1.1 0.1 return
self.astar[i, k]
271 else:
272 3544 3927 1.1 0.1 return
self.astar[k+1, k]
273 25056 16273 0.6 0.2 elif i == k
and j != k and j != k + 1:
274 7016 685746 97.7 10.2 return
-1*self.astar[k+1, j]-self.astar[k+1, k]* \
275 7016 760791 108.4 11.3
self.astar[k, j]
276 18040 12076 0.7 0.2 elif j == k
and i != k and i != k + 1:
277 7016 681617 97.2 10.2 return
-1*self.astar[i, k+1]-self.astar[i, k]* \
278 7016 759046 108.2 11.3
self.astar[k, k+1]
279 11024 9371 0.9 0.1 elif i != k
and i != k+1 and j != k and j != k+1:
280 11024 11820 1.1 0.2 return
self.astar[i, j]
https://github.com/syamajala/KnotContactHomology/blob/master/braids.py
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