

In [1]:

    
%matplotlib inline

Comparisons between different versions of skprocrustes solvers



In [2]:

    
import skprocrustes as skp
import time
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

1. Comparison between old versions of all solvers



In [3]:

    
gkbsolver = skp.GKBSolver(verbose=0)
spgsolver = skp.SPGSolver(verbose=0)
gpisolver = skp.GPISolver(verbose=0)
ebsolver = skp.EBSolver(verbose=0)

Problem 1



In [4]:

    
problem1 = skp.ProcrustesProblem((5000,5000,10,10), problemnumber=1)

Problem 1: GKB



In [5]:

    
t0 = time.time(); results1_gkb = gkbsolver.solve(problem1); t1_gkb = time.time()-t0; print(t1_gkb)









    



1.4648008346557617



In [6]:

    
results1_gkb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.356796838548058e-06
normgrad : 1.8137752238665688e-05
nbiter : 0.09
nfev : 0.10800000000000001
blocksteps : 3

Problem 1: SPG



In [7]:

    
t0 = time.time(); results1_spg = spgsolver.solve(problem1); t1_spg = time.time()-t0; print(t1_spg)









    



2.6056413650512695



In [8]:

    
results1_spg.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 3.650803449675828e-11
normgrad : 0.0002814298063655452
nbiter : 6
nfev : 7.0

Problem 1: GPI



In [9]:

    
t0 = time.time(); results1_gpi = gpisolver.solve(problem1); t1_gpi = time.time()-t0; print(t1_gpi)









    



23.890547275543213



In [10]:

    
results1_gpi.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 2.402815405055444e-07
nbiter : 5
nfev : 6

Problem 1: EB



In [11]:

    
t0 = time.time(); results1_eb = ebsolver.solve(problem1); t1_eb = time.time()-t0; print(t1_eb)









    



720.4642467498779



In [12]:

    
results1_eb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 5.536188817884922e-07
nbiter : 8
nfev : 9

Problem 1: All



In [13]:

    
gkb, spg, gpi, eb = plt.bar([0,1,2,3], [t1_gkb, t1_spg, t1_gpi, t1_eb])
gkb.set_facecolor('r')
spg.set_facecolor('g')
gpi.set_facecolor('b')
eb.set_facecolor('m')
ax = plt.gca()
ax.set_xticks([0,1,2,3])
ax.set_xticklabels(['GKB', 'SPG', 'GPI', 'EB'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 1')









    Out[13]:





Text(0.5,1,'Problem 1')



In [14]:

    
results = pd.DataFrame({ 'GKB' : [t1_gkb], 'SPG' : [t1_spg], 'GPI' : [t1_gpi], 'EB' : [t1_eb]}, index=['problem1'])
results = results.T
results

Problem 2



In [15]:

    
problem2 = skp.ProcrustesProblem((500,500,5,5), problemnumber=2)

Problem 2: GKB



In [16]:

    
t0 = time.time(); results2_gkb = gkbsolver.solve(problem2); t2_gkb = time.time()-t0; print(t2_gkb)









    



141.4156413078308



In [17]:

    
results2_gkb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.0331400013001382e-07
normgrad : 0.0003805496868961612
nbiter : 32471.200000000008
nfev : 55044.400000005306
blocksteps : 97

Problem 2: SPG



In [18]:

    
t0 = time.time(); results2_spg = spgsolver.solve(problem2); t2_spg = time.time()-t0; print(t2_spg)









    



0.6697518825531006



In [19]:

    
results2_spg.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.971594271897369e-08
normgrad : 0.000968998869953896
nbiter : 520
nfev : 876.0

Problem 2: GPI



In [20]:

    
t0 = time.time(); results2_gpi = gpisolver.solve(problem2); t2_gpi = time.time()-t0; print(t2_gpi)









    



2.761721611022949



In [21]:

    
results2_gpi.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 0.0005648845110181697
nbiter : 1241
nfev : 1242

Problem 2: EB



In [22]:

    
t0 = time.time(); results2_eb = ebsolver.solve(problem2); t2_eb = time.time()-t0; print(t2_eb)









    



182.22071957588196



In [23]:

    
results2_eb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 9.978668157791289e-07
nbiter : 2739
nfev : 2740

Problem 2: All



In [24]:

    
gkb, spg, gpi, eb = plt.bar([0,1,2,3], [t2_gkb, t2_spg, t2_gpi, t2_eb])
gkb.set_facecolor('r')
spg.set_facecolor('g')
gpi.set_facecolor('b')
eb.set_facecolor('m')
ax = plt.gca()
ax.set_xticks([0,1,2,3])
ax.set_xticklabels(['GKB', 'SPG', 'GPI', 'EB'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 2')









    Out[24]:





Text(0.5,1,'Problem 2')



In [25]:

    
results['problem2'] = pd.Series([t2_gkb, t2_spg, t2_gpi, t2_eb], index=results.index)
results

Problem 3



In [34]:

    
problem3 = skp.ProcrustesProblem((1000, 1000, 5, 5), problemnumber=3)

Problem 3: GKB



In [35]:

    
t0 = time.time(); results3_gkb = gkbsolver.solve(problem3); t3_gkb = time.time()-t0; print(t3_gkb)









    



98.37644624710083



In [36]:

    
results3_gkb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 2.2042145673987446e-06
normgrad : 0.000948891935006996
nbiter : 4711.175000000001
nfev : 6383.2599999999165
blocksteps : 200

Problem 3: SPG



In [37]:

    
t0 = time.time(); results3_spg = spgsolver.solve(problem3); t3_spg = time.time()-t0; print(t3_spg)









    



0.1624917984008789



In [38]:

    
results3_spg.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 4.243405518052438e-05
normgrad : 0.0007263441639077083
nbiter : 31
nfev : 38.0

Problem 3: GPI



In [39]:

    
t0 = time.time(); results3_gpi = gpisolver.solve(problem3); t3_gpi = time.time()-t0; print(t3_gpi)









    



0.788931131362915



In [40]:

    
results3_gpi.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 5.401435589027177e-05
nbiter : 74
nfev : 75

Problem 3: EB



In [41]:

    
t0 = time.time(); results3_eb = ebsolver.solve(problem3); t3_eb = time.time()-t0; print(t3_eb)









    



99.98649406433105



In [42]:

    
results3_eb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 4.242901381421668e-05
nbiter : 166
nfev : 167

Problem 3: All



In [43]:

    
gkb, spg, gpi, eb = plt.bar([0,1,2,3], [t3_gkb, t3_spg, t3_gpi, t3_eb])
gkb.set_facecolor('r')
spg.set_facecolor('g')
gpi.set_facecolor('b')
eb.set_facecolor('m')
ax = plt.gca()
ax.set_xticks([0,1,2,3])
ax.set_xticklabels(['GKB', 'SPG', 'GPI', 'EB'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 3')









    Out[43]:





Text(0.5,1,'Problem 3')



In [44]:

    
results['problem3'] = pd.Series([t3_gkb, t3_spg, t3_gpi, t3_eb], index=results.index)
results

2. Comparison between blobop and old residual for GKBSolver.



In [45]:

    
gkbsolver_blobop = skp.GKBSolver(verbose=0, bloboptest = True)

Problem 1



In [46]:

    
t0 = time.time(); results1_gkbblobop = gkbsolver_blobop.solve(problem1); t1_blobop = time.time()-t0



In [47]:

    
results1_gkbblobop.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.362771769311597e-06
normgrad : 4.198305440171956e-05
nbiter : 0.07200000000000001
nfev : 0.09000000000000002
blocksteps : 3



In [48]:

    
results1_gkb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.356796838548058e-06
normgrad : 1.8137752238665688e-05
nbiter : 0.09
nfev : 0.10800000000000001
blocksteps : 3



In [49]:

    
gkb, blobop = plt.bar([0,1], [t1_gkb, t1_blobop])
gkb.set_facecolor('r')
blobop.set_facecolor('y')
ax = plt.gca()
ax.set_xticks([0,1])
ax.set_xticklabels(['GKB', 'BLOBOP'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 1')









    Out[49]:





Text(0.5,1,'Problem 1')



In [50]:

    
gkb, spg, gpi, eb, blobop = plt.bar([0,1,2,3,4], [t1_gkb, t1_spg, t1_gpi, t1_eb, t1_blobop])
gkb.set_facecolor('r')
spg.set_facecolor('g')
gpi.set_facecolor('b')
eb.set_facecolor('m')
blobop.set_facecolor('y')
ax = plt.gca()
ax.set_xticks([0,1,2,3,4])
ax.set_xticklabels(['GKB', 'SPG', 'GPI', 'EB', 'BLOBOP'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 1')









    Out[50]:





Text(0.5,1,'Problem 1')

Problem 2



In [51]:

    
t0 = time.time(); results2_gkbblobop = gkbsolver_blobop.solve(problem2); t2_blobop = time.time()-t0



In [52]:

    
results2_gkbblobop.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 2.877625244684322e-08
normgrad : 0.0004151077654649252
nbiter : 1633.18
nfev : 2877.0300000000007
blocksteps : 100



In [53]:

    
results2_gkb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.0331400013001382e-07
normgrad : 0.0003805496868961612
nbiter : 32471.200000000008
nfev : 55044.400000005306
blocksteps : 97



In [54]:

    
gkb, blobop = plt.bar([0,1], [t2_gkb, t2_blobop])
gkb.set_facecolor('r')
blobop.set_facecolor('y')
ax = plt.gca()
ax.set_xticks([0,1])
ax.set_xticklabels(['GKB', 'BLOBOP'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 2')









    Out[54]:





Text(0.5,1,'Problem 2')



In [55]:

    
gkb, spg, gpi, eb, blobop = plt.bar([0,1,2,3,4], [t2_gkb, t2_spg, t2_gpi, t2_eb, t2_blobop])
gkb.set_facecolor('r')
spg.set_facecolor('g')
gpi.set_facecolor('b')
eb.set_facecolor('m')
blobop.set_facecolor('y')
ax = plt.gca()
ax.set_xticks([0,1,2,3,4])
ax.set_xticklabels(['GKB', 'SPG', 'GPI', 'EB', 'BLOBOP'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 2')









    Out[55]:





Text(0.5,1,'Problem 2')

Problem 3



In [56]:

    
t0 = time.time(); results3_gkbblobop = gkbsolver_blobop.solve(problem3); t3_blobop = time.time()-t0



In [57]:

    
results3_gkbblobop.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.3388545979624172e-06
normgrad : 0.0008379390464818944
nbiter : 1400.8650000000002
nfev : 1840.3849999999954
blocksteps : 200



In [58]:

    
results3_gkb.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 2.2042145673987446e-06
normgrad : 0.000948891935006996
nbiter : 4711.175000000001
nfev : 6383.2599999999165
blocksteps : 200



In [59]:

    
gkb, blobop = plt.bar([0,1], [t3_gkb, t3_blobop])
gkb.set_facecolor('r')
blobop.set_facecolor('y')
ax = plt.gca()
ax.set_xticks([0,1])
ax.set_xticklabels(['GKB', 'BLOBOP'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 3')









    Out[59]:





Text(0.5,1,'Problem 3')



In [60]:

    
gkb, spg, gpi, eb, blobop = plt.bar([0,1,2,3,4], [t3_gkb, t3_spg, t3_gpi, t3_eb, t3_blobop])
gkb.set_facecolor('r')
spg.set_facecolor('g')
gpi.set_facecolor('b')
eb.set_facecolor('m')
blobop.set_facecolor('y')
ax = plt.gca()
ax.set_xticks([0,1,2,3,4])
ax.set_xticklabels(['GKB', 'SPG', 'GPI', 'EB', 'BLOBOP'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 3')









    Out[60]:





Text(0.5,1,'Problem 3')



In [61]:

    
r = pd.DataFrame({'problem1' : t1_blobop, 'problem2' : t2_blobop, 'problem3' : t3_blobop}, index=['BLOBOP'])
results = results.append(r)
results

3. Comparison between svd and polar decomposition on GKBSolver



In [62]:

    
gkbpolar = skp.GKBSolver(verbose=0, polar="ns")
gkbpolarblobop = skp.GKBSolver(verbose=0, polar="ns", bloboptest=True)

Problem 1



In [63]:

    
t0 = time.time(); results1_gkbpolar = gkbpolar.solve(problem1); t1_gkbpolar = time.time()-t0



In [64]:

    
results1_gkbpolar.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.356966497640276e-06
normgrad : 1.8140182342238757e-05
nbiter : 0.09
nfev : 0.10800000000000001
blocksteps : 3



In [65]:

    
t0 = time.time(); results1_gkbpolarblobop = gkbpolarblobop.solve(problem1); t1_gkbpolarblobop = time.time()-t0



In [66]:

    
results1_gkbpolarblobop.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.36597474327368e-06
normgrad : 4.201749566593682e-05
nbiter : 0.07200000000000001
nfev : 0.09000000000000002
blocksteps : 3



In [67]:

    
gkb, polarblobop, polar = plt.bar([0,1,2], [t1_gkb, t1_gkbpolarblobop, t1_gkbpolar])
gkb.set_facecolor('r')
polarblobop.set_facecolor('g')
polar.set_facecolor('b')
ax = plt.gca()
ax.set_xticks([0,1,2])
ax.set_xticklabels(['GKB', 'POLAR+BLOBOP', 'POLAR'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 1')









    Out[67]:





Text(0.5,1,'Problem 1')

Problem 2



In [69]:

    
t0 = time.time(); results2_gkbpolar = gkbpolar.solve(problem2); t2_gkbpolar = time.time()-t0



In [70]:

    
results2_gkbpolar.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.7028781386131266e-07
normgrad : 0.0008778077880254848
nbiter : 26778.710000000003
nfev : 45200.560000008125
blocksteps : 93



In [71]:

    
t0 = time.time(); results2_gkbpolarblobop = gkbpolarblobop.solve(problem2); t2_gkbpolarblobop = time.time()-t0



In [72]:

    
results2_gkbpolarblobop.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 1.529732495734995e-08
normgrad : 0.0002809142654184651
nbiter : 1347.37
nfev : 2354.4400000000005
blocksteps : 100



In [73]:

    
gkb, polarblobop, polar = plt.bar([0,1,2], [t2_gkb, t2_gkbpolarblobop, t2_gkbpolar])
gkb.set_facecolor('r')
polarblobop.set_facecolor('g')
polar.set_facecolor('b')
ax = plt.gca()
ax.set_xticks([0,1,2])
ax.set_xticklabels(['GKB', 'POLAR+BLOBOP', 'POLAR'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 2')









    Out[73]:





Text(0.5,1,'Problem 2')

Problem 3



In [75]:

    
t0 = time.time(); results3_gkbpolar = gkbpolar.solve(problem3); t3_gkbpolar = time.time()-t0



In [76]:

    
results3_gkbpolar.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 2.5088717984998106e-06
normgrad : 0.0009965032569177797
nbiter : 5037.8899999999985
nfev : 7084.519999999943
blocksteps : 200



In [77]:

    
t0 = time.time(); results3_gkbpolarblobop = gkbpolarblobop.solve(problem3); t3_gkbpolarblobop = time.time()-t0



In [78]:

    
results3_gkbpolarblobop.show()









    



=========
 Summary:
=========
success : True
status : 0
message : Optimization terminated successfully.
fun : 3.9186066753096486e-05
normgrad : 0.0009593176867913745
nbiter : 1327.83
nfev : 1585.2550000000024
blocksteps : 200



In [79]:

    
gkb, polarblobop, polar = plt.bar([0,1,2], [t3_gkb, t3_gkbpolarblobop, t3_gkbpolar])
gkb.set_facecolor('r')
polarblobop.set_facecolor('g')
polar.set_facecolor('b')
ax = plt.gca()
ax.set_xticks([0,1,2])
ax.set_xticklabels(['GKB', 'POLAR+BLOBOP', 'POLAR'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 3')









    Out[79]:





Text(0.5,1,'Problem 3')



In [82]:

    
r = pd.DataFrame({'problem1' : t1_gkbpolar, 'problem2' : t2_gkbpolar, 'problem3' : t3_gkbpolar}, index=['POLAR'])
results = results.append(r)
r = pd.DataFrame({'problem1' : t1_gkbpolarblobop, 'problem2' : t2_gkbpolarblobop, 'problem3' : t3_gkbpolarblobop}, index=['POLAR+BLOBOP'])
results = results.append(r)
results









    Out[82]:







  
    
      
      problem1
      problem2
      problem3
    
  
  
    
      GKB
      1.464801
      141.415641
      98.376446
    
    
      SPG
      2.605641
      0.669752
      0.162492
    
    
      GPI
      23.890547
      2.761722
      0.788931
    
    
      EB
      720.464247
      182.220720
      99.986494
    
    
      BLOBOP
      1.228617
      7.477077
      44.583440
    
    
      GKB+POLAR
      1.220175
      121.742762
      107.766008
    
    
      POLAR+BLOBOP
      1.254919
      7.202415
      49.948579

4. Comparison between all versions

Problem 1



In [83]:

    
gkb, blobop, polarblobop, polar, spg, gpi, eb = plt.bar([0, 1, 2, 3, 4, 5, 6], [t1_gkb, t1_blobop, t1_gkbpolarblobop, t1_gkbpolar, t1_spg, t1_gpi, t1_eb])
gkb.set_facecolor('r')
blobop.set_facecolor('k')
polarblobop.set_facecolor('g')
polar.set_facecolor('b')
spg.set_facecolor('y')
gpi.set_facecolor('m')
eb.set_facecolor('c')
ax = plt.gca()
ax.set_xticks([0,1,2,3,4,5,6])
ax.set_xticklabels(['GKB', 'BLOBOP', 'POLAR+BLOBOP', 'POLAR', 'SPG', 'GPI', 'EB'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 1')









    Out[83]:





Text(0.5,1,'Problem 1')

Problem 2



In [84]:

    
gkb, blobop, polarblobop, polar, spg, gpi, eb = plt.bar([0, 1, 2, 3, 4, 5, 6], [t2_gkb, t2_blobop, t2_gkbpolarblobop, t2_gkbpolar, t2_spg, t2_gpi, t2_eb])
gkb.set_facecolor('r')
blobop.set_facecolor('k')
polarblobop.set_facecolor('g')
polar.set_facecolor('b')
spg.set_facecolor('y')
gpi.set_facecolor('m')
eb.set_facecolor('c')
ax = plt.gca()
ax.set_xticks([0,1,2,3,4,5,6])
ax.set_xticklabels(['GKB', 'BLOBOP', 'POLAR+BLOBOP', 'POLAR', 'SPG', 'GPI', 'EB'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 2')









    Out[84]:





Text(0.5,1,'Problem 2')

Problem 3



In [85]:

    
gkb, blobop, polarblobop, polar, spg, gpi, eb = plt.bar([0, 1, 2, 3, 4, 5, 6], [t3_gkb, t3_blobop, t3_gkbpolarblobop, t3_gkbpolar, t3_spg, t3_gpi, t3_eb])
gkb.set_facecolor('r')
blobop.set_facecolor('k')
polarblobop.set_facecolor('g')
polar.set_facecolor('b')
spg.set_facecolor('y')
gpi.set_facecolor('m')
eb.set_facecolor('c')
ax = plt.gca()
ax.set_xticks([0,1,2,3,4,5,6])
ax.set_xticklabels(['GKB', 'BLOBOP', 'POLAR+BLOBOP', 'POLAR', 'SPG', 'GPI', 'EB'])
#ax.set_ylim([0, 100])
ax.set_ylabel('CPU Time')
ax.set_title('Problem 3')









    Out[85]:





Text(0.5,1,'Problem 3')



In [ ]:

	problem1	problem2
GKB	1.464801	141.415641
SPG	2.605641	0.669752
GPI	23.890547	2.761722
EB	720.464247	182.220720

	problem1	problem2	problem3
GKB	1.464801	141.415641	98.376446
SPG	2.605641	0.669752	0.162492
GPI	23.890547	2.761722	0.788931
EB	720.464247	182.220720	99.986494