/home/snow/gnga/ Problem C4 Opening /home/snow/gnga/graphs/C4/C4.basis.txt, 4 basis vectors, 4 vertices Opening /home/snow/gnga/graphs/C4/C4.basisInfo.txt, 3 lines read Opening /home/snow/gnga/graphs/C4/C4.stabInfo.txt, 16 symmetries read Opening /home/snow/gnga/graphs/C4/C4.bifInfo.txt, 16 stabilizers read Opening /home/snow/gnga/graphs/C4/C4.weight.txt, 4 coefficients read 0.5 0.5 0.5 0.5 weight_inv Opening /home/snow/gnga/graphs/C4/C4.a_weights.txt, 4 coefficients read 1 1 -1 -1 Opening C4.all.init.txt, nonlinearity type 0 Opening /home/snow/gnga/graphs/C4/C4.aut.txt, 8 symmetry elements read pt.speed = 0.140546 random_number_generator_seed = 1 (------------------- bifpoint 1 starts Branch 0 mother pt -0.8595 = s 0 = J 0 = u.w 0 = MI bifpoint 1 -6.189e-17 = s 0 = J 0 = u.w 1 = dMI bifpoint 2 2 = s 0 = J 0 = u.w 2 = dMI bifpoint 3 4 = s 0 = J 0 = u.w 1 = dMI Last point: 5 = s 0 = J 0 = u.w 4 = MI Last point u = 0 0 0 0 Last point a = 0 0 0 0 Symmetry of the branch was 0 (type 0) List of Newton iterations = 0 0 0 0 0 )--------------------------- end of Branch 0 =======> Processing bifpoint 1 bifpoint sym = 0 (type 0) bifpoint is at -6.189e-17 = s 0 = J 0 = u.w 1 = dMI bifpoint was on branch 0 dim_E_components = 0 0 1 0 irrep_copies = 0 0 1 0 Searching for arrow daughters with symmetry 2 (type 2) Found a new daughter with sym type 2 and MI 1 at s - s* = -0.004938 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 0 (------------------- bifpoint 1 starts Branch 0 1 mother pt -6.189e-17 = s 0 = J 0 = u.w 1 = MI bifpoint 4 -1 = s 1 = J -1.659 = u.w 2 = dMI bifpoint 5 -2 = s 4 = J -2.347 = u.w 1 = dMI Last point: -10 = s 100 = J -5.248 = u.w 4 = MI Last point u = -3.162 -3.162 -3.162 -3.162 Last point a = 0 6.325 0 0 Symmetry of the branch was 2 (type 2) List of Newton iterations = 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 1 =======> Processing bifpoint 2 bifpoint sym = 0 (type 0) bifpoint is at 2 = s 0 = J 0 = u.w 2 = dMI bifpoint was on branch 0 dim_E_components = 0 0 0 2 irrep_copies = 0 0 0 1 Searching for arrow daughters with symmetry 4 (type 3) Found a new daughter with sym type 3 and MI 3 at s - s* = -0.004938 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 0 Searching for arrow daughters with symmetry 6 (type 4) Found a new daughter with sym type 4 and MI 2 at s - s* = -0.009877 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 0 (------------------- bifpoint 2 starts Branch 0 2 mother pt 2 = s 0 = J 0 = u.w 3 = MI bifpoint 6 1 = s 1 = J -0.1549 = u.w 1 = dMI Last point: -10 = s 144 = J -0.5367 = u.w 4 = MI Last point u = -3.464 -3.464 3.464 3.464 Last point a = 0 0 -6.928 0 Symmetry of the branch was 4 (type 3) List of Newton iterations = 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 2 (------------------- bifpoint 2 starts Branch 0 3 mother pt 2 = s 0 = J 0 = u.w 2 = MI Last point: -10 = s 72 = J -1.941 = u.w 2 = MI Last point u = -3.464 0 3.464 0 Last point a = 0 0 -3.464 -3.464 Symmetry of the branch was 6 (type 4) List of Newton iterations = 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 3 =======> Processing bifpoint 3 bifpoint sym = 0 (type 0) bifpoint is at 4 = s 0 = J 0 = u.w 1 = dMI bifpoint was on branch 0 dim_E_components = 0 1 0 0 irrep_copies = 0 1 0 0 Searching for arrow daughters with symmetry 1 (type 1) Found a new daughter with sym type 1 and MI 4 at s - s* = -0.004938 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 0 (------------------- bifpoint 3 starts Branch 0 4 mother pt 4 = s 0 = J 0 = u.w 4 = MI Last point: -10 = s 196 = J -2.014 = u.w 4 = MI Last point u = 3.742 -3.742 3.742 -3.742 Last point a = -7.483 0 0 0 Symmetry of the branch was 1 (type 1) List of Newton iterations = 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 4 =======> Processing bifpoint 4 bifpoint sym = 2 (type 2) bifpoint is at -1 = s 1 = J -1.659 = u.w 2 = dMI bifpoint was on branch 0 1 dim_E_components = 0 0 2 irrep_copies = 0 0 1 Searching for arrow daughters with symmetry 11 (type 7) Found a new daughter with sym type 7 and MI 2 at s - s* = -0.01975 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 2.923e-14 Searching for arrow daughters with symmetry 14 (type 9) Found a new daughter with sym type 9 and MI 2 at s - s* = 0.003796 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 5.899e-14 (------------------- bifpoint 4 starts Branch 0 1 5 mother pt -1 = s 1 = J -1.659 = u.w 2 = MI Last point: -10 = s 59.5 = J -2.759 = u.w 2 = MI Last point u = -0.3028 -0.3028 -3.303 -3.303 Last point a = 0 3.606 3 0 Symmetry of the branch was 11 (type 7) List of Newton iterations = 3 3 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 1 5 (------------------- bifpoint 4 starts Branch 0 1 6 mother pt -1 = s 1 = J -1.659 = u.w 2 = MI fold point -0.9943 = s 0.9887 = J -1.526 = u.w -1 = MI Last point: -10 = s 34.99 = J -0.3497 = u.w 1 = MI Last point u = -0.04881 -0.2928 -3.439 -0.2928 Last point a = 1.451 2.037 1.695 1.695 Symmetry of the branch was 14 (type 9) List of Newton iterations = 3 3 3 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 1 6 =======> Processing bifpoint 5 bifpoint sym = 2 (type 2) bifpoint is at -2 = s 4 = J -2.347 = u.w 1 = dMI bifpoint was on branch 0 1 dim_E_components = 0 1 0 irrep_copies = 0 1 0 Searching for arrow daughters with symmetry 7 (type 5) Found a new daughter with sym type 5 and MI 3 at s - s* = -0.01975 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 2.269e-14 (------------------- bifpoint 5 starts Branch 0 1 7 mother pt -2 = s 4 = J -2.347 = u.w 3 = MI bifpoint 7 -2.243 = s 5 = J -2.515 = u.w -1 = dMI Last point: -10 = s 68 = J -4.08 = u.w 2 = MI Last point u = -0.5858 -3.414 -0.5858 -3.414 Last point a = -2.828 4 0 0 Symmetry of the branch was 7 (type 5) List of Newton iterations = 3 3 2 2 2 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 1 7 =======> Processing bifpoint 6 bifpoint sym = 4 (type 3) bifpoint is at 1 = s 1 = J -0.1549 = u.w 1 = dMI bifpoint was on branch 0 2 dim_E_components = 0 0 0 1 irrep_copies = 0 0 0 1 Searching for arrow daughters with symmetry 8 (type 6) Found a new daughter with sym type 6 and MI 3 at s - s* = -0.01975 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 2.485e-14 (------------------- bifpoint 6 starts Branch 0 2 8 mother pt 1 = s 1 = J -0.1549 = u.w 3 = MI bifpoint 8 -4.386e-12 = s 3.5 = J -0.4423 = u.w -1 = dMI Last point: -10 = s 83.5 = J -1.192 = u.w 2 = MI Last point u = -0.2782 -3.595 3.595 0.2782 Last point a = -3.317 0 -3.873 0 Symmetry of the branch was 8 (type 6) List of Newton iterations = 3 3 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 2 8 =======> Processing bifpoint 7 bifpoint sym = 7 (type 5) bifpoint is at -2.243 = s 5 = J -2.515 = u.w -1 = dMI bifpoint was on branch 0 1 7 dim_E_components = 0 0 1 irrep_copies = 0 0 1 Searching for arrow daughters with symmetry 14 (type 9) Found a new daughter with sym type 9 and MI 3 at s - s* = -0.06806 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 1.777e-14 (------------------- bifpoint 7 starts Branch 0 1 7 9 mother pt -2.243 = s 5 = J -2.515 = u.w 3 = MI Last point: -10 = s 83.68 = J -5.387 = u.w 3 = MI Last point u = -3.147 -3.298 -0.5646 -3.298 Last point a = -1.442 5.154 -1.291 -1.291 Symmetry of the branch was 14 (type 9) List of Newton iterations = 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 1 7 9 =======> Processing bifpoint 8 bifpoint sym = 8 (type 6) bifpoint is at -4.386e-12 = s 3.5 = J -0.4423 = u.w -1 = dMI bifpoint was on branch 0 2 8 dim_E_components = 0 1 irrep_copies = 0 1 Searching for arrow daughters with symmetry 15 (type 10) Found a new daughter with sym type 10 and MI 3 at s - s* = -0.0283 after 1 guesses. Found a pitchfork bifurcation find_daughter made 3 calls to newton_cylinder. Of these calls, 3 conveged. (100 per cent). It found 1 nonconjugate daughter(s) The cutoff for the norm in same_orbit in symmetry.C is 1.405e-05 smallest_norm_above_cutoff = 1e+10 largest_norm_below_cutoff = 6.378e-16 (------------------- bifpoint 8 starts Branch 0 2 8 10 mother pt -4.386e-12 = s 3.5 = J -0.4423 = u.w 3 = MI Last point: -10 = s 108.5 = J 1.229 = u.w 3 = MI Last point u = -0.02414 -3.6 3.476 3.31 Last point a = -1.871 -1.581 -5.205 1.705 Symmetry of the branch was 15 (type 10) List of Newton iterations = 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 )--------------------------- end of Branch 0 2 8 10 Summary of Newton's method and Secant Method Calls: 252 newton() calls, and 614 iterations, for 2.437 iterations per call. 30 newton_cylinder() calls, and 96 iterations, for 3.2 iterations per call. 9 secant() calls, and 37 iterations, for 4.111 iterations per call.