Note
Go to the end to download the full example code.
Using Coala within Shamrock to solve the Smoluchowski equation#
Imports
9 import os
10
11 import numpy as np
12 from matplotlib import pyplot as plt
13 from shamrock.external import coala
14
15 import shamrock
Where is coala located?
19 print(f"coala path : {coala.__file__}")
coala path : /usr/local/lib/python3.10/dist-packages/shamrock/external/coala/__init__.py
Use shamrock documentation style for matplotlib
23 shamrock.matplotlib.set_shamrock_mpl_style()
Parameters of the dust distribution & evolution
Function to run the tests for a given kernel
41 def run_kernel_case(kernel):
42
43 cases = {
44 "order k=0": {
45 "kpol": 0,
46 },
47 "order k=1": {
48 "kpol": 1,
49 },
50 "order k=2": {
51 "kpol": 2,
52 },
53 "order k=3": {
54 "kpol": 3,
55 },
56 # "order k=4": {
57 # "kpol": 4,
58 # },
59 # "order k=5": {
60 # "kpol": 5,
61 # },
62 }
63
64 if kernel == 0:
65 dthydro = 100
66 ndthydro = 300
67 elif kernel == 1:
68 dthydro = 1e-2
69 ndthydro = 300
70 elif kernel == 2 or kernel == 3:
71 dthydro = 1e-1
72 ndthydro = 500
73 else:
74 raise ValueError("need to choose a kernel")
75
76 if kernel == 0:
77 print("Test coala for kconst")
78 elif kernel == 1:
79 print("Test coala for kadd")
80 elif kernel == 2:
81 print("Test coala for k_Br")
82 else:
83 print("Test coala for k_dv")
84
85 massgrid, massbins = coala.init_grid_log(nbins, massmax, massmin)
86
87 for case in cases:
88 kpol = cases[case]["kpol"]
89 print()
90 print("Computing coala solver for k=%d" % (kpol))
91 match kernel:
92 case 0 | 1 | 2:
93 gij_init, gij, time_coag = coala.iterate_coag(
94 kernel,
95 K0,
96 nbins,
97 kpol,
98 dthydro,
99 ndthydro,
100 coeff_CFL,
101 Q,
102 eps,
103 massgrid,
104 massbins,
105 )
106
107 case 3:
108 # Brownian motion dv with constant approximation
109 dv_Br = np.zeros((nbins, nbins))
110 massmeanlog = np.sqrt(massgrid[0:nbins] * massgrid[1:])
111 for i in range(nbins):
112 for j in range(nbins):
113 dv_Br[i, j] = np.sqrt(1.0 / massmeanlog[i] + 1.0 / massmeanlog[j])
114
115 gij_init, gij, time_coag = coala.iterate_coag_kdv(
116 kernel,
117 K0,
118 nbins,
119 kpol,
120 dthydro,
121 ndthydro,
122 coeff_CFL,
123 Q,
124 eps,
125 massgrid,
126 massbins,
127 dv_Br,
128 )
129
130 case _:
131 print("Need to choose available kernel in kernel_collision.py.")
132
133 cases[case]["massgrid"] = massgrid
134 cases[case]["massbins"] = massbins
135 cases[case]["gij_init"] = gij_init
136 cases[case]["gij_end"] = gij
137 cases[case]["time"] = [t0, time_coag]
138
139 # compute ref solutions when needed
140 match kernel:
141 case 2:
142 # dv Brownian with analytic formula
143 nbins_ref = 100
144 massgrid_ref, massbins_ref = coala.init_grid_log(nbins_ref, massmax, massmin)
145
146 print()
147 print("Computing coala solver for k_Br (k=0), ref solution")
148 gij_init_ref, gij_ref, time_coag_ref = coala.iterate_coag(
149 kernel,
150 K0,
151 nbins_ref,
152 0,
153 dthydro,
154 ndthydro,
155 coeff_CFL,
156 Q,
157 eps,
158 massgrid_ref,
159 massbins_ref,
160 )
161
162 case 3:
163 # Brownian motion dv with constant approximation
164 nbins_ref = 100
165 massgrid_ref, massbins_ref = coala.init_grid_log(nbins_ref, massmax, massmin)
166
167 massmeanlog_ref = np.sqrt(massgrid_ref[0:nbins_ref] * massgrid_ref[1:])
168 dv_Br_ref = np.sqrt(1.0 / massmeanlog_ref[:, None] + 1.0 / massmeanlog_ref[None, :])
169
170 print()
171 print("Computing coala solver for k_dv (k=0), ref solution")
172 gij_init_ref, gij_ref, time_coag_ref = coala.iterate_coag_kdv(
173 kernel,
174 K0,
175 nbins_ref,
176 0,
177 dthydro,
178 ndthydro,
179 coeff_CFL,
180 Q,
181 eps,
182 massgrid_ref,
183 massbins_ref,
184 dv_Br_ref,
185 )
186
187 # Plotting
188 plt.rcParams["font.size"] = 16
189 plt.rcParams["lines.linewidth"] = 3
190 plt.rcParams["legend.columnspacing"] = 0.5
191
192 savefig_options = dict(bbox_inches="tight")
193
194 marker_style = dict(
195 marker="o", markersize=8, markerfacecolor="white", linestyle="", markeredgewidth=2
196 )
197
198 match kernel:
199 case 0:
200 str_kernel = "kconst"
201 case 1:
202 str_kernel = "kadd"
203 case 2:
204 str_kernel = "k_Br"
205 case 3:
206 str_kernel = "k_dv"
207 case _:
208 print("Need to choose a simple kernel in the list.")
209
210 x = np.logspace(np.log10(massmin), np.log10(massmax), num=100)
211
212 tend = cases["order k=0"]["time"][-1]
213 plt.figure(1)
214 if kernel < 2:
215 plt.loglog(x, coala.exact_sol_coag(kernel, x, 0.0), "--", c="C0", alpha=0.5)
216 plt.loglog(x, coala.exact_sol_coag(kernel, x, tend), "--", c="C0", label="Analytic")
217 else:
218 plt.loglog(massbins_ref, gij_init_ref, "--", c="C0", alpha=0.5)
219 plt.loglog(massbins_ref, gij_ref, "--", c="C0", label="ref %d bins" % (nbins_ref))
220
221 plt.loglog(
222 cases["order k=0"]["massbins"],
223 cases["order k=0"]["gij_init"],
224 markeredgecolor="black",
225 label="gij init",
226 **marker_style,
227 alpha=0.5,
228 )
229 for case in cases:
230 print("plotting case", case)
231
232 # if cases[case]["gij_end"][0] is a scalar
233 print("gij_end = ", type(cases[case]["gij_end"][0]))
234 if isinstance(cases[case]["gij_end"][0], np.float64):
235 print("gij_end is a scalar")
236 plt.loglog(cases[case]["massbins"], cases[case]["gij_end"], label=case, **marker_style)
237 else:
238 print("gij_end is an array")
239 plt.loglog(
240 cases[case]["massbins"], cases[case]["gij_end"][:, 0], label=case, **marker_style
241 )
242 # print ("gij_end = ",type(cases[case]["gij_end"][0]))
243 # plt.loglog(cases[case]["massbins"],cases[case]["gij_end"],markeredgecolor='black',label=case,**marker_style)
244
245 plt.ylim(1.0e-15, 1.0e1)
246 plt.xlim(massmin, massmax)
247 plt.title(str_kernel + ", nbins=%d" % (nbins))
248 plt.xlabel(r"mass ")
249 plt.ylabel(r"mass density distribution g")
250 plt.legend(loc="lower left", ncol=1)
251 plt.tight_layout()
Run the tests (kconst)
256 run_kernel_case(0)
257 plt.show()
Test coala for kconst
Computing coala solver for k=0
Tensor tabflux generated in 0.23952 s
gij generated in 0.00032 s
gij t0 = [1.90527518e-03 5.34978592e-03 1.49200031e-02 4.08236317e-02
1.05876532e-01 2.36603895e-01 3.53238069e-01 1.92536780e-01
1.28210758e-02 7.88742300e-06 5.05922357e-15 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 429
total ndt = 269
total number time-steps = 698
gij tend = [6.71600230e-12 1.89619194e-11 5.36376952e-11 1.52666572e-10
4.42014352e-10 1.33150816e-09 4.25831439e-09 1.32793559e-08
3.87782455e-08 1.12441169e-07 3.24816715e-07 9.30532385e-07
2.60287335e-06 6.80950280e-06 1.49230883e-05 2.16526482e-05
1.45034809e-05 3.14337289e-06 1.73265197e-07 2.10043162e-09]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202388
diff M1 = 1.2212453270876722e-15
Time solver in 0.09433
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 7.71286 s
gij generated in 0.00084 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04]
[ 5.34978592e-03 2.53498952e-03]
[ 1.49200031e-02 7.00550421e-03]
[ 4.08236317e-02 1.86714390e-02]
[ 1.05876532e-01 4.47777100e-02]
[ 2.36603895e-01 7.68481264e-02]
[ 3.53238069e-01 1.50847901e-02]
[ 1.92536780e-01 -1.40538593e-01]
[ 1.28210758e-02 -1.28210758e-02]
[ 7.88742300e-06 -7.88742300e-06]
[ 5.05922357e-15 -5.05921357e-15]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 424
total ndt = 260
total number time-steps = 684
gij tend = [[ 9.08739021e-12 4.32990254e-12]
[ 2.56210283e-11 1.22038314e-11]
[ 7.22233057e-11 3.43990293e-11]
[ 2.03600738e-10 9.69786292e-11]
[ 5.74175517e-10 2.73513777e-10]
[ 1.62161042e-09 7.71868442e-10]
[ 4.60664870e-09 2.18528668e-09]
[ 1.32536962e-08 6.34652065e-09]
[ 3.70147049e-08 1.78129806e-08]
[ 1.03428322e-07 4.96983195e-08]
[ 2.88363419e-07 1.38224875e-07]
[ 7.99643836e-07 3.80548485e-07]
[ 2.18375171e-06 1.01834375e-06]
[ 5.71460131e-06 2.51196161e-06]
[ 1.32895116e-05 4.84925294e-06]
[ 2.24681425e-05 3.57289104e-06]
[ 1.71690351e-05 -6.21601221e-06]
[ 2.59367847e-06 -2.59367847e-06]
[ 3.50895039e-08 -3.50895039e-08]
[ 4.28413480e-11 -4.28413480e-11]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202366
diff M1 = -9.992007221626409e-16
Time solver in 1.03179
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 33.62428 s
gij generated in 0.00675 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02]
[ 1.28210758e-02 -2.10736118e-02 1.68642939e-02]
[ 7.88742300e-06 -1.01855598e-05 1.31438063e-05]
[ 5.05922357e-15 -6.34995441e-15 8.54561595e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 434
total ndt = 264
total number time-steps = 698
gij tend = [[ 8.61296901e-12 4.10381168e-12 3.82709695e-18]
[ 2.42829914e-11 1.15662380e-11 3.12260672e-17]
[ 6.84481214e-11 3.25991151e-11 2.55283634e-16]
[ 1.92930537e-10 9.18850880e-11 2.05772065e-15]
[ 5.43835171e-10 2.59033579e-10 1.68785159e-14]
[ 1.53334524e-09 7.30577711e-10 1.58999521e-13]
[ 4.32659496e-09 2.06313922e-09 2.12869702e-12]
[ 1.22381686e-08 5.84949862e-09 2.28061007e-11]
[ 3.44657967e-08 1.64643900e-08 7.07318793e-11]
[ 9.69080757e-08 4.61999158e-08 1.56710304e-10]
[ 2.71902818e-07 1.29306089e-07 3.27584038e-10]
[ 7.58964475e-07 3.58447154e-07 6.38737886e-11]
[ 2.08796621e-06 9.66898795e-07 -6.23684199e-09]
[ 5.51499763e-06 2.41063627e-06 -6.24642561e-08]
[ 1.30058543e-05 4.72704799e-06 -4.20140045e-07]
[ 2.25081445e-05 3.44428693e-06 -1.59813299e-06]
[ 1.76019294e-05 -7.64816778e-06 -3.07456793e-07]
[ 2.46217029e-06 -3.83173351e-06 2.18177126e-06]
[ 3.04938580e-08 -4.33007982e-08 4.79549291e-08]
[ 3.31784451e-10 -3.74798607e-10 5.83292416e-10]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202375
diff M1 = -1.1102230246251565e-16
Time solver in 11.17701
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 89.99339 s
gij generated in 0.00709 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07 1.49930663e-10]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06 3.34102550e-09]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05 7.38262831e-08]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04 1.59300983e-06]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03 3.21378086e-05]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02 5.35173800e-04]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02 5.06383102e-03]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02 5.03190777e-03]
[ 1.28210758e-02 -2.13264427e-02 1.70666234e-02 -8.56125651e-03]
[ 7.88742300e-06 -8.86780238e-06 1.14433256e-05 -1.04629462e-05]
[ 5.05922357e-15 -5.35814132e-15 7.21085774e-15 -6.91192999e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 434
total ndt = 261
total number time-steps = 695
gij tend = [[ 8.58190950e-12 4.08901095e-12 3.32598078e-18 -9.32076456e-21]
[ 2.41954044e-11 1.15245077e-11 2.72382806e-17 1.11835712e-19]
[ 6.82010910e-11 3.24813744e-11 2.23365770e-16 4.41780117e-19]
[ 1.92233124e-10 9.15522312e-11 1.79848437e-15 1.24247229e-18]
[ 5.41860314e-10 2.58087502e-10 1.43522044e-14 -5.90228399e-18]
[ 1.52770115e-09 7.27852848e-10 1.13835684e-13 -9.84660185e-16]
[ 4.30981343e-09 2.05503553e-09 8.89859202e-13 -8.95207452e-14]
[ 1.21799797e-08 5.82101344e-09 7.19079036e-12 -2.77686538e-12]
[ 3.42746188e-08 1.63461459e-08 4.09213471e-11 4.33718250e-12]
[ 9.64008979e-08 4.58957678e-08 7.68306254e-11 1.26000830e-11]
[ 2.70595445e-07 1.28510819e-07 1.06447252e-10 4.82331670e-11]
[ 7.55672274e-07 3.56414662e-07 -5.48175904e-10 1.19382420e-10]
[ 2.08001088e-06 9.61942211e-07 -7.89403917e-09 3.66045445e-10]
[ 5.49774985e-06 2.39998251e-06 -6.67672814e-08 1.77926825e-09]
[ 1.29786486e-05 4.71068069e-06 -4.30552805e-07 1.87764710e-08]
[ 2.25012456e-05 3.42917431e-06 -1.61885283e-06 2.01436300e-07]
[ 1.76422697e-05 -7.71901969e-06 -2.24206026e-07 5.83871307e-07]
[ 2.47282804e-06 -3.87782349e-06 2.42050159e-06 -8.03737276e-07]
[ 2.31434354e-08 -2.83195055e-08 3.48844906e-08 -2.97084206e-08]
[ 9.94854007e-11 -7.04079178e-11 1.10464067e-10 -1.39541550e-10]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202356
diff M1 = -1.9984014443252818e-15
Time solver in 13.13930
plotting case order k=0
gij_end = <class 'numpy.float64'>
gij_end is a scalar
plotting case order k=1
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=2
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=3
gij_end = <class 'numpy.ndarray'>
gij_end is an array
Run the tests (kadd)
261 run_kernel_case(1)
262 plt.show()
Test coala for kadd
Computing coala solver for k=0
Tensor tabflux generated in 0.24100 s
gij generated in 0.00035 s
gij t0 = [1.90527518e-03 5.34978592e-03 1.49200031e-02 4.08236317e-02
1.05876532e-01 2.36603895e-01 3.53238069e-01 1.92536780e-01
1.28210758e-02 7.88742300e-06 5.05922357e-15 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 300
total ndt = 227
total number time-steps = 527
gij tend = [9.46923595e-05 2.65043632e-04 7.32678756e-04 1.95693839e-03
4.76890398e-03 9.28871278e-03 1.15251017e-02 7.84524840e-03
4.18790882e-03 2.15758465e-03 1.11809027e-03 5.73274221e-04
2.79582274e-04 1.24810694e-04 4.80539799e-05 1.45278618e-05
3.02547109e-06 3.71308293e-07 2.26007997e-08 5.67256497e-10]
M1 t0 = 0.9999988304202376
M1 tend = 0.999998830420237
diff M1 = -6.661338147750939e-16
Time solver in 0.07085
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 7.86048 s
gij generated in 0.00085 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04]
[ 5.34978592e-03 2.53498952e-03]
[ 1.49200031e-02 7.00550421e-03]
[ 4.08236317e-02 1.86714390e-02]
[ 1.05876532e-01 4.47777100e-02]
[ 2.36603895e-01 7.68481264e-02]
[ 3.53238069e-01 1.50847901e-02]
[ 1.92536780e-01 -1.40538593e-01]
[ 1.28210758e-02 -1.28210758e-02]
[ 7.88742300e-06 -7.88742300e-06]
[ 5.05922357e-15 -5.05921357e-15]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 201
total ndt = 254
total number time-steps = 455
gij tend = [[ 9.46748867e-05 4.49313443e-05]
[ 2.64905195e-04 1.24935394e-04]
[ 7.31591213e-04 3.38957363e-04]
[ 1.94859122e-03 8.57842302e-04]
[ 4.70971706e-03 1.78004402e-03]
[ 8.97837560e-03 2.02344363e-03]
[ 1.09628859e-02 -3.93487186e-04]
[ 8.44513302e-03 -1.48433949e-03]
[ 5.14873253e-03 -1.06071864e-03]
[ 3.03683434e-03 -6.13512395e-04]
[ 1.77279721e-03 -3.39368817e-04]
[ 1.00204189e-03 -2.09442170e-04]
[ 5.04192232e-04 -1.41730972e-04]
[ 1.86341177e-04 -8.79482101e-05]
[ 3.25424160e-05 -2.82716732e-05]
[ 1.23991390e-06 -1.23991390e-06]
[ 1.01484523e-08 -1.01484523e-08]
[ 2.08646952e-11 -2.08646952e-11]
[ 6.75735584e-15 -6.75734584e-15]
[ 3.27695741e-19 -3.17695741e-19]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202378
diff M1 = 2.220446049250313e-16
Time solver in 0.67790
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 34.23130 s
gij generated in 0.00671 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02]
[ 1.28210758e-02 -2.10736118e-02 1.68642939e-02]
[ 7.88742300e-06 -1.01855598e-05 1.31438063e-05]
[ 5.05922357e-15 -6.34995441e-15 8.54561595e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 197
total ndt = 271
total number time-steps = 468
gij tend = [[ 9.46740930e-05 4.49306564e-05 -5.30725953e-08]
[ 2.64898939e-04 1.24930186e-04 -4.16260358e-07]
[ 7.31542559e-04 3.38921500e-04 -3.19048882e-06]
[ 1.94822620e-03 8.57669602e-04 -2.29199278e-05]
[ 4.70720297e-03 1.78056407e-03 -1.37297806e-04]
[ 8.96373187e-03 2.04516882e-03 -4.95078148e-04]
[ 1.09001508e-02 -2.95227344e-04 -3.90237343e-04]
[ 8.36656837e-03 -1.65208521e-03 2.89923760e-04]
[ 5.25686775e-03 -1.25407691e-03 2.62553011e-04]
[ 3.16148600e-03 -7.64386129e-04 1.75976220e-04]
[ 1.87293760e-03 -4.28005126e-04 8.32321583e-05]
[ 1.06532175e-03 -2.58924824e-04 3.24894494e-05]
[ 5.33049416e-04 -1.78936288e-04 1.85477876e-05]
[ 1.85170566e-04 -1.14608901e-04 1.94401344e-05]
[ 2.57319638e-05 -3.31284417e-05 1.23865040e-05]
[ 6.36584472e-07 -1.08681430e-06 7.43906502e-07]
[ 1.38512136e-08 -2.12361893e-08 2.02956586e-08]
[ 2.95845862e-10 -3.62377036e-10 5.05016610e-10]
[ 9.06693425e-13 -1.01043556e-12 1.60078727e-12]
[ 1.91516589e-16 -2.08222215e-16 3.40579088e-16]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202401
diff M1 = 2.4424906541753444e-15
Time solver in 6.81249
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 92.26757 s
gij generated in 0.00719 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07 1.49930663e-10]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06 3.34102550e-09]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05 7.38262831e-08]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04 1.59300983e-06]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03 3.21378086e-05]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02 5.35173800e-04]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02 5.06383102e-03]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02 5.03190777e-03]
[ 1.28210758e-02 -2.13264427e-02 1.70666234e-02 -8.56125651e-03]
[ 7.88742300e-06 -8.86780238e-06 1.14433256e-05 -1.04629462e-05]
[ 5.05922357e-15 -5.35814132e-15 7.21085774e-15 -6.91192999e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 196
total ndt = 265
total number time-steps = 461
gij tend = [[ 9.46740366e-05 4.49306065e-05 -5.30804851e-08 3.52580998e-11]
[ 2.64898494e-04 1.24929793e-04 -4.16322177e-07 7.79431590e-10]
[ 7.31539100e-04 3.38918475e-04 -3.19097755e-06 1.68399414e-08]
[ 1.94820032e-03 8.57647496e-04 -2.29246820e-05 3.41121421e-07]
[ 4.70702822e-03 1.78042512e-03 -1.37395709e-04 5.76899248e-06]
[ 8.96280034e-03 2.04461819e-03 -4.97860693e-04 5.91801922e-05]
[ 1.08965112e-02 -2.94834645e-04 -4.21488542e-04 1.54439962e-04]
[ 8.35754022e-03 -1.65216016e-03 2.83491778e-04 -3.84833538e-05]
[ 5.25990832e-03 -1.27869607e-03 3.04106896e-04 -6.12690152e-05]
[ 3.16670106e-03 -7.72133507e-04 2.06773491e-04 -4.67570716e-05]
[ 1.88178967e-03 -4.31702815e-04 9.46284184e-05 -1.75245250e-05]
[ 1.07321353e-03 -2.60765144e-04 2.71770505e-05 9.80743107e-06]
[ 5.37048763e-04 -1.81852718e-04 1.25032214e-05 1.19632552e-05]
[ 1.85513328e-04 -1.17368267e-04 1.90749723e-05 4.26202961e-06]
[ 2.50437045e-05 -3.32540338e-05 1.45276303e-05 -2.22739771e-06]
[ 5.02994604e-07 -9.23647364e-07 8.46431472e-07 -4.25778712e-07]
[ 4.37691758e-09 -5.38792852e-09 7.29931100e-09 -6.28830007e-09]
[ 3.53097659e-11 -2.53915401e-11 3.91831042e-11 -4.91013301e-11]
[ 2.75641665e-14 -1.76061225e-14 2.83932579e-14 -3.83512918e-14]
[ 6.83806670e-19 -4.19571032e-19 6.86499070e-19 -9.40734708e-19]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202353
diff M1 = -2.3314683517128287e-15
Time solver in 7.77393
plotting case order k=0
gij_end = <class 'numpy.float64'>
gij_end is a scalar
plotting case order k=1
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=2
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=3
gij_end = <class 'numpy.ndarray'>
gij_end is an array
Run the tests (k_Br)
266 run_kernel_case(2)
267 plt.show()
Test coala for k_Br
Computing coala solver for k=0
Tensor tabflux generated in 0.30650 s
gij generated in 0.00057 s
gij t0 = [1.90527518e-03 5.34978592e-03 1.49200031e-02 4.08236317e-02
1.05876532e-01 2.36603895e-01 3.53238069e-01 1.92536780e-01
1.28210758e-02 7.88742300e-06 5.05922357e-15 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1171
total ndt = 62
total number time-steps = 1233
gij tend = [1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
2.18267012e-17 8.76110393e-12 2.38970552e-08 2.63187075e-06
4.02788007e-05 2.01063032e-04 5.08211257e-04 7.76730349e-04
6.77968419e-04 2.75660442e-04 4.23126198e-05 2.11243724e-06
2.92268205e-08 7.94458645e-11 2.24149265e-14 3.25785636e-19]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202382
diff M1 = 5.551115123125783e-16
Time solver in 0.17133
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 9.35736 s
gij generated in 0.00082 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04]
[ 5.34978592e-03 2.53498952e-03]
[ 1.49200031e-02 7.00550421e-03]
[ 4.08236317e-02 1.86714390e-02]
[ 1.05876532e-01 4.47777100e-02]
[ 2.36603895e-01 7.68481264e-02]
[ 3.53238069e-01 1.50847901e-02]
[ 1.92536780e-01 -1.40538593e-01]
[ 1.28210758e-02 -1.28210758e-02]
[ 7.88742300e-06 -7.88742300e-06]
[ 5.05922357e-15 -5.05921357e-15]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1267
total ndt = 0
total number time-steps = 1267
gij tend = [[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 3.80230108e-17 3.80130108e-17]
[ 1.04180553e-11 1.04180553e-11]
[ 2.12413654e-08 2.12413654e-08]
[ 2.06724569e-06 2.06724569e-06]
[ 3.10464534e-05 2.90532609e-05]
[ 1.62931733e-04 1.01215568e-04]
[ 4.53992185e-04 1.78760265e-04]
[ 8.06415263e-04 1.58315087e-04]
[ 8.32672678e-04 -9.66040083e-05]
[ 3.07474733e-04 -2.23852212e-04]
[ 1.72056018e-05 -1.72056018e-05]
[ 1.05089007e-07 -1.05089007e-07]
[ 9.68657332e-11 -9.68657332e-11]
[ 9.67982125e-15 -9.67981125e-15]
[ 4.18978458e-20 -3.18978458e-20]
[ 1.06525473e-20 -1.15813627e-22]]
M1 t0 = 0.9999988304202376
M1 tend = 0.999998830420237
diff M1 = -6.661338147750939e-16
Time solver in 1.89339
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 39.89590 s
gij generated in 0.00662 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02]
[ 1.28210758e-02 -2.10736118e-02 1.68642939e-02]
[ 7.88742300e-06 -1.01855598e-05 1.31438063e-05]
[ 5.05922357e-15 -6.34995441e-15 8.54561595e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1288
total ndt = 0
total number time-steps = 1288
gij tend = [[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 9.22208090e-17 1.58362261e-16 1.04181528e-16]
[ 1.55852582e-11 2.68125034e-11 1.73917717e-11]
[ 2.30770837e-08 3.99233413e-08 2.19542593e-08]
[ 1.89388839e-06 2.57926898e-06 8.29683532e-07]
[ 2.88378714e-05 2.72740676e-05 3.23635140e-06]
[ 1.56063878e-04 9.66208486e-05 -1.80099983e-06]
[ 4.45077215e-04 1.74480400e-04 -1.88426189e-05]
[ 8.09068396e-04 1.56377273e-04 -4.40736262e-05]
[ 8.54982165e-04 -1.25893224e-04 -4.23787533e-05]
[ 3.07395706e-04 -2.91974962e-04 7.34073631e-05]
[ 1.40341901e-05 -2.30819823e-05 1.84348556e-05]
[ 2.56644181e-07 -3.36332127e-07 4.24453007e-07]
[ 3.81182804e-09 -4.26127215e-09 6.72339455e-09]
[ 6.04965637e-12 -6.54949009e-12 1.07719159e-11]
[ 2.55429966e-16 -2.74953300e-16 4.55518909e-16]
[ 1.19659328e-20 -2.13780177e-21 3.49612660e-21]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202403
diff M1 = 2.6645352591003757e-15
Time solver in 17.59792
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 107.19242 s
gij generated in 0.00710 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07 1.49930663e-10]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06 3.34102550e-09]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05 7.38262831e-08]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04 1.59300983e-06]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03 3.21378086e-05]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02 5.35173800e-04]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02 5.06383102e-03]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02 5.03190777e-03]
[ 1.28210758e-02 -2.13264427e-02 1.70666234e-02 -8.56125651e-03]
[ 7.88742300e-06 -8.86780238e-06 1.14433256e-05 -1.04629462e-05]
[ 5.05922357e-15 -5.35814132e-15 7.21085774e-15 -6.91192999e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1280
total ndt = 0
total number time-steps = 1280
gij tend = [[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 8.52146370e-17 1.38556444e-16 1.12501540e-16 5.91497329e-17]
[ 1.57006374e-11 2.74694330e-11 2.15444370e-11 9.77564138e-12]
[ 2.27035339e-08 4.00991816e-08 2.32631231e-08 5.86747547e-09]
[ 1.86907655e-06 2.54442510e-06 8.08662871e-07 2.67193405e-08]
[ 2.85296449e-05 2.69644526e-05 3.08493750e-06 -5.50352445e-07]
[ 1.54989521e-04 9.58265619e-05 -2.07678362e-06 -8.12861815e-07]
[ 4.43401379e-04 1.73331212e-04 -1.95939812e-05 1.59499681e-06]
[ 8.08479191e-04 1.55118521e-04 -4.58068152e-05 6.12312721e-06]
[ 8.57350856e-04 -1.29199008e-04 -4.29762047e-05 1.41726686e-05]
[ 3.09003556e-04 -2.96895810e-04 8.62901531e-05 -6.34592624e-06]
[ 1.36308359e-05 -2.36389740e-05 2.22505254e-05 -1.22423874e-05]
[ 1.21688562e-07 -1.15791446e-07 1.67370558e-07 -1.73267674e-07]
[ 6.27436608e-10 -4.05017808e-10 6.56279204e-10 -8.78698004e-10]
[ 2.99832945e-13 -1.82897250e-13 3.02028250e-13 -4.18963935e-13]
[ 2.34273549e-18 -1.40962219e-18 2.34079638e-18 -3.26390969e-18]
[ 1.06610069e-20 -1.21683304e-22 5.07009915e-24 5.51739347e-23]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202384
diff M1 = 7.771561172376096e-16
Time solver in 22.57850
Computing coala solver for k_Br (k=0), ref solution
Tensor tabflux generated in 34.57367 s
gij generated in 0.00018 s
gij t0 = [1.11388714e-03 1.37002748e-03 1.68496775e-03 2.07215484e-03
2.54808441e-03 3.13297862e-03 3.85160744e-03 4.73428037e-03
5.81803832e-03 7.14807753e-03 8.77943753e-03 1.07789822e-02
1.32276937e-02 1.62232810e-02 1.98830708e-02 2.43470927e-02
2.97811797e-02 3.63797645e-02 4.43678399e-02 5.40012432e-02
6.55639905e-02 7.93607924e-02 9.57021315e-02 1.14878385e-01
1.37118570e-01 1.62528657e-01 1.91004643e-01 2.22117704e-01
2.54974381e-01 2.88065996e-01 3.19140358e-01 3.45155652e-01
3.62406408e-01 3.66929683e-01 3.55276350e-01 3.25626224e-01
2.79008160e-01 2.20098059e-01 1.56889049e-01 9.87692499e-02
5.34071317e-02 2.39766001e-02 8.57583753e-03 2.32454889e-03
4.49417507e-04 5.75867858e-05 4.47365473e-06 1.89022325e-07
3.80222577e-09 3.08903326e-11 8.26626301e-14 5.65758942e-17
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20]
M1 t0 = 0.9999995003330115
Time solver in progress
total nsub = 1413
total ndt = 0
total number time-steps = 1413
gij tend = [1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.58151373e-20 6.71134607e-19 2.01567949e-17
4.42248870e-16 7.29294865e-15 9.27340771e-14 9.30410820e-13
7.52030394e-12 4.99007337e-11 2.76538360e-10 1.30028384e-09
5.26370138e-09 1.85954802e-08 5.80605476e-08 1.62114128e-07
4.09211290e-07 9.43160357e-07 2.00290113e-06 3.95100281e-06
7.29300900e-06 1.26797680e-05 2.08876101e-05 3.27760988e-05
4.92285262e-05 7.10843594e-05 9.90739851e-05 1.33764011e-04
1.75516976e-04 2.24463942e-04 2.80483688e-04 3.43179298e-04
4.11842202e-04 4.85395420e-04 5.62311440e-04 6.40506227e-04
7.17219736e-04 7.88906211e-04 8.51175400e-04 8.98848040e-04
9.26211113e-04 9.27568947e-04 8.98163776e-04 8.35453947e-04
7.40563329e-04 6.19462096e-04 4.83203238e-04 3.46533816e-04
2.24682747e-04 1.29144513e-04 6.43336204e-05 2.70728417e-05
9.35565793e-06 2.57595808e-06 5.48084180e-07 8.76105830e-08
1.02989152e-08 8.82936803e-10 5.58011088e-11 2.68014562e-12
1.01776045e-13 3.15322804e-15 8.08351891e-17 1.72365410e-18
4.18655966e-20 1.25510281e-20 1.19688112e-20 1.17831580e-20
1.16049241e-20 1.14363246e-20 1.12834293e-20 1.11501313e-20
1.10371865e-20 1.09425110e-20 1.08624092e-20 1.07930443e-20
1.07314405e-20 1.06757281e-20 1.06248605e-20 1.05782242e-20]
M1 t0 = 0.9999995003330115
M1 tend = 0.9999995003330108
diff M1 = -7.771561172376096e-16
Time solver in 9.93499
plotting case order k=0
gij_end = <class 'numpy.float64'>
gij_end is a scalar
plotting case order k=1
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=2
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=3
gij_end = <class 'numpy.ndarray'>
gij_end is an array
Run the tests (k_dv)
271 run_kernel_case(3)
272 plt.show()
Test coala for k_dv
Computing coala solver for k=0
Tensor tabflux generated in 0.25729 s
gij generated in 0.00032 s
gij t0 = [1.90527518e-03 5.34978592e-03 1.49200031e-02 4.08236317e-02
1.05876532e-01 2.36603895e-01 3.53238069e-01 1.92536780e-01
1.28210758e-02 7.88742300e-06 5.05922357e-15 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1206
total ndt = 48
total number time-steps = 1254
gij tend = [1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.31892386e-17 6.38032582e-12 1.94799381e-08 2.28200883e-06
3.62269061e-05 1.84425482e-04 4.70169142e-04 7.25605636e-04
6.50272254e-04 2.78866711e-04 4.62995766e-05 2.55881283e-06
4.07228839e-08 1.35651760e-10 5.05782277e-14 9.94500806e-19]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202355
diff M1 = -2.1094237467877974e-15
Time solver in 0.31254
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 8.27928 s
gij generated in 0.00083 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04]
[ 5.34978592e-03 2.53498952e-03]
[ 1.49200031e-02 7.00550421e-03]
[ 4.08236317e-02 1.86714390e-02]
[ 1.05876532e-01 4.47777100e-02]
[ 2.36603895e-01 7.68481264e-02]
[ 3.53238069e-01 1.50847901e-02]
[ 1.92536780e-01 -1.40538593e-01]
[ 1.28210758e-02 -1.28210758e-02]
[ 7.88742300e-06 -7.88742300e-06]
[ 5.05922357e-15 -5.05921357e-15]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1288
total ndt = 0
total number time-steps = 1288
gij tend = [[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00]
[ 9.70510916e-19 -9.60510916e-19]
[ 1.15559032e-12 -1.11713699e-12]
[ 6.06315559e-09 -5.31576522e-09]
[ 1.05076481e-06 -7.24461756e-07]
[ 2.20606788e-05 -9.96948261e-06]
[ 1.38916479e-04 -3.23630902e-05]
[ 4.22334257e-04 -2.66024954e-05]
[ 7.79715862e-04 -8.59487083e-06]
[ 8.21791842e-04 -1.53219455e-04]
[ 3.12568877e-04 -2.27842536e-04]
[ 1.85690653e-05 -1.85690653e-05]
[ 1.21676131e-07 -1.21676131e-07]
[ 1.21500409e-10 -1.21500409e-10]
[ 1.42205022e-14 -1.42204922e-14]
[ 6.75962801e-20 -5.75962801e-20]
[ 1.06563712e-20 -1.15006299e-22]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202383
diff M1 = 6.661338147750939e-16
Time solver in 6.42304
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 35.59829 s
gij generated in 0.00679 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02]
[ 1.28210758e-02 -2.10736118e-02 1.68642939e-02]
[ 7.88742300e-06 -1.01855598e-05 1.31438063e-05]
[ 5.05922357e-15 -6.34995441e-15 8.54561595e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1319
total ndt = 0
total number time-steps = 1319
gij tend = [[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00]
[ 6.03955483e-19 -6.79190415e-19 3.02038994e-19]
[ 8.44411506e-13 -8.68834247e-13 3.60246560e-13]
[ 4.88239401e-09 -4.55035263e-09 1.84002152e-09]
[ 8.95896782e-07 -6.64076140e-07 2.50588309e-07]
[ 2.00841079e-05 -9.84202472e-06 3.12937577e-06]
[ 1.31743516e-04 -3.39237292e-05 9.13527658e-06]
[ 4.13574868e-04 -3.27552343e-05 6.28468658e-06]
[ 7.86792549e-04 -1.94431772e-05 -1.31262293e-05]
[ 8.50342352e-04 -1.94549244e-04 -1.53957116e-05]
[ 3.11818644e-04 -3.00267310e-04 7.92599760e-05]
[ 1.46536032e-05 -2.41768426e-05 1.91132197e-05]
[ 2.71229057e-07 -3.56859592e-07 4.47625235e-07]
[ 4.25136962e-09 -4.75980169e-09 7.49516979e-09]
[ 7.59616740e-12 -8.22592641e-12 1.35246133e-11]
[ 3.51440554e-16 -3.78492459e-16 6.26660010e-16]
[ 1.25349075e-20 -2.73868351e-21 4.51622697e-21]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202353
diff M1 = -2.3314683517128287e-15
Time solver in 28.41653
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 96.50130 s
gij generated in 0.00706 s
gij t0 = [[ 1.90527518e-03 9.05725016e-04 -5.49509960e-07 1.49930663e-10]
[ 5.34978592e-03 2.53498952e-03 -4.34223153e-06 3.34102550e-09]
[ 1.49200031e-02 7.00550421e-03 -3.39884114e-05 7.38262831e-08]
[ 4.08236317e-02 1.86714390e-02 -2.59000879e-04 1.59300983e-06]
[ 1.05876532e-01 4.47777100e-02 -1.82867015e-03 3.21378086e-05]
[ 2.36603895e-01 7.68481264e-02 -1.03458457e-02 5.35173800e-04]
[ 3.53238069e-01 1.50847901e-02 -2.89427354e-02 5.06383102e-03]
[ 1.92536780e-01 -1.40538593e-01 1.94501341e-02 5.03190777e-03]
[ 1.28210758e-02 -2.13264427e-02 1.70666234e-02 -8.56125651e-03]
[ 7.88742300e-06 -8.86780238e-06 1.14433256e-05 -1.04629462e-05]
[ 5.05922357e-15 -5.35814132e-15 7.21085774e-15 -6.91192999e-15]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]]
M1 t0 = 0.9999988304202376
Time solver in progress
total nsub = 1310
total ndt = 0
total number time-steps = 1310
gij tend = [[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 1.00000000e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00]
[ 5.68101941e-19 -6.41124819e-19 2.96165723e-19 -9.53975237e-20]
[ 8.11587057e-13 -8.37390651e-13 3.58304026e-13 -1.08172248e-13]
[ 4.75488584e-09 -4.44359728e-09 1.85407011e-09 -5.66819237e-10]
[ 8.78880882e-07 -6.53030844e-07 2.52414909e-07 -7.61154442e-08]
[ 1.98187128e-05 -9.77979876e-06 3.14393063e-06 -7.57682312e-07]
[ 1.30647875e-04 -3.39731553e-05 8.95910294e-06 -1.43917565e-06]
[ 4.11907821e-04 -3.35572617e-05 5.66810249e-06 4.63738218e-07]
[ 7.86745815e-04 -2.10938293e-05 -1.44335915e-05 5.32080213e-06]
[ 8.53644536e-04 -1.98925364e-04 -1.49290197e-05 1.10159604e-05]
[ 3.13382392e-04 -3.06095800e-04 9.29522346e-05 -7.86946230e-06]
[ 1.41566100e-05 -2.48440953e-05 2.31358535e-05 -1.24483682e-05]
[ 1.25809728e-07 -1.22116648e-07 1.75644275e-07 -1.79337355e-07]
[ 6.82890022e-10 -4.41998579e-10 7.15956795e-10 -9.56848238e-10]
[ 3.68615890e-13 -2.24938390e-13 3.71385035e-13 -5.15062526e-13]
[ 3.32434318e-18 -2.00379596e-18 3.32662772e-18 -4.63717494e-18]
[ 1.06612138e-20 -1.21818590e-22 3.13339746e-24 6.13463787e-23]]
M1 t0 = 0.9999988304202376
M1 tend = 0.9999988304202418
diff M1 = 4.218847493575595e-15
Time solver in 40.21354
Computing coala solver for k_dv (k=0), ref solution
Tensor tabflux generated in 30.06042 s
gij generated in 0.00019 s
gij t0 = [1.11388714e-03 1.37002748e-03 1.68496775e-03 2.07215484e-03
2.54808441e-03 3.13297862e-03 3.85160744e-03 4.73428037e-03
5.81803832e-03 7.14807753e-03 8.77943753e-03 1.07789822e-02
1.32276937e-02 1.62232810e-02 1.98830708e-02 2.43470927e-02
2.97811797e-02 3.63797645e-02 4.43678399e-02 5.40012432e-02
6.55639905e-02 7.93607924e-02 9.57021315e-02 1.14878385e-01
1.37118570e-01 1.62528657e-01 1.91004643e-01 2.22117704e-01
2.54974381e-01 2.88065996e-01 3.19140358e-01 3.45155652e-01
3.62406408e-01 3.66929683e-01 3.55276350e-01 3.25626224e-01
2.79008160e-01 2.20098059e-01 1.56889049e-01 9.87692499e-02
5.34071317e-02 2.39766001e-02 8.57583753e-03 2.32454889e-03
4.49417507e-04 5.75867858e-05 4.47365473e-06 1.89022325e-07
3.80222577e-09 3.08903326e-11 8.26626301e-14 5.65758942e-17
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20]
M1 t0 = 0.9999995003330115
Time solver in progress
total nsub = 1414
total ndt = 0
total number time-steps = 1414
gij tend = [1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.00000000e-20 1.00000000e-20 1.00000000e-20
1.00000000e-20 1.54753101e-20 6.57978620e-19 1.97964719e-17
4.35043591e-16 7.18473259e-15 9.14817747e-14 9.18984647e-13
7.43637744e-12 4.93948931e-11 2.73991816e-10 1.28939477e-09
5.22354647e-09 1.84659328e-08 5.76898601e-08 1.61161575e-07
4.06988198e-07 9.38400928e-07 1.99347088e-06 3.93357308e-06
7.26274189e-06 1.26300575e-05 2.08099117e-05 3.26598542e-05
4.90611619e-05 7.08513224e-05 9.87587721e-05 1.33348172e-04
1.74980100e-04 2.23783683e-04 2.79635940e-04 3.42138664e-04
4.10582967e-04 4.83893253e-04 5.60546080e-04 6.38465406e-04
7.14904488e-04 7.86337515e-04 8.48401646e-04 8.95952097e-04
9.23314730e-04 9.24831068e-04 8.95768646e-04 8.33585557e-04
7.39366252e-04 6.18995834e-04 4.83406407e-04 3.47220379e-04
2.25586233e-04 1.30002646e-04 6.49748304e-05 2.74547665e-05
9.53508080e-06 2.64103287e-06 5.65829996e-07 9.11516206e-08
1.08043064e-08 9.33935830e-10 5.94665317e-11 2.87354069e-12
1.09615554e-13 3.40776928e-15 8.76091178e-17 1.87199758e-18
4.45145178e-20 1.25894115e-20 1.19700598e-20 1.17842427e-20
1.16061795e-20 1.14376235e-20 1.12846341e-20 1.11511427e-20
1.10379676e-20 1.09430830e-20 1.08628263e-20 1.07933632e-20
1.07317020e-20 1.06759545e-20 1.06250617e-20 1.05784049e-20]
M1 t0 = 0.9999995003330115
M1 tend = 0.9999995003330124
diff M1 = 8.881784197001252e-16
Time solver in 27.67756
plotting case order k=0
gij_end = <class 'numpy.float64'>
gij_end is a scalar
plotting case order k=1
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=2
gij_end = <class 'numpy.ndarray'>
gij_end is an array
plotting case order k=3
gij_end = <class 'numpy.ndarray'>
gij_end is an array
Total running time of the script: (13 minutes 46.587 seconds)
Estimated memory usage: 179 MB