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 import shamrock.external.coala as coala
13 from matplotlib import pyplot as plt
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:
71 dthydro = 1e-1
72 ndthydro = 500
73 elif kernel == 3:
74 dthydro = 1e-1
75 ndthydro = 500
76 else:
77 raise ValueError("need to choose a kernel")
78
79 if kernel == 0:
80 print("Test coala for kconst")
81 elif kernel == 1:
82 print("Test coala for kadd")
83 elif kernel == 2:
84 print("Test coala for k_Br")
85 else:
86 print("Test coala for k_dv")
87
88 massgrid, massbins = coala.init_grid_log(nbins, massmax, massmin)
89
90 for case in cases:
91 kpol = cases[case]["kpol"]
92 print("")
93 print("Computing coala solver for k=%d" % (kpol))
94 match kernel:
95 case 0 | 1 | 2:
96 gij_init, gij, time_coag = coala.iterate_coag(
97 kernel,
98 K0,
99 nbins,
100 kpol,
101 dthydro,
102 ndthydro,
103 coeff_CFL,
104 Q,
105 eps,
106 massgrid,
107 massbins,
108 )
109
110 case 3:
111 # Brownian motion dv with constant approximation
112 dv_Br = np.zeros((nbins, nbins))
113 massmeanlog = np.sqrt(massgrid[0:nbins] * massgrid[1:])
114 for i in range(nbins):
115 for j in range(nbins):
116 dv_Br[i, j] = np.sqrt(1.0 / massmeanlog[i] + 1.0 / massmeanlog[j])
117
118 gij_init, gij, time_coag = coala.iterate_coag_kdv(
119 kernel,
120 K0,
121 nbins,
122 kpol,
123 dthydro,
124 ndthydro,
125 coeff_CFL,
126 Q,
127 eps,
128 massgrid,
129 massbins,
130 dv_Br,
131 )
132
133 case _:
134 print("Need to choose available kernel in kernel_collision.py.")
135
136 cases[case]["massgrid"] = massgrid
137 cases[case]["massbins"] = massbins
138 cases[case]["gij_init"] = gij_init
139 cases[case]["gij_end"] = gij
140 cases[case]["time"] = [t0, time_coag]
141
142 # compute ref solutions when needed
143 match kernel:
144 case 2:
145 # dv Brownian with analytic formula
146 nbins_ref = 100
147 massgrid_ref, massbins_ref = coala.init_grid_log(nbins_ref, massmax, massmin)
148
149 print("")
150 print("Computing coala solver for k_Br (k=0), ref solution")
151 gij_init_ref, gij_ref, time_coag_ref = coala.iterate_coag(
152 kernel,
153 K0,
154 nbins_ref,
155 0,
156 dthydro,
157 ndthydro,
158 coeff_CFL,
159 Q,
160 eps,
161 massgrid_ref,
162 massbins_ref,
163 )
164
165 case 3:
166 # Brownian motion dv with constant approximation
167 nbins_ref = 100
168 massgrid_ref, massbins_ref = coala.init_grid_log(nbins_ref, massmax, massmin)
169
170 massmeanlog_ref = np.sqrt(massgrid_ref[0:nbins_ref] * massgrid_ref[1:])
171 dv_Br_ref = np.sqrt(1.0 / massmeanlog_ref[:, None] + 1.0 / massmeanlog_ref[None, :])
172
173 print("")
174 print("Computing coala solver for k_dv (k=0), ref solution")
175 gij_init_ref, gij_ref, time_coag_ref = coala.iterate_coag_kdv(
176 kernel,
177 K0,
178 nbins_ref,
179 0,
180 dthydro,
181 ndthydro,
182 coeff_CFL,
183 Q,
184 eps,
185 massgrid_ref,
186 massbins_ref,
187 dv_Br_ref,
188 )
189
190 # Plotting
191 plt.rcParams["font.size"] = 16
192 plt.rcParams["lines.linewidth"] = 3
193 plt.rcParams["legend.columnspacing"] = 0.5
194
195 savefig_options = dict(bbox_inches="tight")
196
197 marker_style = dict(
198 marker="o", markersize=8, markerfacecolor="white", linestyle="", markeredgewidth=2
199 )
200
201 match kernel:
202 case 0:
203 str_kernel = "kconst"
204 case 1:
205 str_kernel = "kadd"
206 case 2:
207 str_kernel = "k_Br"
208 case 3:
209 str_kernel = "k_dv"
210 case _:
211 print("Need to choose a simple kernel in the list.")
212
213 x = np.logspace(np.log10(massmin), np.log10(massmax), num=100)
214
215 tend = cases["order k=0"]["time"][-1]
216 plt.figure(1)
217 if kernel < 2:
218 plt.loglog(x, coala.exact_sol_coag(kernel, x, 0.0), "--", c="C0", alpha=0.5)
219 plt.loglog(x, coala.exact_sol_coag(kernel, x, tend), "--", c="C0", label="Analytic")
220 else:
221 plt.loglog(massbins_ref, gij_init_ref, "--", c="C0", alpha=0.5)
222 plt.loglog(massbins_ref, gij_ref, "--", c="C0", label="ref %d bins" % (nbins_ref))
223
224 plt.loglog(
225 cases["order k=0"]["massbins"],
226 cases["order k=0"]["gij_init"],
227 markeredgecolor="black",
228 label="gij init",
229 **marker_style,
230 alpha=0.5,
231 )
232 for case in cases:
233 print("plotting case", case)
234
235 # if cases[case]["gij_end"][0] is a scalar
236 print("gij_end = ", type(cases[case]["gij_end"][0]))
237 if isinstance(cases[case]["gij_end"][0], np.float64):
238 print("gij_end is a scalar")
239 plt.loglog(cases[case]["massbins"], cases[case]["gij_end"], label=case, **marker_style)
240 else:
241 print("gij_end is an array")
242 plt.loglog(
243 cases[case]["massbins"], cases[case]["gij_end"][:, 0], label=case, **marker_style
244 )
245 # print ("gij_end = ",type(cases[case]["gij_end"][0]))
246 # plt.loglog(cases[case]["massbins"],cases[case]["gij_end"],markeredgecolor='black',label=case,**marker_style)
247
248 plt.ylim(1.0e-15, 1.0e1)
249 plt.xlim(massmin, massmax)
250 plt.title(str_kernel + ", nbins=%d" % (nbins))
251 plt.xlabel(r"mass ")
252 plt.ylabel(r"mass density distribution g")
253 plt.legend(loc="lower left", ncol=1)
254 plt.tight_layout()
Run the tests (kconst)
259 run_kernel_case(0)
260 plt.show()
Test coala for kconst
Computing coala solver for k=0
Tensor tabflux generated in 0.13527 s
gij generated in 0.00021 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 0.04827
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 4.47939 s
gij generated in 0.00058 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 0.55749
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 19.39482 s
gij generated in 0.00398 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 6.25480
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 51.67647 s
gij generated in 0.00393 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 -9.32076598e-21]
[ 2.41954044e-11 1.15245077e-11 2.72382806e-17 1.11835724e-19]
[ 6.82010910e-11 3.24813744e-11 2.23365770e-16 4.41779966e-19]
[ 1.92233124e-10 9.15522312e-11 1.79848437e-15 1.24247212e-18]
[ 5.41860314e-10 2.58087502e-10 1.43522044e-14 -5.90228353e-18]
[ 1.52770115e-09 7.27852848e-10 1.13835684e-13 -9.84660186e-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 = 0.999998830420235
diff M1 = -2.6645352591003757e-15
Time solver in 7.22259
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)
264 run_kernel_case(1)
265 plt.show()
Test coala for kadd
Computing coala solver for k=0
Tensor tabflux generated in 0.13803 s
gij generated in 0.00019 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 0.03636
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 4.50094 s
gij generated in 0.00054 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 0.36863
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 19.32643 s
gij generated in 0.00396 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 = 0.9999988304202398
diff M1 = 2.220446049250313e-15
Time solver in 3.77221
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 52.24841 s
gij generated in 0.00406 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 = 0.9999988304202364
diff M1 = -1.2212453270876722e-15
Time solver in 4.36910
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)
269 run_kernel_case(2)
270 plt.show()
Test coala for k_Br
Computing coala solver for k=0
Tensor tabflux generated in 0.17276 s
gij generated in 0.00019 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 0.08606
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 5.33595 s
gij generated in 0.00053 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 1.00229
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 22.67073 s
gij generated in 0.00381 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 9.72381
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 61.65492 s
gij generated in 0.00415 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 = 0.99999883042024
diff M1 = 2.3314683517128287e-15
Time solver in 13.04927
Computing coala solver for k_Br (k=0), ref solution
Tensor tabflux generated in 19.64510 s
gij generated in 0.00014 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 4.15078
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)
274 run_kernel_case(3)
275 plt.show()
Test coala for k_dv
Computing coala solver for k=0
Tensor tabflux generated in 0.14986 s
gij generated in 0.00028 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 0.17591
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 4.70329 s
gij generated in 0.00056 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 3.29229
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 20.64112 s
gij generated in 0.00377 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 = 0.9999988304202372
diff M1 = -4.440892098500626e-16
Time solver in 15.64346
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 55.00851 s
gij generated in 0.00420 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 = 0.9999988304202422
diff M1 = 4.551914400963142e-15
Time solver in 22.44401
Computing coala solver for k_dv (k=0), ref solution
Tensor tabflux generated in 17.47249 s
gij generated in 0.00016 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 17.29790
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: (7 minutes 50.381 seconds)
Estimated memory usage: 177 MB