Note
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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
Where is coala located?
17 print(f"coala path : {coala.__file__}")
coala path : /usr/local/lib/python3.10/dist-packages/shamrock/external/coala/__init__.py
Parameters of the dust distribution & evolution
Function to run the tests for a given kernel
35 def run_kernel_case(kernel):
36
37 cases = {
38 "order k=0": {
39 "kpol": 0,
40 },
41 "order k=1": {
42 "kpol": 1,
43 },
44 "order k=2": {
45 "kpol": 2,
46 },
47 "order k=3": {
48 "kpol": 3,
49 },
50 # "order k=4": {
51 # "kpol": 4,
52 # },
53 # "order k=5": {
54 # "kpol": 5,
55 # },
56 }
57
58 if kernel == 0:
59 dthydro = 100
60 ndthydro = 300
61 elif kernel == 1:
62 dthydro = 1e-2
63 ndthydro = 300
64 elif kernel == 2:
65 dthydro = 1e-1
66 ndthydro = 500
67 elif kernel == 3:
68 dthydro = 1e-1
69 ndthydro = 500
70 else:
71 raise ValueError("need to choose a kernel")
72
73 if kernel == 0:
74 print("Test coala for kconst")
75 elif kernel == 1:
76 print("Test coala for kadd")
77 elif kernel == 2:
78 print("Test coala for k_Br")
79 else:
80 print("Test coala for k_dv")
81
82 massgrid, massbins = coala.init_grid_log(nbins, massmax, massmin)
83
84 for case in cases:
85 kpol = cases[case]["kpol"]
86 print("")
87 print("Computing coala solver for k=%d" % (kpol))
88 match kernel:
89 case 0 | 1 | 2:
90 gij_init, gij, time_coag = coala.iterate_coag(
91 kernel,
92 K0,
93 nbins,
94 kpol,
95 dthydro,
96 ndthydro,
97 coeff_CFL,
98 Q,
99 eps,
100 massgrid,
101 massbins,
102 )
103
104 case 3:
105 # Brownian motion dv with constant approximation
106 dv_Br = np.zeros((nbins, nbins))
107 massmeanlog = np.sqrt(massgrid[0:nbins] * massgrid[1:])
108 for i in range(nbins):
109 for j in range(nbins):
110 dv_Br[i, j] = np.sqrt(1.0 / massmeanlog[i] + 1.0 / massmeanlog[j])
111
112 gij_init, gij, time_coag = coala.iterate_coag_kdv(
113 kernel,
114 K0,
115 nbins,
116 kpol,
117 dthydro,
118 ndthydro,
119 coeff_CFL,
120 Q,
121 eps,
122 massgrid,
123 massbins,
124 dv_Br,
125 )
126
127 case _:
128 print("Need to choose available kernel in kernel_collision.py.")
129
130 cases[case]["massgrid"] = massgrid
131 cases[case]["massbins"] = massbins
132 cases[case]["gij_init"] = gij_init
133 cases[case]["gij_end"] = gij
134 cases[case]["time"] = [t0, time_coag]
135
136 # compute ref solutions when needed
137 match kernel:
138 case 2:
139 # dv Brownian with analytic formula
140 nbins_ref = 100
141 massgrid_ref, massbins_ref = coala.init_grid_log(nbins_ref, massmax, massmin)
142
143 print("")
144 print("Computing coala solver for k_Br (k=0), ref solution")
145 gij_init_ref, gij_ref, time_coag_ref = coala.iterate_coag(
146 kernel,
147 K0,
148 nbins_ref,
149 0,
150 dthydro,
151 ndthydro,
152 coeff_CFL,
153 Q,
154 eps,
155 massgrid_ref,
156 massbins_ref,
157 )
158
159 case 3:
160 # Brownian motion dv with constant approximation
161 nbins_ref = 100
162 massgrid_ref, massbins_ref = coala.init_grid_log(nbins_ref, massmax, massmin)
163
164 massmeanlog_ref = np.sqrt(massgrid_ref[0:nbins_ref] * massgrid_ref[1:])
165 dv_Br_ref = np.sqrt(1.0 / massmeanlog_ref[:, None] + 1.0 / massmeanlog_ref[None, :])
166
167 print("")
168 print("Computing coala solver for k_dv (k=0), ref solution")
169 gij_init_ref, gij_ref, time_coag_ref = coala.iterate_coag_kdv(
170 kernel,
171 K0,
172 nbins_ref,
173 0,
174 dthydro,
175 ndthydro,
176 coeff_CFL,
177 Q,
178 eps,
179 massgrid_ref,
180 massbins_ref,
181 dv_Br_ref,
182 )
183
184 # Plotting
185 plt.rcParams["font.size"] = 16
186 plt.rcParams["lines.linewidth"] = 3
187 plt.rcParams["legend.columnspacing"] = 0.5
188
189 savefig_options = dict(bbox_inches="tight")
190
191 marker_style = dict(
192 marker="o", markersize=8, markerfacecolor="white", linestyle="", markeredgewidth=2
193 )
194
195 match kernel:
196 case 0:
197 str_kernel = "kconst"
198 case 1:
199 str_kernel = "kadd"
200 case 2:
201 str_kernel = "k_Br"
202 case 3:
203 str_kernel = "k_dv"
204 case _:
205 print("Need to choose a simple kernel in the list.")
206
207 x = np.logspace(np.log10(massmin), np.log10(massmax), num=100)
208
209 tend = cases["order k=0"]["time"][-1]
210 plt.figure(1)
211 if kernel < 2:
212 plt.loglog(x, coala.exact_sol_coag(kernel, x, 0.0), "--", c="C0", alpha=0.5)
213 plt.loglog(x, coala.exact_sol_coag(kernel, x, tend), "--", c="C0", label="Analytic")
214 else:
215 plt.loglog(massbins_ref, gij_init_ref, "--", c="C0", alpha=0.5)
216 plt.loglog(massbins_ref, gij_ref, "--", c="C0", label="ref %d bins" % (nbins_ref))
217
218 plt.loglog(
219 cases["order k=0"]["massbins"],
220 cases["order k=0"]["gij_init"],
221 markeredgecolor="black",
222 label="gij init",
223 **marker_style,
224 alpha=0.5,
225 )
226 for case in cases:
227 print("plotting case", case)
228
229 # if cases[case]["gij_end"][0] is a scalar
230 print("gij_end = ", type(cases[case]["gij_end"][0]))
231 if isinstance(cases[case]["gij_end"][0], np.float64):
232 print("gij_end is a scalar")
233 plt.loglog(cases[case]["massbins"], cases[case]["gij_end"], label=case, **marker_style)
234 else:
235 print("gij_end is an array")
236 plt.loglog(
237 cases[case]["massbins"], cases[case]["gij_end"][:, 0], label=case, **marker_style
238 )
239 # print ("gij_end = ",type(cases[case]["gij_end"][0]))
240 # plt.loglog(cases[case]["massbins"],cases[case]["gij_end"],markeredgecolor='black',label=case,**marker_style)
241
242 plt.ylim(1.0e-15, 1.0e1)
243 plt.xlim(massmin, massmax)
244 plt.title(str_kernel + ", nbins=%d" % (nbins))
245 plt.xlabel(r"mass ")
246 plt.ylabel(r"mass density distribution g")
247 plt.legend(loc="lower left", ncol=1)
248 plt.tight_layout()
Run the tests (kconst)
253 run_kernel_case(0)
254 plt.show()
Test coala for kconst
Computing coala solver for k=0
Tensor tabflux generated in 0.21807 s
gij generated in 0.00026 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 0.10143
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 7.19022 s
gij generated in 0.00086 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 1.03491
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 31.27104 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 = 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 11.63684
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 83.70186 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 = 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 13.74876
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)
258 run_kernel_case(1)
259 plt.show()
Test coala for kadd
Computing coala solver for k=0
Tensor tabflux generated in 0.22420 s
gij generated in 0.00023 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 0.07856
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 7.34040 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 0.68452
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 31.94126 s
gij generated in 0.00669 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 7.17277
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 85.71241 s
gij generated in 0.00724 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 8.10196
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)
263 run_kernel_case(2)
264 plt.show()
Test coala for k_Br
Computing coala solver for k=0
Tensor tabflux generated in 0.26995 s
gij generated in 0.00025 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 0.18099
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 8.42691 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 = 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 1.91132
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 36.43321 s
gij generated in 0.00672 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 18.60714
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 97.62542 s
gij generated in 0.00722 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 23.72429
Computing coala solver for k_Br (k=0), ref solution
Tensor tabflux generated in 31.01839 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 = 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 10.38580
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)
268 run_kernel_case(3)
269 plt.show()
Test coala for k_dv
Computing coala solver for k=0
Tensor tabflux generated in 0.23493 s
gij generated in 0.00026 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 0.30224
Computing coala solver for k=1
Tensor tabflux tabintflux generated in 7.58921 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 = 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 7.18417
Computing coala solver for k=2
Tensor tabflux tabintflux generated in 32.95828 s
gij generated in 0.00665 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 30.18110
Computing coala solver for k=3
Tensor tabflux tabintflux generated in 88.72452 s
gij generated in 0.00722 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 42.28120
Computing coala solver for k_dv (k=0), ref solution
Tensor tabflux generated in 27.33535 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 = 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 24.62182
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 2.140 seconds)
Estimated memory usage: 158 MB