Probability of Failure Estimation with Gaussian Processes
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import qmcpy as qp
import gpytorch
import torch
import os
import warnings
import pandas as pd
from gpytorch.utils.warnings import NumericalWarning
warnings.filterwarnings("ignore")
pd.set_option(
'display.max_rows', None,
'display.max_columns', None,
'display.width', 1000,
'display.colheader_justify', 'center',
'display.precision',2,
'display.float_format',lambda x:'%.1e'%x)
from matplotlib import pyplot
pyplot.style.use("../qmcpy/qmcpy.mplstyle")
!pip install botorch -U --quiet
import qmcpy as qp
import pandas as pd
pd.set_option(
'display.max_rows', None,
'display.max_columns', None,
'display.width', 1000,
'display.colheader_justify', 'center',
'display.precision',2,
'display.float_format',lambda x:'%.1e'%x)
from matplotlib import pyplot
pyplot.style.use("../qmcpy/qmcpy.mplstyle")
gpytorch_use_gpu = torch.cuda.is_available()
gpytorch_use_gpu
False
Sin 1d Problem
mcispfgp = qp.PFGPCI(
integrand = qp.Sin1d(qp.DigitalNetB2(1,seed=17),k=3),
failure_threshold = 0,
failure_above_threshold=True,
abs_tol = 1e-2,
alpha = 1e-1,
n_init = 4,
init_samples = None,
batch_sampler = qp.PFSampleErrorDensityAR(verbose=True),
n_batch = 4,
n_max = 20,
n_approx = 2**18,
gpytorch_prior_mean = gpytorch.means.ZeroMean(),
gpytorch_prior_cov = gpytorch.kernels.ScaleKernel(
gpytorch.kernels.MaternKernel(nu=2.5,
lengthscale_constraint = gpytorch.constraints.Interval(.01,.1)
),
outputscale_constraint = gpytorch.constraints.Interval(1e-3,10)
),
gpytorch_likelihood = gpytorch.likelihoods.GaussianLikelihood(noise_constraint = gpytorch.constraints.Interval(1e-12,1e-8)),
gpytorch_marginal_log_likelihood_func = lambda likelihood,gpyt_model: gpytorch.mlls.ExactMarginalLogLikelihood(likelihood,gpyt_model),
torch_optimizer_func = lambda gpyt_model: torch.optim.Adam(gpyt_model.parameters(),lr=0.1),
gpytorch_train_iter = 100,
gpytorch_use_gpu = False,
verbose = 50,
n_ref_approx = 2**22,
seed_ref_approx = None)
solution,data = mcispfgp.integrate(seed=7,refit=False)
print(data)
df = pd.DataFrame(data.get_results_dict())
print("\nIteration Summary")
print(df)
data.plot();
reference approximation with d=1: 0.5000002384185791
batch 0
gpytorch model fitting
iter 50 of 100
likelihood.noise_covar.raw_noise.................. -8.63e-02
covar_module.raw_outputscale...................... -3.04e+00
covar_module.base_kernel.raw_lengthscale.......... 5.04e+00
iter 100 of 100
likelihood.noise_covar.raw_noise.................. -1.01e-01
covar_module.raw_outputscale...................... -2.96e+00
covar_module.base_kernel.raw_lengthscale.......... 6.29e+00
batch 1
AR sampling with efficiency 2.6e-01, expect 15 draws: 12, 15, 18, 21, 24,
batch 2
AR sampling with efficiency 1.7e-01, expect 23 draws: 16, 20,
batch 3
AR sampling with efficiency 1.3e-01, expect 30 draws: 20, 25,
batch 4
AR sampling with efficiency 6.1e-02, expect 65 draws: 48, 72,
PFGPCIData (AccumulateData Object)
solution 0.500
error_bound 0.073
bound_low 0.426
bound_high 0.573
n_total 20
time_integrate 0.644
PFGPCI (StoppingCriterion Object)
Sin1d (Integrand Object)
Uniform (TrueMeasure Object)
lower_bound 0
upper_bound 18.850
DigitalNetB2 (DiscreteDistribution Object)
d 1
dvec 0
randomize LMS_DS
graycode 0
entropy 17
spawn_key ()
Iteration Summary
n_sum n_batch error_bounds ci_low ci_high solutions solutions_ref error_ref in_ci
0 4 4 5.1e-01 0.0e+00 1.0e+00 4.9e-01 5.0e-01 1.4e-02 True
1 8 4 5.0e-01 0.0e+00 1.0e+00 5.0e-01 5.0e-01 2.2e-03 True
2 12 4 5.2e-01 0.0e+00 1.0e+00 4.8e-01 5.0e-01 1.6e-02 True
3 16 4 3.0e-01 2.1e-01 8.1e-01 5.1e-01 5.0e-01 1.0e-02 True
4 20 4 7.3e-02 4.3e-01 5.7e-01 5.0e-01 5.0e-01 4.7e-04 True
Multimodal 2d Problem
mcispfgp = qp.PFGPCI(
integrand = qp.Multimodal2d(qp.DigitalNetB2(2,seed=17)),
failure_threshold = 0,
failure_above_threshold=True,
abs_tol = 1e-2,
alpha = 1e-1,
n_init = 64,
init_samples = None,
batch_sampler = qp.PFSampleErrorDensityAR(verbose=True),
n_batch = 16,
n_max = 128,
n_approx = 2**18,
gpytorch_prior_mean = gpytorch.means.ZeroMean(),
gpytorch_prior_cov = gpytorch.kernels.ScaleKernel(
gpytorch.kernels.MaternKernel(nu=1.5,
lengthscale_constraint = gpytorch.constraints.Interval(.1,1)
),
outputscale_constraint = gpytorch.constraints.Interval(1e-3,.5)
),
gpytorch_likelihood = gpytorch.likelihoods.GaussianLikelihood(noise_constraint = gpytorch.constraints.Interval(1e-12,1e-8)),
gpytorch_marginal_log_likelihood_func = lambda likelihood,gpyt_model: gpytorch.mlls.ExactMarginalLogLikelihood(likelihood,gpyt_model),
torch_optimizer_func = lambda gpyt_model: torch.optim.Adam(gpyt_model.parameters(),lr=0.1),
gpytorch_train_iter = 800,
gpytorch_use_gpu = gpytorch_use_gpu,
verbose = 200,
n_ref_approx = 2**22,
seed_ref_approx = None)
solution,data = mcispfgp.integrate(seed=7,refit=False)
print(data)
df = pd.DataFrame(data.get_results_dict())
print("\nIteration Summary")
print(df)
data.plot();
reference approximation with d=2: 0.3020772933959961
batch 0
gpytorch model fitting
iter 200 of 800
likelihood.noise_covar.raw_noise.................. 1.45e+00
covar_module.raw_outputscale...................... 2.92e+00
covar_module.base_kernel.raw_lengthscale.......... -3.02e+00
iter 400 of 800
likelihood.noise_covar.raw_noise.................. 1.49e+00
covar_module.raw_outputscale...................... 3.70e+00
covar_module.base_kernel.raw_lengthscale.......... -3.32e+00
iter 600 of 800
likelihood.noise_covar.raw_noise.................. 1.53e+00
covar_module.raw_outputscale...................... 4.24e+00
covar_module.base_kernel.raw_lengthscale.......... -3.43e+00
iter 800 of 800
likelihood.noise_covar.raw_noise.................. 1.58e+00
covar_module.raw_outputscale...................... 4.66e+00
covar_module.base_kernel.raw_lengthscale.......... -3.48e+00
batch 1
AR sampling with efficiency 7.6e-02, expect 211 draws: 144, 198,
batch 2
AR sampling with efficiency 3.8e-02, expect 416 draws: 288,
batch 3
AR sampling with efficiency 2.8e-02, expect 581 draws: 400, 500, 525,
batch 4
AR sampling with efficiency 2.0e-02, expect 785 draws: 544, 748, 816, 884,
PFGPCIData (AccumulateData Object)
solution 0.298
error_bound 0.079
bound_low 0.219
bound_high 0.377
n_total 128
time_integrate 4.295
PFGPCI (StoppingCriterion Object)
Multimodal2d (Integrand Object)
Uniform (TrueMeasure Object)
lower_bound [-4 -3]
upper_bound [7 8]
DigitalNetB2 (DiscreteDistribution Object)
d 2^(1)
dvec [0 1]
randomize LMS_DS
graycode 0
entropy 17
spawn_key ()
Iteration Summary
n_sum n_batch error_bounds ci_low ci_high solutions solutions_ref error_ref in_ci
0 64 64 3.8e-01 0.0e+00 6.7e-01 3.0e-01 3.0e-01 5.7e-03 True
1 80 16 1.9e-01 8.1e-02 4.7e-01 2.7e-01 3.0e-01 2.8e-02 True
2 96 16 1.4e-01 1.5e-01 4.2e-01 2.9e-01 3.0e-01 1.5e-02 True
3 112 16 1.0e-01 2.0e-01 4.0e-01 3.0e-01 3.0e-01 4.5e-03 True
4 128 16 7.9e-02 2.2e-01 3.8e-01 3.0e-01 3.0e-01 4.0e-03 True
Four Branch 2d Problem
mcispfgp = qp.PFGPCI(
integrand = qp.FourBranch2d(qp.DigitalNetB2(2,seed=17)),
failure_threshold = 0,
failure_above_threshold=True,
abs_tol = 1e-2,
alpha = 1e-1,
n_init = 64,
init_samples = None,
batch_sampler = qp.PFSampleErrorDensityAR(verbose=True),
n_batch = 12,
n_max = 200,
n_approx = 2**18,
gpytorch_prior_mean = gpytorch.means.ZeroMean(),
gpytorch_prior_cov = gpytorch.kernels.ScaleKernel(
gpytorch.kernels.MaternKernel(nu=1.5,
lengthscale_constraint = gpytorch.constraints.Interval(.5,1)
),
outputscale_constraint = gpytorch.constraints.Interval(1e-8,.5)
),
gpytorch_likelihood = gpytorch.likelihoods.GaussianLikelihood(noise_constraint = gpytorch.constraints.Interval(1e-12,1e-8)),
gpytorch_marginal_log_likelihood_func = lambda likelihood,gpyt_model: gpytorch.mlls.ExactMarginalLogLikelihood(likelihood,gpyt_model),
torch_optimizer_func = lambda gpyt_model: torch.optim.Adam(gpyt_model.parameters(),lr=0.1),
gpytorch_train_iter = 800,
gpytorch_use_gpu = gpytorch_use_gpu,
verbose = 200,
n_ref_approx = 2**22,
seed_ref_approx = None)
solution,data = mcispfgp.integrate(seed=7,refit=False)
print(data)
df = pd.DataFrame(data.get_results_dict())
print("\nIteration Summary")
print(df)
data.plot();
reference approximation with d=2: 0.20872807502746582
batch 0
gpytorch model fitting
iter 200 of 800
likelihood.noise_covar.raw_noise.................. 2.89e+00
covar_module.raw_outputscale...................... 3.88e+00
covar_module.base_kernel.raw_lengthscale.......... -4.50e+00
iter 400 of 800
likelihood.noise_covar.raw_noise.................. 3.63e+00
covar_module.raw_outputscale...................... 4.78e+00
covar_module.base_kernel.raw_lengthscale.......... -5.44e+00
iter 600 of 800
likelihood.noise_covar.raw_noise.................. 4.17e+00
covar_module.raw_outputscale...................... 5.36e+00
covar_module.base_kernel.raw_lengthscale.......... -6.04e+00
iter 800 of 800
likelihood.noise_covar.raw_noise.................. 4.59e+00
covar_module.raw_outputscale...................... 5.80e+00
covar_module.base_kernel.raw_lengthscale.......... -6.48e+00
batch 1
AR sampling with efficiency 9.0e-03, expect 1337 draws: 924, 1232,
batch 2
AR sampling with efficiency 4.9e-03, expect 2461 draws: 1704, 2556,
batch 3
AR sampling with efficiency 3.7e-03, expect 3250 draws: 2256,
batch 4
AR sampling with efficiency 2.5e-03, expect 4858 draws: 3372, 3653, 3934,
PFGPCIData (AccumulateData Object)
solution 0.207
error_bound 0.009
bound_low 0.198
bound_high 0.217
n_total 112
time_integrate 4.376
PFGPCI (StoppingCriterion Object)
FourBranch2d (Integrand Object)
Uniform (TrueMeasure Object)
lower_bound -8
upper_bound 2^(3)
DigitalNetB2 (DiscreteDistribution Object)
d 2^(1)
dvec [0 1]
randomize LMS_DS
graycode 0
entropy 17
spawn_key ()
Iteration Summary
n_sum n_batch error_bounds ci_low ci_high solutions solutions_ref error_ref in_ci
0 64 64 4.5e-02 1.6e-01 2.5e-01 2.0e-01 2.1e-01 3.8e-03 True
1 76 12 2.4e-02 1.9e-01 2.3e-01 2.1e-01 2.1e-01 1.4e-03 True
2 88 12 1.8e-02 1.9e-01 2.3e-01 2.1e-01 2.1e-01 1.0e-03 True
3 100 12 1.2e-02 1.9e-01 2.2e-01 2.1e-01 2.1e-01 1.6e-03 True
4 112 12 9.4e-03 2.0e-01 2.2e-01 2.1e-01 2.1e-01 1.4e-03 True
Ishigami 3d Problem
mcispfgp = qp.PFGPCI(
integrand = qp.Ishigami(qp.DigitalNetB2(3,seed=17)),
failure_threshold = 0,
failure_above_threshold=False,
abs_tol = 1e-2,
alpha = 1e-1,
n_init = 128,
init_samples = None,
batch_sampler = qp.PFSampleErrorDensityAR(verbose=True),
n_batch = 16,
n_max = 256,
n_approx = 2**18,
gpytorch_prior_mean = gpytorch.means.ZeroMean(),
gpytorch_prior_cov = gpytorch.kernels.ScaleKernel(
gpytorch.kernels.MaternKernel(nu=2.5,
lengthscale_constraint = gpytorch.constraints.Interval(.5,1)
),
outputscale_constraint = gpytorch.constraints.Interval(1e-8,.5)
),
gpytorch_likelihood = gpytorch.likelihoods.GaussianLikelihood(noise_constraint = gpytorch.constraints.Interval(1e-12,1e-8)),
gpytorch_marginal_log_likelihood_func = lambda likelihood,gpyt_model: gpytorch.mlls.ExactMarginalLogLikelihood(likelihood,gpyt_model),
torch_optimizer_func = lambda gpyt_model: torch.optim.Adam(gpyt_model.parameters(),lr=0.1),
gpytorch_train_iter = 800,
gpytorch_use_gpu = gpytorch_use_gpu,
verbose = 200,
n_ref_approx = 2**22,
seed_ref_approx = None)
solution,data = mcispfgp.integrate(seed=7,refit=False)
print(data)
df = pd.DataFrame(data.get_results_dict())
print("\nIteration Summary")
print(df)
data.plot();
reference approximation with d=3: 0.16239547729492188
batch 0
gpytorch model fitting
iter 200 of 800
likelihood.noise_covar.raw_noise.................. 2.18e+00
covar_module.raw_outputscale...................... 3.43e+00
covar_module.base_kernel.raw_lengthscale.......... -4.09e+00
iter 400 of 800
likelihood.noise_covar.raw_noise.................. 2.66e+00
covar_module.raw_outputscale...................... 4.26e+00
covar_module.base_kernel.raw_lengthscale.......... -4.99e+00
iter 600 of 800
likelihood.noise_covar.raw_noise.................. 3.08e+00
covar_module.raw_outputscale...................... 4.81e+00
covar_module.base_kernel.raw_lengthscale.......... -5.56e+00
iter 800 of 800
likelihood.noise_covar.raw_noise.................. 3.43e+00
covar_module.raw_outputscale...................... 5.24e+00
covar_module.base_kernel.raw_lengthscale.......... -6.00e+00
batch 1
AR sampling with efficiency 6.1e-03, expect 2626 draws: 1824,
batch 2
AR sampling with efficiency 5.3e-03, expect 3019 draws: 2096, 3013, 3668, 3930, 4061, 4192, 4323, 4454, 4585,
batch 3
AR sampling with efficiency 4.4e-03, expect 3631 draws: 2512, 4082, 4710, 4867, 5024,
batch 4
AR sampling with efficiency 4.0e-03, expect 4003 draws: 2784,
batch 5
AR sampling with efficiency 3.5e-03, expect 4576 draws: 3168, 4158, 4554, 4950,
batch 6
AR sampling with efficiency 3.0e-03, expect 5315 draws: 3680, 4600, 5060, 5520,
batch 7
AR sampling with efficiency 2.5e-03, expect 6313 draws: 4384,
batch 8
AR sampling with efficiency 2.4e-03, expect 6570 draws: 4560, 5985, 6270, 6555, 6840, 7125, 7410,
PFGPCIData (AccumulateData Object)
solution 0.166
error_bound 0.011
bound_low 0.155
bound_high 0.177
n_total 256
time_integrate 14.351
PFGPCI (StoppingCriterion Object)
Ishigami (Integrand Object)
Uniform (TrueMeasure Object)
lower_bound -3.142
upper_bound 3.142
DigitalNetB2 (DiscreteDistribution Object)
d 3
dvec [0 1 2]
randomize LMS_DS
graycode 0
entropy 17
spawn_key ()
Iteration Summary
n_sum n_batch error_bounds ci_low ci_high solutions solutions_ref error_ref in_ci
0 128 128 3.0e-02 1.4e-01 2.0e-01 1.7e-01 1.6e-01 1.1e-02 True
1 144 16 2.6e-02 1.4e-01 2.0e-01 1.7e-01 1.6e-01 9.1e-03 True
2 160 16 2.2e-02 1.5e-01 1.9e-01 1.7e-01 1.6e-01 8.1e-03 True
3 176 16 2.0e-02 1.5e-01 1.9e-01 1.7e-01 1.6e-01 7.4e-03 True
4 192 16 1.7e-02 1.5e-01 1.8e-01 1.7e-01 1.6e-01 3.7e-03 True
5 208 16 1.5e-02 1.5e-01 1.8e-01 1.7e-01 1.6e-01 4.7e-03 True
6 224 16 1.3e-02 1.5e-01 1.8e-01 1.7e-01 1.6e-01 3.4e-03 True
7 240 16 1.2e-02 1.5e-01 1.8e-01 1.6e-01 1.6e-01 2.3e-03 True
8 256 16 1.1e-02 1.6e-01 1.8e-01 1.7e-01 1.6e-01 3.5e-03 True
Hartmann 6d Problem
mcispfgp = qp.PFGPCI(
integrand = qp.Hartmann6d(qp.DigitalNetB2(6,seed=17)),
failure_threshold = -2,
failure_above_threshold=False,
abs_tol = 2.5e-3,
alpha = 1e-1,
n_init = 512,
init_samples = None,
batch_sampler = qp.PFSampleErrorDensityAR(verbose=True),
n_batch = 64,
n_max = 2500,
n_approx = 2**18,
gpytorch_prior_mean = gpytorch.means.ZeroMean(),
gpytorch_prior_cov = gpytorch.kernels.ScaleKernel(gpytorch.kernels.MaternKernel(nu=2.5)),
gpytorch_likelihood = gpytorch.likelihoods.GaussianLikelihood(noise_constraint = gpytorch.constraints.Interval(1e-12,1e-8)),
gpytorch_marginal_log_likelihood_func = lambda likelihood,gpyt_model: gpytorch.mlls.ExactMarginalLogLikelihood(likelihood,gpyt_model),
torch_optimizer_func = lambda gpyt_model: torch.optim.Adam(gpyt_model.parameters(),lr=0.1),
gpytorch_train_iter = 150,
gpytorch_use_gpu = gpytorch_use_gpu,
verbose = 50,
n_ref_approx = 2**23,
seed_ref_approx = None)
solution,data = mcispfgp.integrate(seed=7,refit=False)
print(data)
df = pd.DataFrame(data.get_results_dict())
print("\nIteration Summary")
print(df)
data.plot();
reference approximation with d=6: 0.007387995719909668
batch 0
gpytorch model fitting
iter 50 of 150
likelihood.noise_covar.raw_noise.................. 1.65e+00
covar_module.raw_outputscale...................... 5.53e-01
covar_module.base_kernel.raw_lengthscale.......... 2.79e-01
iter 100 of 150
likelihood.noise_covar.raw_noise.................. 2.80e+00
covar_module.raw_outputscale...................... 5.10e-01
covar_module.base_kernel.raw_lengthscale.......... 2.67e-01
iter 150 of 150
likelihood.noise_covar.raw_noise.................. 3.38e+00
covar_module.raw_outputscale...................... 5.14e-01
covar_module.base_kernel.raw_lengthscale.......... 2.68e-01
batch 1
AR sampling with efficiency 1.4e-03, expect 45089 draws: 31232, 35624,
batch 2
AR sampling with efficiency 2.1e-03, expect 30750 draws: 21312, 27306, 29304, 30969, 31635, 32301,
batch 3
AR sampling with efficiency 1.8e-03, expect 35103 draws: 24320, 32680, 36860, 38000,
batch 4
AR sampling with efficiency 1.6e-03, expect 41262 draws: 28608, 40230, 41571,
batch 5
AR sampling with efficiency 1.4e-03, expect 46939 draws: 32576, 43265, 47846, 50900,
batch 6
AR sampling with efficiency 1.2e-03, expect 54986 draws: 38144, 51852, 53044, 54236, 54832,
batch 7
AR sampling with efficiency 1.0e-03, expect 61209 draws: 42432, 59670, 66300, 68289, 69615, 70278,
batch 8
AR sampling with efficiency 9.2e-04, expect 69388 draws: 48128, 63168, 65424, 66176, 66928, 67680, 68432,
batch 9
AR sampling with efficiency 8.4e-04, expect 75933 draws: 52672, 66663, 71601, 73247,
batch 10
AR sampling with efficiency 7.6e-04, expect 84744 draws: 58752, 80784, 89046,
batch 11
AR sampling with efficiency 6.9e-04, expect 93317 draws: 64704, 93012, 99078, 101100, 103122, 105144,
batch 12
AR sampling with efficiency 6.3e-04, expect 101312 draws: 70208, 95439, 103118, 105312, 107506,
batch 13
AR sampling with efficiency 6.0e-04, expect 106776 draws: 74048, 87932, 92560,
batch 14
AR sampling with efficiency 5.7e-04, expect 112270 draws: 77824, 98496, 100928, 102144,
batch 15
AR sampling with efficiency 5.6e-04, expect 115250 draws: 79872, 113568, 124800, 126048, 127296, 128544, 129792, 131040, 132288, 133536, 134784,
batch 16
AR sampling with efficiency 5.2e-04, expect 123202 draws: 85376, 88044, 89378, 90712,
PFGPCIData (AccumulateData Object)
solution 0.007
error_bound 0.002
bound_low 0.005
bound_high 0.010
n_total 1536
time_integrate 250.998
PFGPCI (StoppingCriterion Object)
Hartmann6d (Integrand Object)
Uniform (TrueMeasure Object)
lower_bound 0
upper_bound 1
DigitalNetB2 (DiscreteDistribution Object)
d 6
dvec [0 1 2 3 4 5]
randomize LMS_DS
graycode 0
entropy 17
spawn_key ()
Iteration Summary
n_sum n_batch error_bounds ci_low ci_high solutions solutions_ref error_ref in_ci
0 512 512 7.1e-03 0.0e+00 8.6e-03 1.5e-03 7.4e-03 5.9e-03 True
1 576 64 1.0e-02 0.0e+00 1.7e-02 6.6e-03 7.4e-03 8.3e-04 True
2 640 64 9.1e-03 0.0e+00 1.6e-02 7.3e-03 7.4e-03 1.1e-04 True
3 704 64 7.8e-03 0.0e+00 1.5e-02 7.5e-03 7.4e-03 1.1e-04 True
4 768 64 6.8e-03 7.4e-04 1.4e-02 7.6e-03 7.4e-03 1.7e-04 True
5 832 64 5.8e-03 1.8e-03 1.3e-02 7.6e-03 7.4e-03 2.3e-04 True
6 896 64 5.2e-03 2.4e-03 1.3e-02 7.6e-03 7.4e-03 2.0e-04 True
7 960 64 4.6e-03 2.9e-03 1.2e-02 7.5e-03 7.4e-03 1.5e-04 True
8 1024 64 4.2e-03 3.2e-03 1.2e-02 7.5e-03 7.4e-03 6.6e-05 True
9 1088 64 3.8e-03 3.6e-03 1.1e-02 7.4e-03 7.4e-03 1.6e-05 True
10 1152 64 3.4e-03 4.0e-03 1.1e-02 7.4e-03 7.4e-03 2.4e-05 True
11 1216 64 3.2e-03 4.3e-03 1.1e-02 7.4e-03 7.4e-03 3.2e-05 True
12 1280 64 3.0e-03 4.4e-03 1.0e-02 7.4e-03 7.4e-03 1.3e-05 True
13 1344 64 2.9e-03 4.6e-03 1.0e-02 7.4e-03 7.4e-03 1.3e-05 True
14 1408 64 2.8e-03 4.6e-03 1.0e-02 7.4e-03 7.4e-03 1.8e-05 True
15 1472 64 2.6e-03 4.8e-03 1.0e-02 7.4e-03 7.4e-03 2.6e-05 True
16 1536 64 2.5e-03 4.9e-03 9.8e-03 7.4e-03 7.4e-03 3.3e-05 True
