Note
Click here to download the full example code
Algorithm: RegAdaptive#
# Windows users have to encapsulate the code into a main function to avoid multiprocessing errors.
# def main():
import pygpc
import numpy as np
from collections import OrderedDict
fn_results = 'tmp/regadaptive' # filename of output
save_session_format = ".pkl" # file format of saved gpc session ".hdf5" (slow) or ".pkl" (fast)
Loading the model and defining the problem#
# define model
model = pygpc.testfunctions.Ishigami()
# define problem
parameters = OrderedDict()
parameters["x1"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[-np.pi, np.pi])
parameters["x2"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[-np.pi, np.pi])
parameters["x3"] = 0.
parameters["a"] = 7.
parameters["b"] = 0.1
problem = pygpc.Problem(model, parameters)
Setting up the algorithm#
# gPC options
options = dict()
options["order_start"] = 5
options["order_end"] = 20
options["solver"] = "LarsLasso"
options["interaction_order"] = 2
options["order_max_norm"] = 0.7
options["n_cpu"] = 0
options["adaptive_sampling"] = True
options["gradient_enhanced"] = True
options["gradient_calculation"] = "FD_fwd"
options["gradient_calculation_options"] = {"dx": 0.001, "distance_weight": -2}
options["fn_results"] = fn_results
options["save_session_format"] = save_session_format
options["eps"] = 0.0075
options["grid"] = pygpc.Random
options["grid_options"] = {"seed": 1}
# define algorithm
algorithm = pygpc.RegAdaptive(problem=problem, options=options)
Running the gpc#
# Initialize gPC Session
session = pygpc.Session(algorithm=algorithm)
# run gPC algorithm
session, coeffs, results = session.run()
Out:
Initializing gPC object...
Creating initial grid (<class 'pygpc.Grid.Random'>) with n_grid=28.0
Initializing gPC matrix...
Starting adaptive sampling:
Extending grid from 28 to 28 by 0 sampling points
Performing simulations 1 to 28
It/Sub-it: 5/2 Performing simulation 01 from 28 [= ] 3.6%
Total parallel function evaluation: 0.006276369094848633 sec
It/Sub-it: 5/2 Performing simulation 01 from 56 [ ] 1.8%
Gradient evaluation: 0.0005824565887451172 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV 24 from 25 [====================================== ] 96.0%
LOOCV 25 from 25 [========================================] 100.0%
LOOCV computation time: 0.043991804122924805 sec
-> relative loocv error = 5.377542041076339
Extending grid from 28 to 29 by 1 sampling points
Performing simulations 29 to 29
It/Sub-it: 5/2 Performing simulation 1 from 1 [========================================] 100.0%
Total parallel function evaluation: 0.005603790283203125 sec
It/Sub-it: 5/2 Performing simulation 1 from 2 [==================== ] 50.0%
Gradient evaluation: 0.0005440711975097656 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.043187856674194336 sec
-> relative loocv error = 5.4389255100332
Order/Interaction order: 6/1
============================
Starting adaptive sampling:
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.05651235580444336 sec
-> relative loocv error = 2.7424898356615115
Starting adaptive sampling:
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.05181598663330078 sec
-> relative loocv error = 0.2706490419013213
Order/Interaction order: 7/1
============================
Starting adaptive sampling:
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.1637439727783203 sec
-> relative loocv error = 2.166994676373574
Extending grid from 29 to 31 by 2 sampling points
Performing simulations 30 to 31
It/Sub-it: 7/1 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.00604701042175293 sec
It/Sub-it: 7/1 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0006062984466552734 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.07811856269836426 sec
-> relative loocv error = 0.5750523757165803
Extending grid from 31 to 33 by 2 sampling points
Performing simulations 32 to 33
It/Sub-it: 7/1 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.0058994293212890625 sec
It/Sub-it: 7/1 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0005195140838623047 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.07593035697937012 sec
-> relative loocv error = 0.24863210863921048
Extending grid from 33 to 35 by 2 sampling points
Performing simulations 34 to 35
It/Sub-it: 7/1 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.00604701042175293 sec
It/Sub-it: 7/1 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.00048422813415527344 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.08003425598144531 sec
-> relative loocv error = 0.28953840725742275
Starting adaptive sampling:
Extending grid from 35 to 37 by 2 sampling points
Performing simulations 36 to 37
It/Sub-it: 7/2 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.005279541015625 sec
It/Sub-it: 7/2 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0005128383636474609 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.07238507270812988 sec
-> relative loocv error = 0.5931898041382196
Extending grid from 37 to 39 by 2 sampling points
Performing simulations 38 to 39
It/Sub-it: 7/2 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.006007194519042969 sec
It/Sub-it: 7/2 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0005488395690917969 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.060982465744018555 sec
-> relative loocv error = 0.577730672588717
Order/Interaction order: 8/1
============================
Starting adaptive sampling:
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.11690235137939453 sec
-> relative loocv error = 0.07013088550854302
Starting adaptive sampling:
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.09050297737121582 sec
-> relative loocv error = 0.11129548131752019
Extending grid from 39 to 41 by 2 sampling points
Performing simulations 40 to 41
It/Sub-it: 8/2 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.006171464920043945 sec
It/Sub-it: 8/2 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0005750656127929688 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.08337211608886719 sec
-> relative loocv error = 0.11827342483956584
Order/Interaction order: 9/1
============================
Starting adaptive sampling:
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.16336321830749512 sec
-> relative loocv error = 0.12504479993150708
Extending grid from 41 to 43 by 2 sampling points
Performing simulations 42 to 43
It/Sub-it: 9/1 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.006613254547119141 sec
It/Sub-it: 9/1 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0006575584411621094 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.13547492027282715 sec
-> relative loocv error = 0.07020897203877206
Extending grid from 43 to 45 by 2 sampling points
Performing simulations 44 to 45
It/Sub-it: 9/1 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.009029865264892578 sec
It/Sub-it: 9/1 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0007212162017822266 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.13698387145996094 sec
-> relative loocv error = 0.06337373123600874
Starting adaptive sampling:
Extending grid from 45 to 47 by 2 sampling points
Performing simulations 46 to 47
It/Sub-it: 9/2 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.006031513214111328 sec
It/Sub-it: 9/2 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0005385875701904297 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.13159584999084473 sec
-> relative loocv error = 0.031183973071024478
Extending grid from 47 to 49 by 2 sampling points
Performing simulations 48 to 49
It/Sub-it: 9/2 Performing simulation 1 from 2 [==================== ] 50.0%
Total parallel function evaluation: 0.006354570388793945 sec
It/Sub-it: 9/2 Performing simulation 1 from 4 [========== ] 25.0%
Gradient evaluation: 0.0008597373962402344 sec
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.12259411811828613 sec
-> relative loocv error = 0.02068268619927386
Order/Interaction order: 10/1
=============================
Starting adaptive sampling:
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
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LOOCV computation time: 0.16002273559570312 sec
-> relative loocv error = 0.0037572748491800927
Determine gPC coefficients using 'LarsLasso' solver (gradient enhanced)...
Postprocessing#
# read session
session = pygpc.read_session(fname=session.fn_session, folder=session.fn_session_folder)
# Post-process gPC
pygpc.get_sensitivities_hdf5(fn_gpc=options["fn_results"],
output_idx=None,
calc_sobol=True,
calc_global_sens=True,
calc_pdf=True,
algorithm="sampling",
n_samples=1e3)
Out:
> Loading gpc session object: tmp/regadaptive.pkl
> Loading gpc coeffs: tmp/regadaptive.hdf5
> Adding results to: tmp/regadaptive.hdf5
Validation#
Validate gPC vs original model function (2D-surface)#
pygpc.validate_gpc_plot(session=session,
coeffs=coeffs,
random_vars=list(problem.parameters_random.keys()),
n_grid=[51, 51],
output_idx=[0],
fn_out=None,
folder=None,
n_cpu=session.n_cpu)
Validate gPC vs original model function (Monte Carlo)#
nrmsd = pygpc.validate_gpc_mc(session=session,
coeffs=coeffs,
n_samples=int(1e4),
output_idx=[0],
fn_out=None,
folder=None,
plot=True,
n_cpu=session.n_cpu)
print("> Maximum NRMSD (gpc vs original): {:.2}%".format(max(nrmsd)))
# On Windows subprocesses will import (i.e. execute) the main module at start.
# You need to insert an if __name__ == '__main__': guard in the main module to avoid
# creating subprocesses recursively.
#
# if __name__ == '__main__':
# main()
Out:
> Maximum NRMSD (gpc vs original): 0.0025%
Total running time of the script: ( 0 minutes 3.509 seconds)