Algorithm: Static (Quadrature)

# Windows users have to encapsulate the code into a main function to avoid multiprocessing errors.
# def main():
import pygpc
from collections import OrderedDict

fn_results = 'tmp/static_quad'   # 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.Peaks()

# define problem
parameters = OrderedDict()
parameters["x1"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[1.2, 2])
parameters["x2"] = 1.25
parameters["x3"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[0, 0.6])
problem = pygpc.Problem(model, parameters)

Setting up the algorithm

# gPC options
options = dict()
options["method"] = "quad"
options["solver"] = "NumInt"
options["settings"] = None
options["order"] = [9, 9]
options["order_max"] = 9
options["interaction_order"] = 2
options["error_type"] = "nrmsd"
options["n_samples_validation"] = 1e3
options["n_cpu"] = 0
options["fn_results"] = fn_results
options["save_session_format"] = save_session_format
options["backend"] = "omp"
options["grid"] = None
options["grid_options"] = {"grid_type": ["jacobi", "jacobi"], "n_dim": [9, 9]}

# generate grid
grid = pygpc.TensorGrid(parameters_random=problem.parameters_random,
                        options=options["grid_options"])

# initialize algorithm
algorithm = pygpc.Static(problem=problem, options=options, grid=grid)

Running the gpc

# initialize gPC Session
session = pygpc.Session(algorithm=algorithm)

# run gPC algorithm
session, coeffs, results = session.run()

Out:

Performing 81 simulations!

It/Sub-it: 9/2 Performing simulation 01 from 81 [                                        ] 1.2%
Total parallel function evaluation: 0.00034165382385253906 sec
Determine gPC coefficients using 'NumInt' solver ...
-> relative nrmsd error = 3.308670348173378e-08

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="standard",
                             n_samples=1e3)

Out:

> Loading gpc session object: tmp/static_quad.pkl
> Loading gpc coeffs: tmp/static_quad.hdf5
> Adding results to: tmp/static_quad.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): 3.4e-08%