.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_algorithms/plot_algorithm_static_quad.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_algorithms_plot_algorithm_static_quad.py: Algorithm: Static (Quadrature) ============================== .. GENERATED FROM PYTHON SOURCE LINES 5-13 .. code-block:: default # 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) .. GENERATED FROM PYTHON SOURCE LINES 14-16 Loading the model and defining the problem ------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 16-27 .. code-block:: default # 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) .. GENERATED FROM PYTHON SOURCE LINES 28-30 Setting up the algorithm ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 30-55 .. code-block:: default # 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) .. GENERATED FROM PYTHON SOURCE LINES 56-58 Running the gpc --------------- .. GENERATED FROM PYTHON SOURCE LINES 58-65 .. code-block:: default # initialize gPC Session session = pygpc.Session(algorithm=algorithm) # run gPC algorithm session, coeffs, results = session.run() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 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 .. GENERATED FROM PYTHON SOURCE LINES 66-68 Postprocessing -------------- .. GENERATED FROM PYTHON SOURCE LINES 68-81 .. code-block:: default # 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) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none > Loading gpc session object: tmp/static_quad.pkl > Loading gpc coeffs: tmp/static_quad.hdf5 > Adding results to: tmp/static_quad.hdf5 .. GENERATED FROM PYTHON SOURCE LINES 82-86 Validation ---------- Validate gPC vs original model function (2D-surface) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 86-94 .. code-block:: default 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) .. image-sg:: /auto_algorithms/images/sphx_glr_plot_algorithm_static_quad_001.png :alt: Original model, gPC approximation, Difference (Original vs gPC) :srcset: /auto_algorithms/images/sphx_glr_plot_algorithm_static_quad_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 95-97 Validate gPC vs original model function (Monte Carlo) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 97-114 .. code-block:: default 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() .. image-sg:: /auto_algorithms/images/sphx_glr_plot_algorithm_static_quad_002.png :alt: plot algorithm static quad :srcset: /auto_algorithms/images/sphx_glr_plot_algorithm_static_quad_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none > Maximum NRMSD (gpc vs original): 3.4e-08% .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 1.549 seconds) .. _sphx_glr_download_auto_algorithms_plot_algorithm_static_quad.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_algorithm_static_quad.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_algorithm_static_quad.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_