{ "info": { "author": "Felipe Souza Lima", "author_email": "felipe.lima@eq.ufcg.edu.br", "bugtrack_url": null, "classifiers": [ "License :: OSI Approved :: Apache Software License", "Operating System :: OS Independent", "Programming Language :: Python :: 3.6", "Topic :: Scientific/Engineering" ], "description": "# Description\n\nThis project is an adaptation from the work of Hans Bruun Nielsen, S\u00c3\u00b8ren Nymand and Lophaven Jacob S\u00c3\u00b8ndergaard.\n\n## Notes\n**This is a implementation that relies heavily on linear algebra solvers** (least-squares solvers, Cholesky and QR \ndecompositions, etc.). Therefore, it is strongly advised that your numpy library be integrated to a \n[BLAS library](http://markus-beuckelmann.de/blog/boosting-numpy-blas.html) (e.g.: Intel-MKL, OpenBLAS, ATLAS, etc.) \nin order to attain satisfactory performances of calculation.\n\nFor the sake of convenience, Anaconda handles the gritty details of how to combine numpy and those libraries natively.\n\n## Installation\n\nTo install through PyPi Repository:\n\n pip install pydace\n\nTo install via conda\n\n conda install -c felipes21 pydace\n\n## Usage\n\n### Example with dace model\n\n```python \n import numpy as np\n import scipy.io as sio\n from pydace import Dace\n import matplotlib.pyplot as plt\n\n # Load the training and validation data. (Here we are using a file from the\n # github repo located in the folder pydace\\tests with the name \n # 'doe_final_infill_mat'\n\n mat_contents = sio.loadmat('doe_final_infill.mat')\n\n design_data = mat_contents['MV'] # design sites\n observed_data = mat_contents['CV'] # experiment results\n\n # define the hyperparameters bounds and initial estimate\n theta0 = 1 * np.ones((design_data.shape[1],))\n lob = 1e-5 * np.ones(theta0.shape)\n upb = 1e5 * np.ones(theta0.shape)\n\n # select the training and validation data\n design_val = design_data[:99, :]\n observed_val = observed_data[:99, :]\n\n design_train = design_data[100:, :]\n observed_train = observed_data[100:, :]\n\n # build the univariate kriging models with a first order polynomial \n # regression and a gaussian regression model\n observed_prediction = np.empty(observed_val.shape)\n for j in np.arange(design_data.shape[1]):\n # initialize the dace object\n dace_obj = Dace('poly1', 'corrgauss', optimizer='boxmin')\n\n # fit the training data using the default hyperparameter optimizer\n dace_obj.fit(design_train, observed_train[:, j], theta0, lob, upb)\n\n # predict the validation data\n observed_prediction[:, [j]], *_ = dace_obj.predict(design_val)\n\n # labels for the observed data\n var_labels = ['L/F', 'V/F', 'xD', 'xB', 'J', 'QR'] \n\n # plot the validation data\n for var in np.arange(design_data.shape[1]):\n plt.figure(var + 1)\n plt.plot(observed_val[:, var], observed_prediction[:,var], 'b+')\n plt.xlabel(var_labels[var] + ' - Observed')\n plt.ylabel(var_labels[var] + ' - Kriging Prediction')\n\n plt.show()\n```\n\n### Example of design of experiment data generation\nIt is also possible to generate design of experiment data with a variation reduction technique called Latin Hypercube\nSampling (LHS) that is already implemented in this toolbox.\n\nLets say we have a 4-th dimensional problem (i.e. 4 design/input variables). They are defined by the following bounds.\n\n![Variables to sample](lhsvariables.png)\n\nIf we want to build a latin hypercube within these bounds we would do the following:\n\n```python \n import numpy as np\n from pydace.aux_functions import lhsdesign\n\n lb = np.array([8.5, 0., 102., 0.])\n ub = np.array([20., 100., 400., 400.])\n\n lhs = lhsdesign(53, lb, ub, include_vertices=False)\n```\n\n## Contact/Talk to me\n\nMy e-email is felipe.lima@eq.ufcg.edu.br. 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