README.md

Description

This project is an adaptation from the work of Hans Bruun Nielsen, Søren Nymand and Lophaven Jacob Søndergaard.

Notes

This is a implementation that relies heavily on linear algebra solvers (least-squares solvers, Cholesky and QR decompositions, etc.). Therefore, it is strongly advised that your numpy library be integrated to a BLAS library (e.g.: Intel-MKL, OpenBLAS, ATLAS, etc.) in order to attain satisfactory performances of calculation.

For the sake of convenience, Anaconda handles the gritty details of how to combine numpy and those libraries natively.

Installation

To install through PyPi Repository:

pip install pydace

To install via conda

conda install -c felipes21 pydace

Usage

Example with dace model

    import numpy as np
    import scipy.io as sio
    from pydace import Dace
    import matplotlib.pyplot as plt
    
    # Load the training and validation data. (Here we are using a file from the
    # github repo located in the folder pydace\tests with the name 
    # 'doe_final_infill_mat'
    
    mat_contents = sio.loadmat('doe_final_infill.mat')
    
    design_data = mat_contents['MV']  # design sites
    observed_data = mat_contents['CV']  # experiment results
    
    # define the hyperparameters bounds and initial estimate
    theta0 = 1 * np.ones((design_data.shape[1],))
    lob = 1e-5 * np.ones(theta0.shape)
    upb = 1e5 * np.ones(theta0.shape)
    
    # select the training and validation data
    design_val = design_data[:99, :]
    observed_val = observed_data[:99, :]
    
    design_train = design_data[100:, :]
    observed_train = observed_data[100:, :]
    
    # build the univariate kriging models with a first order polynomial 
    # regression and a gaussian regression model
    observed_prediction = np.empty(observed_val.shape)
    for j in np.arange(design_data.shape[1]):
        # initialize the dace object
        dace_obj = Dace('poly1', 'corrgauss', optimizer='boxmin')

        # fit the training data using the default hyperparameter optimizer
        dace_obj.fit(design_train, observed_train[:, j], theta0, lob, upb)

        # predict the validation data
        observed_prediction[:, [j]], *_ = dace_obj.predict(design_val)
    
    # labels for the observed data
    var_labels = ['L/F', 'V/F', 'xD', 'xB', 'J', 'QR'] 
    
    # plot the validation data
    for var in np.arange(design_data.shape[1]):
        plt.figure(var + 1)
        plt.plot(observed_val[:, var], observed_prediction[:,var], 'b+')
        plt.xlabel(var_labels[var] + ' - Observed')
        plt.ylabel(var_labels[var] + ' - Kriging Prediction')
    
    plt.show()

Example of design of experiment data generation

It is also possible to generate design of experiment data with a variation reduction technique called Latin Hypercube Sampling (LHS) that is already implemented in this toolbox.

Lets say we have a 4-th dimensional problem (i.e. 4 design/input variables). They are defined by the following bounds.

If we want to build a latin hypercube within these bounds we would do the following:

    import numpy as np
    from pydace.aux_functions import lhsdesign
    
    lb = np.array([8.5, 0., 102., 0.])
    ub = np.array([20., 100., 400., 400.])

    lhs = lhsdesign(53, lb, ub, include_vertices=False)

Contact/Talk to me

My e-email is felipe.lima@eq.ufcg.edu.br. Feel free to contact me anytime, or just nag me if I'm being lazy.