The purpose of this clone is to have a python version of the popular dacefit toolbox in MATLAB [1]. The toolbox can be found here.

This framework is an exact clone of the original code and the correctness has been checked. Please contact me if you should be scenarios where the values are significantly different (10^6).


The test problems are uploaded to the PyPi Repository.

pip install pydacefit


In general, the function calls are very similar to the MATLAB Version. The only difference is that in Python an actual object is used which provide the functions fit and predict.

The following shows how to use this framework:

import numpy as np

from pydacefit.corr import corr_gauss, corr_cubic, corr_exp, corr_expg, corr_spline, corr_spherical
from pydacefit.dace import DACE, regr_linear, regr_quadratic
from pydacefit.regr import regr_constant

import matplotlib.pyplot as plt

# -----------------------------------------------
# Different ways of initialization
# -----------------------------------------------

# regression can be: regr_constant, regr_linear or regr_quadratic
regression = regr_constant
# regression = regr_linear
# regression = regr_quadratic

# then define the correlation (all possible correlations are shown below)
# please have a look at the MATLAB document for more details
correlation = corr_gauss
# correlation = corr_cubic
# correlation = corr_exp
# correlation = corr_expg
# correlation = corr_spline
# correlation = corr_spherical
# correlation = corr_cubic

# This initializes a DACEFIT objective using the provided regression and correlation
# because an initial theta is provided and also thetaL and thetaU the hyper parameter
# optimization is done
dacefit = DACE(regr=regression, corr=correlation,
               theta=1.0, thetaL=0.00001, thetaU=100)

# if no lower and upper bounds are defined, then no hyperparameter optimization is executed
dacefit_no_hyperparameter_optimization = DACE(regr=regression, corr=correlation,
                                              theta=1.0, thetaL=None, thetaU=None)

# to turn on the automatic relevance detection use a vector for theta and define bounds
dacefit_with_ard = DACE(regr=regression, corr=correlation,
                        theta=[1.0, 1.0], thetaL=[0.001, 0.0001], thetaU=[20, 20])

# -----------------------------------------------
# Create some data for the purpose of testing
# -----------------------------------------------

def fun(X):
    return np.sum(np.sin(X * 2 * np.pi), axis=1)

X = np.random.random((20, 1))
F = fun(X)

# -----------------------------------------------
# Fit the model with the data and predict
# -----------------------------------------------

# create the model and fit it, F)

# predict values for plotting
_X = np.linspace(0, 1, 100)[:, None]
_F = dacefit.predict(_X)

# -----------------------------------------------
# Plot the results
# -----------------------------------------------

plt.scatter(X, F, label="prediction")
plt.plot(_X, _F, label="data")

print("MSE: ", np.mean(np.abs(fun(_X)[:, None] - _F)))



H. B. Nielsen, S. N. Lophaven, and J. Søndergaard. DACE - a matlab kriging toolbox. 2002. URL:


Feel free to contact me if you have any question:

Julian Blank (blankjul [at]
Michigan State University
Computational Optimization and Innovation Laboratory (COIN)
East Lansing, MI 48824, USA