# Source code for surrogate.sampling.samBoxBehnken

```
# Copyright 2016 Quan Pan
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Quan Pan <quanpan302@hotmail.com>
# License: Apache License, Version 2.0
# Create: 2016-12-02
import numpy as np
from .samFullFact import samFF2n
from .utils.doe_repeatCenter import repeatCenter
[docs]def samBoxBehnken(n, center=None):
"""Create a Box-Behnken design
:param n: The number of factors in the design
:param center: The number of center points to include (default = 1).
:return: The design matrix
This code was originally published by the following individuals for use with
Scilab:
- Copyright (C) 2012 - 2013 - Michael Baudin
- Copyright (C) 2012 - Maria Christopoulou
- Copyright (C) 2010 - 2011 - INRIA - Michael Baudin
- Copyright (C) 2009 - Yann Collette
- Copyright (C) 2009 - CEA - Jean-Marc Martinez
website: forge.scilab.org/index.php/p/scidoe/sourcetree/master/macros
Much thanks goes to these individuals. It has been converted to Python by
Abraham Lee.
:Example:
>>> samBoxBehnken(3)
array([[-1., -1., 0.],
[ 1., -1., 0.],
[-1., 1., 0.],
[ 1., 1., 0.],
[-1., 0., -1.],
[ 1., 0., -1.],
[-1., 0., 1.],
[ 1., 0., 1.],
[ 0., -1., -1.],
[ 0., 1., -1.],
[ 0., -1., 1.],
[ 0., 1., 1.],
[ 0., 0., 0.],
[ 0., 0., 0.],
[ 0., 0., 0.]])
"""
assert n >= 3, 'Number of variables must be at least 3'
# First, compute a factorial DOE with 2 parameters
H_fact = samFF2n(2)
# Now we populate the real DOE with this DOE
# We made a factorial design on each pair of dimensions
# - So, we created a factorial design with two factors
# - Make two loops
Index = 0
nb_lines = (n * (n - 1) / 2) * H_fact.shape[0]
H = repeatCenter(n, nb_lines)
for i in range(n - 1):
for j in range(i + 1, n):
Index = Index + 1
H[max([0, (Index - 1) * H_fact.shape[0]]):Index * H_fact.shape[0], i] = H_fact[:, 0]
H[max([0, (Index - 1) * H_fact.shape[0]]):Index * H_fact.shape[0], j] = H_fact[:, 1]
if center is None:
if n <= 16:
points = [0, 0, 0, 3, 3, 6, 6, 6, 8, 9, 10, 12, 12, 13, 14, 15, 16]
center = points[n]
else:
center = n
H = np.c_[H.T, repeatCenter(n, center).T].T
return H
```