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pyDOE_corrected.py
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pyDOE_corrected.py
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"""
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.
"""
import re
import numpy as np
#__all__ = ['np', 'fullfact_corrected', 'ff2n', 'fracfact']
def fullfact_corrected(levels):
"""
Create a general full-factorial design
Parameters
----------
levels : array-like
An array of integers that indicate the number of levels of each input
design factor.
Returns
-------
mat : 2d-array
The design matrix with coded levels 0 to k-1 for a k-level factor
Example
-------
::
>>> fullfact([2, 4, 3])
array([[ 0., 0., 0.],
[ 1., 0., 0.],
[ 0., 1., 0.],
[ 1., 1., 0.],
[ 0., 2., 0.],
[ 1., 2., 0.],
[ 0., 3., 0.],
[ 1., 3., 0.],
[ 0., 0., 1.],
[ 1., 0., 1.],
[ 0., 1., 1.],
[ 1., 1., 1.],
[ 0., 2., 1.],
[ 1., 2., 1.],
[ 0., 3., 1.],
[ 1., 3., 1.],
[ 0., 0., 2.],
[ 1., 0., 2.],
[ 0., 1., 2.],
[ 1., 1., 2.],
[ 0., 2., 2.],
[ 1., 2., 2.],
[ 0., 3., 2.],
[ 1., 3., 2.]])
"""
n = len(levels) # number of factors
nb_lines = np.prod(levels) # number of trial conditions
H = np.zeros((nb_lines, n))
level_repeat = 1
range_repeat = np.prod(levels)
for i in range(n):
range_repeat //= levels[i]
lvl = []
for j in range(levels[i]):
lvl += [j]*level_repeat
rng = lvl*range_repeat
level_repeat *= levels[i]
H[:, i] = rng
return H
################################################################################
def ff2n(n):
"""
Create a 2-Level full-factorial design
Parameters
----------
n : int
The number of factors in the design.
Returns
-------
mat : 2d-array
The design matrix with coded levels -1 and 1
Example
-------
::
>>> ff2n(3)
array([[-1., -1., -1.],
[ 1., -1., -1.],
[-1., 1., -1.],
[ 1., 1., -1.],
[-1., -1., 1.],
[ 1., -1., 1.],
[-1., 1., 1.],
[ 1., 1., 1.]])
"""
return 2*fullfact_corrected([2]*n) - 1
################################################################################
def fracfact(gen):
"""
Create a 2-level fractional-factorial design with a generator string.
Parameters
----------
gen : str
A string, consisting of lowercase, uppercase letters or operators "-"
and "+", indicating the factors of the experiment
Returns
-------
H : 2d-array
A m-by-n matrix, the fractional factorial design. m is 2^k, where k
is the number of letters in ``gen``, and n is the total number of
entries in ``gen``.
Notes
-----
In ``gen`` we define the main factors of the experiment and the factors
whose levels are the products of the main factors. For example, if
gen = "a b ab"
then "a" and "b" are the main factors, while the 3rd factor is the product
of the first two. If we input uppercase letters in ``gen``, we get the same
result. We can also use the operators "+" and "-" in ``gen``.
For example, if
gen = "a b -ab"
then the 3rd factor is the opposite of the product of "a" and "b".
The output matrix includes the two level full factorial design, built by
the main factors of ``gen``, and the products of the main factors. The
columns of ``H`` follow the sequence of ``gen``.
For example, if
gen = "a b ab c"
then columns H[:, 0], H[:, 1], and H[:, 3] include the two level full
factorial design and H[:, 2] includes the products of the main factors.
Examples
--------
::
>>> fracfact("a b ab")
array([[-1., -1., 1.],
[ 1., -1., -1.],
[-1., 1., -1.],
[ 1., 1., 1.]])
>>> fracfact("A B AB")
array([[-1., -1., 1.],
[ 1., -1., -1.],
[-1., 1., -1.],
[ 1., 1., 1.]])
>>> fracfact("a b -ab c +abc")
array([[-1., -1., -1., -1., -1.],
[ 1., -1., 1., -1., 1.],
[-1., 1., 1., -1., 1.],
[ 1., 1., -1., -1., -1.],
[-1., -1., -1., 1., 1.],
[ 1., -1., 1., 1., -1.],
[-1., 1., 1., 1., -1.],
[ 1., 1., -1., 1., 1.]])
"""
# Recognize letters and combinations
A = [item for item in re.split('\-?\s?\+?', gen) if item] # remove empty strings
C = [len(item) for item in A]
# Indices of single letters (main factors)
I = [i for i, item in enumerate(C) if item==1]
# Indices of letter combinations (we need them to fill out H2 properly).
J = [i for i, item in enumerate(C) if item!=1]
# Check if there are "-" or "+" operators in gen
U = [item for item in gen.split(' ') if item] # remove empty strings
# If R1 is either None or not, the result is not changed, since it is a
# multiplication of 1.
R1 = _grep(U, '+')
R2 = _grep(U, '-')
# Fill in design with two level factorial design
H1 = ff2n(len(I))
H = np.zeros((H1.shape[0], len(C)))
H[:, I] = H1
# Recognize combinations and fill in the rest of matrix H2 with the proper
# products
for k in J:
# For lowercase letters
xx = np.array([ord(c) for c in A[k]]) - 97
# For uppercase letters
if np.any(xx<0):
xx = np.array([ord(c) for c in A[k]]) - 65
H[:, k] = np.prod(H1[:, xx], axis=1)
# Update design if gen includes "-" operator
if R2:
H[:, R2] *= -1
# Return the fractional factorial design
return H
def _grep(haystack, needle):
try:
haystack[0]
except (TypeError, AttributeError):
return [0] if needle in haystack else []
else:
locs = []
for idx, item in enumerate(haystack):
if needle in item:
locs += [idx]
return locs
#__all__ = ['bbdesign_corrected']
def bbdesign_corrected(n, center=None):
"""
Create a Box-Behnken design
Parameters
----------
n : int
The number of factors in the design
Optional
--------
center : int
The number of center points to include (default = 1).
Returns
-------
mat : 2d-array
The design matrix
Example
-------
::
>>> bbdesign(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 = ff2n(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 = int((0.5*n*(n-1))*H_fact.shape[0])
H = repeat_center(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, repeat_center(n, center).T].T
return H
def repeat_center(n, repeat):
"""
Create the center-point portion of a design matrix
Parameters
----------
n : int
The number of factors in the original design
repeat : int
The number of center points to repeat
Returns
-------
mat : 2d-array
The center-point portion of a design matrix (elements all zero).
Example
-------
::
>>> repeat_center(3, 2)
array([[ 0., 0., 0.],
[ 0., 0., 0.]])
"""
return np.zeros((repeat, n))