def bbdesign(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 = (n*(n-1)/2)*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 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_corrected(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 ccdesign_corrected(n,
center=(4, 4),
alpha="orthogonal",
face="circumscribed"):
"""
Central composite design
Parameters
----------
n : int
The number of factors in the design.
Optional
--------
center : int array
A 1-by-2 array of integers, the number of center points in each block
of the design. (Default: (4, 4)).
alpha : str
A string describing the effect of alpha has on the variance. ``alpha``
can take on the following values:
1. 'orthogonal' or 'o' (Default)
2. 'rotatable' or 'r'
face : str
The relation between the start points and the corner (factorial) points.
There are three options for this input:
1. 'circumscribed' or 'ccc': This is the original form of the central
composite design. The star points are at some distance ``alpha``
from the center, based on the properties desired for the design.
The start points establish new extremes for the low and high
settings for all factors. These designs have circular, spherical,
or hyperspherical symmetry and require 5 levels for each factor.
Augmenting an existing factorial or resolution V fractional
factorial design with star points can produce this design.
2. 'inscribed' or 'cci': For those situations in which the limits
specified for factor settings are truly limits, the CCI design
uses the factors settings as the star points and creates a factorial
or fractional factorial design within those limits (in other words,
a CCI design is a scaled down CCC design with each factor level of
the CCC design divided by ``alpha`` to generate the CCI design).
This design also requires 5 levels of each factor.
3. 'faced' or 'ccf': In this design, the star points are at the center
of each face of the factorial space, so ``alpha`` = 1. This
variety requires 3 levels of each factor. Augmenting an existing
factorial or resolution V design with appropriate star points can
also produce this design.
Notes
-----
- Fractional factorial designs are not (yet) available here.
- 'ccc' and 'cci' can be rotatable design, but 'ccf' cannot.
- If ``face`` is specified, while ``alpha`` is not, then the default value
of ``alpha`` is 'orthogonal'.
Returns
-------
mat : 2d-array
The design matrix with coded levels -1 and 1
Example
-------
::
>>> ccdesign(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. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[-1.82574186, 0. , 0. ],
[ 1.82574186, 0. , 0. ],
[ 0. , -1.82574186, 0. ],
[ 0. , 1.82574186, 0. ],
[ 0. , 0. , -1.82574186],
[ 0. , 0. , 1.82574186],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ]])
"""
# Check inputs
assert isinstance(n,
int) and n > 1, '"n" must be an integer greater than 1.'
assert alpha.lower() in (
"orthogonal",
"o",
"rotatable",
"r",
), 'Invalid value for "alpha": {:}'.format(alpha)
assert face.lower() in (
"circumscribed",
"ccc",
"inscribed",
"cci",
"faced",
"ccf",
), 'Invalid value for "face": {:}'.format(face)
try:
nc = len(center)
except:
raise TypeError(
'Invalid value for "center": {:}. Expected a 1-by-2 array.'.format(
center))
else:
if nc != 2:
raise ValueError(
'Invalid number of values for "center" (expected 2, but got {:})'
.format(nc))
# Orthogonal Design
if alpha.lower() in ("orthogonal", "o"):
H2, a = star(n, alpha="orthogonal", center=center)
# Rotatable Design
if alpha.lower() in ("rotatable", "r"):
H2, a = star(n, alpha="rotatable")
# Inscribed CCD
if face.lower() in ("inscribed", "cci"):
H1 = ff2n_corrected(n)
H1 = H1 / a # Scale down the factorial points
H2, a = star(n)
# Faced CCD
if face.lower() in ("faced", "ccf"):
H2, a = star(n) # Value of alpha is always 1 in Faced CCD
H1 = ff2n_corrected(n)
# Circumscribed CCD
if face.lower() in ("circumscribed", "ccc"):
H1 = ff2n_corrected(n)
C1 = repeat_center(n, center[0])
C2 = repeat_center(n, center[1])
H1 = union(H1, C1)
H2 = union(H2, C2)
H = union(H1, H2)
return H
def ccdesign(n, center=(4, 4), alpha='orthogonal', face='circumscribed'):
"""
Central composite design
Parameters
----------
n : int
The number of factors in the design.
Optional
--------
center : int array
A 1-by-2 array of integers, the number of center points in each block
of the design. (Default: (4, 4)).
alpha : str
A string describing the effect of alpha has on the variance. ``alpha``
can take on the following values:
1. 'orthogonal' or 'o' (Default)
2. 'rotatable' or 'r'
face : str
The relation between the start points and the corner (factorial) points.
There are three options for this input:
1. 'circumscribed' or 'ccc': This is the original form of the central
composite design. The star points are at some distance ``alpha``
from the center, based on the properties desired for the design.
The start points establish new extremes for the low and high
settings for all factors. These designs have circular, spherical,
or hyperspherical symmetry and require 5 levels for each factor.
Augmenting an existing factorial or resolution V fractional
factorial design with star points can produce this design.
2. 'inscribed' or 'cci': For those situations in which the limits
specified for factor settings are truly limits, the CCI design
uses the factors settings as the star points and creates a factorial
or fractional factorial design within those limits (in other words,
a CCI design is a scaled down CCC design with each factor level of
the CCC design divided by ``alpha`` to generate the CCI design).
This design also requires 5 levels of each factor.
3. 'faced' or 'ccf': In this design, the star points are at the center
of each face of the factorial space, so ``alpha`` = 1. This
variety requires 3 levels of each factor. Augmenting an existing
factorial or resolution V design with appropriate star points can
also produce this design.
Notes
-----
- Fractional factorial designs are not (yet) available here.
- 'ccc' and 'cci' can be rotatable design, but 'ccf' cannot.
- If ``face`` is specified, while ``alpha`` is not, then the default value
of ``alpha`` is 'orthogonal'.
Returns
-------
mat : 2d-array
The design matrix with coded levels -1 and 1
Example
-------
::
>>> ccdesign(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. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[-1.82574186, 0. , 0. ],
[ 1.82574186, 0. , 0. ],
[ 0. , -1.82574186, 0. ],
[ 0. , 1.82574186, 0. ],
[ 0. , 0. , -1.82574186],
[ 0. , 0. , 1.82574186],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ]])
"""
# Check inputs
assert isinstance(n, int) and n>1, '"n" must be an integer greater than 1.'
assert alpha.lower() in ('orthogonal', 'o', 'rotatable',
'r'), 'Invalid value for "alpha": {:}'.format(alpha)
assert face.lower() in ('circumscribed', 'ccc', 'inscribed', 'cci',
'faced', 'ccf'), 'Invalid value for "face": {:}'.format(face)
try:
nc = len(center)
except:
raise TypeError('Invalid value for "center": {:}. Expected a 1-by-2 array.'.format(center))
else:
if nc!=2:
raise ValueError('Invalid number of values for "center" (expected 2, but got {:})'.format(nc))
# Orthogonal Design
if alpha.lower() in ('orthogonal', 'o'):
H2, a = star(n, alpha='orthogonal', center=center)
# Rotatable Design
if alpha.lower() in ('rotatable', 'r'):
H2, a = star(n, alpha='rotatable')
# Inscribed CCD
if face.lower() in ('inscribed', 'cci'):
H1 = ff2n(n)
H1 = H1/a # Scale down the factorial points
H2, a = star(n)
# Faced CCD
if face.lower() in ('faced', 'ccf'):
H2, a = star(n) # Value of alpha is always 1 in Faced CCD
H1 = ff2n(n)
# Circumscribed CCD
if face.lower() in ('circumscribed', 'ccc'):
H1 = ff2n(n)
C1 = repeat_center(n, center[0])
C2 = repeat_center(n, center[1])
H1 = union(H1, C1)
H2 = union(H2, C2)
H = union(H1, H2)
return H