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efvega
Mobile-robotics
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a9ec76a4
Commit
a9ec76a4
authored
2 years ago
by
efvega
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Adds a file for working with multivariate t distribution
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src/distribution_tools/multivariatet.py
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a9ec76a4
"""
Multivariate t-distribution.
Author: Gregory Gundersen 2020. Architecture based on SciPy
'
s
`_multivariate.py` module by Joris Vankerschaver 2013.
"""
import
numpy
as
np
from
scipy._lib._util
import
check_random_state
from
scipy.stats._multivariate
import
_PSD
,
multi_rv_generic
,
multi_rv_frozen
from
scipy.special
import
gammaln
# -----------------------------------------------------------------------------
class
multivariate_t_gen
(
multi_rv_generic
):
def
__init__
(
self
,
seed
=
None
):
"""
Initialize a multivariate t-distributed random variable.
Parameters
----------
seed : Random state.
"""
self
.
_random_state
=
check_random_state
(
seed
)
def
__call__
(
self
,
mean
=
None
,
shape
=
1
,
df
=
1
,
seed
=
None
):
"""
Create a frozen multivariate t-distribution. See
`multivariate_t_frozen` for parameters.
"""
return
multivariate_t_frozen
(
mean
=
mean
,
shape
=
shape
,
df
=
df
,
seed
=
seed
)
def
pdf
(
self
,
x
,
mean
=
None
,
shape
=
1
,
df
=
1
):
"""
Multivariate t-distribution probability density function.
Parameters
----------
x : array_like
Points at which to evaluate the log of the probability density
function.
mean : array_like, optional
Mean of the distribution (default zero).
shape : array_like, optional
Positive definite shape matrix. This is not the distribution
'
s
covariance matrix (default one).
df : Degrees of freedom.
Returns
-------
logpdf : Probability density function evaluated at `x`.
Examples
--------
FIXME.
"""
dim
,
mean
,
shape
,
df
=
self
.
_process_parameters
(
mean
,
shape
,
df
)
x
=
self
.
_process_quantiles
(
x
,
dim
)
shape_info
=
_PSD
(
shape
)
lp
=
self
.
_logpdf
(
x
,
mean
,
shape_info
.
U
,
shape_info
.
log_pdet
,
df
,
dim
)
return
np
.
exp
(
lp
)
def
logpdf
(
self
,
x
,
mean
=
None
,
shape
=
1
,
df
=
1
):
"""
Log of the multivariate t-distribution probability density function.
Parameters
----------
x : array_like
Points at which to evaluate the log of the probability density
function.
mean : array_like, optional
Mean of the distribution (default zero).
shape : array_like, optional
Positive definite shape matrix. This is not the distribution
'
s
covariance matrix (default one).
df : Degrees of freedom.
Returns
-------
logpdf : Log of the probability density function evaluated at `x`.
Examples
--------
FIXME.
"""
dim
,
mean
,
shape
,
df
=
self
.
_process_parameters
(
mean
,
shape
,
df
)
x
=
self
.
_process_quantiles
(
x
,
dim
)
shape_info
=
_PSD
(
shape
)
return
self
.
_logpdf
(
x
,
mean
,
shape_info
.
U
,
shape_info
.
log_pdet
,
df
,
dim
)
def
_logpdf
(
self
,
x
,
mean
,
U
,
log_pdet
,
df
,
dim
):
"""
Utility method `pdf`, `logpdf` for parameters.
"""
dev
=
x
-
mean
maha
=
np
.
square
(
np
.
dot
(
dev
,
U
)).
sum
(
axis
=-
1
)
t
=
0.5
*
(
df
+
dim
)
A
=
gammaln
(
t
)
B
=
gammaln
(
0.5
*
df
)
C
=
dim
/
2.
*
np
.
log
(
df
*
np
.
pi
)
D
=
0.5
*
log_pdet
E
=
-
t
*
np
.
log
(
1
+
(
1.
/
df
)
*
maha
)
return
A
-
B
-
C
-
D
+
E
def
rvs
(
self
,
mean
=
None
,
shape
=
1
,
df
=
1
,
size
=
1
,
random_state
=
None
):
"""
Draw random samples from a multivariate t-distribution.
Parameters
----------
x : array_like
Points at which to evaluate the log of the probability density
function.
mean : array_like, optional
Mean of the distribution (default zero).
shape : array_like, optional
Positive definite shape matrix. This is not the distribution
'
s
covariance matrix (default one).
df : Degrees of freedom.
Returns
-------
Examples
--------
FIXME.
"""
dim
,
mean
,
shape
,
df
=
self
.
_process_parameters
(
mean
,
shape
,
df
)
if
random_state
is
not
None
:
rng
=
check_random_state
(
random_state
)
else
:
rng
=
self
.
_random_state
if
df
==
np
.
inf
:
x
=
np
.
ones
(
size
)
else
:
x
=
rng
.
chisquare
(
df
,
size
=
size
)
/
df
z
=
rng
.
multivariate_normal
(
np
.
zeros
(
dim
),
shape
,
size
=
size
)
samples
=
mean
+
z
/
np
.
sqrt
(
x
)[:,
None
]
return
samples
def
_process_quantiles
(
self
,
x
,
dim
):
"""
Adjust quantiles array so that last axis labels the components of
each data point.
"""
x
=
np
.
asarray
(
x
,
dtype
=
float
)
if
x
.
ndim
==
0
:
x
=
x
[
np
.
newaxis
]
elif
x
.
ndim
==
1
:
if
dim
==
1
:
x
=
x
[:,
np
.
newaxis
]
else
:
x
=
x
[
np
.
newaxis
,
:]
return
x
def
_process_parameters
(
self
,
mean
,
shape
,
df
):
"""
Infer dimensionality from mean array and shape matrix, handle
defaults, and ensure compatible dimensions.
"""
if
mean
is
None
and
shape
is
None
:
shape
=
np
.
asarray
(
1
,
dtype
=
float
)
dim
=
1
elif
mean
is
None
:
shape
=
np
.
asarray
(
shape
,
dtype
=
float
)
if
shape
.
ndim
<
2
:
dim
=
1
else
:
dim
=
shape
.
shape
[
0
]
mean
=
np
.
zeros
(
dim
)
else
:
shape
=
np
.
asarray
(
shape
,
dtype
=
float
)
mean
=
np
.
asarray
(
mean
,
dtype
=
float
)
dim
=
mean
.
size
# FIXME: Why is this here?
if
dim
==
1
:
mean
.
shape
=
(
1
,)
shape
.
shape
=
(
1
,
1
)
if
mean
.
ndim
!=
1
or
mean
.
shape
[
0
]
!=
dim
:
raise
ValueError
(
"
Array
'
mean
'
must be a vector of length %d.
"
%
dim
)
if
shape
.
ndim
==
0
:
shape
=
shape
*
np
.
eye
(
dim
)
elif
shape
.
ndim
==
1
:
shape
=
np
.
diag
(
shape
)
elif
shape
.
ndim
==
2
and
shape
.
shape
!=
(
dim
,
dim
):
rows
,
cols
=
shape
.
shape
if
rows
!=
cols
:
msg
=
(
"
Array
'
cov
'
must be square if it is two dimensional,
"
"
but cov.shape = %s.
"
%
str
(
shape
.
shape
))
else
:
msg
=
(
"
Dimension mismatch: array
'
cov
'
is of shape %s,
"
"
but
'
mean
'
is a vector of length %d.
"
)
msg
=
msg
%
(
str
(
shape
.
shape
),
len
(
mean
))
raise
ValueError
(
msg
)
elif
shape
.
ndim
>
2
:
raise
ValueError
(
"
Array
'
cov
'
must be at most two-dimensional,
"
"
but cov.ndim = %d
"
%
shape
.
ndim
)
# Process degrees of freedom.
if
df
is
None
:
df
=
1
if
not
isinstance
(
df
,
int
)
and
not
np
.
isinf
(
df
):
raise
ValueError
(
"'
df
'
must be an integer or
'
np.inf
'
but is of
"
"
type %s
"
%
type
(
df
))
return
dim
,
mean
,
shape
,
df
class
multivariate_t_frozen
(
multi_rv_frozen
):
def
__init__
(
self
,
mean
=
None
,
shape
=
1
,
df
=
1
,
seed
=
None
):
"""
Create a frozen multivariate normal distribution.
Parameters
----------
x : array_like
Points at which to evaluate the log of the probability density
function.
mean : array_like, optional
Mean of the distribution (default zero).
shape : array_like, optional
Positive definite shape matrix. This is not the distribution
'
s
covariance matrix (default one).
df : Degrees of freedom.
Examples
--------
FIXME.
"""
self
.
_dist
=
multivariate_t_gen
(
seed
)
dim
,
mean
,
shape
,
df
=
self
.
_dist
.
_process_parameters
(
mean
,
shape
,
df
)
self
.
dim
,
self
.
mean
,
self
.
shape
,
self
.
df
=
dim
,
mean
,
shape
,
df
self
.
shape_info
=
_PSD
(
shape
)
def
logpdf
(
self
,
x
):
x
=
self
.
_dist
.
_process_quantiles
(
x
,
self
.
dim
)
U
=
self
.
shape_info
.
U
log_pdet
=
self
.
shape_info
.
log_pdet
return
self
.
_dist
.
_logpdf
(
x
,
self
.
mean
,
U
,
log_pdet
,
self
.
df
,
self
.
dim
)
def
pdf
(
self
,
x
):
return
np
.
exp
(
self
.
logpdf
(
x
))
def
rvs
(
self
,
size
=
1
,
random_state
=
None
):
"""
Draw random samples from a multivariate normal distribution.
Parameters
----------
size : integer, optional
Number of samples to draw (default 1).
random_state : np.random.RandomState instance
RandomState used for drawing the random variates.
Returns
-------
rvs : ndarray or scalar
Random variates of size (`size`, `N`), where `N` is the
dimension of the random variable.
"""
return
self
.
_dist
.
rvs
(
mean
=
self
.
mean
,
shape
=
self
.
shape
,
df
=
self
.
df
,
size
=
size
,
random_state
=
random_state
)
# -----------------------------------------------------------------------------
multivariate_t
=
multivariate_t_gen
()
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