def __init__(self, n, init_pdf, p_bt_btp, kalman_args, kalman_class = KalmanFilter):
r"""Initialise marginalized particle filter.
:param int n: number of particles
:param init_pdf: probability density which initial particles are sampled from. (both
:math:`a_t` and :math:`b_t` parts)
:type init_pdf: :class:`~pybayes.pdfs.Pdf`
:param p_bt_btp: :math:`p(b_t|b_{t-1})` cpdf of the (b part of the) state in *t* given
state in *t-1*
:type p_bt_btp: :class:`~pybayes.pdfs.CPdf`
:param dict kalman_args: arguments for the Kalman filter, passed as dictionary; *state_pdf*
key should not be speficied as it is supplied by the marginalized particle filter
:param class kalman_class: class of the filter used for the :math:`a_t` part of the system;
defaults to :class:`KalmanFilter`
"""
if not isinstance(n, int) or n < 1:
raise TypeError("n must be a positive integer")
if not isinstance(init_pdf, Pdf) or not isinstance(p_bt_btp, CPdf):
raise TypeError("init_pdf must be a Pdf and p_bt_btp must be a CPdf")
if not issubclass(kalman_class, KalmanFilter):
raise TypeError("kalman_class must be a subclass (not an instance) of KalmanFilter")
b_shape = p_bt_btp.shape()
if p_bt_btp.cond_shape() != b_shape:
raise ValueError("p_bt_btp's shape ({0}) and cond shape ({1}) must both be {2}".format(
p_bt_btp.shape(), p_bt_btp.cond_shape(), b_shape))
self.p_bt_btp = p_bt_btp
a_shape = init_pdf.shape() - b_shape
# this will be removed when hardcoding Q,R into kalman filter will be removed
kalman_args['Q'] = np.array([[-123.]])
kalman_args['R'] = np.array([[-494658.]])
# generate both initial parts of particles
init_particles = init_pdf.samples(n)
# create all Kalman filters first
self.kalmans = np.empty(n, dtype=KalmanFilter) # array of references to Kalman filters
gausses = np.empty(n, dtype=GaussPdf) # array of Kalman filter state pdfs
for i in range(n):
gausses[i] = GaussPdf(init_particles[i,0:a_shape], np.array([[1.]]))
kalman_args['state_pdf'] = gausses[i]
self.kalmans[i] = kalman_class(**kalman_args)
# construct apost pdf. Important: reference to ith GaussPdf is shared between ith Kalman
# filter's state_pdf and ith memp't gauss
self.memp = MarginalizedEmpPdf(gausses, init_particles[:,a_shape:])
def __init__(self, A, B = None, C = None, D = None, Q = None, R = None, state_pdf = None):
r"""Initialise Kalman filter.
:param A: process model matrix :math:`A_t` from :class:`class description <KalmanFilter>`
:type A: 2D :class:`numpy.ndarray`
:param B: process control model matrix :math:`B_t` from :class:`class description
<KalmanFilter>`; may be None or unspecified for control-less systems
:type B: 2D :class:`numpy.ndarray`
:param C: observation model matrix :math:`C_t` from :class:`class description
<KalmanFilter>`; must be full-ranked
:type C: 2D :class:`numpy.ndarray`
:param D: observation control model matrix :math:`D_t` from :class:`class description
<KalmanFilter>`; may be None or unspecified for control-less systems
:type D: 2D :class:`numpy.ndarray`
:param Q: process noise covariance matrix :math:`Q_t` from :class:`class description
<KalmanFilter>`; must be positive definite
:type Q: 2D :class:`numpy.ndarray`
:param R: observation noise covariance matrix :math:`R_t` from :class:`class description
<KalmanFilter>`; must be positive definite
:type R: 2D :class:`numpy.ndarray`
:param state_pdf: initial state pdf; this object is referenced and used throughout whole
life of KalmanFilter, so it is not safe to reuse state pdf for other purposes
:type state_pdf: :class:`~pybayes.pdfs.GaussPdf`
All matrices can be time-varying - you can modify or replace all above stated matrices
providing that you don't change their shape and all constraints still hold. On the other
hand, you **should not modify state_pdf** unless you really know what you are doing.
>>> # initialise control-less Kalman filter:
>>> kf = pb.KalmanFilter(A=np.array([[1.]]),
C=np.array([[1.]]),
Q=np.array([[0.7]]), R=np.array([[0.3]]),
state_pdf=pb.GaussPdf(...))
"""
# check type of pdf
if not isinstance(state_pdf, GaussPdf):
raise TypeError("state_pdf must be (a subclass of) GaussPdf")
# check type of input arrays
matrices = {"A":A, "B":B, "C":C, "D":D, "Q":Q, "R":R}
for name in matrices:
matrix = matrices[name]
if name == 'B' and matrix is None: # we allow B to be unspecified
matrices['B'] = matrix = B = np.empty((A.shape[0], 0))
if name == 'D' and matrix is None: # we allow D to be unspecified
matrices['D'] = matrix = D = np.empty((C.shape[0], 0))
if not isinstance(matrix, np.ndarray):
raise TypeError("{0} must be numpy.ndarray, {1} given".format(name, type(matrix)))
if matrix.ndim != 2:
raise ValueError("{0} must have 2 dimensions (forming a matrix) {1} given".format(
name, matrix.ndim))
# remember vector shapes
self.n = state_pdf.shape() # dimension of state vector
self.k = B.shape[1] # dimension of control vector
self.j = C.shape[0] # dimension of observation vector
# dict of required matrice shapes (sizes)
shapes = {
"A":(self.n, self.n),
"B":(self.n, self.k),
"C":(self.j, self.n),
"D":(self.j, self.k),
"Q":(self.n, self.n),
"R":(self.j, self.j)
}
# check input matrix sizes
for name in matrices:
matrix = matrices[name]
if matrix.shape != shapes[name]:
raise ValueError("Given shapes of state_pdf, B and C, matrix " + name +
" must have shape " + str(shapes[name]) + ", " +
str(matrix.shape) + " given")
self.A, self.B, self.C, self.D, self.Q, self.R = A, B, C, D, Q, R
self.P = state_pdf
self.S = GaussPdf(np.array([0.]), np.array([[1.]])) # observation probability density function
class KalmanFilter(Filter):
r"""Implementation of standard Kalman filter. **cond** in :meth:`bayes` is interpreted as
control (intervention) input :math:`u_t` to the system.
Kalman filter forms *optimal Bayesian solution* for the following system:
.. math::
x_t &= A_t x_{t-1} + B_t u_t + v_{t-1} \quad \quad
A_t \in \mathbb{R}^{n,n} \;\;
B_t \in \mathbb{R}^{n,k} \;\;
\;\; n \in \mathbb{N}
\;\; k \in \mathbb{N}_0 \text{ (may be zero)}
\\
y_t &= C_t x_t + D_t u_t + w_t \quad \quad \quad \;\;
C_t \in \mathbb{R}^{j,n} \;\;
D_t \in \mathbb{R}^{j,k} \;\;
j \in \mathbb{N} \;\; j \leq n
where :math:`x_t \in \mathbb{R}^n` is hidden state vector, :math:`y_t \in \mathbb{R}^j` is
observation vector and :math:`u_t \in \mathbb{R}^k` is control vector. :math:`v_t` is normally
distributed zero-mean process noise with covariance matrix :math:`Q_t`, :math:`w_t` is normally
distributed zero-mean observation noise with covariance matrix :math:`R_t`. Additionally, intial
pdf (**state_pdf**) has to be Gaussian.
"""
def __init__(self, A, B = None, C = None, D = None, Q = None, R = None, state_pdf = None):
r"""Initialise Kalman filter.
:param A: process model matrix :math:`A_t` from :class:`class description <KalmanFilter>`
:type A: 2D :class:`numpy.ndarray`
:param B: process control model matrix :math:`B_t` from :class:`class description
<KalmanFilter>`; may be None or unspecified for control-less systems
:type B: 2D :class:`numpy.ndarray`
:param C: observation model matrix :math:`C_t` from :class:`class description
<KalmanFilter>`; must be full-ranked
:type C: 2D :class:`numpy.ndarray`
:param D: observation control model matrix :math:`D_t` from :class:`class description
<KalmanFilter>`; may be None or unspecified for control-less systems
:type D: 2D :class:`numpy.ndarray`
:param Q: process noise covariance matrix :math:`Q_t` from :class:`class description
<KalmanFilter>`; must be positive definite
:type Q: 2D :class:`numpy.ndarray`
:param R: observation noise covariance matrix :math:`R_t` from :class:`class description
<KalmanFilter>`; must be positive definite
:type R: 2D :class:`numpy.ndarray`
:param state_pdf: initial state pdf; this object is referenced and used throughout whole
life of KalmanFilter, so it is not safe to reuse state pdf for other purposes
:type state_pdf: :class:`~pybayes.pdfs.GaussPdf`
All matrices can be time-varying - you can modify or replace all above stated matrices
providing that you don't change their shape and all constraints still hold. On the other
hand, you **should not modify state_pdf** unless you really know what you are doing.
>>> # initialise control-less Kalman filter:
>>> kf = pb.KalmanFilter(A=np.array([[1.]]),
C=np.array([[1.]]),
Q=np.array([[0.7]]), R=np.array([[0.3]]),
state_pdf=pb.GaussPdf(...))
"""
# check type of pdf
if not isinstance(state_pdf, GaussPdf):
raise TypeError("state_pdf must be (a subclass of) GaussPdf")
# check type of input arrays
matrices = {"A":A, "B":B, "C":C, "D":D, "Q":Q, "R":R}
for name in matrices:
matrix = matrices[name]
if name == 'B' and matrix is None: # we allow B to be unspecified
matrices['B'] = matrix = B = np.empty((A.shape[0], 0))
if name == 'D' and matrix is None: # we allow D to be unspecified
matrices['D'] = matrix = D = np.empty((C.shape[0], 0))
if not isinstance(matrix, np.ndarray):
raise TypeError("{0} must be numpy.ndarray, {1} given".format(name, type(matrix)))
if matrix.ndim != 2:
raise ValueError("{0} must have 2 dimensions (forming a matrix) {1} given".format(
name, matrix.ndim))
# remember vector shapes
self.n = state_pdf.shape() # dimension of state vector
self.k = B.shape[1] # dimension of control vector
self.j = C.shape[0] # dimension of observation vector
# dict of required matrice shapes (sizes)
shapes = {
"A":(self.n, self.n),
"B":(self.n, self.k),
"C":(self.j, self.n),
"D":(self.j, self.k),
"Q":(self.n, self.n),
"R":(self.j, self.j)
}
# check input matrix sizes
for name in matrices:
matrix = matrices[name]
if matrix.shape != shapes[name]:
raise ValueError("Given shapes of state_pdf, B and C, matrix " + name +
" must have shape " + str(shapes[name]) + ", " +
str(matrix.shape) + " given")
self.A, self.B, self.C, self.D, self.Q, self.R = A, B, C, D, Q, R
self.P = state_pdf
self.S = GaussPdf(np.array([0.]), np.array([[1.]])) # observation probability density function
def __copy__(self):
# type(self) is used because this method may be called for a derived class
ret = type(self).__new__(type(self))
ret.A = self.A
ret.B = self.B
ret.C = self.C
ret.D = self.D
ret.Q = self.Q
ret.R = self.R
ret.n = self.n
ret.k = self.k
ret.j = self.j
ret.P = self.P
ret.S = self.S
return ret
def __deepcopy__(self, memo):
# type(self) is used because this method may be called for a derived class
ret = type(self).__new__(type(self))
ret.A = deepcopy(self.A, memo) # numpy arrays:
ret.B = deepcopy(self.B, memo)
ret.C = deepcopy(self.C, memo)
ret.D = deepcopy(self.D, memo)
ret.Q = deepcopy(self.Q, memo)
ret.R = deepcopy(self.R, memo)
ret.n = self.n # no need to copy integers
ret.k = self.k
ret.j = self.j
ret.P = deepcopy(self.P, memo) # GaussPdfs:
ret.S = deepcopy(self.S, memo)
return ret
def bayes(self, yt, cond = np.empty(0)):
r"""Perform exact bayes rule.
:param yt: observation at time t
:type yt: 1D :class:`numpy.ndarray`
:param cond: control (intervention) vector at time t. May be unspecified if the filter is
control-less.
:type cond: 1D :class:`numpy.ndarray`
:return: always returns True (see :meth:`~Filter.posterior` to get posterior density)
"""
if not isinstance(yt, np.ndarray):
raise TypeError("yt must be and instance of numpy.ndarray ({0} given)".format(type(yt)))
if yt.ndim != 1 or yt.shape[0] != self.j:
raise ValueError("yt must have shape {0}. ({1} given)".format((self.j,), (yt.shape[0],)))
if not isinstance(cond, np.ndarray):
raise TypeError("cond must be and instance of numpy.ndarray ({0} given)".format(type(cond)))
if cond.ndim != 1 or cond.shape[0] != self.k:
raise ValueError("cond must have shape {0}. ({1} given)".format((self.k,), (cond.shape[0],)))
# predict
self.P.mu = np.dot(self.A, self.P.mu) + np.dot(self.B, cond) # prior state mean estimate
self.P.R = np.dot(np.dot(self.A, self.P.R), self.A.T) + self.Q # prior state covariance estimate
# data update
self.S.mu = np.dot(self.C, self.P.mu) + np.dot(self.D, cond) # prior observation mean estimate
self.S.R = np.dot(np.dot(self.C, self.P.R), self.C.T) + self.R # prior observation covariance estimate
# kalman gain
K = np.dot(np.dot(self.P.R, self.C.T), linalg.inv(self.S.R))
# update according to observation
self.P.mu += np.dot(K, (yt - self.S.mu)) # posterior state mean estimate
self.P.R -= np.dot(np.dot(K, self.C), self.P.R) # posterior state covariance estimate
return True
def posterior(self):
return self.P
def evidence_log(self, yt):
return self.S.eval_log(yt)
import pdb
from mle import *
#import julia
import scipy.optimize as opt
#from julia.api import Julia
#j=julia.Julia(compiled_modules=False)
#from julia import Main
import pybayes
from scipy.integrate import quad,dblquad
from pybayes.pdfs import CPdf,MLinGaussCPdf,GaussPdf,MyEmpPdf
k=pd.read_pickle('/home/sahil/projdir/dailydata.pkl')
k1=k[k.Symbol==k.Symbol.unique()[2]].iloc[1000:1030]
k1['ret']=((k1.Close-k1.Open)/(k1.Close))*100
init_param=[0,1.38,4.74,2.95]
a=MLinGaussCPdf(np.identity(4),np.identity(4),np.zeros(4))
init=GaussPdf(np.array(init_param),np.identity(4))
def pdf(x,xmean,*args):
z,beta,q=args
ser=x
pd =(1/z)*(1+beta*(q-1)*(x-xmean)**2)**(-1/(q-1))
return pd
sample=[init.sample() for _ in range(20)]
w=[]
for i in range(30):
if(i==0):
sample=np.array([init.sample() for _ in range(20)])
w=[pdf(k1.ret.iloc[i],*j) for j in sample]
