def __init__(self, pct_drift=None, pct_vol=None, time_unit=dt.timedelta(days=1)):
if pct_drift is None and pct_vol is None:
pct_drift = 0.; pct_vol = 1.
self._pct_drift, self._pct_vol = None, None
if pct_drift is not None:
self._pct_drift = npu.to_ndim_2(pct_drift, ndim_1_to_col=True, copy=True)
process_dim = npu.nrow(self._pct_drift)
if pct_vol is not None:
self._pct_vol = npu.to_ndim_2(pct_vol, ndim_1_to_col=True, copy=True)
process_dim = npu.nrow(self._pct_vol)
if self._pct_drift is None: self._pct_drift = npu.col_of(process_dim, 0.)
if self._pct_vol is None: self._pct_vol = np.eye(process_dim)
npc.check_col(self._pct_drift)
npc.check_nrow(self._pct_drift, process_dim)
npc.check_nrow(self._pct_vol, process_dim)
noise_dim = npu.ncol(self._pct_vol)
self._pct_cov = stats.vol_to_cov(self._pct_vol)
npu.make_immutable(self._pct_drift)
npu.make_immutable(self._pct_vol)
npu.make_immutable(self._pct_cov)
self._to_string_helper_GeometricBrownianMotion = None
self._str_GeometricBrownianMotion = None
super(GeometricBrownianMotion, self).__init__(process_dim=process_dim, noise_dim=noise_dim,
drift=lambda t, x: self._pct_drift * x,
diffusion=lambda t, x: x * self._pct_vol,
time_unit=time_unit)
def __init__(self, mean=None, vol=None):
if mean is None and vol is None:
mean = 0.
vol = 1.
self.__mean, self.__vol = None, None
if mean is not None:
self.__mean = npu.tondim2(mean, ndim1tocol=True, copy=True)
processdim = npu.nrow(self.__mean)
if vol is not None:
self.__vol = npu.tondim2(vol, ndim1tocol=True, copy=True)
processdim = npu.nrow(self.__vol)
if self.__mean is None: self.__mean = npu.colof(processdim, 0.)
if self.__vol is None: self.__vol = np.eye(processdim)
npc.checkcol(self.__mean)
npc.checknrow(self.__mean, processdim)
npc.checknrow(self.__vol, processdim)
noisedim = npu.ncol(self.__vol)
self.__cov = np.dot(self.__vol, self.__vol.T)
npu.makeimmutable(self.__mean)
npu.makeimmutable(self.__vol)
npu.makeimmutable(self.__cov)
super(WienerProcess, self).__init__(processdim=processdim,
noisedim=noisedim,
drift=lambda t, x: self.__mean,
diffusion=lambda t, x: self.__vol)
def __init__(self, mean=None, vol=None):
if mean is None and vol is None:
mean = 0.
vol = 1.
self._mean, self._vol = None, None
if mean is not None:
self._mean = npu.to_ndim_2(mean, ndim_1_to_col=True, copy=True)
process_dim = npu.nrow(self._mean)
if vol is not None:
self._vol = npu.to_ndim_2(vol, ndim_1_to_col=True, copy=True)
process_dim = npu.nrow(self._vol)
if self._mean is None: self._mean = npu.col_of(process_dim, 0.)
if self._vol is None: self._vol = np.eye(process_dim)
npc.check_col(self._mean)
npc.check_nrow(self._mean, process_dim)
npc.check_nrow(self._vol, process_dim)
noise_dim = npu.ncol(self._vol)
self._cov = np.dot(self._vol, self._vol.T)
npu.make_immutable(self._mean)
npu.make_immutable(self._vol)
npu.make_immutable(self._cov)
self._to_string_helper_WienerProcess = None
self._str_WienerProcess = None
super(WienerProcess, self).__init__(process_dim=process_dim,
noise_dim=noise_dim,
drift=lambda t, x: self._mean,
diffusion=lambda t, x: self._vol)
def test_nrow(self):
r = npu.row(429., 5., 2., 14.)
self.assertEqual(npu.nrow(r), 1)
c = npu.col(429., 5., 2., 14.)
self.assertEqual(npu.nrow(c), 4)
m = npu.matrix_of(3, 5, 0.)
self.assertEqual(npu.nrow(m), 3)
def __init__(self, transition=None, mean=None, vol=None):
if transition is None and mean is None and vol is None:
transition = 1.
mean = 0.
vol = 1.
self._transition, self._mean, self._vol = None, None, None
if transition is not None:
self._transition = npu.to_ndim_2(transition,
ndim_1_to_col=True,
copy=True)
process_dim = npu.nrow(self._transition)
if mean is not None:
self._mean = npu.to_ndim_2(mean, ndim_1_to_col=True, copy=True)
process_dim = npu.nrow(self._mean)
if vol is not None:
self._vol = npu.to_ndim_2(vol, ndim_1_to_col=True, copy=True)
process_dim = npu.nrow(self._vol)
if self._transition is None: self._transition = np.eye(process_dim)
if self._mean is None: self._mean = npu.col_of(process_dim, 0.)
if self._vol is None: self._vol = np.eye(process_dim)
npc.check_square(self._transition)
npc.check_nrow(self._transition, process_dim)
npc.check_col(self._mean)
npc.check_nrow(self._mean, process_dim)
npc.check_nrow(self._vol, process_dim)
noise_dim = npu.ncol(self._vol)
self._transition_x_2 = npu.kron_sum(self._transition, self._transition)
self._transition_x_2_inverse = np.linalg.inv(self._transition_x_2)
self._cov = np.dot(self._vol, self._vol.T)
self._cov_vec = npu.vec(self._cov)
self._cached_mean_reversion_factor = None
self._cached_mean_reversion_factor_time_delta = None
self._cached_mean_reversion_factor_squared = None
self._cached_mean_reversion_factor_squared_time_delta = None
npu.make_immutable(self._transition)
npu.make_immutable(self._transition_x_2)
npu.make_immutable(self._transition_x_2_inverse)
npu.make_immutable(self._mean)
npu.make_immutable(self._vol)
npu.make_immutable(self._cov)
npu.make_immutable(self._cov_vec)
self._to_string_helper_OrnsteinUhlenbeckProcess = None
self._str_OrnsteinUhlenbeckProcess = None
super(OrnsteinUhlenbeckProcess, self).__init__(
process_dim=process_dim,
noise_dim=noise_dim,
drift=lambda t, x: -np.dot(self._transition, x - self._mean),
diffusion=lambda t, x: self._vol)
def __init__(self,
initial_value=None,
final_value=None,
initial_time=0.,
final_time=1.,
vol=None,
time_unit=dt.timedelta(days=1)):
process_dim = 1
self.__initial_value = None
self.__final_value = None
if initial_value is not None:
self.__initial_value = npu.to_ndim_2(initial_value,
ndim_1_to_col=True,
copy=True)
process_dim = npu.nrow(self.__initial_value)
if final_value is not None:
self.__final_value = npu.to_ndim_2(final_value,
ndim_1_to_col=True,
copy=True)
process_dim = npu.nrow(self.__final_value)
if self.__initial_value is None:
self.__initial_value = npu.col_of(process_dim, 0.)
if self.__final_value is None:
self.__final_value = npu.col_of(process_dim, 0.)
self.__vol = None
if vol is not None:
self.__vol = npu.to_ndim_2(vol, ndim_1_to_col=True, copy=True)
process_dim = npu.nrow(self.__vol)
if self.__vol is None: self.__vol = np.eye(process_dim)
self.__initial_time = initial_time
self.__final_time = final_time
npc.check_col(self.__initial_value)
npc.check_col(self.__final_value)
npc.check_nrow(self.__initial_value, process_dim)
npc.check_nrow(self.__final_value, process_dim)
noise_dim = npu.ncol(self.__vol)
self.__cov = stats.vol_to_cov(self.__vol)
npu.make_immutable(self.__initial_value)
npu.make_immutable(self.__final_value)
npu.make_immutable(self.__vol)
npu.make_immutable(self.__cov)
self._to_string_helper_BrownianBridge = None
self._str_BrownianBridge = None
super(BrownianBridge,
self).__init__(process_dim=process_dim,
noise_dim=noise_dim,
drift=lambda t, x: (self.__final_value - x) /
(self.__final_time - t),
diffusion=lambda t, x: self.__vol,
time_unit=time_unit)
def __init__(self,
particles=None,
weights=None,
dim=None,
use_n_minus_1_stats=False,
sampler=None,
copy=True):
self._particles, self._weights, self._dim = None, None, None
if particles is not None:
self._particles = npu.to_ndim_2(particles,
ndim_1_to_col=True,
copy=copy)
self._dim = npu.ncol(self._particles)
if weights is None:
weights = np.ones((npu.nrow(self._particles), 1))
weights /= float(npu.nrow(self._particles))
if weights is not None:
checks.check_not_none(particles)
self._weights = npu.to_ndim_2(weights,
ndim_1_to_col=True,
copy=copy)
self._dim = npu.ncol(self._particles)
if dim is not None:
self._dim = dim
if self._particles is not None:
npc.check_ncol(self._particles, self._dim)
if self._weights is not None:
npc.check_nrow(self._weights, npu.nrow(self._particles))
npu.make_immutable(self._particles, allow_none=True)
npu.make_immutable(self._weights, allow_none=True)
self._use_n_minus_1_stats = use_n_minus_1_stats
# "n minus 1" (unbiased) stats only make sense when using "repeat"-type weights, meaning that each weight
# represents the number of occurrences of one observation.
#
# See https://stats.stackexchange.com/questions/61225/correct-equation-for-weighted-unbiased-sample-covariance
self._effective_particle_count = None
self._weight_sum = None
self._mean = None
self._var_n = None
self._var_n_minus_1 = None
self._cov_n = None
self._cov_n_minus_1 = None
self._vol_n = None
self._vol_n_minus_1 = None
self._to_string_helper_EmpiricalDistr = None
self._str_EmpiricalDistr = None
super().__init__(do_not_init=True)
def __init__(self, transition=None, mean=None, vol=None):
if transition is None and mean is None and vol is None:
transition = 1.
mean = 0.
vol = 1.
self.__transition, self.__mean, self.__vol = None, None, None
if transition is not None:
self.__transition = npu.tondim2(transition,
ndim1tocol=True,
copy=True)
processdim = npu.nrow(self.__transition)
if mean is not None:
self.__mean = npu.tondim2(mean, ndim1tocol=True, copy=True)
processdim = npu.nrow(self.__mean)
if vol is not None:
self.__vol = npu.tondim2(vol, ndim1tocol=True, copy=True)
processdim = npu.nrow(self.__vol)
if self.__transition is None: self.__transition = np.eye(processdim)
if self.__mean is None: self.__mean = npu.colof(processdim, 0.)
if self.__vol is None: self.__vol = np.eye(processdim)
npc.checksquare(self.__transition)
npc.checknrow(self.__transition, processdim)
npc.checkcol(self.__mean)
npc.checknrow(self.__mean, processdim)
npc.checknrow(self.__vol, processdim)
noisedim = npu.ncol(self.__vol)
self.__transitionx2 = npu.kronsum(self.__transition, self.__transition)
self.__transitionx2inverse = np.linalg.inv(self.__transitionx2)
self.__cov = np.dot(self.__vol, self.__vol.T)
self.__covvec = npu.vec(self.__cov)
self.__cachedmeanreversionfactor = None
self.__cachedmeanreversionfactortimedelta = None
self.__cachedmeanreversionfactorsquared = None
self.__cachedmeanreversionfactorsquaredtimedelta = None
npu.makeimmutable(self.__transition)
npu.makeimmutable(self.__transitionx2)
npu.makeimmutable(self.__transitionx2inverse)
npu.makeimmutable(self.__mean)
npu.makeimmutable(self.__vol)
npu.makeimmutable(self.__cov)
npu.makeimmutable(self.__covvec)
super(OrnsteinUhlenbeckProcess, self).__init__(
processdim=processdim,
noisedim=noisedim,
drift=lambda t, x: -np.dot(self.__transition, x - self.__mean),
diffusion=lambda t, x: self.__vol)
def test_kron_sum(self):
a = np.array([[5., 1.], [2., 5.]])
b = np.array([[14., 42., 1.], [132., 14., 2.], [5., 2., 42.]])
c = npu.kron_sum(a, b)
m = npu.nrow(a)
self.assertEqual(npu.ncol(a), m)
n = npu.nrow(b)
self.assertEqual(npu.ncol(b), n)
known_kron_sum = np.kron(a, np.eye(n)) + np.kron(np.eye(m), b)
npt.assert_almost_equal(c, known_kron_sum)
def __init__(self,
mean=None,
cov=None,
vol=None,
dim=None,
copy=True,
do_not_init=False):
if not do_not_init:
if mean is not None and dim is not None and np.size(mean) == 1:
mean = npu.col_of(dim, npu.to_scalar(mean))
if mean is None and vol is None and cov is None:
self._dim = 1 if dim is None else dim
mean = npu.col_of(self._dim, 0.)
cov = np.eye(self._dim)
vol = np.eye(self._dim)
self._dim, self._mean, self._vol, self._cov = None, None, None, None
# TODO We don't currently check whether cov and vol are consistent, i.e. that cov = np.dot(vol, vol.T) -- should we?
if mean is not None:
self._mean = npu.to_ndim_2(mean, ndim_1_to_col=True, copy=copy)
self._dim = npu.nrow(self._mean)
if cov is not None:
self._cov = npu.to_ndim_2(cov, ndim_1_to_col=True, copy=copy)
self._dim = npu.nrow(self._cov)
if vol is not None:
self._vol = npu.to_ndim_2(vol, ndim_1_to_col=True, copy=copy)
self._dim = npu.nrow(self._vol)
if self._mean is None: self._mean = npu.col_of(self._dim, 0.)
if self._cov is None and self._vol is None:
self._cov = np.eye(self._dim)
self._vol = np.eye(self._dim)
npc.check_col(self._mean)
npc.check_nrow(self._mean, self._dim)
if self._cov is not None:
npc.check_nrow(self._cov, self._dim)
npc.check_square(self._cov)
if self._vol is not None:
npc.check_nrow(self._vol, self._dim)
npu.make_immutable(self._mean)
if self._cov is not None: npu.make_immutable(self._cov)
if self._vol is not None: npu.make_immutable(self._vol)
self._to_string_helper_WideSenseDistr = None
self._str_WideSenseDistr = None
super().__init__()
def __init__(self, mean_of_log=None, cov_of_log=None, vol_of_log=None, dim=None, copy=True):
if mean_of_log is not None and dim is not None and np.size(mean_of_log) == 1:
mean_of_log = npu.col_of(dim, npu.to_scalar(mean_of_log))
if mean_of_log is None and vol_of_log is None and cov_of_log is None:
self._dim = 1 if dim is None else dim
mean_of_log = npu.col_of(self._dim, 0.)
cov_of_log = np.eye(self._dim)
vol_of_log = np.eye(self._dim)
self._dim, self._mean_of_log, self._vol_of_log, self._cov_of_log = None, None, None, None
# TODO We don't currently check whether cov_of_log and vol_of_log are consistent, i.e. that cov_of_log = np.dot(vol_of_log, vol_of_log.T) -- should we?
if mean_of_log is not None:
self._mean_of_log = npu.to_ndim_2(mean_of_log, ndim_1_to_col=True, copy=copy)
self._dim = npu.nrow(self._mean_of_log)
if cov_of_log is not None:
self._cov_of_log = npu.to_ndim_2(cov_of_log, ndim_1_to_col=True, copy=copy)
self._dim = npu.nrow(self._cov_of_log)
if vol_of_log is not None:
self._vol_of_log = npu.to_ndim_2(vol_of_log, ndim_1_to_col=True, copy=copy)
self._dim = npu.nrow(self._vol_of_log)
if self._mean_of_log is None: self._mean_of_log = npu.col_of(self._dim, 0.)
if self._cov_of_log is None and self._vol_of_log is None:
self._cov_of_log = np.eye(self._dim)
self._vol_of_log = np.eye(self._dim)
npc.check_col(self._mean_of_log)
npc.check_nrow(self._mean_of_log, self._dim)
if self._cov_of_log is not None:
npc.check_nrow(self._cov_of_log, self._dim)
npc.check_square(self._cov_of_log)
if self._vol_of_log is not None:
npc.check_nrow(self._vol_of_log, self._dim)
if self._cov_of_log is None: self._cov_of_log = stats.vol_to_cov(self._vol_of_log)
if self._vol_of_log is None: self._vol_of_log = stats.cov_to_vol(self._cov_of_log)
npu.make_immutable(self._mean_of_log)
npu.make_immutable(self._cov_of_log)
npu.make_immutable(self._vol_of_log)
mean = np.exp(self._mean_of_log + .5 * npu.col(*[self._cov_of_log[i,i] for i in range(self._dim)]))
cov = np.array([[np.exp(self._mean_of_log[i,0] + self._mean_of_log[j,0] + .5 * (self._cov_of_log[i,i] + self._cov_of_log[j,j])) * (np.exp(self._cov_of_log[i,j]) - 1.) for j in range(self._dim)] for i in range(self._dim)])
vol = stats.cov_to_vol(cov)
self._to_string_helper_LogNormalDistr = None
self._str_LogNormalDistr = None
super().__init__(mean, cov, vol, self._dim, copy)
def test_kron(self):
a = np.array([[5., 1., 14., 2., 42.], [132., 2., 429., 1., 1.],
[1., 2., 1430., 2., 2.]])
b = np.array([[42., 2.], [5., 1.], [5., 2.], [14., 132.]])
c = np.kron(a, b)
n = npu.nrow(a)
p = npu.ncol(a)
m = npu.nrow(b)
q = npu.ncol(b)
self.assertEqual(npu.nrow(c), m * n)
self.assertEqual(npu.ncol(c), p * q)
for i in range(n):
for j in range(p):
npt.assert_almost_equal(
c[i * m:(i + 1) * m, j * q:(j + 1) * q], a[i, j] * b)
def __init__(self, mean=None, cov=None, vol=None, dim=None, copy=True):
if mean is None and vol is None and cov is None:
self.__dim = 1 if dim is None else dim
mean = npu.colof(self.__dim, 0.)
cov = np.eye(self.__dim)
vol = np.eye(self.__dim)
self.__dim, self.__mean, self.__vol, self.__cov = None, None, None, None
# TODO We don't currently check whether cov and vol are consistent, i.e. that cov = np.dot(vol, vol.T) -- should we?
if mean is not None:
self.__mean = npu.tondim2(mean, ndim1tocol=True, copy=copy)
self.__dim = npu.nrow(self.__mean)
if cov is not None:
self.__cov = npu.tondim2(cov, ndim1tocol=True, copy=copy)
self.__dim = npu.nrow(self.__cov)
if vol is not None:
self.__vol = npu.tondim2(vol, ndim1tocol=True, copy=copy)
self.__dim = npu.nrow(self.__vol)
if self.__mean is None: self.__mean = npu.colof(self.__dim, 0.)
if self.__cov is None and self.__vol is None:
self.__cov = np.eye(self.__dim)
self.__vol = np.eye(self.__dim)
npc.checkcol(self.__mean)
npc.checknrow(self.__mean, self.__dim)
if self.__cov is not None:
npc.checknrow(self.__cov, self.__dim)
npc.checksquare(self.__cov)
if self.__vol is not None:
npc.checknrow(self.__vol, self.__dim)
npu.makeimmutable(self.__mean)
if self.__cov is not None: npu.makeimmutable(self.__cov)
if self.__vol is not None: npu.makeimmutable(self.__vol)
super(NormalDistr, self).__init__()
def check_nrow(
arg,
nrow,
message='Unexpected number of rows: actual=%(actual)d, expected=%(expected)d',
level=1):
n = npu.nrow(arg)
check(n == nrow,
message=lambda: message % {
'actual': n,
'expected': nrow
},
level=level)
return arg
def predict(self, time, true_value=None):
self.filter.predict(time, true_value)
predicted_obs = self._obs_model.predict_obs(time, self._sub_state_distr(self.filter._state_distr), self)
cc = predicted_obs.cross_cov
# While cc is the cross-covariance between the "observed" processes and the observation, we need the
# cross-covariance between the full compound process and the observation. Therefore we enlarge this matrix
# by inserting columns of zeros at appropriate indices
cc_nrow = npu.nrow(cc)
cross_cov = np.zeros((cc_nrow, self.filter._state_distr.dim))
col = 0
for r in self._state_mean_rects:
size = r[0].stop - r[0].start
cross_cov[0:cc_nrow, r[0].start:r[0].start+size] = cc[0:cc_nrow, col:col+size]
col += size
return filtering.PredictedObs(self, time, predicted_obs.distr, cross_cov)
def multivariate_normal(mean=None,
cov=None,
size=None,
ndim=None,
random_state=None):
global _rs
if ndim is None:
if mean is not None: ndim = np.size(mean)
elif cov is not None: ndim = npu.nrow(cov)
else: ndim = 1
if ndim is not None:
if mean is None: mean = npu.ndim_1_of(ndim, 0.)
if cov is None: cov = np.eye(ndim, ndim)
mean = npu.to_ndim_1(mean)
cov = npu.to_ndim_2(cov)
npc.check_size(mean, ndim)
npc.check_nrow(cov, ndim)
npc.check_square(cov)
if random_state is None: random_state = _rs()
return random_state.multivariate_normal(mean, cov, size)
def __init__(self, mean=None, dim=None, copy=True):
if mean is not None and dim is not None and np.size(mean) == 1:
mean = npu.col_of(dim, npu.to_scalar(mean))
if mean is None:
dim = 1 if dim is None else dim
mean = npu.col_of(dim, 0.)
self._mean = npu.to_ndim_2(mean, ndim_1_to_col=True, copy=copy)
if dim is None: dim = npu.nrow(self._mean)
self._dim = dim
npc.check_col(self._mean)
npc.check_nrow(self._mean, self._dim)
npu.make_immutable(self._mean)
self._zero_cov = None
self._to_string_helper_DiracDeltaDistr = None
self._str_DiracDeltaDistr = None
def multivariate_lognormal(mean_of_log=0.,
cov_of_log=1.,
size=None,
ndim=None,
random_state=None):
global _rs
if ndim is None:
if mean_of_log is not None: ndim = np.size(mean_of_log)
elif cov_of_log is not None: ndim = npu.nrow(cov_of_log)
else: ndim = 1
if ndim is not None:
if mean_of_log is None: mean_of_log = npu.ndim_1_of(ndim, 0.)
if cov_of_log is None: cov_of_log = np.eye(ndim, ndim)
mean_of_log = npu.to_ndim_1(mean_of_log)
cov_of_log = npu.to_ndim_2(cov_of_log)
npc.check_size(mean_of_log, ndim)
npc.check_nrow(cov_of_log, ndim)
npc.check_square(cov_of_log)
if random_state is None: random_state = _rs()
normal = random_state.multivariate_normal(mean_of_log, cov_of_log, size)
return np.exp(normal)
def isnrow(arg, nrow):
return npu.nrow(arg) == nrow
def particle_count(self):
return npu.nrow(self._particles) if self._particles is not None else 0
