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,
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 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 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)
