def __next__(self):
if self._time is None:
self._time = next(self.__times)
else:
newtime = next(self.__times)
time_delta = newtime - self._time
if isinstance(time_delta, dt.timedelta):
time_delta = time_delta.total_seconds(
) / self._time_unit.total_seconds()
npu.col_of(self.__process.noise_dim, 0.)
variate_delta = np.sqrt(time_delta) * npu.to_ndim_2(
next(self.__variates), ndim_1_to_col=True, copy=False)
drift = npu.to_ndim_2(self.__process.drift(self._time,
self.__value),
ndim_1_to_col=True,
copy=False)
diffusion = npu.to_ndim_2(self.__process.diffusion(
self._time, self.__value),
ndim_1_to_col=True,
copy=False)
self.__value += drift * time_delta + diffusion.dot(variate_delta)
self._time = newtime
v = np.copy(self.__value)
if self.__flatten: v = v.flatten()
return self._time, v
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,
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_wide_sense_distr(self):
std_wide_sense_1d = distrs.WideSenseDistr(dim=1)
npt.assert_almost_equal(std_wide_sense_1d.mean, 0.)
npt.assert_almost_equal(std_wide_sense_1d.cov, 1.)
npt.assert_almost_equal(std_wide_sense_1d.vol, 1.)
with self.assertRaises(NotImplementedError):
std_wide_sense_1d.sample()
std_wide_sense_2d = distrs.WideSenseDistr(dim=2)
npt.assert_almost_equal(std_wide_sense_2d.mean, npu.col_of(2, 0.))
npt.assert_almost_equal(std_wide_sense_2d.cov, np.eye(2))
npt.assert_almost_equal(std_wide_sense_2d.vol, np.eye(2))
with self.assertRaises(NotImplementedError):
std_wide_sense_2d.sample()
sd1=3.; sd2=4.; cor=-.5
wide_sense_2d = distrs.WideSenseDistr(mean=[1., 2.], cov=stats.make_cov_2d(sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(wide_sense_2d.mean, npu.col(1., 2.))
npt.assert_almost_equal(wide_sense_2d.cov, [[sd1*sd1, cor*sd1*sd2], [cor*sd1*sd2, sd2*sd2]])
npt.assert_almost_equal(wide_sense_2d.vol, [[sd1, 0.], [cor*sd2, np.sqrt(1.-cor*cor)*sd2]])
with self.assertRaises(NotImplementedError):
wide_sense_2d.sample()
wide_sense_2d = distrs.WideSenseDistr(mean=[1., 2.], vol=stats.make_vol_2d(sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(wide_sense_2d.mean, npu.col(1., 2.))
npt.assert_almost_equal(wide_sense_2d.cov, [[sd1*sd1, cor*sd1*sd2], [cor*sd1*sd2, sd2*sd2]])
npt.assert_almost_equal(wide_sense_2d.vol, [[sd1, 0.], [cor*sd2, np.sqrt(1.-cor*cor)*sd2]])
with self.assertRaises(NotImplementedError):
wide_sense_2d.sample()
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 __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, 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, 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 __init__(self,
process,
initial_value=None,
times=None,
variates=None,
time_unit=dt.timedelta(days=1),
flatten=False):
checks.check_instance(process, proc.ItoProcess)
self.__process = process
self.__value = npu.to_ndim_2(
initial_value, ndim_1_to_col=True,
copy=True) if initial_value is not None else npu.col_of(
process.process_dim, 0.)
self.__times = times if times is not None else xtimes(0., None, 1.)
self.__variates = variates if variates is not None else rnd.multivatiate_normals(
ndim=process.noise_dim)
self._time = None
self._time_unit = time_unit
self.__flatten = flatten
def test_multivariate_normal_distr(self):
std_normal_1d = distrs.NormalDistr(dim=1)
npt.assert_almost_equal(std_normal_1d.mean, 0.)
npt.assert_almost_equal(std_normal_1d.cov, 1.)
npt.assert_almost_equal(std_normal_1d.vol, 1.)
std_normal_1d = distrs.NormalDistr(dim=2)
npt.assert_almost_equal(std_normal_1d.mean, npu.col_of(2, 0.))
npt.assert_almost_equal(std_normal_1d.cov, np.eye(2))
npt.assert_almost_equal(std_normal_1d.vol, np.eye(2))
sd1 = 3.
sd2 = 4.
cor = -.5
normal_2d = distrs.NormalDistr(mean=[1., 2.],
cov=distrs.NormalDistr.make_cov_2d(
sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(normal_2d.mean, npu.col(1., 2.))
npt.assert_almost_equal(
normal_2d.cov,
[[sd1 * sd1, cor * sd1 * sd2], [cor * sd1 * sd2, sd2 * sd2]])
npt.assert_almost_equal(
normal_2d.vol,
[[sd1, 0.], [cor * sd2, np.sqrt(1. - cor * cor) * sd2]])
normal_2d = distrs.NormalDistr(mean=[1., 2.],
vol=distrs.NormalDistr.make_vol_2d(
sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(normal_2d.mean, npu.col(1., 2.))
npt.assert_almost_equal(
normal_2d.cov,
[[sd1 * sd1, cor * sd1 * sd2], [cor * sd1 * sd2, sd2 * sd2]])
npt.assert_almost_equal(
normal_2d.vol,
[[sd1, 0.], [cor * sd2, np.sqrt(1. - cor * cor) * sd2]])
def test_normal_distr(self):
rnd.random_state(np.random.RandomState(seed=42), force=True)
std_normal_1d = distrs.NormalDistr(dim=1)
npt.assert_almost_equal(std_normal_1d.mean, 0.)
npt.assert_almost_equal(std_normal_1d.cov, 1.)
npt.assert_almost_equal(std_normal_1d.vol, 1.)
sample = std_normal_1d.sample()
self.assertEqual(np.shape(sample), (1, 1))
npt.assert_almost_equal(sample, [[ 0.49671415]])
sample = std_normal_1d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 1))
npt.assert_almost_equal(sample, [
[-0.1382643 ],
[ 0.64768854],
[ 1.52302986],
[-0.23415337],
[-0.23413696],
[ 1.57921282],
[ 0.76743473],
[-0.46947439],
[ 0.54256004],
[-0.46341769]])
std_normal_2d = distrs.NormalDistr(dim=2)
npt.assert_almost_equal(std_normal_2d.mean, npu.col_of(2, 0.))
npt.assert_almost_equal(std_normal_2d.cov, np.eye(2))
npt.assert_almost_equal(std_normal_2d.vol, np.eye(2))
sample = std_normal_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[-0.46572975, 0.24196227],
[-1.91328024, -1.72491783],
[-0.56228753, -1.01283112],
[ 0.31424733, -0.90802408],
[-1.4123037 , 1.46564877],
[-0.2257763 , 0.0675282 ],
[-1.42474819, -0.54438272],
[ 0.11092259, -1.15099358],
[ 0.37569802, -0.60063869],
[-0.29169375, -0.60170661]])
sd1=3.; sd2=4.; cor=-.5
normal_2d = distrs.NormalDistr(mean=[1., 2.], cov=stats.make_cov_2d(sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(normal_2d.mean, npu.col(1., 2.))
npt.assert_almost_equal(normal_2d.cov, [[sd1*sd1, cor*sd1*sd2], [cor*sd1*sd2, sd2*sd2]])
npt.assert_almost_equal(normal_2d.vol, [[sd1, 0.], [cor*sd2, np.sqrt(1.-cor*cor)*sd2]])
sample = normal_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[-3.09581812, 9.06710684],
[ 5.00400357, -1.07912958],
[ 4.10821238, -2.42324481],
[ 2.58989516, -7.05256838],
[ 2.07671635, 3.61955714],
[ 0.38728403, 2.5195548 ],
[-1.36010204, -0.88681309],
[ 1.63968707, -1.29329703],
[-0.61960168, 6.44566548],
[ 5.53451941, -4.36131646]])
normal_2d = distrs.NormalDistr(mean=[1., 2.], vol=stats.make_vol_2d(sd1=sd1, sd2=sd2, cor=cor))
npt.assert_almost_equal(normal_2d.mean, npu.col(1., 2.))
npt.assert_almost_equal(normal_2d.cov, [[sd1*sd1, cor*sd1*sd2], [cor*sd1*sd2, sd2*sd2]])
npt.assert_almost_equal(normal_2d.vol, [[sd1, 0.], [cor*sd2, np.sqrt(1.-cor*cor)*sd2]])
sample = normal_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[ 0.4624506 , -0.26705979],
[ 1.76344545, 5.54913479],
[-2.76038957, 4.57609973],
[ 2.35608833, 1.20642031],
[-2.1218454 , 5.16796697],
[-0.85307657, -0.00850715],
[ 5.28771297, -1.62048489],
[-2.12592264, 7.1016208 ],
[-0.46508111, 6.26189296],
[ 3.15543223, -0.04269231]])
def test_dirac_delta_distr(self):
std_dirac_delta_1d = distrs.DiracDeltaDistr(dim=1)
npt.assert_almost_equal(std_dirac_delta_1d.mean, 0.)
npt.assert_almost_equal(std_dirac_delta_1d.cov, 0.)
npt.assert_almost_equal(std_dirac_delta_1d.vol, 0.)
sample = std_dirac_delta_1d.sample()
self.assertEqual(np.shape(sample), (1, 1))
npt.assert_almost_equal(sample, [[ 0. ]])
sample = std_dirac_delta_1d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 1))
npt.assert_almost_equal(sample, [
[ 0.],
[ 0.],
[ 0.],
[ 0.],
[ 0.],
[ 0.],
[ 0.],
[ 0.],
[ 0.],
[ 0.]])
std_dirac_delta_2d = distrs.DiracDeltaDistr(dim=2)
npt.assert_almost_equal(std_dirac_delta_2d.mean, npu.col_of(2, 0.))
npt.assert_almost_equal(std_dirac_delta_2d.cov, np.zeros((2, 2)))
npt.assert_almost_equal(std_dirac_delta_2d.vol, np.zeros((2, 2)))
sample = std_dirac_delta_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[ 0., 0.],
[ 0., 0.],
[ 0., 0.],
[ 0., 0.],
[ 0., 0.],
[ 0., 0.],
[ 0., 0.],
[ 0., 0.],
[ 0., 0.],
[ 0., 0.]])
dirac_delta_2d = distrs.DiracDeltaDistr(mean=[1., 2.], dim=2)
npt.assert_almost_equal(dirac_delta_2d.mean, [[1.], [2.]])
npt.assert_almost_equal(dirac_delta_2d.cov, np.zeros((2, 2)))
npt.assert_almost_equal(dirac_delta_2d.vol, np.zeros((2, 2)))
sample = dirac_delta_2d.sample(size=10)
self.assertEqual(np.shape(sample), (10, 2))
npt.assert_almost_equal(sample, [
[ 1., 2.],
[ 1., 2.],
[ 1., 2.],
[ 1., 2.],
[ 1., 2.],
[ 1., 2.],
[ 1., 2.],
[ 1., 2.],
[ 1., 2.],
[ 1., 2.]])
def test_col_of(self):
col = npu.col_of(5, 429.)
npt.assert_almost_equal(col, np.array([[429.], [429.], [429.], [429.], [429.]]))
