def interpret_complete_cdf(
cdfs_p: List[Union[list, np.ndarray]],
cdfs_v: List[Union[list, np.ndarray]],
distribution: str = None,
) -> Union[List[Union[list, np.ndarray]], Tuple[List[Union[list, np.ndarray]],
List[Union[list, np.ndarray]]],
ot.DistributionImplementation, ]:
"""Interpret the given points on the cumulative distribution function to represent a complete CDF. The default
policy is to assume discrete probabilities.
If a distribution name is specified, the CDF is returned as an openturns distribution object.
Supported openturns distributions are the following:
- discrete: all residual probability is attributed to the highest given value
- normal or gaussian: derived from the first two point only
- uniform: interpolates linearly between points, with residual probability attributed to the min and max values
"""
# Todo: refactor, currently too many possible types of output
if distribution is None:
for cdf_p in cdfs_p:
cdf_p[-1] = 1 # Last value is the highest
return cdfs_p, cdfs_v
cdfs = []
if distribution == "discrete":
for cdf_p, cdf_v in zip(cdfs_p, cdfs_v):
cdf_p[-1] = 1 # Last value is the highest
cdfs.append(ot.UserDefined([[v] for v in cdf_v], cp_to_p(cdf_p)))
elif distribution in ["normal", "gaussian"]:
for cdf_p, cdf_v in zip(cdfs_p, cdfs_v):
if len(cdf_v) > 1:
x1 = cdf_v[0]
x2 = cdf_v[1]
y1 = cdf_p[0]
y2 = cdf_p[1]
mu = (x1 * pyerf.erfinv(1 - 2 * y2) -
x2 * pyerf.erfinv(1 - 2 * y1)) / (
pyerf.erfinv(1 - 2 * y2) - pyerf.erfinv(1 - 2 * y1))
sigma = (2**0.5 * x1 -
2**0.5 * x2) / (2 * pyerf.erfinv(1 - 2 * y2) -
2 * pyerf.erfinv(1 - 2 * y1))
cdfs.append(ot.Normal(mu, sigma))
else:
cdfs.append(ot.UserDefined([[v] for v in cdf_v], cdf_p))
elif distribution == "uniform":
for cdf_p, cdf_v in zip(cdfs_p, cdfs_v):
if len(cdf_v) == 1:
cdfs.append(ot.UserDefined([cdf_v]))
elif len(cdf_v) > 1:
coll = ([ot.UserDefined([[cdf_v[0]]])] + [
ot.Uniform(float(cdf_v[i]), float(cdf_v[i + 1]))
for i in range(len(cdf_v) - 1)
] + [ot.UserDefined([[cdf_v[-1]]])])
weights = np.append(cp_to_p(cdf_p), 1 - cdf_p[-1])
cdfs.append(ot.Mixture(coll, weights))
else:
return NotImplementedError
return cdfs
def interpret_complete_cdf(
cdfs_p: List[Union[list, np.ndarray]],
cdfs_v: List[Union[list, np.ndarray]],
distribution: str = None,
) -> Union[List[Union[list, np.ndarray]], Tuple[List[Union[list, np.ndarray]],
List[Union[list, np.ndarray]]],
ot.DistributionImplementation, ]:
"""Interpret the given points on the cumulative distribution function to represent a complete CDF. The default
policy is to assume discrete probabilities.
If a distribution name is specified, the CDF is returned as an openturns distribution object.
Supported openturns distributions are the following:
- discrete: all residual probability is attributed to the highest given value
- normal or gaussian: derived from the first two point only
- uniform: derived from the first and last points and extended to range from cp=0 to cp=1
"""
# Todo: refactor, currently too many possible types of output
if distribution is None:
for cdf_p in cdfs_p:
cdf_p[-1] = 1 # Last value is the highest
return cdfs_p, cdfs_v
cdfs = []
if distribution == "discrete":
for cdf_p, cdf_v in zip(cdfs_p, cdfs_v):
cdf_p[-1] = 1 # Last value is the highest
cdfs.append(ot.UserDefined([[v] for v in cdf_v], cdf_p))
elif distribution in ["normal", "gaussian"]:
for cdf_p, cdf_v in zip(cdfs_p, cdfs_v):
x1 = cdf_v[0]
x2 = cdf_v[1]
y1 = cdf_p[0]
y2 = cdf_p[1]
mu = (x1 * pyerf.erfinv(1 - 2 * y2) - x2 * pyerf.erfinv(1 - 2 * y1)
) / (pyerf.erfinv(1 - 2 * y2) - pyerf.erfinv(1 - 2 * y1))
sigma = (2**0.5 * x1 - 2**0.5 * x2) / (
2 * pyerf.erfinv(1 - 2 * y2) - 2 * pyerf.erfinv(1 - 2 * y1))
cdfs.append(ot.Normal(mu, sigma))
elif distribution is "uniform":
for cdf_p, cdf_v in zip(cdfs_p, cdfs_v):
x1 = cdf_v[0]
x2 = cdf_v[-1]
y1 = cdf_p[0]
y2 = cdf_p[-1]
dydx = (y2 - y1) / (x2 - x1)
a = x1 - y1 / dydx
b = x2 + (1 - y2) / dydx
cdfs.append(ot.Uniform(a, b))
else:
return NotImplementedError
return cdfs
def _nppf_py(x):
return s2 * pyerf.erfinv(2 * x - 1)
def fractile(p):
return math.sqrt(2) * pyerf.erfinv(2 * p - 1)