copula¶
High performance copula generators

pyscenarios.copula.
gaussian_copula
(cov: Union[List[List[float]], numpy.ndarray], samples: int, seed: int = 0, chunks: Union[None, int, Tuple[int, int], Tuple[Tuple[int, ...], Tuple[int, ...]]] = None, rng: str = 'Mersenne Twister') → Union[numpy.ndarray, dask.array.core.Array]¶ Gaussian Copula scenario generator.
Simplified algorithm:
>>> l = numpy.linalg.cholesky(cov) >>> y = numpy.random.standard_normal(size=(samples, cov.shape[0])) >>> p = (l @ y.T).T
 Parameters
cov (numpy.ndarray) – covariance matrix, a.k.a. correlation matrix. It must be a Hermitian, positivedefinite matrix in any square arraylike format. The width of cov determines the number of dimensions of the output.
samples (int) –
Number of random samples to generate
Note
When using Sobol, to obtain a uniform distribution one must use \(2^{n}  1\) samples (for any n > 0).
chunks –
Chunk size for the return array, which has shape (samples, dimensions). It can be anything accepted by dask (a positive integer, a tuple of two ints, or a tuple of two tuples of ints) for the output shape.
Set to None to return a numpy array.
Warning
When using the Mersenne Twister random generator, the chunk size changes the random sequence. To guarantee repeatability, it must be fixed together with the seed. chunks=None also produces different results from using dask.
seed (int) –
Random seed.
With
rng='Sobol'
, this is the initial dimension; when generating multiple copulas with different seeds, one should never use seeds that are less thancov.shape[0]
apart from each other.The maximum seed when using sobol is:
pyscenarios.sobol.max_dimensions()  cov.shape[0]  1
rng (str) – Either
Mersenne Twister
orSobol
 Returns
array of shape (samples, dimensions), with all series being normal (0, 1) distributions.
 Return type
If chunks is not None,
dask.array.Array
; elsenumpy.ndarray

pyscenarios.copula.
t_copula
(cov: Union[List[List[float]], numpy.ndarray], df: Union[int, List[int], numpy.ndarray], samples: int, seed: int = 0, chunks: Union[None, int, Tuple[int, int], Tuple[Tuple[int, ...], Tuple[int, ...]]] = None, rng: str = 'Mersenne Twister') → Union[numpy.ndarray, dask.array.core.Array]¶ Student T Copula / IT Copula scenario generator.
Simplified algorithm:
>>> l = numpy.linalg.cholesky(cov) >>> y = numpy.random.standard_normal(size=(samples, cov.shape[0])) >>> p = (l @ y.T).T # Gaussian Copula >>> r = numpy.random.uniform(size=(samples, 1)) >>> s = scipy.stats.chi2.ppf(r, df=df) >>> z = numpy.sqrt(df / s) * p >>> u = scipy.stats.t.cdf(z, df=df) >>> t = scipy.stats.norm.ppf(u)
 Parameters
cov (numpy.ndarray) – covariance matrix, a.k.a. correlation matrix. It must be a Hermitian, positivedefinite matrix in any square arraylike format. The width of cov determines the number of dimensions of the output.
df – Number of degrees of freedom. Can be either a scalar int for Student T Copula, or a onedimensional arraylike with one point per dimension for IT Copula.
samples (int) –
Number of random samples to generate
Note
When using Sobol, to obtain a uniform distribution one must use \(2^{n}  1\) samples (for any n > 0).
chunks –
Chunk size for the return array, which has shape (samples, dimensions). It can be anything accepted by dask (a positive integer, a tuple of two ints, or a tuple of two tuples of ints) for the output shape.
Set to None to return a numpy array.
Warning
When using the Mersenne Twister random generator, the chunk size changes the random sequence. To guarantee repeatability, it must be fixed together with the seed. chunks=None also produces different results from using dask.
seed (int) –
Random seed.
With
rng='Sobol'
, this is the initial dimension; when generating multiple copulas with different seeds, one should never use seeds that are less thancov.shape[0] + 1
apart from each other.The maximum seed when using sobol is:
pyscenarios.sobol.max_dimensions()  cov.shape[0]  2
rng (str) – Either
Mersenne Twister
orSobol
 Returns
array of shape (samples, dimensions), with all series being normal (0, 1) distributions.
 Return type
If chunks is not None,
dask.array.Array
; elsenumpy.ndarray