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Module « scipy.stats »

Fonction uniform_direction - module scipy.stats

Signature de la fonction uniform_direction

def uniform_direction(dim=None, seed=None) 

Description

help(scipy.stats.uniform_direction)

A vector-valued uniform direction.

Return a random direction (unit vector). The `dim` keyword specifies
the dimensionality of the space.

Methods
-------
rvs(dim=None, size=1, random_state=None)
    Draw random directions.

Parameters
----------
dim : scalar
    Dimension of directions.
seed : {None, int, `numpy.random.Generator`,
        `numpy.random.RandomState`}, optional

    Used for drawing random variates.
    If `seed` is `None`, the `~np.random.RandomState` singleton is used.
    If `seed` is an int, a new ``RandomState`` instance is used, seeded
    with seed.
    If `seed` is already a ``RandomState`` or ``Generator`` instance,
    then that object is used.
    Default is `None`.

Notes
-----
This distribution generates unit vectors uniformly distributed on
the surface of a hypersphere. These can be interpreted as random
directions.
For example, if `dim` is 3, 3D vectors from the surface of :math:`S^2`
will be sampled.

References
----------
.. [1] Marsaglia, G. (1972). "Choosing a Point from the Surface of a
       Sphere". Annals of Mathematical Statistics. 43 (2): 645-646.

Examples
--------
>>> import numpy as np
>>> from scipy.stats import uniform_direction
>>> x = uniform_direction.rvs(3)
>>> np.linalg.norm(x)
1.

This generates one random direction, a vector on the surface of
:math:`S^2`.

Alternatively, the object may be called (as a function) to return a frozen
distribution with fixed `dim` parameter. Here,
we create a `uniform_direction` with ``dim=3`` and draw 5 observations.
The samples are then arranged in an array of shape 5x3.

>>> rng = np.random.default_rng()
>>> uniform_sphere_dist = uniform_direction(3)
>>> unit_vectors = uniform_sphere_dist.rvs(5, random_state=rng)
>>> unit_vectors
array([[ 0.56688642, -0.1332634 , -0.81294566],
       [-0.427126  , -0.74779278,  0.50830044],
       [ 0.3793989 ,  0.92346629,  0.05715323],
       [ 0.36428383, -0.92449076, -0.11231259],
       [-0.27733285,  0.94410968, -0.17816678]])

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