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Module « scipy.stats »

Fonction ortho_group - module scipy.stats

Signature de la fonction ortho_group

def ortho_group(dim=None, seed=None) 

Description

help(scipy.stats.ortho_group)

An Orthogonal matrix (O(N)) random variable.

Return a random orthogonal matrix, drawn from the O(N) Haar
distribution (the only uniform distribution on O(N)).

The `dim` keyword specifies the dimension N.

Methods
-------
rvs(dim=None, size=1, random_state=None)
    Draw random samples from O(N).

Parameters
----------
dim : scalar
    Dimension of matrices
seed : {None, int, np.random.RandomState, np.random.Generator}, 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 class is closely related to `special_ortho_group`.

Some care is taken to avoid numerical error, as per the paper by Mezzadri.

References
----------
.. [1] F. Mezzadri, "How to generate random matrices from the classical
       compact groups", :arXiv:`math-ph/0609050v2`.

Examples
--------
>>> import numpy as np
>>> from scipy.stats import ortho_group
>>> x = ortho_group.rvs(3)

>>> np.dot(x, x.T)
array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
       [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
       [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])

>>> import scipy.linalg
>>> np.fabs(scipy.linalg.det(x))
1.0

This generates one random matrix from O(3). It is orthogonal and
has a determinant of +1 or -1.

Alternatively, the object may be called (as a function) to fix the `dim`
parameter, returning a "frozen" ortho_group random variable:

>>> rv = ortho_group(5)
>>> # Frozen object with the same methods but holding the
>>> # dimension parameter fixed.

See Also
--------
special_ortho_group

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