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Module « numpy.linalg »

Fonction matrix_power - module numpy.linalg

Signature de la fonction matrix_power

def matrix_power(a, n) 

Description

help(numpy.linalg.matrix_power)

Raise a square matrix to the (integer) power `n`.

For positive integers `n`, the power is computed by repeated matrix
squarings and matrix multiplications. If ``n == 0``, the identity matrix
of the same shape as M is returned. If ``n < 0``, the inverse
is computed and then raised to the ``abs(n)``.

.. note:: Stacks of object matrices are not currently supported.

Parameters
----------
a : (..., M, M) array_like
    Matrix to be "powered".
n : int
    The exponent can be any integer or long integer, positive,
    negative, or zero.

Returns
-------
a**n : (..., M, M) ndarray or matrix object
    The return value is the same shape and type as `M`;
    if the exponent is positive or zero then the type of the
    elements is the same as those of `M`. If the exponent is
    negative the elements are floating-point.

Raises
------
LinAlgError
    For matrices that are not square or that (for negative powers) cannot
    be inverted numerically.

Examples
--------
>>> import numpy as np
>>> from numpy.linalg import matrix_power
>>> i = np.array([[0, 1], [-1, 0]]) # matrix equiv. of the imaginary unit
>>> matrix_power(i, 3) # should = -i
array([[ 0, -1],
       [ 1,  0]])
>>> matrix_power(i, 0)
array([[1, 0],
       [0, 1]])
>>> matrix_power(i, -3) # should = 1/(-i) = i, but w/ f.p. elements
array([[ 0.,  1.],
       [-1.,  0.]])

Somewhat more sophisticated example

>>> q = np.zeros((4, 4))
>>> q[0:2, 0:2] = -i
>>> q[2:4, 2:4] = i
>>> q # one of the three quaternion units not equal to 1
array([[ 0., -1.,  0.,  0.],
       [ 1.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  1.],
       [ 0.,  0., -1.,  0.]])
>>> matrix_power(q, 2) # = -np.eye(4)
array([[-1.,  0.,  0.,  0.],
       [ 0., -1.,  0.,  0.],
       [ 0.,  0., -1.,  0.],
       [ 0.,  0.,  0., -1.]])

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