xorbits.numpy.linalg.matrix_power#

xorbits.numpy.linalg.matrix_power(a, n)#

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 – 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.

Return type

(…, M, M) ndarray or matrix object

Raises

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

Examples

>>> 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.]])

Warning

This method has not been implemented yet. Xorbits will try to execute it with numpy.linalg.

This docstring was copied from numpy.linalg.