SciPy

scipy.linalg.fractional_matrix_power

scipy.linalg.fractional_matrix_power(A, t)[source]

Compute the fractional power of a matrix.

Proceeds according to the discussion in section (6) of [R82].

Parameters:

A : (N, N) array_like

Matrix whose fractional power to evaluate.

t : float

Fractional power.

Returns:

X : (N, N) array_like

The fractional power of the matrix.

References

[R82](1, 2) Nicholas J. Higham and Lijing lin (2011) “A Schur-Pade Algorithm for Fractional Powers of a Matrix.” SIAM Journal on Matrix Analysis and Applications, 32 (3). pp. 1056-1078. ISSN 0895-4798

Examples

>>> from scipy.linalg import fractional_matrix_power
>>> a = np.array([[1.0, 3.0], [1.0, 4.0]])
>>> b = fractional_matrix_power(a, 0.5)
>>> b
array([[ 0.75592895,  1.13389342],
       [ 0.37796447,  1.88982237]])
>>> np.dot(b, b)      # Verify square root
array([[ 1.,  3.],
       [ 1.,  4.]])