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 [1].
- Parameters:
- A(N, N) array_like
Matrix whose fractional power to evaluate.
- tfloat
Fractional power.
- Returns:
- X(N, N) array_like
The fractional power of the matrix.
References
[1]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
>>> import numpy as np >>> 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.]])