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scipy.linalg.

# fractional_matrix_power

scipy.linalg.fractional_matrix_power(A, t)

  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.

    t float

      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.]])