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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].

  The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. Note that calls with zero-size batches are unsupported and will raise a `ValueError`.

  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. DOI:10.1137/10081232X

  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.]])