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scipy.linalg.

# logm

scipy.linalg.logm(A, disp=True)

  Compute matrix logarithm.

  The matrix logarithm is the inverse of expm: expm(logm(A)) == A

  Parameters:
    A(N, N) array_like

      Matrix whose logarithm to evaluate

    disp bool, optional

      Emit warning if error in the result is estimated large instead of returning estimated error. (Default: True)

  Returns:
    logm(N, N) ndarray

      Matrix logarithm of A

    errest float

      (if disp == False)

      1-norm of the estimated error, ||err||_1 / ||A||_1

  References

  [1]

  Awad H. Al-Mohy and Nicholas J. Higham (2012) “Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm.” SIAM Journal on Scientific Computing, 34 (4). C152-C169. ISSN 1095-7197

  [2]

  Nicholas J. Higham (2008) “Functions of Matrices: Theory and Computation” ISBN 978-0-898716-46-7

  [3]

  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 logm, expm
      >>> a = np.array([[1.0, 3.0], [1.0, 4.0]])
      >>> b = logm(a)
      >>> b
      array([[-1.02571087,  2.05142174],
             [ 0.68380725,  1.02571087]])
      >>> expm(b)         # Verify expm(logm(a)) returns a
      array([[ 1.,  3.],
             [ 1.,  4.]])