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scipy.linalg.

# logm

scipy.linalg.logm(A)

  Compute matrix logarithm.

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

  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 logarithm to evaluate

  Returns:
    logm(N, N) ndarray

      Matrix logarithm of A

  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.]])