scipy.linalg.logm#
- scipy.linalg.logm(A, disp=True)[source]#
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
- dispbool, optional
Print 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
- errestfloat
(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
>>> 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.]])