scipy.linalg.

logm#

scipy.linalg.logm(A, disp=True)[source]#

計算矩陣對數。

矩陣對數是 expm 的反函數：expm(logm(A)) == A

參數:

A(N, N) array_like: 要評估對數的矩陣
dispbool, optional: 若結果中的誤差估計值過大，則發出警告，而不是返回估計誤差。（預設值：True）

返回值:

logm(N, N) ndarray

A 的矩陣對數

errestfloat

（若 disp == False）

估計誤差的 1-範數，||err||_1 / ||A||_1

參考文獻

[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

範例

>>> 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.]])