def logm(A,disp=1):
"""Matrix logarithm, inverse of expm."""
# Compute using general funm but then use better error estimator and
# make one step in improving estimate using a rotation matrix.
A = mat(asarray(A))
F, errest = funm(A,log,disp=0)
errtol = 1000*eps
# Only iterate if estimate of error is too large.
if errest >= errtol:
# Use better approximation of error
errest = norm(expm(F)-A,1) / norm(A,1)
if not isfinite(errest) or errest >= errtol:
N,N = A.shape
X,Y = ogrid[1:N+1,1:N+1]
R = mat(orth(eye(N,dtype='d')+X+Y))
F, dontcare = funm(R*A*R.H,log,disp=0)
F = R.H*F*R
if (norm(imag(F),1)<=1000*errtol*norm(F,1)):
F = mat(real(F))
E = mat(expm(F))
temp = mat(solve(E.T,(E-A).T))
F = F - temp.T
errest = norm(expm(F)-A,1) / norm(A,1)
if disp:
if not isfinite(errest) or errest >= errtol:
print "Result may be inaccurate, approximate err =", errest
return F
else:
return F, errest
def logm(A,disp=1):
"""Compute matrix logarithm.
The matrix logarithm is the inverse of expm: expm(logm(A)) == A
Parameters
----------
A : array, shape(M,M)
Matrix whose logarithm to evaluate
disp : boolean
Print warning if error in the result is estimated large
instead of returning estimated error. (Default: True)
Returns
-------
logA : array, shape(M,M)
Matrix logarithm of A
(if disp == False)
errest : float
1-norm of the estimated error, ||err||_1 / ||A||_1
"""
# Compute using general funm but then use better error estimator and
# make one step in improving estimate using a rotation matrix.
A = mat(asarray(A))
F, errest = funm(A,log,disp=0)
errtol = 1000*eps
# Only iterate if estimate of error is too large.
if errest >= errtol:
# Use better approximation of error
errest = norm(expm(F)-A,1) / norm(A,1)
if not isfinite(errest) or errest >= errtol:
N,N = A.shape
X,Y = ogrid[1:N+1,1:N+1]
R = mat(orth(eye(N,dtype='d')+X+Y))
F, dontcare = funm(R*A*R.H,log,disp=0)
F = R.H*F*R
if (norm(imag(F),1)<=1000*errtol*norm(F,1)):
F = mat(real(F))
E = mat(expm(F))
temp = mat(solve(E.T,(E-A).T))
F = F - temp.T
errest = norm(expm(F)-A,1) / norm(A,1)
if disp:
if not isfinite(errest) or errest >= errtol:
print "Result may be inaccurate, approximate err =", errest
return F
else:
return F, errest
