def sqrtm(A,disp=1):
"""Matrix square root
If disp is non-zero display warning if singular matrix.
If disp is zero then return residual ||A-X*X||_F / ||A||_F
Uses algorithm by Nicholas J. Higham
"""
A = asarray(A)
if len(A.shape)!=2:
raise ValueError, "Non-matrix input to matrix function."
T, Z = schur(A)
T, Z = rsf2csf(T,Z)
n,n = T.shape
R = sb.zeros((n,n),T.dtype.char)
for j in range(n):
R[j,j] = sqrt(T[j,j])
for i in range(j-1,-1,-1):
s = 0
for k in range(i+1,j):
s = s + R[i,k]*R[k,j]
R[i,j] = (T[i,j] - s)/(R[i,i] + R[j,j])
R, Z = all_mat(R,Z)
X = (Z * R * Z.H)
if disp:
nzeig = sb.any(sb.diag(T)==0)
if nzeig:
print "Matrix is singular and may not have a square root."
return X.A
else:
arg2 = norm(X*X - A,'fro')**2 / norm(A,'fro')
return X.A, arg2
def sqrtm(A,disp=1):
"""Matrix square root.
Parameters
----------
A : array, shape(M,M)
Matrix whose square root to evaluate
disp : boolean
Print warning if error in the result is estimated large
instead of returning estimated error. (Default: True)
Returns
-------
sgnA : array, shape(M,M)
Value of the sign function at A
(if disp == False)
errest : float
Frobenius norm of the estimated error, ||err||_F / ||A||_F
Notes
-----
Uses algorithm by Nicholas J. Higham
"""
A = asarray(A)
if len(A.shape)!=2:
raise ValueError, "Non-matrix input to matrix function."
T, Z = schur(A)
T, Z = rsf2csf(T,Z)
n,n = T.shape
R = np.zeros((n,n),T.dtype.char)
for j in range(n):
R[j,j] = sqrt(T[j,j])
for i in range(j-1,-1,-1):
s = 0
for k in range(i+1,j):
s = s + R[i,k]*R[k,j]
R[i,j] = (T[i,j] - s)/(R[i,i] + R[j,j])
R, Z = all_mat(R,Z)
X = (Z * R * Z.H)
if disp:
nzeig = np.any(diag(T)==0)
if nzeig:
print "Matrix is singular and may not have a square root."
return X.A
else:
arg2 = norm(X*X - A,'fro')**2 / norm(A,'fro')
return X.A, arg2
