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