def solve_newton_with_dt(func, u0, args, kargs, dt,
max_iter, abs_tol, rel_tol, verbose):
u = adarray(value(u0).copy())
_DEBUG_perturb_new(u)
for i_Newton in range(max_iter):
if dt == np.inf:
res = func(u, *args, **kargs)
else:
res = (u - u0) / dt + func(u, *args, **kargs)
res_norm = np.linalg.norm(res._value.reshape(res.size), np.inf)
if verbose:
print(' ', i_Newton, res_norm)
if i_Newton == 0:
res_norm0 = res_norm
if res_norm < max(abs_tol, rel_tol * res_norm0):
return adsolution(u, res, i_Newton + 1)
if not np.isfinite(res_norm) or res_norm > res_norm0 * 1E6:
break
# Newton update
J = res.diff(u).tocsr()
if J.shape[0] > 1:
minus_du = splinalg.spsolve(J, np.ravel(res._value),
use_umfpack=False)
else:
minus_du = res._value / J.toarray()[0,0]
u._value -= minus_du.reshape(u.shape)
u = adarray(u._value) # unlink operation history if any
_DEBUG_perturb_new(u)
# not converged
u = adarray(value(u0).copy())
res = func(u, *args, **kargs)
return adsolution(u, res, np.inf)
def solve(func, u0, args=(), kargs={},
max_iter=10, abs_tol=1E-6, rel_tol=1E-6, verbose=True):
u = adarray(value(u0).copy())
_DEBUG_perturb_new(u)
func = replace__globals__(func)
for i_Newton in range(max_iter):
res = func(u, *args, **kargs)
res_norm = np.linalg.norm(res._value, np.inf)
if verbose:
print(' ', i_Newton, res_norm)
if not np.isfinite(res_norm):
break
if i_Newton == 0:
res_norm0 = res_norm
if res_norm < max(abs_tol, rel_tol * res_norm0):
return adsolution(u, res, i_Newton + 1)
# Newton update
J = res.diff(u).tocsr()
if J.shape[0] > 1:
minus_du = splinalg.spsolve(J, np.ravel(res._value),
use_umfpack=False)
else:
minus_du = res._value / J.toarray()[0,0]
u._value -= minus_du.reshape(u.shape)
u = adarray(u._value) # unlink operation history if any
_DEBUG_perturb_new(u)
# not converged
return adsolution(u, res, np.inf)
def __init__(self, solution, residual, n_Newton):
assert isinstance(solution, adarray)
assert isinstance(residual, adarray)
residual._current_state = ResidualState(residual._current_state)
adarray.__init__(self, solution._value)
self._current_state = SolutionState(self, residual._current_state,
residual.diff(solution))
self._n_Newton = n_Newton
self._res_norm = np.linalg.norm(residual._value.reshape(residual.size))
_DEBUG_perturb_new(self)
def solve(func, u0, args=(), kargs={},
max_iter=10, abs_tol=1E-6, rel_tol=1E-6, verbose=True):
u = adarray(base(u0).copy())
_DEBUG_perturb_new(u)
for i_Newton in range(max_iter):
start = time.time()
res = func(u, *args, **kargs) # TODO: how to put into adarray context?
res_norm = np.linalg.norm(res._base, np.inf)
if verbose:
print(' ', i_Newton, res_norm)
if not np.isfinite(res_norm):
break
if i_Newton == 0:
res_norm0 = res_norm
if res_norm < max(abs_tol, rel_tol * res_norm0):
return adsolution(u, res, i_Newton + 1)
# Newton update
J = res.diff(u).tocsr()
start2 = time.time()
minus_du = splinalg.spsolve(J, np.ravel(res._base))
print time.time()-start2
# P = splinalg.spilu(J, drop_tol=1e-5)
# M_x = lambda x: P.solve(x)
# M = splinalg.LinearOperator((n * m, n * m), M_x)
# minus_du = splinalg.gmres(J, np.ravel(res._base), M=M,tol=1e-6)
u._base -= minus_du.reshape(u.shape)
u = adarray(u._base) # unlink operation history if any
_DEBUG_perturb_new(u)
print time.time()-start
# not converged
return adsolution(u, res, np.inf)
