def __init__(self, fun, t0, y0, t_bound, max_step=np.inf,
rtol=1e-7, atol=1e-12, safety_factor=0.9,
min_step_change=0.333, max_step_change=6.0,
beta_stabilizer=0.00, max_nsteps=100000,
vectorized=False, **extraneous):
warn_extraneous(extraneous)
super().__init__(fun, t0, y0, t_bound, vectorized,
support_complex=True)
self.y_old = None
self.max_step = validate_max_step(max_step)
self.beta_stabilizer = validate_beta_stabilizer(beta_stabilizer)
self.max_nsteps = validate_max_nsteps(max_nsteps)
self.safety_factor = validate_safety_factor(safety_factor)
self.rtol, self.atol = validate_tol(rtol, atol, self.n)
self.min_step_change = min_step_change
self.max_step_change = max_step_change
self.order = 8
self.f = self.fun(self.t, self.y)
self.h_abs = select_initial_step(self.fun, self.t, self.y, self.f, self.direction,
self.order, self.rtol, self.atol)
self.nfev += 2
self.n_steps = 0
self.n_accepted = 0
self.n_rejected = 0
self.factor_old = 1e-4 # Lund-stabilization factor
self.K = np.zeros((16, self.n))
self.interpolation = np.zeros((8, self.n))
def __init__(self,
fun,
get_energy_gradient,
t0,
y0,
t_bound,
max_step=np.inf,
rtol=1e-3,
atol=1e-6,
ls_ctol=1e-4,
ls_max_iter=10,
ls_dec_scale=0.5,
vectorized=False,
line_search_class=None,
**extraneous):
warn_extraneous(extraneous)
super(RungeKutta_LS, self).__init__(fun,
t0,
y0,
t_bound,
vectorized,
support_complex=True)
self.y_old = None
self.max_step = validate_max_step(max_step)
self.rtol, self.atol = validate_tol(rtol, atol, self.n)
self.f = self.fun(self.t, self.y)
self.h_abs = select_initial_step(self.fun, self.t, self.y, self.f,
self.direction, self.order, self.rtol,
self.atol)
self.K = np.empty((self.n_stages + 1, self.n), dtype=self.y.dtype)
self.ls_ctol = ls_ctol
self.ls_max_iter = ls_max_iter
self.ls_dec_scale = ls_dec_scale
self.get_energy_gradient = get_energy_gradient
self.line_search_class = line_search_class
def __init__(self, *args, **kwargs):
self.options = VariableStepOptions(
**{k: kwargs.pop(k)
for k in variable_step_options if k in kwargs})
h = kwargs.pop("first_step", None)
super().__init__(*args, **kwargs)
validate_max_step(self.options.max_step)
validate_tol(self.options.rtol, self.options.atol, self.y.size)
if h is None:
h = select_initial_step(
self.rhs,
self.t,
self.y,
self.f,
1,
self.error_estimator_order,
self.options.rtol,
self.options.atol,
)
self.h = np.array(h, dtype=float)
def __init__(self,
fun,
t0,
y0,
t_bound,
max_step=np.inf,
rtol=1e-7,
atol=1e-12,
safety_factor=0.9,
min_step_change=0.333,
max_step_change=6.0,
beta_stabilizer=0.00,
max_nsteps=100000,
vectorized=False,
**extraneous):
warn_extraneous(extraneous)
super().__init__(fun,
t0,
y0,
t_bound,
vectorized,
support_complex=True)
self.y_old = None
self.max_step = validate_max_step(max_step)
self.beta_stabilizer = validate_beta_stabilizer(beta_stabilizer)
self.max_nsteps = validate_max_nsteps(max_nsteps)
self.safety_factor = validate_safety_factor(safety_factor)
self.rtol, self.atol = validate_tol(rtol, atol, self.n)
self.min_step_change = min_step_change
self.max_step_change = max_step_change
self.order = 8
self.f = self.fun(self.t, self.y)
self.h_abs = select_initial_step(
self.fun,
self.t,
self.y,
self.f,
self.direction,
self.order,
self.rtol,
self.atol,
)
self.nfev += 2
self.n_steps = 0
self.n_accepted = 0
self.n_rejected = 0
self.factor_old = 1e-4 # Lund-stabilization factor
self.K = np.zeros((16, self.n))
self.interpolation = np.zeros((8, self.n))
def __init__(self, fun, t0, y0, t_bound, max_step=np.inf,
rtol=1e-3, atol=1e-6, min_step=0, vectorized=False,
first_step=None, **extraneous):
warn_extraneous(extraneous)
super(RungeKutta, self).__init__(fun, t0, y0, t_bound, vectorized,
support_complex=True)
self.min_step_user = min_step
self.y_old = None
self.max_step = validate_max_step(max_step)
self.rtol, self.atol = validate_tol(rtol, atol, self.n)
self.f = self.fun(self.t, self.y)
if first_step is None:
self.h_abs = select_initial_step(
self.fun, self.t, self.y, self.f, self.direction,
self.order, self.rtol, self.atol)
else:
self.h_abs = validate_first_step(first_step, t0, t_bound)
self.K = np.empty((self.n_stages + 1, self.n), dtype=self.y.dtype)
def __init__(self,
fun,
t0,
y0,
t_bound,
max_step=np.inf,
rtol=1e-3,
atol=1e-6,
jac=None,
jac_sparsity=None,
vectorized=False,
first_step=None,
mass=None,
bPrint=False,
newton_tol=None,
constant_dt=False,
bPrintProgress=False,
**extraneous):
warn_extraneous(extraneous)
super(RadauDAE, self).__init__(fun, t0, y0, t_bound, vectorized)
self.y_old = None
self.max_step = validate_max_step(max_step)
self.rtol, self.atol = validate_tol(rtol, atol, self.n)
self.f = self.fun(self.t, self.y)
# Select initial step assuming the same order which is used to control
# the error.
if first_step is None:
self.h_abs = select_initial_step(self.fun, self.t, self.y, self.f,
self.direction, 3, self.rtol,
self.atol)
else:
self.h_abs = validate_first_step(first_step, t0, t_bound)
self.h_abs_old = None
self.error_norm_old = None
if newton_tol is None:
self.newton_tol = max(10 * EPS / rtol, min(0.03, rtol**0.5))
else:
self.newton_tol = newton_tol
self.sol = None
self.constant_dt = constant_dt
self.jac_factor = None
self.jac, self.J = self._validate_jac(jac, jac_sparsity)
self.nlusove = 0
self.bPrintProgress = bPrintProgress
global BPRINT
BPRINT = bPrint
if BPRINT:
zzzjac = self.jac
def debugJacprint(t, y, f):
print('\tupdating jacobian')
return zzzjac(t, y, f)
self.jac = debugJacprint
if issparse(self.J):
def lu(A):
self.nlu += 1
return splu(A)
def solve_lu(LU, b):
self.nlusove += 1
return LU.solve(b)
I = eye(self.n, format='csc')
else:
def lu(A):
self.nlu += 1
return lu_factor(A, overwrite_a=True)
def solve_lu(LU, b):
self.nlusove += 1
return lu_solve(LU, b, overwrite_b=True)
I = np.identity(self.n)
self.lu = lu
self.solve_lu = solve_lu
self.I = I
if not (mass is None):
if issparse(mass):
self.mass_matrix = csc_matrix(mass)
self.index_algebraic_vars = np.where(
np.all(self.mass_matrix.toarray() == 0,
axis=1))[0] # TODO: avoid the toarray()
else:
self.mass_matrix = mass
self.index_algebraic_vars = np.where(
np.all(self.mass_matrix == 0, axis=1))[0]
self.nvars_algebraic = self.index_algebraic_vars.size
else:
self.mass_matrix = None
self.index_algebraic_vars = None
self.nvars_algebraic = 0
self.current_jac = True
self.LU_real = None
self.LU_complex = None
self.Z = None
self.info = {
'cond': {
'LU_real': [],
'LU_complex': [],
't': [],
'h': []
}
}