def __init__(self, fun, t0, y0, t_bound, max_step=np.inf, rtol=1e-3,
atol=1e-6, vectorized=False, first_step=None,
const_jac=False, rho_jac=None, **extraneous):
warn_extraneous(extraneous)
super(SSV2stab, self).__init__(
fun, t0, y0, t_bound, vectorized, support_complex=False)
if first_step is None:
self.absh = None
else:
self.absh = validate_first_step(first_step, t0, t_bound)
self.hold = None
if not isinstance(const_jac, bool):
raise TypeError('`const_jac` should be True or False')
if rho_jac is not None:
if not callable(rho_jac):
raise TypeError(
'`rho_jac` should be None or a function: '
'`sprad = rho_jac(t, y)`')
elif not isinstance(rho_jac(self.t, self.y), float):
raise TypeError('`rho_jac` should return a float')
elif rho_jac(self.t, self.y) <= 0:
raise ValueError('`rho_jac` should return a positive float')
self.const_jac = const_jac
self.rho_jac = rho_jac
self.max_step = validate_max_step(max_step)
self.rtol, self.atol = validate_tol(rtol, atol, self.y)
self.uround = np.nextafter(np.finfo(self.y.dtype).epsneg, 1)
self.sqrtu = sqrt(self.uround)
self.sqrtmin = sqrt(np.finfo(self.y.dtype).tiny)
self.W = np.empty((4, self.n), self.y.dtype)
self.V = None # eigenvector for spectral radius estimation. It
# was WORK(5) in Fortran. Init in self._rho().
# reset counters
nrejct[()] = 0
nfesig[()] = 0
maxm[()] = 0
self.nstsig = 0
self.mlim = 0 # added, for stiffness warning
# Initialize on the first call.
mmax = int(round(sqrt(self.rtol/(10.0 * self.uround))))
self.mmax = max(mmax, 2)
self.newspc = True
self.jacatt = False
self.W[0] = self.y
self.W[1] = self.fun(self.t, self.y) # evaluate
max_step = min(self.max_step, abs(self.t_bound - self.t))
self.max_step = min(max_step, sqrt(np.finfo(self.y.dtype).max))
hmin = abs(self.t)
if self.t_bound != np.inf:
hmin = max(hmin, abs(self.max_step))
self.hmin = max(self.sqrtmin, 10.0 * self.uround * hmin)
def __init__(self,
fun,
t0,
y0,
t_bound,
max_step=np.inf,
rtol=1e-3,
atol=1e-6,
vectorized=False,
first_step=None,
nfev_stiff_detect=5000,
sc_params=None,
**extraneous):
warn_extraneous(extraneous)
super(RungeKutta, self).__init__(fun,
t0,
y0,
t_bound,
vectorized,
support_complex=True)
self.max_step = validate_max_step(max_step)
self.rtol, self.atol = validate_tol(rtol, atol, self.y)
self.f = self.fun(self.t, self.y)
if self.f.dtype != self.y.dtype:
raise TypeError('dtypes of solution and derivative do not match')
self.error_exponent = -1 / (self.error_estimator_order + 1)
self._init_stiffness_detection(nfev_stiff_detect)
self.h_min_a, self.h_min_b = self._init_min_step_parameters()
self._init_sc_control(sc_params)
# size of first step:
if first_step is None:
b = self.t + self.direction * min(abs(self.t_bound - self.t),
self.max_step)
self.h_abs = abs(
h_start(self.fun, self.t, b, self.y, self.f,
self.error_estimator_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), self.y.dtype)
self.FSAL = 1 if self.E[self.n_stages] else 0
self.h_previous = None
self.y_old = None
NFS[()] = 0 # global failed step counter
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, vectorized=False, first_step=None, k_max=12,
**extraneous):
if not (isinstance(k_max, int) and k_max > 0 and k_max < 13):
raise ValueError("`k_max` should be an integer between 1 and 12.")
warn_extraneous(extraneous)
super(SWAG, self).__init__(
fun, t0, y0, t_bound, vectorized, support_complex=True)
self.max_step = validate_max_step(max_step)
self.rtol, self.atol = validate_tol(rtol, atol, self.y)
# starting step size
self.yp = self.fun(self.t, self.y) # initial evaluation
if first_step is None:
b = self.t + copysign(min(abs(self.t_bound - self.t),
self.max_step), self.direction)
self.h = h_start(self.fun, self.t, b, self.y, self.yp,
1, self.rtol, self.atol)
else:
h_abs = validate_first_step(first_step, t0, t_bound)
self.h = copysign(h_abs, self.direction)
# constants
small = np.nextafter(np.finfo(self.y.dtype).epsneg, 1)
self.twou = 2.0 * small
self.fouru = 4.0 * small
self.two = (2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0, 256.0, 512.0,
1024.0, 2048.0, 4096.0, 8192.0)
self.gstr = (0.5, 0.0833, 0.0417, 0.0264, 0.0188, 0.0143, 0.0114,
0.00936, 0.00789, 0.00679, 0.00592, 0.00524, 0.00468)
iq = np.arange(1, k_max + 2)
self.iqq = 1.0 / (iq * (iq + 1)) # added
self.k_max = k_max # added
self.eps = 1.0 # tolerances in wt
self.p5eps = 0.5 # tolerances in wt
# allocate arrays
self.phi = np.empty((self.n, k_max + 2), self.y.dtype, 'F')
self.psi = np.empty(k_max)
self.alpha = np.empty(k_max)
self.beta = np.empty(k_max)
self.sig = np.empty(k_max + 1)
self.v = np.empty(k_max)
self.w = np.empty(k_max)
self.g = np.empty(k_max + 1)
self.gi = np.empty(k_max - 1)
self.iv = np.zeros(max(0, k_max - 2), np.short)
# Tolerances are dealt with like in scipy: wt is like scipy's scale
# and will be update each step. This is only the initial value:
self.wt = self.atol + self.rtol * 0.5*(
np.abs(self.y) + np.abs(self.y - self.h*self.yp))
# initialization
# from *** block 0 *** of dsteps.f, under IF START:
_round = 0.0
if self.y.size: # to pass scipy's unit tests
_round = self.twou * norm(self.y / self.wt)
if self.p5eps < 100.0 * _round:
# The compensated summation of the original code that would be
# executed if nornd == False has been removed. Instead, this
# warning is given to the user.
warn("Numerical rounding may limit the accuracy "
"at this tolerance.")
self.phi[:, 0] = self.yp
self.phi[:, 1] = 0.0
self.sig[0] = 1.0
self.g[0] = 1.0
self.g[1] = 0.5
self.hold = 0.0
self.k = 1
self.kold = 0
self.kprev = 0
self.phase1 = True
self.ivc = 0
self.kgi = 0
self.ns = 0
# from ddes.f, for stiffness detection
self.kle4 = 0
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': []
}
}