def __init__(self, setup):
self.setup = setup
sigma2 = pow(setup.sigma, 2)
dx_opt = abs(setup.C_opt / (.5 * sigma2 - setup.r) * setup.l2_opt * sigma2)
dt_opt = pow(dx_opt, 2) / sigma2 / setup.l2_opt
# adjusting dt so that nt is integer
self.dt = setup.T
self.nt = 0
while self.dt > dt_opt:
self.nt += 1
self.dt = setup.T / self.nt
# adjusting dx to match requested l^2
dx = np.sqrt(setup.l2_opt * self.dt) * setup.sigma
# calculating actual u number and lambda
self.C = - (.5 * sigma2 - setup.r) * (-self.dt) / dx
self.l2 = dx * dx / sigma2 / self.dt
# adjusting nx and setting S_beg, S_end
S_beg = setup.S_match
self.nx = 1
while S_beg > setup.S_min:
self.nx += 1
S_beg = np.exp(np.log(setup.S_match) - self.nx * dx)
self.ix_match = self.nx
S_end = setup.S_match
while S_end < setup.S_max:
self.nx += 1
S_end = np.exp(np.log(S_beg) + (self.nx-1) * dx)
# asset price
self.S = np.exp(np.log(S_beg) + np.arange(self.nx) * dx)
self.mu_coeff = (0.5 / self.l2,)
self.solvers = {}
self.solvers[1] = Factories.advection_diffusion_1d(
advectee=setup.payoff(self.S),
advector=self.C,
options=Options(n_iters=1, non_zero_mu_coeff=True),
boundary_conditions=(ExtrapolatedBoundaryCondition(),)
)
self.solvers[2] = Factories.advection_diffusion_1d(
advectee=setup.payoff(self.S),
advector=self.C,
options=Options(**OPTIONS),
boundary_conditions=(ExtrapolatedBoundaryCondition(),)
)
def __init__(self, setup: Setup, options: Options):
x, y, z = from_pdf_2d(setup.pdf,
xrange=setup.xrange,
yrange=setup.yrange,
gridsize=setup.grid)
self.mpdata = Factories.stream_function_2d_basic(
setup.grid, setup.size, setup.dt, setup.stream_function, z,
options)
self.nt = setup.nt
def __init__(self, setup, grid_layout, psi_coord, opts, GC_max):
self.setup = setup
self.psi_coord = psi_coord
# units of calculation
self.__t_unit = self.setup.si.seconds
self.__r_unit = self.setup.si.micrometre
self.__n_unit = self.setup.si.centimetres**-3 / self.setup.si.micrometre
self.solver, self.__r, self.__rh, self.dx, dt = Factories.condensational_growth(
self.setup.nr, self.__mgn(self.setup.r_min, self.__r_unit),
self.__mgn(self.setup.r_max, self.__r_unit), GC_max,
grid_layout, psi_coord, lambda r: self.__mgn(
self.setup.pdf(r * self.__r_unit), self.__n_unit),
lambda r: self.__mgn(self.setup.drdt(r * self.__r_unit), self.
__r_unit / self.__t_unit), opts)
self.out_steps = Simulation.find_out_steps(setup=self.setup, dt=dt)
self.dt = dt * self.__t_unit