# -*- coding: utf-8 -*-
r"""
"""
import sys
if './' not in sys.path:
sys.path.append('./')
from tools.frozen import Frozen
from src.time_sequence import AbstractTimeSequence
from typing import Dict
[docs]
class TemporalDiscretization(Frozen):
"""A wrapper of the temporal discretization setting of a weak formulation."""
def __init__(self, wf):
""""""
self._wf = wf
self._initialize_odes()
self._ats = None
self._freeze()
def _initialize_odes(self):
"""Initialize odes."""
from src.ode.main import ode
# must import locally here to avoid a circular import
wf = self._wf
valid_ode = dict()
for i in wf._term_dict:
terms = wf._term_dict[i]
signs = wf._sign_dict[i]
v_ode = ode(terms_and_signs=[terms, signs])
valid_ode[i] = v_ode
self._valid_ode = valid_ode
def __getitem__(self, item):
"""Return the ode."""
return self._valid_ode[item].discretize
def __iter__(self):
"""iter over valid ode numbers."""
for valid_ode_number in self._valid_ode:
yield valid_ode_number
def __call__(self, *args, clean=True, **kwargs):
"""Return a new weak formulation by combining all equations."""
wfs: Dict = dict()
for i in self:
wfs[i] = self[i]()
for i in self._wf._term_dict:
if i not in wfs:
wfs[i] = {
'_term_dict': self._wf._term_dict[i],
'_sign_dict': self._wf._sign_dict[i]
}
else:
pass
wf = self._wf.__class__(self._wf._test_forms, merge=wfs)
wf._bc = self._wf._bc
# we get the new weak formulation by combining each pde.
if clean: # make sure this temporal discretization is used only once.
self._wf = None
self._valid_ode = None
else:
pass
return wf
@property
def ts(self):
return self._ats
@property
def time_sequence(self):
"""The time sequence this temporal discretization is working on."""
return self._ats
[docs]
def set_time_sequence(self, ts=None):
"""The method of setting time sequence.
.. note::
Note that each wf only use one time sequence.
If your time sequence is complex, you should carefully design
it instead of using multiple time sequences.
"""
if ts is None: # make a new one
ts = AbstractTimeSequence()
else:
pass
assert ts.__class__.__name__ == 'AbstractTimeSequence', f"I need an abstract time sequence object."
assert self._ats is None, f"time_sequence existing, change it may leads to unexpected issue."
self._ats = ts
for i in self:
self[i].set_time_sequence(self._ats)
[docs]
def define_abstract_time_instants(self, *atis):
"""Define abstract time instants for the temporal discretization."""
for i in self:
self[i].define_abstract_time_instants(*atis)
[docs]
def differentiate(self, index, *args):
"""Differentiate the term indexed ``index`` at abstract time instances."""
assert index in self._wf, f"index={index} is illegal, print representations to check the indices."
i, j = index.split('-')
ode_d = self[int(i)]
ode_d.differentiate(j, *args)
[docs]
def average(self, index, f, *args, which='all'):
"""Average the term indexed ``index`` at abstract time instances."""
assert index in self._wf, f"index={index} is illegal, print representations to check the indices."
i, j = index.split('-')
ode_d = self[int(i)]
if len(args) == 1:
ode_d.average(j, f, *args, which=which)
else:
ode_d.average(j, f, args, which=which)
if __name__ == '__main__':
# python src/wf/td.py
import __init__ as ph
samples = ph.samples
oph = samples.pde_canonical_pH(n=3, p=3)[0]
oph.pr()
a3, b2 = oph.unknowns
wf = oph.test_with(oph.unknowns, sym_repr=[r'v^3', r'u^2'])
wf = wf.derive.integration_by_parts('1-1')
wf.pr(indexing=True)
td = wf.td
td.set_time_sequence() # initialize a time sequence
td.define_abstract_time_instants('k-1', 'k-1/2', 'k')
td.differentiate('0-0', 'k-1', 'k')
td.average('0-1', b2, ['k-1', 'k'])
td.differentiate('1-0', 'k-1', 'k')
td.average('1-1', a3, ['k-1', 'k'])
td.average('1-2', a3, ['k-1/2'])
dt = td.time_sequence.make_time_interval('k-1', 'k')
wf = td()
wf.pr()
wf.unknowns = [a3 @ td.time_sequence['k'], b2 @ td.time_sequence['k']]
wf = wf.derive.split('0-0', 'f0',
[a3 @ td.ts['k'], a3 @ td.ts['k-1']],
['+', '-'],
factors=[1/dt, 1/dt])
wf = wf.derive.split('0-2', 'f0',
[ph.d(b2 @ td.ts['k-1']), ph.d(b2 @ td.ts['k'])],
['+', '+'],
factors=[1/2, 1/2])
wf = wf.derive.split('1-0', 'f0',
[b2 @ td.ts['k'], b2 @ td.ts['k-1']],
['+', '-'],
factors=[1/dt, 1/dt])
wf = wf.derive.split('1-2', 'f0',
[a3 @ td.ts['k-1'], a3 @ td.ts['k']],
['+', '+'],
factors=[1/2, 1/2])
wf = wf.derive.rearrange(
{
0: '0, 3 = 1, 2',
1: '3, 0 = 2, 1, 4',
}
)
ph.space.finite(3)
ap = wf.ap
wf.pr()
# wf.pr()
# print(wf.elementary_forms)
