現在，除了我之前的兩篇ODE 實作的帖子之外，我還 嘗試重構我的代碼并修復一些問題。我決定，從邏輯上創建這樣的類：Solver, Problem.
所以 ODE_Solver 和 FE 類的代碼最終編碼并作業。
# ODS.py
import numpy as np
class ODE_Solver(object):
def __init__(self, f):
if not callable(f):
raise TypeError('f is not %s, function' % type(f))
self.f = lambda u, x: np.asarray(f(u, x), float)
self.err_sch = None
def solver_st(self):
raise NotImplementedError
def err_st(self):
raise NotImplementedError
def set_initial_condition(self, u0):
if isinstance(u0, (float, int)):
self.neq = 1
u0 = float(u0)
else:
u0 = np.asarray(u0)
self.neq = u0.size
self.u0 = u0
try:
f0 = self.f(self.u0, 0)
except IndexError:
raise IndexError(
'index out of bounds f(u,x). correct index %s' % (str(range(self.neq))))
if f0.size != self.neq:
raise ValueError('f(u,x) returend %d elems, vector u has %d elems' % (f0.size, self.neq))
def solve(self, coord_points, terminate=None):
if terminate is None:
terminate = lambda u, x, step_no: False
if isinstance(coord_points, (float, int)):
raise TypeError('solve: x points not numpy array or numbers.')
self.x = np.asarray(coord_points)
if self.x.size <= 1:
raise ValueError('ODESolver.solve points of coords less than two')
n = self.x.size
if self.neq == 1: # ОДУ
self.u = np.zeros(n)
self.err_sch = np.zeros(n)
else:
self.u = np.zeros((n, self.neq))
self.err_sch = np.zeros((n, self.neq))
self.u[0] = self.u0
self.err_sch[0] = 0
for k in range(n - 1):
self.k = k
self.u[k 1] = self.solver_st()
self.err_sch[k 1] = self.err_st()
if terminate(self.u, self.x, self.k 1):
break
return self.u[:k 2], self.x[:k 2]
# ES.py
from ODS import ODE_Solver
import numpy as np
class FE(ODE_Solver):
def solver_st(self):
u, f, k, x = self.u, self.f, self.k, self.x
dx = x[k 1] - x[k]
u_new = u[k] dx * f(u[k], x[k])
return u_new
def err_st(self):
u, f, k, x, err_sch = self.u, self.f, self.k, self.x, self.err_sch
dx = x[k 1] - x[k]
err_sch = np.max(dx)**2
return err_sch
我嘗試實作類Problem（回傳 ODE 并獲取初始條件）
import numpy as np
class Problem(object):
def __init__(self, u0, End):
self.u0 = np.asarray(u0)
self.End = End # end point of coords
def __call__(self, u, x):
return (u[1], u[2], u[3], u[4],
- 15 * u[4] - 90 * u[3] - 270 * u[2] - 405 * u[1] - 243 * u[0])
Solver以及呼叫數值方案的代碼類，繪制最終結果，繪制和評估錯誤：
import numpy as np
import matplotlib as plt
import ES
import ODS
from ADS import ABM4
from ES import FE
from MLNS import MLN
from RKS import RK4
class Solver(object):
def __init__(self, problem, dx,
method=ES.FE): # choose FE scheme for tetsting
"""
"""
self.problem, self.dx = problem, dx
self.solver = method
@staticmethod
def choose_sch(type):
if type == 1:
method = FE
return method
elif type == 2:
method = RK4
return method
elif type == 3:
method = ABM4
return method
elif type == 4:
method = MLN
return method
else:
raise ValueError('not choose numerical scheme!')
def dsolve(self):
solver = self.method(self.problem)
solver.set_initial_condition(self.problem.u0)
n = int(round(self.problem.End / self.dx))
x_points = np.linspace(0, self.problem.End, n 1)
self.u, self.x = solver.solve(x_points)
if solver.k 1 == n:
self.plot()
raise ValueError('not converge this scheme,' % self.problem.End)
def plot(self):
plt.plot(self.x, self.u)
plt.show()
現在，當我打電話給Solver這個Problem
import numpy as np
from ODE_Problem import Problem
from SLV_Prob import Solver
def test():
problem = Problem(u0=[0, 3, -9, -8, 0], End=5)
solver = Solver(problem, dx=0.1)
solver.dsolve()
solver.plot()
if __name__ == '__main__':
test()
我得到錯誤：
Traceback (most recent call last):
File "C:\Fin_Proj_ODE\test2.py", line 14, in <module>
test()
File "C:\Fin_Proj_ODE\test2.py", line 9, in test
solver.dsolve()
File "C:\Fin_Proj_ODE\SLV_Prob.py", line 37, in dsolve
solver = self.method(self.problem)
AttributeError: 'Solver' object has no attribute 'method'
而且我不明白并假設這個錯誤的原因是什么......
所以，我有 2 個問題要實作這個 Solver：
- 如何修復這個錯誤？
- 如何更正重寫 def choose_sch(type):，我可以呼叫求解器并發送 args 型別（并且取決于它，一個特定的數值方案將已經開始）？
uj5u.com熱心網友回復：
問題一：
好吧，正如錯誤所述，您的 Solver 類沒有名為“方法”的屬性。您的屬性實際上是“求解器”，所以不要呼叫
self.method(self.problem)
嘗試
self.solver(self.problem)
問題二：
如果我對您的理解正確，您想知道如何從求解器建構式中呼叫 choose_sch 方法并直接采用型別而不是方法。為此，只需執行以下操作：
class Solver(object):
def __init__(self, problem, dx, solver_type=1): # choose FE scheme for tetsting
"""
"""
self.problem, self.dx = problem, dx
self.solver = self._choose_sch(solver_type)
@staticmethod
def _choose_sch(solver_type):
methods = {1: FE, 2: RK4, 3: ABM4, 4: MLN}
if solver_type in methods:
return methods[solver_type]
else:
raise ValueError('not choose numerical scheme!')
對于這類任務，這里的字典比 if 陳述句要好得多。
如果您不需要從靜態背景關系中呼叫它，也可以不將 _choose_ach 設為靜態方法，而是直接設定求解器。
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