PyDSTool求解ODE系统时积分步长设置报错求助

问题回顾 #

你尝试用PyDSTool求解自定义ODE系统，但在构造Generator时遇到了参数错误，报错提示Invalid keyword arguments for this class，你的代码和报错信息如下：

原代码 #

import PyDSTool as ds
from PyDSTool import Par, Var
import time
from PyDSTool import *
import math  # 注意：原代码漏了导入math，需要补上！

# 声明（符号）参数的名称和初始值
varepsilon = pow(10, -2)
j = 2.5*pow(10, -5)
e = 3.0
y8 = lambda y1,y5,y7: 1 / (1 - 2 / y1) * math.sqrt(y5 ** 2 + (1 - 2 / y1) * (1 + y1 ** 2 * y7 ** 2))
E0 = lambda y1,y8: (1 - 2 / y1) * y8
Phi0 = lambda y1,y7: y1 ** 2 * y7

# 根据参数计算非平凡边界平衡初始条件（推导见参考文献）
u0 = -math.sqrt(-1 + math.sqrt(varepsilon ** 2 + 12) / varepsilon) * math.sqrt(2) / 6
v0 = 1 / (1 - 2 / e) * math.sqrt(j ** 2 + (1 - 2 / e) * (e ** 2 * u0 ** 2 + 1))
y08 = y8(y1=e, y5=j, y7=u0); E = E0(y1=e, y8=y08); Phi = Phi0(y1=e, y7=u0)
z01, z03, z04, z05, z07, z08 = e, 0.0, 0.0, j, u0, v0

# 声明符号变量
z1, z3, z4, z5, z7, z8 = Var('z1'), Var('z3'), Var('z4'), Var('z5'), Var('z7'), Var('z8')

# 创建符号量对象用于定义
p1 = -z1*z5/(z1 - 2); p3 = -z1**2 *z7; p4 = z8*(1 - 2/z1);
Q1 = -z5**2/(z1*(z1 - 2)) + (z8**2/z1**3 - z7**2)*(z1 - 2);
Q3 = 2*z5*z7/z1; Q4 = 2*z5*z8/(z1*(z1 - 2));
c1 = z1*z7*varepsilon; c3 = -z1*z5*varepsilon; C = z7*varepsilon/z1 - z8*(1 - 2/z1);
d1 = -z1*z8*varepsilon; d3 = z1*z5*varepsilon; B = z1**2*z7 - z8*varepsilon*(1 - 2/z1);
Omega = 1/(c1*d3*p3+c3*d1*p4-c3*d3*p1);

# 微分方程
z1dot = z5; z3dot = z7; z4dot = z8;
z5dot = Omega*(-Q1*c1*d3*p3 - Q1*c3*d1*p4 + Q1*c3*d3*p1 + B*c3*p4 + C*d3*p3 + E*d3*p3 - Phi*c3*p4);
z7dot = -Omega*(Q3*c1*d3*p3 + Q3*c3*d1*p4 - Q3*c3*d3*p1 + B*c1*p4 - C*d1*p4 + C*d3*p1 - E*d1*p4 + E*d3*p1 - Phi*c1*p4);
z8dot = Omega*(-Q4*c1*d3*p3 - Q4*c3*d1*p4 + Q4*c3*d3*p1 + B*c1*p3 - B*c3*p1 - C*d1*p3 - E*d1*p3 - Phi*c1*p3 + Phi*c3*p1);

# 构建生成器
DSargs = args(name='Sining particle')
#print(dir(DSargs))
#DSargs.pars = [varepsilon, j, e]
DSargs.MaxNumPoints = 450
DSargs.MaxStepSize = 2e-2
DSargs.MinStepSize = 1e-5
DSargs.StepSize = e-2
DSargs.tdata = [0.0, 0.1]
DSargs.varspecs = args(z1=z1dot, z3=z3dot, z4=z4dot, z5=z5dot, z7=z7dot, z8=z8dot)
# 使用eval方法从参数值的符号定义中获取浮点值
DSargs.ics = args(z1=z01, z3=z03, z4=z04, z5=z05, z7=z07, z8=z08)

ode = Generator.Vode_ODEsystem(DSargs)
t = time.time()
result = ode.compute('test')
print("time for integration: %f" %(time.time() - t))
pts = result.sample()
plt.plot(pts['t'], pts['z7'], label='x')
plt.legend()
plt.xlabel('t')
plt.show()

报错信息 #

Traceback (most recent call last):
  File "C:\Users\mykola\Downloads\pydstool.py", line 65, in <module>
    ode = Generator.Vode_ODEsystem(DSargs)
  File "C:\Users\mykola\AppData\Local\Programs\Python\Python36-32\lib\site-packages\PyDSTool\Generator\Vode_ODEsystem.py", line 47, in __init__
    ODEsystem.__init__(self, kw)
  File "C:\Users\mykola\AppData\Local\Programs\Python\Python36-32\lib\site-packages\PyDSTool\Generator\ODEsystem.py", line 61, in __init__
    self.checkArgs(kw)
  File "C:\Users\mykola\AppData\Local\Programs\Python\Python36-32\lib\site-packages\PyDSTool\Generator\baseclasses.py", line 1069, in checkArgs
    raise PyDSTool_KeyError('Invalid keyword arguments for this class')
PyDSTool.errors.PyDSTool_KeyError: 'Invalid keyword arguments for this class'

错误原因 #

你犯了几个关键错误：

1. 积分步长参数的位置错误：PyDSTool的Vode_ODEsystem不接受MaxStepSize、MinStepSize、StepSize这些参数作为顶层键，这些属于VODE求解器的算法配置参数，必须放在algparams字典中。
2. 参数名称不匹配：PyDSTool对VODE的参数名有特定要求，比如你用的StepSize应该是initial_step，MaxStepSize对应max_step，MinStepSize对应min_step。
3. 额外问题：原代码漏了导入math模块，会导致运行时报错；另外MaxNumPoints不是VODE的参数，如果你需要固定输出点数，应该在采样时设置。

修正后的代码 #

下面是修改后的完整代码，重点标注了修改部分：

import PyDSTool as ds
from PyDSTool import Par, Var
import time
from PyDSTool import *
import math  # 补上缺失的math导入

# 声明（符号）参数的名称和初始值
varepsilon = pow(10, -2)
j = 2.5*pow(10, -5)
e = 3.0
y8 = lambda y1,y5,y7: 1 / (1 - 2 / y1) * math.sqrt(y5 ** 2 + (1 - 2 / y1) * (1 + y1 ** 2 * y7 ** 2))
E0 = lambda y1,y8: (1 - 2 / y1) * y8
Phi0 = lambda y1,y7: y1 ** 2 * y7

# 根据参数计算非平凡边界平衡初始条件（推导见参考文献）
u0 = -math.sqrt(-1 + math.sqrt(varepsilon ** 2 + 12) / varepsilon) * math.sqrt(2) / 6
v0 = 1 / (1 - 2 / e) * math.sqrt(j ** 2 + (1 - 2 / e) * (e ** 2 * u0 ** 2 + 1))
y08 = y8(y1=e, y5=j, y7=u0); E = E0(y1=e, y8=y08); Phi = Phi0(y1=e, y7=u0)
z01, z03, z04, z05, z07, z08 = e, 0.0, 0.0, j, u0, v0

# 声明符号变量
z1, z3, z4, z5, z7, z8 = Var('z1'), Var('z3'), Var('z4'), Var('z5'), Var('z7'), Var('z8')

# 创建符号量对象用于定义
p1 = -z1*z5/(z1 - 2); p3 = -z1**2 *z7; p4 = z8*(1 - 2/z1);
Q1 = -z5**2/(z1*(z1 - 2)) + (z8**2/z1**3 - z7**2)*(z1 - 2);
Q3 = 2*z5*z7/z1; Q4 = 2*z5*z8/(z1*(z1 - 2));
c1 = z1*z7*varepsilon; c3 = -z1*z5*varepsilon; C = z7*varepsilon/z1 - z8*(1 - 2/z1);
d1 = -z1*z8*varepsilon; d3 = z1*z5*varepsilon; B = z1**2*z7 - z8*varepsilon*(1 - 2/z1);
Omega = 1/(c1*d3*p3+c3*d1*p4-c3*d3*p1);

# 微分方程
z1dot = z5; z3dot = z7; z4dot = z8;
z5dot = Omega*(-Q1*c1*d3*p3 - Q1*c3*d1*p4 + Q1*c3*d3*p1 + B*c3*p4 + C*d3*p3 + E*d3*p3 - Phi*c3*p4);
z7dot = -Omega*(Q3*c1*d3*p3 + Q3*c3*d1*p4 - Q3*c3*d3*p1 + B*c1*p4 - C*d1*p4 + C*d3*p1 - E*d1*p4 + E*d3*p1 - Phi*c1*p4);
z8dot = Omega*(-Q4*c1*d3*p3 - Q4*c3*d1*p4 + Q4*c3*d3*p1 + B*c1*p3 - B*c3*p1 - C*d1*p3 - E*d1*p3 - Phi*c1*p3 + Phi*c3*p1);

# 构建生成器
DSargs = args(name='Sining particle')
DSargs.tdata = [0.0, 0.1]
DSargs.varspecs = args(z1=z1dot, z3=z3dot, z4=z4dot, z5=z5dot, z7=z7dot, z8=z8dot)
DSargs.ics = args(z1=z01, z3=z03, z4=z04, z5=z05, z7=z07, z8=z08)

# 关键修改：将积分步长参数放入algparams字典，使用正确的参数名
DSargs.algparams = {
    'max_step': 2e-2,       # 对应原来的MaxStepSize
    'min_step': 1e-5,       # 对应原来的MinStepSize
    'initial_step': 1e-2    # 对应原来的StepSize，这里我改成了1e-2，如果需要e-2=1.0可以替换回去
}

ode = Generator.Vode_ODEsystem(DSargs)
t = time.time()
result = ode.compute('test')
print("time for integration: %f" %(time.time() - t))

# 关键修改：用numpts参数控制输出点数，替代原来的MaxNumPoints
pts = result.sample(numpts=450)
plt.plot(pts['t'], pts['z7'], label='x')
plt.legend()
plt.xlabel('t')
plt.show()

关键修改说明 #

• 参数位置调整：所有与积分步长相关的配置都移到了algparams字典中，这是PyDSTool中VODE求解器要求的参数结构。
• 参数名称修正：使用VODE求解器认可的参数名：max_step、min_step、initial_step，而非自定义的名称。
• 输出点数控制：通过result.sample(numpts=450)来生成固定数量的采样点，替代原来无效的MaxNumPoints参数。
• 补全依赖：添加了import math，避免运行时出现NameError。

内容的提问来源于stack exchange，提问作者Mykola Fenyk