Question

Heaviside函数应该内置到Sympy和Numpy中，但是以下代码给出错误if image_params[:tags] @image.tags = image_params[:tags].map { |tag| Tag.create(title: tag) unless Tag.where(title: tag).exists? Tag.find_by(title: tag) } end class TagRelation < ApplicationRecord belongs_to :tag belongs_to :taggable, polymorphic: true # Destroy tag if no other items are related after_destroy do self.tag.check_count end end class Tag < ApplicationRecord has_many :tag_relations, dependent: :destroy, after_remove: :check_count has_many :gallery_images, through: :tag_relations, source_type: 'GalleryImage', source: :taggable has_many :streams, through: :tag_relations, source_type: 'Stream', source: :taggable validates :title, uniqueness: true def count self.tag_relations.count end def check_count self.destroy if self.count === 0 end end。尝试在将要使用它的数值计算之前（基于Traceback）在代码中自己定义Heaviside函数无济于事-我想应该在Name Heaviside not defined中定义它。有解决方法吗？

lambdifygenerated

回溯如下：

from sympy import *
from IPython.display import display
mux, s, Px, Py, Pxe, Pye = symbols("mu_X s P_X P_Y P_X^* P_Y^*", positive=True)
vx, vy, cx, cy = symbols("v_X v_Y c_X c_Y", real=True)
pix = (Px-cx)*( mux*integrate(integrate(1,(vx,Min(1,Max(0,Px+Max(0,vy-Pye-s))),1)),(vy,0,1))
      +(1-mux)*integrate(integrate(1,(vx,Min(1,Max(0,Max(Pxe+s,Px)+Max(0,vy-Pye))),1)),(vy,0,1))
     )
piy = (Py-cy)*( (1-mux)*integrate(integrate(1,(vy,Min(1,Max(0,Py+Max(0,vx-Pxe-s))),1)),(vx,0,1))
      +mux*integrate(integrate(1,(vy,Min(1,Max(0,Max(Pye+s,Py)+Max(0,vx-Pxe))),1)),(vx,0,1))
     )
focx =diff(pix,Px)
focy =diff(piy,Py)
focxeq=focx.subs(Px,Pxe)
focyeq=focy.subs(Py,Pye)

import numpy as np
focx_lambda = lambdify((Pxe,Pye), focxeq, modules=['numpy', 'sympy'])
focy_lambda = lambdify((Pxe,Pye), focyeq, modules=['numpy', 'sympy'])
nsolve([focxeq.subs({mux:0.4,s:0.05,cx:0,cy:0.1}).evalf(),focyeq.subs({mux:0.4,s:0.05,cx:0,cy:0.1}).evalf()],(Pxe,Pye),(0.3,0.4))

我根据对(Some function) is not defined with SymPy Lambdify的回答添加了-------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-10-b7bc7e96827d> in <module> 26 focx_lambda = lambdify((Pxe,Pye), focxeq, modules=['numpy', 'sympy']) 27 focy_lambda = lambdify((Pxe,Pye), focyeq, modules=['numpy', 'sympy']) ---> 28 nsolve([focxeq.subs({mux:0.4,s:0.05,cx:0,cy:0.1}).evalf(),focyeq.subs({mux:0.4,s:0.05,cx:0,cy:0.1}).evalf()],(Pxe,Pye),(0.3,0.4)) 29 mux=0.4 30 s=0.05 ~/anaconda3/lib/python3.6/site-packages/sympy/utilities/decorator.py in func_wrapper(*args, **kwargs) 88 dps = mpmath.mp.dps 89 try: ---> 90 return func(*args, **kwargs) 91 finally: 92 mpmath.mp.dps = dps ~/anaconda3/lib/python3.6/site-packages/sympy/solvers/solvers.py in nsolve(*args, **kwargs) 3045 J = lambdify(fargs, J, modules) 3046 # solve the system numerically -> 3047 x = findroot(f, x0, J=J, **kwargs) 3048 if as_dict: 3049 return [dict(zip(fargs, [sympify(xi) for xi in x]))] ~/anaconda3/lib/python3.6/site-packages/mpmath/calculus/optimization.py in findroot(ctx, f, x0, solver, tol, verbose, verify, **kwargs) 926 # detect multidimensional functions 927 try: --> 928 fx = f(*x0) 929 multidimensional = isinstance(fx, (list, tuple, ctx.matrix)) 930 except TypeError: <lambdifygenerated-23> in _lambdifygenerated(Dummy_4515, _Dummy_4514) 1 def _lambdifygenerated(Dummy_4515, _Dummy_4514): ----> 2 return (ImmutableDenseMatrix([[Dummy_4515*(mpf((0, 3602879701896397, -53, 52))*((-(_Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Heaviside(1 - Dummy_4515)*Heaviside(1 - Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + Heaviside(1 - Dummy_4515)*Heaviside(1 - Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + Min(mpf((0, 1, 0, 1)), _Dummy_4514 + mpf((0, 3602879701896397, -56, 52))) - Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))) if (Dummy_4515 >= 1) else (-(_Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Heaviside(1 - Dummy_4515)*Heaviside(1 - Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + Heaviside(1 - Dummy_4515)*Heaviside(1 - Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) - Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))))) + mpf((0, 5404319552844595, -53, 53))*((0) if (Dummy_4515 >= mpf((0, 4278419646001971, -52, 52))) else (-(_Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Heaviside(1 - Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + 1))*Heaviside(_Dummy_4514 - Dummy_4515 - Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52))) + 1) + Heaviside(1 - Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + 1))*Heaviside(_Dummy_4514 - Dummy_4515 - Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52))) + 1)*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 1, 0, 1))))) if (Dummy_4515 >= 1) else (0))) + mpf((0, 3602879701896397, -53, 52))*((-(_Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), _Dummy_4514 + mpf((0, 3602879701896397, -56, 52))) + (_Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), _Dummy_4514 + mpf((0, 3602879701896397, -56, 52)))**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))**2) if (Dummy_4515 >= 1) else ((mpf((0, 1, 0, 1)) - Dummy_4515)*Min(mpf((0, 1, 0, 1)), _Dummy_4514 + mpf((0, 3602879701896397, -56, 52))) - (_Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), _Dummy_4514 + mpf((0, 3602879701896397, -56, 52))) + (_Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), _Dummy_4514 + mpf((0, 3602879701896397, -56, 52)))**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514 + mpf((0, 3602879701896397, -56, 52)), _Dummy_4514 - Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))**2)) + mpf((0, 5404319552844595, -53, 53))*((-(_Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), _Dummy_4514) + (_Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), _Dummy_4514)**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52))))**2) if (Dummy_4515 >= mpf((0, 4278419646001971, -52, 52))) else (-(_Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), _Dummy_4514) + (_Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 1, 0, 1)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), _Dummy_4514)**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 1, 0, 1))))**2) if (Dummy_4515 >= 1) else ((mpf((0, 4278419646001971, -52, 52)) - Dummy_4515)*Min(mpf((0, 1, 0, 1)), _Dummy_4514) - (_Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), _Dummy_4514) + (_Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), _Dummy_4514)**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(_Dummy_4514, _Dummy_4514 - Dummy_4515 + mpf((0, 4278419646001971, -52, 52))))**2))], [(_Dummy_4514 + mpf((1, 3602879701896397, -55, 52)))*(mpf((0, 5404319552844595, -53, 53))*((-(-_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Heaviside(1 - _Dummy_4514)*Heaviside(1 - Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + Heaviside(1 - _Dummy_4514)*Heaviside(1 - Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + Min(mpf((0, 1, 0, 1)), Dummy_4515 + mpf((0, 3602879701896397, -56, 52))) - Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))) if (_Dummy_4514 >= 1) else (-(-_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Heaviside(1 - _Dummy_4514)*Heaviside(1 - Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + Heaviside(1 - _Dummy_4514)*Heaviside(1 - Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) - Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))))) + mpf((0, 3602879701896397, -53, 52))*((0) if (_Dummy_4514 >= mpf((0, 4278419646001971, -52, 52))) else (-(-_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Heaviside(1 - Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + 1))*Heaviside(-_Dummy_4514 + Dummy_4515 - Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52))) + 1) + Heaviside(1 - Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + 1))*Heaviside(-_Dummy_4514 + Dummy_4515 - Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52))) + 1)*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 1, 0, 1))))) if (_Dummy_4514 >= 1) else (0))) + mpf((0, 5404319552844595, -53, 53))*((-(-_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), Dummy_4515 + mpf((0, 3602879701896397, -56, 52))) + (-_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Dummy_4515 + mpf((0, 3602879701896397, -56, 52)))**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))**2) if (_Dummy_4514 >= 1) else ((mpf((0, 1, 0, 1)) - _Dummy_4514)*Min(mpf((0, 1, 0, 1)), Dummy_4515 + mpf((0, 3602879701896397, -56, 52))) - (-_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), Dummy_4515 + mpf((0, 3602879701896397, -56, 52))) + (-_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Dummy_4515 + mpf((0, 3602879701896397, -56, 52)))**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515 + mpf((0, 3602879701896397, -56, 52)), -_Dummy_4514 + Dummy_4515 + mpf((0, 4728779608739021, -52, 53))))**2)) + mpf((0, 3602879701896397, -53, 52))*((-(-_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Dummy_4515) + (-_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Dummy_4515)**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52))))**2) if (_Dummy_4514 >= mpf((0, 4278419646001971, -52, 52))) else (-(-_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Dummy_4515) + (-_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 1, 0, 1)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Dummy_4515)**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 1, 0, 1))))**2) if (_Dummy_4514 >= 1) else ((mpf((0, 4278419646001971, -52, 52)) - _Dummy_4514)*Min(mpf((0, 1, 0, 1)), Dummy_4515) - (-_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Dummy_4515) + (-_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52)))) + mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Dummy_4515)**2 - mpf((0, 1, -1, 1))*Min(mpf((0, 1, 0, 1)), Max(Dummy_4515, -_Dummy_4514 + Dummy_4515 + mpf((0, 4278419646001971, -52, 52))))**2))]])) NameError: name 'Heaviside' is not defined 但这并没有改变任何东西。

我自己定义Heaviside的方式是

focx_lambda = lambdify((Pxe,Pye), focxeq, modules=['numpy', 'sympy'])

我也尝试了def Heaviside(x): if x<0: out=0 else: out=1 return out以防万一。这并没有改变任何东西。

Answer 1

lambdify的多个问题似乎同时发生。我想我可以解决问题，但是您应该检查它是否有意义，因为我对特定的方程式不熟悉。

通常，将from sympy import *与from numpy import *一起调用会造成很多混乱。这两个库中的许多函数都具有相同的名称，并且它们确实真的不喜欢与其他变量一起使用。

从另一方面来说，lambdify在Heaviside上表现不佳。此外，numpy中的函数是小写的和，需要两个参数：一个x值和一个x2来决定对x==0会发生什么。作为补救措施，下面的代码用lambda x: np.heaviside(x, 1)替换了“ Heaviside”。

我无法让sympy的nsolve使用这些功能，所以我尝试了scipy的fsolve。 fsolve还需要进行一些调整才能使用元组功能。

在创建focx_lambda时，重要的是除函数参数Pxe和Pye以外的所有变量都应具有固定值。因此，我在执行lambdify时替换了它们。

from sympy import symbols, integrate, Min, Max, diff, lambdify
from IPython.display import display

mux, s, Px, Py, Pxe, Pye = symbols("mu_X s P_X P_Y P_X^* P_Y^*", positive=True)
vx, vy, cx, cy = symbols("v_X v_Y c_X c_Y", real=True)
pix = (Px - cx) * (mux * integrate(integrate(1, (vx, Min(1, Max(0, Px + Max(0, vy - Pye - s))), 1)), (vy, 0, 1))
                   + (1 - mux) * integrate(integrate(1, (vx, Min(1, Max(0, Max(Pxe + s, Px) + Max(0, vy - Pye))), 1)),
                                           (vy, 0, 1))
                   )
piy = (Py - cy) * ((1 - mux) * integrate(integrate(1, (vy, Min(1, Max(0, Py + Max(0, vx - Pxe - s))), 1)), (vx, 0, 1))
                   + mux * integrate(integrate(1, (vy, Min(1, Max(0, Max(Pye + s, Py) + Max(0, vx - Pxe))), 1)),
                                     (vx, 0, 1))
                   )
focx = diff(pix, Px)
focy = diff(piy, Py)
focxeq = focx.subs(Px, Pxe)
focyeq = focy.subs(Py, Pye)

import numpy as np
from scipy.optimize import fsolve

modules = [{'Heaviside': lambda x: np.heaviside(x, 1)}, 'numpy']
values_for_parameters = {mux: 0.4, s: 0.05, cx: 0, cy: 0.1}
focx_lambda = lambdify((Pxe, Pye), focxeq.subs(values_for_parameters), modules=modules)
focy_lambda = lambdify((Pxe, Pye), focyeq.subs(values_for_parameters), modules=modules)

print(focx_lambda(0.3, 0.4))  # we need to check that the lambdify works, so this should print a floating point number
print(focy_lambda(0.3, 0.4))

def equations(p):
    x, y = p
    return focx_lambda(x, y), focy_lambda(x, y)

sol = fsolve(equations, (0.3, 0.4))
print(sol)  # [0.64701372 0.61726372]

在lambdifygenerate中未定义符号名称Heaviside

1 个答案: