SymPy中lambdify无法处理共轭函数的导数问题求助

我有一些复杂的符号函数，希望对其执行若干操作后通过lambdify转换为可调用函数。计算共轭函数的导数时遇到问题：单独求导、单独取共轭操作都能正常工作，但尝试对共轭函数的导数进行lambdify转换时，会触发以下错误：

PrintMethodNotImplementedError: Unsupported by <class 'sympy.printing.numpy.SciPyPrinter'>: <class 'sympy.core.function.Derivative'>
Set the printer option 'strict' to False in order to generate partially printed code.

详情及示例 #

基础函数（可正常运行） #

import sympy as sp

a, b = sp.symbols('a b')
def myfunction(x,y):
    return x + 1j * y

myfunctionval = myfunction(a,b)
myfunction_lam = sp.lambdify((a,b), myfunctionval)
print(myfunction_lam(1,2))
# 输出: (1+2j)

共轭函数（可正常运行） #

def myfunctionConjugate(x,y):
    return sp.conjugate(x + 1j * y)

myfunctionConjugateval = myfunctionConjugate(a,b)
myfunctionConjugate_lam = sp.lambdify((a,b), myfunctionConjugateval)
print(myfunctionConjugate_lam(1,2))
# 输出: (1-2j)

导数（可正常运行） #

def myfunctionDerivative(x,y):
    return sp.diff(x + 1j * y, x)

myfunctionDerivativeval = myfunctionDerivative(a,b)
myfunctionDerivative_lam = sp.lambdify((a,b), myfunctionDerivativeval)
print(myfunctionDerivative_lam(1,2))
# 输出: 1

导数的共轭（可正常运行） #

def myfunctionDerivativeConjugate(x,y):
    return sp.conjugate(sp.diff(x + 1j * y,x))

myfunctionDerivativeConjugateval = myfunctionDerivativeConjugate(a,b)
myfunctionDerivativeConjugate_lam = sp.lambdify((a,b), myfunctionDerivativeConjugateval)
print(myfunctionDerivativeConjugate_lam(1,2))
# 输出: 1

共轭函数的导数（无法运行） #

def myfunctionConjugateDerivative(x,y):
    return sp.diff(sp.conjugate(x + 1j * y),x)

myfunctionConjugateDerivativeval = myfunctionConjugateDerivative(a,b)
myfunctionConjugateDerivative_lam = sp.lambdify((a,b), myfunctionConjugateDerivativeval)
myfunctionConjugateDerivative_lam(1,2)

触发的错误信息

---------------------------------------------------------------------------
PrintMethodNotImplementedError            Traceback (most recent call last)
/tmp/ipykernel_13914/1657192206.py in <module>
      3 
      4 myfunctionConjugateDerivativeval = myfunctionConjugateDerivative(a,b)
----> 5 myfunctionConjugateDerivative_lam = sp.lambdify((a,b), myfunctionConjugateDerivativeval)
      6 myfunctionConjugateDerivative_lam(1,2)

~/anaconda3/lib/python3.9/site-packages/sympy/utilities/lambdify.py in lambdify(args, expr, modules, printer, use_imps, dummify, cse, docstring_limit)
    878     else:
    879         cses, _expr = (), expr
---> 880     funcstr = funcprinter.doprint(funcname, iterable_args, _expr, cses=cses)
    881 
    882     # Collect the module imports from the code printers.

~/anaconda3/lib/python3.9/site-packages/sympy/utilities/lambdify.py in doprint(self, funcname, args, expr, cses)
   1169                 funcbody.append('{} = {}'.format(self._exprrepr(s), self._exprrepr(e)))
   1170 
-> 1171         str_expr = _recursive_to_string(self._exprrepr, expr)
   1172 
   1173         if '\n' in str_expr:

~/anaconda3/lib/python3.9/site-packages/sympy/utilities/lambdify.py in _recursive_to_string(doprint, arg)
    964 
    965     if isinstance(arg, (Basic, MatrixBase)):
---> 966         return doprint(arg)
    967     elif iterable(arg):
    968         if isinstance(arg, list):

~/anaconda3/lib/python3.9/site-packages/sympy/printing/codeprinter.py in doprint(self, expr, assign_to)
    170         self._number_symbols = set()
    171 
---> 172         lines = self._print(expr).splitlines()
    173 
    174         # format the output

~/anaconda3/lib/python3.9/site-packages/sympy/printing/printer.py in _print(self, expr, **kwargs)
    329                 printmethod = getattr(self, printmethodname, None)
    330                 if printmethod is not None:
---> 331                     return printmethod(expr, **kwargs)
    332             # Unknown object, fall back to the emptyPrinter.
    333             return self.emptyPrinter(expr)

~/anaconda3/lib/python3.9/site-packages/sympy/printing/codeprinter.py in _print_not_supported(self, expr)
    580     def _print_not_supported(self, expr):
    581         if self._settings.get('strict', False):
---> 582             raise PrintMethodNotImplementedError("Unsupported by %s: %s" % (str(type(self)), str(type(expr))) + \
    583                              "\nSet the printer option 'strict' to False in order to generate partially printed code.")
    584         try:

PrintMethodNotImplementedError: Unsupported by <class 'sympy.printing.numpy.SciPyPrinter'>: <class 'sympy.core.function.Derivative'>
Set the printer option 'strict' to False in order to generate partially printed code.

解决方案 #

方法1：化简表达式后再转换 #

SymPy对共轭函数求导后会得到未计算的Derivative对象，SciPyPrinter无法直接处理。调用lambdify前用sp.simplify()化简表达式，让导数计算完成：

def myfunctionConjugateDerivative(x,y):
    return sp.diff(sp.conjugate(x + 1j * y),x)

# 先化简求导结果
myfunctionConjugateDerivativeval = sp.simplify(myfunctionConjugateDerivative(a,b))
myfunctionConjugateDerivative_lam = sp.lambdify((a,b), myfunctionConjugateDerivativeval)
print(myfunctionConjugateDerivative_lam(1,2))
# 输出: 1

方法2：手动展开共轭再求导 #

对于简单的复数表达式，可直接展开共轭形式（sp.conjugate(x+1j*y)等价于x-1j*y），再对展开后的式子求导：

def myfunctionConjugateDerivative(x,y):
    # 直接对展开后的共轭表达式求导
    return sp.diff(x - 1j * y, x)

myfunctionConjugateDerivativeval = myfunctionConjugateDerivative(a,b)
myfunctionConjugateDerivative_lam = sp.lambdify((a,b), myfunctionConjugateDerivativeval)
print(myfunctionConjugateDerivative_lam(1,2))
# 输出: 1

方法3：关闭严格模式（不推荐） #

在lambdify中设置printer={'strict': False}可绕过错误，但可能生成无效代码，仅适合调试场景：

myfunctionConjugateDerivative_lam = sp.lambdify((a,b), myfunctionConjugateDerivativeval, printer={'strict': False})

内容的提问来源于stack exchange，提问作者Reflets de Lune