使用SymPy将符号表达式转换为Python函数 [英] Convert symbolic expressions to Python functions using SymPy

问题描述

我有一个相当大的符号函数，该函数针对循环中参数的不同值进行求值.在每次迭代中，在找到函数的表达式之后，将导出偏导数.像这样:

I have a rather large symbolic function that is evaluated for different values of a parameter in a loop. In each iteration, after finding the expression of the function, partial derivatives are derived. Something like this:

from sympy import diff, symbols,exp

def lagrange_eqs(a):
    x,y,z= symbols('x y z')
    FUNC=x**2-2*x*y**2+z+a*exp(z)
    d_lgrng_1=diff(FUNC,x)
    d_lgrng_2=diff(FUNC,y)
    d_lgrng_3=diff(FUNC,z)
    return [d_lgrng_1,d_lgrng_2,d_lgrng_3]

接下来，我需要将此函数的输出转换为Python函数，以便可以使用fsolve查找导数为零的x，y，z值.该函数必须以x，y，z作为列表.

Next, I need to convert the output of this function to a Python function so that I can use fsolve to find x, y, z values for which derivatives are zero. The function must take x,y,z as a list.

现在这是我的问题:如何将上述函数的输出转换为Python函数，然后可以将其传递给求解器.这样的函数应如下所示(对于a = 3):

Now here is my problem: how do I convert the output of the above function to a Python function which could be passed on to a solver. Such a function should look like this (for a=3):

def lagrange_eqs_solve(X): 
    x,y,z=X
    return [2*x - 2*y**2, -4*x*y, 3*exp(z) + 1]

我只是复制了第一个函数的输出以构建第二个函数.有什么办法可以编码吗? (Matlab为此具有一个内置函数，称为matlabFunction)

I simply copied the output of the first function to build the second one. Is there a way I could code it? (Matlab has a built-in function for this, called matlabFunction)

推荐答案

您要 lambdify .

f = lambdify(((x, y, z),), lagrange_eqs(a))

将为您提供Python函数f，您可以像f((1, 2, 3))那样对其进行评估(对于x=1，y=2，z=3).我已经在元组中进行了论证，以便可以与scipy的fsolve一起使用.

will give you a Python function f that you can evaluate like f((1, 2, 3)) (for x=1, y=2, z=3). I have made the arguments in a tuple so that it will work with scipy's fsolve.

您可以将modules标志设置为lambdify，以确定exp函数的来源.例如，要使用numpy，请使用lambdify((x, y, z), lagrange_eqs(a), modules="numpy").要使用标准库数学库，请使用modules="math".默认情况下，如果已安装，则使用numpy，否则使用math.

You can set the modules flag to lambdify to determine where the exp function will come from. For instance, to use numpy, use lambdify((x, y, z), lagrange_eqs(a), modules="numpy"). To use the standard library math library, use modules="math". By default, numpy is used if it is installed, otherwise math is used.

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