sympy.subs 无法将点替换为数组

Question

import sympy
import numpy
from sympy import ordered, Matrix
x1,x2=sympy.symbols('x1 x2')
f=x1**2-x1*x2-4*x1+x2**2-x2
X0=numpy.array([[1],[1]])
v = list(ordered(f.free_symbols))
gradient = lambda f, v: Matrix([f]).jacobian(v)
gradf=sympy.transpose(gradient(f, v))
gradfx0=(gradf.subs([(x1, X0[0]), (x2, X0[1])]))
print(gradfx0)

我想计算python中某点的二变函数的梯度。我定义函数并找到函数的梯度向量 (grad)。现在，当我尝试将 X0 替换为 grad 时，结果是

Matrix([[2*x1 - x2 - 4], [-x1 + 2*x2 - 1]]).

我想要的结果应该是

Matrix([[-3], [0]]).

如何将点替换为 sympy 数组？

Answer 1

使用.subs and derive_by_array：

from sympy import symbols
from sympy.tensor.array import derive_by_array

x1, x2 = symbols('x1 x2')
f = x1 ** 2 - x1 * x2 + x2 ** 2 - 4 * x1 - x2

grad = derive_by_array(f, (x1, x2))
#    = [2*x1 - x2 - 4, -x1 + 2*x2 - 1]

gradx0 = grad.subs({x1: 1, x2: 1})
#      = [-3, 0]

如果你想先调用你的点x0，然后使用变量x0:

x0 = (1, 1)
gradx0 = grad.subs(zip((x1,x2), x0))
#      = [-3, 0]

sympy.subs 无法将点替换为数组

sympy.subs cannot substituting a point to array

python

math

sympy