无法将表达式转换为浮点数 - 使用 sympy

Question

我有下面这段代码，但我运行出错了，我不确定该怎么做。我试过更改数组上的数据类型，但这也不起作用。

import sympy as sym
import numpy as np
from numpy.linalg import norm
from numpy import transpose
from numpy import array
from numpy import sum
from matplotlib import pyplot as plt

def equations():
    a, b, c = sym.symbols('x y z')

    f_xyz_1 = 15*a + b**2 - 4*c - 15
    f_xyz_2 = a**2 + 10*b - c - 10 
    f_xyz_3 = b**3 - 25*c + 24

    return [f_xyz_1, f_xyz_2, f_xyz_3]

def f_bold(x):
    a, b, c = sym.symbols('x y z')
    vals = {a: x[0], b: x[1], c: x[2]}

    f_new_1 = equations()[0].subs(vals)
    f_new_2 = equations()[1].subs(vals)
    f_new_3 = equations()[2].subs(vals)    
    return array([[f_new_1], [f_new_2], [f_new_3]], dtype='float64')

def f(x):
    f_n = []
    for i in range(len(x)):
        f_i = f_bold(x)[i]**2
        f_n.append(f_i)

    return sum(f_n)

def M(x):
    a, b, c = sym.symbols('x y z')
    vals = {a: x[0], b: x[1], c: x[2]}

    f_xyz_1_diff_x = sym.diff(equations()[0], a).subs(vals)
    f_xyz_1_diff_y = sym.diff(equations()[0], b).subs(vals)
    f_xyz_1_diff_z = sym.diff(equations()[0], c).subs(vals)

    f_xyz_2_diff_x = sym.diff(equations()[1], a).subs(vals)
    f_xyz_2_diff_y = sym.diff(equations()[1], b).subs(vals)
    f_xyz_2_diff_z = sym.diff(equations()[1], c).subs(vals)

    f_xyz_3_diff_x = sym.diff(equations()[2], a).subs(vals)
    f_xyz_3_diff_y = sym.diff(equations()[2], b).subs(vals)
    f_xyz_3_diff_z = sym.diff(equations()[2], c).subs(vals)

    return array([[f_xyz_1_diff_x, f_xyz_2_diff_x, f_xyz_3_diff_x], [f_xyz_1_diff_y, f_xyz_2_diff_y, f_xyz_3_diff_y], [f_xyz_1_diff_z, f_xyz_2_diff_z, f_xyz_3_diff_z]], dtype='float64')

def grad_f(x):
    return 2*np.dot(M(x), f_bold(x))

def d(x):
    return -1*grad_f(x)/norm(grad_f(x), ord=2)

def s_prime(x, alpha, d):
    return np.dot(transpose(grad_f(x + alpha*d)))

x = [0.5, 0.5, 0.5]
alpha = 0.75
print(s_prime(x, alpha, d(x)))

当我打印 s_prime 时，它会打印以下追溯：

Traceback (most recent call last):
  File "/Users/aidanpayne/Desktop/Scripts/Python/University of Greenwich/MATH1157/Scripts/Steepest Descent Method for three equations.py", line 64, in <module>
    print(s_prime(x, alpha, d(x)))
  File "/Users/aidanpayne/Desktop/Scripts/Python/University of Greenwich/MATH1157/Scripts/Steepest Descent Method for three equations.py", line 60, in s_prime
    return np.dot(transpose(grad_f(x + alpha*d)))
  File "/Users/aidanpayne/Desktop/Scripts/Python/University of Greenwich/MATH1157/Scripts/Steepest Descent Method for three equations.py", line 54, in grad_f
    return 2*np.dot(M(x), f_bold(x))
  File "/Users/aidanpayne/Desktop/Scripts/Python/University of Greenwich/MATH1157/Scripts/Steepest Descent Method for three equations.py", line 51, in M
    return array([[f_xyz_1_diff_x, f_xyz_2_diff_x, f_xyz_3_diff_x], [f_xyz_1_diff_y, f_xyz_2_diff_y, f_xyz_3_diff_y], [f_xyz_1_diff_z, f_xyz_2_diff_z, f_xyz_3_diff_z]], dtype='float64')
  File "/Users/aidanpayne/opt/anaconda3/lib/python3.8/site-packages/sympy/core/expr.py", line 327, in __float__
    raise TypeError("can't convert expression to float")
TypeError: can't convert expression to float

但是当我打印其他 defs 时，它没有打印任何错误。

Answer 1

正确代码：

import sympy as sym
import numpy as np
from numpy.linalg import norm
from numpy import transpose
from numpy import array
from numpy import sum
from matplotlib import pyplot as plt

def equations():
    a, b, c = sym.symbols('x y z')

    f_xyz_1 = 15*a + b**2 - 4*c - 15
    f_xyz_2 = a**2 + 10*b - c - 10 
    f_xyz_3 = b**3 - 25*c + 24

    return [f_xyz_1, f_xyz_2, f_xyz_3]

def f_bold(x):
    a, b, c = sym.symbols('x y z')
    vals = {a: x[0][0], b: x[1][0], c: x[2][0]}

    f_new_1 = equations()[0].subs(vals)
    f_new_2 = equations()[1].subs(vals)
    f_new_3 = equations()[2].subs(vals)

    out_arr = [[f_new_1], [f_new_2], [f_new_3]]

    return array(out_arr, dtype='float32')

def f(x):
    f_n = []
    for i in range(len(x)):
        f_i = f_bold(x)[i]**2
        f_n.append(f_i)

    return sum(f_n)

def M(x):
    a, b, c = sym.symbols('x y z')
    vals = {a: x[0][0], b: x[1][0], c: x[2][0]}

    f_xyz_1_diff_x = sym.diff(equations()[0], a).subs(vals)
    f_xyz_1_diff_y = sym.diff(equations()[0], b).subs(vals)
    f_xyz_1_diff_z = sym.diff(equations()[0], c).subs(vals)

    f_xyz_2_diff_x = sym.diff(equations()[1], a).subs(vals)
    f_xyz_2_diff_y = sym.diff(equations()[1], b).subs(vals)
    f_xyz_2_diff_z = sym.diff(equations()[1], c).subs(vals)

    f_xyz_3_diff_x = sym.diff(equations()[2], a).subs(vals)
    f_xyz_3_diff_y = sym.diff(equations()[2], b).subs(vals)
    f_xyz_3_diff_z = sym.diff(equations()[2], c).subs(vals)

    out_arr = [[f_xyz_1_diff_x, f_xyz_2_diff_x, f_xyz_3_diff_x], [f_xyz_1_diff_y, f_xyz_2_diff_y, f_xyz_3_diff_y], [f_xyz_1_diff_z, f_xyz_2_diff_z, f_xyz_3_diff_z]]

    return array(out_arr, dtype='float32')

def grad_f(x):
    return 2*np.dot(M(x), f_bold(x))

def d(x):
    return -1*grad_f(x)/norm(grad_f(x), ord=2)

def s_prime(x, alpha, d):
    return np.dot(transpose(grad_f(x + alpha*d)), d)

x = [0.5, 0.5, 0.5]
x = np.reshape(x, (3, 1))
alpha = 0.75
d_k = d(x)

print(s_prime(x, alpha, d_k))

无法将表达式转换为浮点数 - 使用 sympy

Can't convert expression to float - using sympy

python

numpy

sympy