無法將運算式轉換為浮點數-使用sympy

我在下面有這個代碼，但我遇到了一個錯誤，我不確定該怎么做。我曾嘗試更改陣列上的 dtype，但這也不起作用。

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)))

當我列印 s_prime 時，它??會列印以下回溯：

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

但是當我列印其他 defs 時，它不會列印任何錯誤。

uj5u.com熱心網友回復：

正確的代碼：

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))

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