我试图用python解决9个非线性方程，但输出是错误的。我发布的代码如下： 该代码已将P1 P2 P3 A1 A2 A3解析为存储的[x，y，z]坐标数。我试图用这些位置来找出最后三个点（x1，y1，z1），（x2，y2，z2），（x3，y3，z3）。
# For symbolic calculations use sympy
import sympy
import scipy
from scipy.optimize import fsolve
import math
import numpy as np
from numpy import cos,sin
###Set up B1 point
x1, y1, z1 = sympy.symbols('x1 y1 z1')
###Set up B2 point
x2, y2, z2 = sympy.symbols('x2 y2 z2')
### Set up B3 point
x3, y3, z3 = sympy.symbols('x3 y3 z3')
# Each lower arm has length Lc, this is length for A B
Lc = 3.0
#Define second points into seperate variables
a11 = A1[0]
a12 = A1[1]
a13 = A1[2]
a21 = A2[0]
a22 = A2[1]
a23 = A2[2]
a31 = A3[0]
a32 = A3[1]
a33 = A3[2]
##Constrain for Bar AB
eq1 = (x1 - A1[0])**2 + (y1 - A1[1])**2 + (z1 - A1[2])**2 - Lc**2
eq2 = (x2 - A2[0])**2 + (y2 - A2[1])**2 + (z2 - A2[2])**2 - Lc**2
eq3 = (x3 - A3[0])**2 + (y3 - A3[1])**2 + (z3 - A2[2])**2 - Lc**2
### Length for plate B points
Ld = 0.2
##Constrain for plate B points
eq4 = (x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2 - Ld**2
eq5 = (x3 - x1)**2 + (y3 - y1)**2 + (z3 - z1)**2 - Ld**2
eq6 = (x3 - x2)**2 + (y3 - y2)**2 + (z3 - z2)**2 - Ld**2
###Vectors for points P and points A
Upa1 = [A1[0] - P1[0], A1[1] - P1[1], A1[2] - P1[2] ]
Upa2 = [A2[0] - P2[0], A2[1] - P2[1], A2[2] - P2[2] ]
Upa3 = [A3[0] - P3[0], A3[1] - P3[1], A3[2] - P3[2] ]
###Vectors for points A and B
Uab1 = [x1 - A1[0], y1 - A1[1], z1 - A1[2]]
Uab2 = [x2 - A2[0], y2 - A2[1], z2 - A2[2]]
Uab3 = [x3 - A3[0], y3 - A3[1], z3 - A3[2]]
eq7 = np.dot(np.cross(Upa1, Uab1),u1)
eq8 = np.dot(np.cross(Upa2, Uab2),u2)
eq9 = np.dot(np.cross(Upa3, Uab3),u3)
###Using Scipy to solve equations
def equations(z):
x1 = z[0]
y1 = z[1]
z1 = z[2]
x2 = z[3]
y2 = z[4]
z2 = z[5]
x3 = z[6]
y3 = z[7]
z3 = z[8]
F = empty((9))
F[0] = (x1 - A1[0])**2 + (y1 - A1[1])**2 + (z1 - A1[2])**2 - Lc**2
F[1] = (x2 - A2[0])**2 + (y2 - A2[1])**2 + (z2 - A2[2])**2 - Lc**2
F[2] = (x3 - A3[0])**2 + (y3 - A3[1])**2 + (z3 - A2[2])**2 - Lc**2
F[3] = (x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2 - Ld**2
F[4] = (x3 - x1)**2 + (y3 - y1)**2 + (z3 - z1)**2 - Ld**2
F[5] = (x3 - x2)**2 + (y3 - y2)**2 + (z3 - z2)**2 - Ld**2
F[6] = np.dot(np.cross(Upa1, Uab1),u1)
F[7] = np.dot(np.cross(Upa2, Uab2),u2)
F[8] = np.dot(np.cross(Upa3, Uab3),u3)
return F
zGuess = [1., 1., 1., 1., 1., 1., 1., 1., 1.]
z = fsolve(equations, zGuess)
输出如下：
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-14-fbac9f95877a> in <module>()
----> 1 z = fsolve(equations, zGuess)
/Users/j/anaconda2/lib/python2.7/site-packages/scipy/optimize/minpack.pyc in fsolve(func, x0, args, fprime, full_output, col_deriv, xtol, maxfev, band, epsfcn, factor, diag)
144 'diag': diag}
145
--> 146 res = _root_hybr(func, x0, args, jac=fprime, **options)
147 if full_output:
148 x = res['x']
/Users/j/anaconda2/lib/python2.7/site-packages/scipy/optimize/minpack.pyc in _root_hybr(func, x0, args, jac, col_deriv, xtol, maxfev, band, eps, factor, diag, **unknown_options)
210 if not isinstance(args, tuple):
211 args = (args,)
--> 212 shape, dtype = _check_func('fsolve', 'func', func, x0, args, n, (n,))
213 if epsfcn is None:
214 epsfcn = finfo(dtype).eps
/Users/j/anaconda2/lib/python2.7/site-packages/scipy/optimize/minpack.pyc in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
24 def _check_func(checker, argname, thefunc, x0, args, numinputs,
25 output_shape=None):
---> 26 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
27 if (output_shape is not None) and (shape(res) != output_shape):
28 if (output_shape[0] != 1):
<ipython-input-12-951ec1513690> in equations(z)
18 F[4] = (x3 - x1)**2 + (y3 - y1)**2 + (z3 - z1)**2 - Ld**2
19 F[5] = (x3 - x2)**2 + (y3 - y2)**2 + (z3 - z2)**2 - Ld**2
---> 20 F[6] = np.dot(np.cross(Upa1, Uab1),u1)
21 F[7] = np.dot(np.cross(Upa2, Uab2),u2)
22 F[8] = np.dot(np.cross(Upa3, Uab3),u3)
/Users/j/anaconda2/lib/python2.7/site-packages/sympy/core/expr.pyc in __float__(self)
237 if result.is_number and result.as_real_imag()[1]:
238 raise TypeError("can't convert complex to float")
--> 239 raise TypeError("can't convert expression to float")
240
241 def __complex__(self):
TypeError: can't convert expression to float
TypeError: can't convert expression to float