Python fsolve（）抱怨形状。 为什么？

Question

具有函数f（x，y，z），我需要求解限制f（x，y，z）= 0，然后将其绘制出来。 我试图为每对（y，z）查找f（x，y，z）= 0的值x：

from numpy import *
from scipy.optimize import fsolve

def func(x,y,z):
    return x+y+z

y = linspace(0,1,100)
z = linspace(0,1,100)
x0 = zeros((y.size,z.size)) + 0.5 # the initial guess
yz = (y[:,newaxis],z[newaxis,:]) # the other parameters
x, info, iterations, message = fsolve(func,x0,yz)
contour(y,z,x)

Python（2.7.5）说：“ TypeError：fsolve：'func'参数'func'的输入和输出形状不匹配。”

但是，如果我自己进行测试，它会具有相同的形状：

func(x0,y[:,newaxis],z[:,newaxis]).shape == x0.shape

返回True。

为什么fsolve（）抱怨？

Answer 1

fsolve期望x参数和func的返回值是标量或一维数组。 您必须修改代码才能使用展平的x值。 例如

def func(x, y, z):
    x = x.reshape(y.size, z.size)
    return (x + y + z).ravel()

和类似的东西打电话给fsolve ：

sol, info, ier, mesg = fsolve(func, x0.ravel(), args=yz, full_output=True)
x = sol.reshape(y.size, z.size)

Answer 2

这是与scipy.optimize教程中广告的krylov方法的比较：

from numpy import linspace, zeros, newaxis
import time
from scipy.optimize import root

def func(x,y,z):
    x = x.reshape(y.size, z.size)
    f = x + y + z
    f = f.ravel()
    return f

n = 50
y = linspace(0,1,n)
z = linspace(0,1,n)
x0 = zeros((y.size,z.size)) + 0.5 # the initial guess
yz = (y[:,newaxis],z[newaxis,:]) # the other parameters

start = time.time()
sol1 = root(func, x0.ravel(), args=yz, method='hybr', tol=1e-7)  # same as fsolve
x1 = sol1.x.reshape(y.size, z.size)
print("(fsolve) time taken (sec): %g" % (time.time() - start,))
print("(fsolve) successful: %r (%s)" % (sol1.success, sol1.message))
print("(fsolve) max error: %g" % (abs(func(x1, *yz)).max(),))

start = time.time()
sol2 = root(func, x0.ravel(), args=yz, method='krylov', tol=1e-9)
x2 = sol2.x.reshape(y.size, z.size)
print("(krylov) time taken (sec): %g" % (time.time() - start,))
print("(krylov) successful: %r (%s)" % (sol2.success, sol2.message))
print("(krylov) max error: %g" % (abs(func(x2, *yz)).max(),))

版画

(fsolve) time taken (sec): 26.9296
(fsolve) successful: False (The iteration is not making good progress, as measured by the 
  improvement from the last ten iterations.)
(fsolve) max error: 1.52656e-16
(krylov) time taken (sec): 0.0173709
(krylov) successful: True (A solution was found at the specified tolerance.)
(krylov) max error: 1.11022e-16