优化参数之一是数组的函数

Question

我想通过改变其中两个参数实际上是数组的参数来优化函数。我试过了

...
# initial parameters
params0 = np.array([p1, p2, ... , p_array1, p_array2])
p_min = minimize(myfunc, params0, args)
...

pj 是标量，p_array1 和 p_array2 是长度相同的数组，但这给了我一个错误提示

ValueError: setting an array element with a sequence.

我还尝试将 p_array1 和 p_array2 作为标量传递到 myfunc 中，然后从 myfunc 中的这两个创建预定数组（例如，设置 p_array1 = p_array1*np.arange(6) 并类似地设置 p_array2），消除了错误，但是我不希望它们被预先确定——相反，我希望“最小化”以弄清楚它们应该是什么。

有什么方法可以利用 Scipy 的优化函数之一而不会出现此错误，同时仍将 p_array1 和 p_array2 保留为数组而不是标量？

编辑

对不起，这里是我的代码：

注意：这里的'myfunc'实际上是norm_residual。

import pandas as pd
import numpy as np

def f(yvec, t, a, b, c, d, M, theta):
    # the system of ODEs to be solved
    x, y = yvec
    dydt = [ a*x - b*y**2 + 1, -c*x - d*x*y + np.sum(M * np.cos(theta*t)) ]
    return dydt

ni = 3 # the number of periodic forcing functions to add to the DE system
M = 0.56*np.random.rand(ni) # the initial amplitudes of forcing functions
theta = np.pi/6*np.arange(ni) # the initial coefficients of the forcing functions

# initialize the parameters
params0 = [0.75, 0.23, 1.0, 0.2, M, theta]

# grabbing the data to be used later
data = pd.read_csv('data.csv')
y_data = data['Y']

N = y_data.shape[0] #20
t = np.linspace(0, N, N) # array of t values to integrate over
yvec0 = [0.3, 0.34] # initial conditions for x and y respectively

def norm_residual(params, *args):
    """
    Computes the L^2 norm of the residual of y and the data (y as defined above).
    Input:    params = array of parameters (scalars or arrays) for the DE system
              args = other arguments to pass into the function f or to use
                   to compute the residual.
    Output: err = L^2 error of the solution vector (scalar).
    """
    data, yvec0, t = args
    a, b, c, d, M, theta = params
    sol = odeint(f, yvec0, t, args=(a, b, c, d, M, theta))
    x = sol[:, 0]; y = sol[:, 1]
    res = data - y
    err = np.linalg.norm(res, 2)
    return err

from scipy.optimize import minimize

p_min = minimize(norm_residual, params0, args=(y_data, yvec0, t))
print(p_min)

还有回溯

Traceback (most recent call last):
  File "model_ex_1.py", line 62, in <module>
    p_min = minimize(norm_residual, params0, args=(y_anom, yvec0, t))
  File "/usr/lib/python2.7/dist-packages/scipy/optimize/_minimize.py", line 354, in minimize
    x0 = np.asarray(x0)
  File "/usr/lib/python2.7/dist-packages/numpy/core/numeric.py", line 482, in asarray
    return array(a, dtype, copy=False, order=order)
ValueError: setting an array element with a sequence.

Answer 1

如果其他元素是标量，则不能将列表放入 numpy 数组中。

>>> import numpy as np
>>> foo_array = np.array([1,2,3,[5,6,7]])
Traceback (most recent call last):
  File "<pyshell#1>", line 1, in <module>
    foo_array = np.array([1,2,3,[5,6,7]])
ValueError: setting an array element with a sequence.

Answer 2

如果你发帖myfunc会很有帮助 但你可以这样做 -

def foo():
    return [p0,p1,p2..pn]

params0 = numpy.array([foo(), p_array1, p_array2])
p_min = minimize(myfunc, params0, args) 

或来自Multiple variables in SciPy's optimize.minimize

import scipy.optimize as optimize

def f(params):
    # print(params)  # <-- you'll see that params is a NumPy array
    a, b, c = params # <-- for readability you may wish to assign names to the component variables
    return a**2 + b**2 + c**2

initial_guess = [1, 1, 1]
result = optimize.minimize(f, initial_guess)
if result.success:
    fitted_params = result.x
    print(fitted_params)
else:
    raise ValueError(result.message)

Answer 3

我想通了！我发现可行的解决方案是改变

params0 = [0.75, 0.23, 1.0, 0.2, M, theta]

在第 6 行到

params0 = np.array([ 0.75, 0.23, 1.0, 0.2, *M, *theta], dtype=np.float64)

在我的 ODE 系统的函数定义中，而不是有

def f(yvec, t, a, b, c, d, M, theta):
    x, y = yvec
    dydt = [ a*x - b*y**2 + 1, -c*x - d*x*y + np.sum(M * np.cos(theta*t)) ]
    return dydt

我现在有

def f(yvec, t, myparams):
    x, y = yvec
    a, b, c, d = myparams[:4]
    ni = (myparams[4:].shape[0])//2 # halved b/c M and theta are of the same shape
    M = myparams[4:ni+4]
    theta = myparams[ni+4:]
    dydt = [ a*x - b*y**2 + 1, -c*x - d*x*y + np.sum(M * np.cos(theta*t)) ]
    return dydt

注意：我必须为“params0”添加“dtype=np.float64”，因为我遇到了错误

AttributeError: 'numpy.float64' object has no attribute 'cos'

当我没有它时，'cos' 似乎不知道如何处理'ndarray' 对象。解决方法可以在here找到。

感谢大家的建议！