使用Scipy curve_fit和可变数量的参数进行优化

Question

假设我们具有以下针对4个参数进行优化的函数，我们必须按如下方式编写该函数，但是如果希望具有更多参数的同一个函数，则必须重写该函数定义。

def radius (z,a0,a1,k0,k1,):
    k = np.array([k0,k1,])
    a = np.array([a0,a1,])
    w   = 1.0
    phi = 0.0
    rs = r0 + np.sum(a*np.sin(k*z +w*t +phi), axis=1)
    return rs

问题是，是否可以通过比this question提示的自动化方式更轻松，更直观地完成此操作。

示例如下，必须手动编写。

def radius (z,a0,a1,a2,a3,a4,a5,a6,a7,a8,a9,k0,k1,k2,k3,k4,k5,k6,k7,k8,k9,):
    k = np.array([k0,k1,k2,k3,k4,k5,k6,k7,k8,k9,])
    a = np.array([a0,a1,a2,a3,a4,a5,a6,a7,a8,a9,])
    w   = 1.0
    phi = 0.0
    rs = r0 + np.sum(a*np.sin(k*z +w*t +phi), axis=1)
    return rs

Answer 1

[将函数构造为循环内的字符串，并使用'exec'将其作为python代码执行，然后在Scipy curve_fit中使用它可能会更容易：

N = 5

arg_k = ''
arg_a = ''

for i in range(N):
    arg_a += 'a'+str(i)+','
    arg_k += 'k'+str(i)+','

function_def = 'def radius (z,' +  arg_a+arg_k+ '):'
a = 'a = np.array(['+arg_a+'])' 
k = 'k = np.array(['+arg_k+'])'  
indent = '    '
function_def += ('\n'+indent+ k
                +'\n'+indent+ a 
                +'\n'+indent+'w   = 1.0'
                +'\n'+indent+'phi = 0.0'
                +'\n'+indent+'rs = r0 + np.sum(a*np.sin(k*z +w*t +phi), axis=1)'
                +'\n'+indent+'return rs')


exec(function_def)

打印字符串会得到以下结果：

print(function_def)

def radius (z,a0,a1,a2,a3,a4,k0,k1,k2,k3,k4,):
    k = np.array([k0,k1,k2,k3,k4,])
    a = np.array([a0,a1,a2,a3,a4,])
    w   = 1.0
    phi = 0.0
    rs = r0 + np.sum(a*np.sin(k*z +w*t +phi), axis=1)
    return rs

然后在定义的函数上使用Scipy curve_fit：

popt, pcov = curve_fit(radius, xdata=z, ydata=r)