是否有办法在lambdas内本地绑定函数?我有一个循环，在每个循环中，我创建了一个函数数组。我想创建另一个函数它是所有这些函数的和并将它存储在另一个数组中。这个新数组应该保存每个循环的所有函数的和。然后我想创建另一个函数它是所有函数和的和
然而，我的问题是，原来的函数不断更新，所以我没有得到我想要的结果。我可以在本地绑定函数吗?我是不是说错了?
import numpy as np
lmax = 4
lapprox = []
# Function to estimate
def curve_func(x):
return np.sin(x*np.pi)*x**2
# Initialise residual function
def residual_func(x):
return curve_func(x)
# For each l, create 2**l+1 nodes and determine new nodes.
for l in range(lmax):
nodes = np.linspace(0, 1, 2**l+1, endpoint = True)
if (l==0):
old_nodes = nodes
new_nodes = nodes
else:
old_nodes = np.linspace(0, 1, 2**(l-1)+1, endpoint = True)
new_nodes = [x for x in nodes if x not in old_nodes]
# Create basis function corresponding to each new node
if (l==0):
phi = [lambda x, i=i: max(1 - abs(2**l * x - i), 0) for i in range(len(new_nodes))]
else:
phi = [lambda x, i=i: max(1 - abs(2**l * x - (2*i+1)), 0) for i in range(len(new_nodes))]
# Calculate hierarchical surpluses
coeff = [residual_func(n) for n in new_nodes]
# Array of functions: coeff*phi
coeff_phi = [lambda x, func=func, alpha=alpha: coeff[alpha]*func(x) for alpha, func in enumerate(phi)]
# Array of length lmax, where each value is sum of functions in coeff_phi for fixed l
lapprox.append(lambda x: sum(f(x) for f in coeff_phi))
# Sum of all functions in lapprox
totapprox = lambda x: sum(f(x) for f in lapprox)
# Compute new residual function
residual_func = lambda x: curve_func(x) - totapprox(x)
关于代码所做的额外细节:代码被设计为近似函数，例如使用分层线性样条的sin(pi*x)*x^2。对于每一级l，都有一些基函数，由数组phi给出。用一些系数乘以这些基函数的线性组合来近似该函数。近似是按顺序进行的，从具有很少基函数的低级开始，直到具有许多基函数的高级。我需要跟踪函数的滚动近似来确定新系数的值。
lmax=3的"脏"解决方案，但我想将其推广到任何lmax。我该怎么做呢?def curve_func(x):
return np.sin(x*np.pi)*x**2
def residual_func_0(x):
return curve_func(x)
# Define nodes function
def make_nodes(l):
return np.linspace(0, 1, 2**l+1, endpoint = True)
# Define new_nodes function
def make_new_nodes(l):
if (l==0):
new_nodes = np.linspace(0, 1, 2**l+1, endpoint = True)
else:
old_nodes = np.linspace(0, 1, 2**(l-1)+1, endpoint = True)
new_nodes = [x for x in make_nodes(l) if x not in old_nodes]
return new_nodes
# Define basis functions
def make_basis(l, i):
if l == 0:
return lambda x: max(1 - abs(2**l * x - i), 0)
else:
return lambda x: max(1 - abs(2**l * x - (2*i+1)), 0)
# Define coeff*basis functions
def make_scaled_basis(alpha, fn):
return lambda x: alpha * fn(x)
new_nodes_0 = make_new_nodes(0)
new_nodes_1 = make_new_nodes(1)
new_nodes_2 = make_new_nodes(2)
new_nodes_3 = make_new_nodes(3)
phi_0 = [make_basis(0, i) for i in range(len(new_nodes_0))]
phi_1 = [make_basis(1, i) for i in range(len(new_nodes_1))]
phi_2 = [make_basis(2, i) for i in range(len(new_nodes_2))]
phi_3 = [make_basis(3, i) for i in range(len(new_nodes_3))]
coeff_0 = [curve_func(n) for n in new_nodes_0]
coeff_phi_0 = [make_scaled_basis(alpha, fn) for alpha, fn in zip(coeff_0, phi_0)]
residual_func_0 = lambda x: curve_func(x) - sum(f(x) for f in coeff_phi_0)
coeff_1 = [residual_func_0(n) for n in new_nodes_1]
coeff_phi_1 = [make_scaled_basis(alpha, fn) for alpha, fn in zip(coeff_1, phi_1)]
residual_func_1 = lambda x: residual_func_0(x) - sum(f(x) for f in coeff_phi_1)
coeff_2 = [residual_func_1(n) for n in new_nodes_2]
coeff_phi_2 = [make_scaled_basis(alpha, fn) for alpha, fn in zip(coeff_2, phi_2)]
residual_func_2 = lambda x: residual_func_1(x) - sum(f(x) for f in coeff_phi_2)
coeff_3 = [residual_func_2(n) for n in new_nodes_3]
coeff_phi_3 = [make_scaled_basis(alpha, fn) for alpha, fn in zip(coeff_3, phi_3)]
residual_func_3 = lambda x: residual_func_2(x) - sum(f(x) for f in coeff_phi_3)
在函数体中本地化l和i的一个简单方法是创建一个函数，该函数返回一个关闭局部变量l和i的函数。
例如:
def make_basis(l, i):
if l == 0:
return lambda x: max(1 - abs(2**l * x - i), 0)
else:
return lambda x: max(1 - abs(2**l * x - (2*i+1)), 0)
...
for l in range(lmax):
...
phi = [make_basis(l, i) for i in range(len(new_nodes))]
循环不创建新的作用域;只有函数体可以。