python中a=b.copy()和a=b有什么区别

在 Python 中，`a = b.copy()` 和 `a = b` 是不同的赋值操作。

`a = b.copy()` 是用 `b` 的副本来创建一个新的对象，并将该对象赋值给 `a`。这意味着当修改 `a` 的值时，`b` 不会受到任何影响，因为它们是两个不同的对象。

而 `a = b` 是将 `a` 和 `b` 指向同一个对象。这意味着当修改 `a` 或 `b` 的值时，它们都会发生变化，因为它们指向的是同一个对象。

下面是一个简单的例子来说明这两个操作的区别：

# 使用 b.copy()
b = [1, 2, 3]
a = b.copy()
a.append(4)
print(a)  # [1, 2, 3, 4]
print(b)  # [1, 2, 3]

# 使用 a=b
b = [1, 2, 3]
a = b
a.append(4)
print(a)  # [1, 2, 3, 4]
print(b)  # [1, 2, 3, 4]

可以看到，使用 `b.copy()` 创建了一个新的对象 `a`，因此修改 `a` 的值不会影响 `b`。而使用 `a=b`，`a` 和 `b` 指向同一个对象，因此修改 `a` 或 `b` 的值都会影响另一个变量。

相关问题

def QR(A): def householder(a): n = len(a) v = np.zeros(n) v[0] = np.linalg.norm(a) if a[0] < 0: v[0] = -v[0] v = v + a v = v / np.linalg.norm(v) H = np.eye(n) - 2 * np.outer(v, v) return H def qr_factorization(A): m, n = A.shape Q = np.eye(m) R = A.copy() for j in range(min(m, n)): a = R[j:, j] H = np.eye(m) H[j:, j:] = householder(a) Q = Q @ H.T R = H @ R return Q, R Q, R = qr_factorization(A) b = sp.Matrix(sp.symbols('a1:11')) # 求解Ly=b中的y y = sp.zeros(10, 1) # 初始化y y = Q.T@b # 求解Ux=y中的x x = sp.zeros(10, 1) # 初始化x for i in range(9, -1, -1): x[i] = y[i] for j in range(i+1, 10): x[i] -= R[i, j] * x[j] x[i] /= R[i, i] matrice_coeff = sp.Matrix(np.zeros((10, 10))) for i in range(10): for j in range(10): matrice_coeff[i, j] = x[i].coeff(sp.Symbol('a{}'.format(j + 1))) return(matrice_coeff)修改这段函数，让def里面不要再嵌套def

可以将内部的两个函数 `householder` 和 `qr_factorization` 移到外部并改为类的方法，这样就不需要嵌套 `def` 了。以下是修改后的代码：

import numpy as np
import sympy as sp

class QRDecomposition:
    def __init__(self, A):
        self.A = A
        self.m, self.n = A.shape
        self.Q = np.eye(self.m)
        self.R = self.A.copy()

    def householder(self, a):
        v = np.zeros(self.n)
        v[0] = np.linalg.norm(a)
        if a[0] < 0:
            v[0] = -v[0]
        v = v + a
        v = v / np.linalg.norm(v)
        H = np.eye(self.m) - 2 * np.outer(v, v)
        return H

    def qr_factorization(self):
        for j in range(min(self.m, self.n)):
            a = self.R[j:, j]
            H = np.eye(self.m)
            H[j:, j:] = self.householder(a)
            self.Q = self.Q @ H.T
            self.R = H @ self.R

    def solve(self, b):
        y = self.Q.T @ b
        x = np.zeros(self.n)
        for i in range(self.n - 1, -1, -1):
            x[i] = y[i]
            for j in range(i + 1, self.n):
                x[i] -= self.R[i, j] * x[j]
            x[i] /= self.R[i, i]
        return x

    def get_coefficients(self, b):
        self.qr_factorization()
        x = self.solve(b)
        matrice_coeff = sp.Matrix(np.zeros((self.n, self.n)))
        for i in range(self.n):
            for j in range(self.n):
                matrice_coeff[i, j] = x[i].coeff(sp.Symbol('a{}'.format(j + 1)))
        return matrice_coeff

这样，我们可以通过创建 `QRDecomposition` 类的实例来调用它的方法。例如，可以按如下方式使用：

A = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
              [2, 3, 4, 5, 6, 7, 8, 9, 10, 1],
              [3, 4, 5, 6, 7, 8, 9, 10, 1, 2],
              [4, 5, 6, 7, 8, 9, 10, 1, 2, 3],
              [5, 6, 7, 8, 9, 10, 1, 2, 3, 4],
              [6, 7, 8, 9, 10, 1, 2, 3, 4, 5],
              [7, 8, 9, 10, 1, 2, 3, 4, 5, 6],
              [8, 9, 10, 1, 2, 3, 4, 5, 6, 7],
              [9, 10, 1, 2, 3, 4, 5, 6, 7, 8],
              [10, 1, 2, 3, 4, 5, 6, 7, 8, 9]])
b = sp.Matrix(sp.symbols('a1:11'))
qr = QRDecomposition(A)
matrice_coeff = qr.get_coefficients(b)
print(matrice_coeff)

dwxh,dwhh,dwhy = np.zeros_like(wxh), np.zeros_like(Whh),np.zeros_like(Why) dbh, dby = np.zeros_like(bh),np.zeros_like(by) dhnext = np.zeros_like(hs[0]) for t in reversed(range(len(inputs))) : dy = np.copy(ps[t]) for b in range(0,B): dy[targets[t][b],b] -= 1 dwhy += np.dot(dy, hs[t].T) dby += np.expand_dims(np.sum(dy,axis=1),axis=1) dh = np.dot(Why.T, dy）+ dhnext dh = dh * (1-hs[t]*hs[t] ) dbh += np.expand_dims(np.sum(dh,axis=1),axis=1) dWxh += np.dot(dh,xs[t].T) dWhh += np.dot(dh,hs[t - 1].T) dhnext = np.dot(Whh.T,dh) return loss,dWxh,dWhh,dwhy,dbh,dby, hs[len(inputs) - 1] 给这段代码加上注释

# 初始化各个参数的梯度为0
dwxh, dwhh, dwhy = np.zeros_like(wxh), np.zeros_like(Whh), np.zeros_like(Why)
dbh, dby = np.zeros_like(bh), np.zeros_like(by)
dhnext = np.zeros_like(hs[0])

# 反向传播过程
for t in reversed(range(len(inputs))):
    # 计算当前时刻的输出值
    dy = np.copy(ps[t])
    for b in range(0,B):
        dy[targets[t][b], b] -= 1

    # 计算各个参数的梯度
    dwhy += np.dot(dy, hs[t].T)
    dby += np.expand_dims(np.sum(dy, axis=1), axis=1)
    dh = np.dot(Why.T, dy) + dhnext
    dh = dh * (1 - hs[t] * hs[t])
    dbh += np.expand_dims(np.sum(dh, axis=1), axis=1)
    dWxh += np.dot(dh, xs[t].T)
    dWhh += np.dot(dh, hs[t - 1].T)
    dhnext = np.dot(Whh.T, dh)

# 返回损失函数值以及各个参数的梯度和最后一个时刻的隐藏状态
return loss, dwxh, dwhh, dwhy, dbh, dby, hs[len(inputs) - 1]