解决Python计算矩阵乘向量,矩阵乘实数的一些小错误

脚本专栏 2025/1/10 佚名

3 2 1

计算：Ax-b

A: 2*2
x: 2*1
b: 2*1
so, Ax-b: 2*1

if __name__ == "__main__":
  A = np.array([[4.0, 1.0],
         [1.0, 3.0]])
  b = np.array([[1.0], [2.0]])
  x_0 = np.array([[2.0], [1.0]])

  r_k = A * x_0 - b

  print(r_k)

错误！！！

修改：

if __name__ == "__main__":
  A= mat([[4.0, 1.0],
      [1.0, 3.0]])
  b = mat([[1.0], [2.0]])
  x_0 = mat([[2.0], [1.0]])

  r_k = A * x_0 - b

  print(r_k)

if __name__ == "__main__":
  A= mat([[4.0, 1.0],
      [1.0, 3.0]])
  b = mat([[1.0], [2.0]])
  x_k = mat([[2.0], [1.0]])

  p_k = -x_k # 2行1列
  r_k = A * x_k - b # 2行1列
  alpha_k = (np.transpose(r_k) * r_k) / (np.transpose(p_k) * A * p_k) # 1行1列
   -----------------------------------------------
  x_k = x_k + alpha_k * p_k #2行1列 ！！！！这里报错
   -----------------------------------------------
  print(x_k)

修改：

if __name__ == "__main__":
  A= mat([[4.0, 1.0],
      [1.0, 3.0]])
  b = mat([[1.0], [2.0]])
  x_k = mat([[2.0], [1.0]])

  p_k = -x_k # 2*1
  r_k = A * x_k - b # 2*1
  alpha_k = (np.transpose(r_k) * r_k) / (np.transpose(p_k) * A * p_k) # 1*1
  -----------------------------------------------
  x_k = x_k +  p_k *alpha_k
  -----------------------------------------------
  print(x_k)