嗨，我嘗試用 python 編寫這段代碼，但是我有一個錯誤，我希望有人可以幫助我

Question

這是我在 python 中的代碼，sx 的維度應該是 100X4 和 sy 100X1 乘法 (sx) (B) (sy)。

import numpy as np                                                                             
  
B= [[-6.08066634428988e-10, -8.61023850910464e-11, 5.48222828615260e-12, -9.49229025004441e-14], 
    [-3.38148313553674e-11, 6.47759097087283e-12, 1.14900158474371e-13, -5.70078947874486e-15], 
    [-2.55893304237669e-13, -1.40941560399352e-13, 5.76510238931847e-15, -5.52980385181738e-17], 
    [3.39795122177475e-15, 7.95704191204353e-16, -5.31260642039813e-17, 7.83532802015832e-19]]                                                                         

[X, Y] = np.meshgrid(np.arange(0, 3, 0.01*3),np.arange(0, 15, 0.01*(15)))                           
sx=[]                                                                                                              
sy=[]                                                                                                               
F=[]                                                                                            
for i in range(len(X)):
    for j in range(len(X)):
        for k in range(len(B)):
            sx[i,k].append(X[i,j]**k)
        for l in range(len(B)):
            sy[l].append((Y[i,j]**l))
        F[i,j] = sx*B*sy 

錯誤：

sx[i,k].append(X[i,j]**k) TypeError: list indices must be integers or slices, not tuple   

---

從注釋中復制的 MATLAB 代碼（猜測格式）

 [x,y]=meshgrid(0:0.01*3:3,0:0.01*15:15); 
 for i=1:size(x) 
     for j=1:size(x) 
         for k=0:size(B) -1 
             sx(1,k+1)=(x(i,j)^k); 
         end 
         for k=0:size(B) -1 
             sy(k+1,1)=(y(i,j)^k); 
         end 
      G(i,j)=sx*B*sy; 
   end 
end 

Answer 1

如果sx或X是二維列表，則索引必須為[i][j] 。 如果您嘗試附加到兩個索引i和j那么它應該是單獨的 append 調用。

Answer 2

在八度音程中：

B =

  -6.0807e-10  -8.6102e-11   5.4822e-12  -9.4923e-14
  -3.3815e-11   6.4776e-12   1.1490e-13  -5.7008e-15
  -2.5589e-13  -1.4094e-13   5.7651e-15  -5.5298e-17
   3.3980e-15   7.9570e-16  -5.3126e-17   7.8353e-19

>>
>>  [x,y]=meshgrid(0:0.01*3:3,0:0.01*15:15);
>>  for i=1:size(x)
     for j=1:size(x)
         for k=0:size(B) -1
             sx(1,k+1)=(x(i,j)^k);
         end
         for k=0:size(B) -1
             sy(k+1,1)=(y(i,j)^k);
         end
      G(i,j)=sx*B*sy;
   end
end

產生

x, y, G (101 x 101)
>> sx         (1,4)
sx =
    1    3    9   27
>> sy          (4,1)
sy =
      1
     15
    225
   3375

所以G元素是 (1,4) * (4,4) * (4,1) => (1,1)

看起來我應該能夠做一個

In [100]: B= [[-6.08066634428988e-10, -8.61023850910464e-11, 5.48222828615260e-12, -9.49229025004441e-14],
     ...:     [-3.38148313553674e-11, 6.47759097087283e-12, 1.14900158474371e-13, -5.70078947874486e-15],
     ...:     [-2.55893304237669e-13, -1.40941560399352e-13, 5.76510238931847e-15, -5.52980385181738e-17],
     ...:     [3.39795122177475e-15, 7.95704191204353e-16, -5.31260642039813e-17, 7.83532802015832e-19]]
     ...: 
In [101]: B = np.array(B)
In [106]: [X, Y] = np.meshgrid(np.linspace(0, 3, 101),np.linspace(0, 15, 101),indexing='ij')
In [107]: X.shape
Out[107]: (101, 101)
In [108]: k = np.arange(0,4)
In [109]: k
Out[109]: array([0, 1, 2, 3])

In [110]: SX = X[:,:,None]**k         # (101,101,4)
In [111]: SY = Y[:,:,None]**k
In [114]: G = np.einsum('ijk,kl,ijl->ij',SX,B,SY)
In [115]: G.shape
Out[115]: (101, 101)

考慮到 MATLAB 的“F”階（即轉置），看起來這些結果匹配：

>> G(1,1)
ans = -0.00000000060807
In [118]: G[0,0]
Out[118]: -6.08066634428988e-10
>> G(50,23)
ans = -0.00000000097117
In [119]: G[22,49]
Out[119]: -9.71172989297259e-10

通過broadcasting我不會制作meshgrid陣列

In [121]: x, y = np.linspace(0,3,101), np.linspace(0,15,101)
In [124]: sx = x[:,None]**k
In [125]: sy = y[:,None]**k
In [126]: sx.shape
Out[126]: (101, 4)

In [129]: g = sx@B@sy.T
In [130]: g.shape
Out[130]: (101, 101)
In [131]: np.allclose(G,g)
Out[131]: True

在這里，我正在做一個矩陣乘積

(101,4) (4,4) (4,100) => (101,101)