索引矩阵

Question

我有一个使用四个索引i，j，k和l创建的矩阵。我用下面的方案来创建矩阵，

for i = 1:N 
for j = 1:2 
    for k = 1:2 
    for l = 1:N 
    Matrix(l,2(j+2*i-3)+k) = Value 
    end 
    end 
end 
end 

当我做到这一点产生变化如下矩阵：

       Columns 
     i = 1 i = 1 i = 1 i = 1 i = 2 i = 2 i = 2 i = 2 ... 
     j = 1 j = 1 j = 2 j = 2 j = 1 j = 1 j = 2 j = 2 ... 
     k = 1 k = 2 k = 1 k = 2 k = 1 k = 2 k = 1 k = 2 ... 
l = 1 
l = 2 
    . 
    . 
    . 

不幸的是我索引是错误的，需要去改变它。我不想改变任何计算。我需要将上述矩阵变成一个代码如下：

       Columns 
      l = 1 l = 1 l = 2 l = 2 l = 1 l = 1 l = 2 l = 2 ... 
      k = 1 k = 2 k = 1 k = 2 k = 1 k = 2 k = 1 k = 2 ... 
i = 1 j = 1    
i = 1 j = 2    
i = 2 j = 1 
i = 2 j = 2  
     . 
     . 
     . 

换句话说一个代码，看起来像，

for i = 1:N 
for j = 1:2 
    for k = 1:2 
    for l = 1:N 
    Matrix(New Index) = Matrix(Old Index) 
    end 
    end 
end 
end 

我该怎么办呢？谢谢。

Answer 1

让我们看看，如果我理解正确的问题：

你有一个Matrix（称之为a）大小N x 4N的，你要创建一个矩阵（称之为b）大小2N x 2N的。

的a元素是由一组(i,j,k,l)如此定义的：

a = f(1,1,1,1) f(1,1,2,1) f(1,2,1,1) f(1,2,2,1) ... f(N,2,2,1) 
    f(1,1,1,2) f(1,1,2,2) f(1,2,1,2) f(1,2,2,2) ... f(N,2,2,2) 
    f(1,1,1,3) f(1,1,2,3) f(1,2,1,3) f(1,2,2,3) ... f(N,2,2,3) 
    f(1,1,1,4) f(1,1,2,4) f(1,2,1,4) f(1,2,2,4) ... f(N,2,2,4) 
    ... 
    f(1,1,1,N) f(1,1,2,N) f(1,2,1,N) f(1,2,2,N) ... f(N,2,2,N) 

现在你想b这样的：

b = f(1,1,1,1) f(1,1,2,1) f(1,1,1,2) f(1,1,2,2) ... f(1,1,2,N) 
    f(1,2,1,1) f(1,2,2,1) f(1,2,1,2) f(1,2,2,2) ... f(1,2,2,N) 
    f(2,1,1,1) f(2,1,2,1) f(2,1,1,2) f(2,1,2,2) ... f(2,1,2,N) 
    f(2,2,1,1) f(2,2,2,1) f(2,2,1,2) f(2,2,2,2) ... f(2,2,2,N) 
    ... 
    f(N,2,1,N) f(N,2,2,N) f(N,2,1,N) f(N,2,2,N) ... f(N,2,2,N) 

---

以上是正确的，那么所有你需要做的是：

b = zeros(2*N); 
b(:, 1:2:end) = a(:, 1:2:end)'; 
b(:, 2:2:end) = a(:, 2:2:end)'; 

---

例子：

n = 5; 
a = 1:(4*n*n); 
a = reshape(a, n, 4*n); 

b = zeros(2*n); 
b(:, 1:2:end) = a(:, 1:2:end)'; 
b(:, 2:2:end) = a(:, 2:2:end)'; 

输出：

a = 

Columns 1 through 13: 

    1  6 11 16 21 26 31 36 41 46 51 56 61 
    2  7 12 17 22 27 32 37 42 47 52 57 62 
    3  8 13 18 23 28 33 38 43 48 53 58 63 
    4  9 14 19 24 29 34 39 44 49 54 59 64 
    5 10 15 20 25 30 35 40 45 50 55 60 65 

Columns 14 through 20: 

    66 71 76 81 86 91 96 
    67 72 77 82 87 92 97 
    68 73 78 83 88 93 98 
    69 74 79 84 89 94 99 
    70 75 80 85 90 95 100 

b = 

    1  6  2  7  3  8  4  9  5 10 
    11 16 12 17 13 18 14 19 15 20 
    21 26 22 27 23 28 24 29 25 30 
    31 36 32 37 33 38 34 39 35 40 
    41 46 42 47 43 48 44 49 45 50 
    51 56 52 57 53 58 54 59 55 60 
    61 66 62 67 63 68 64 69 65 70 
    71 76 72 77 73 78 74 79 75 80 
    81 86 82 87 83 88 84 89 85 90 
    91 96 92 97 93 98 94 99 95 100