我有一个A = 3×3矩阵，其中要根据多项式函数结果对元素的位置进行混洗 [英] I have a A = 3×3 matrix in which position of elements are to be shuffled based on polynomial function result
问题描述
A = [1 2 3; 4 5 6; 7 8 9];
现在，重塑矩阵A以形成行向量将得到B.
Now reshaping the matrix A to form a row vector gives B.
B = [1 4 7 2 5 8 3 6 9];
求多项式函数
f(x)=(7x + 6x ^ 2 + 3x ^ 3)mod 9 因为存在9个元素，所以将'x'的值放在(1，...，9)范围内.
f(x) = (7x+6x^2+3x^3)mod 9 by putting values for 'x' ranging from (1,...,9) since there are 9 elements.
例如对于x = 1，f(x)= 16 mod 9 = 7
Ex. For x=1, f(x) = 16 mod 9 = 7
对于x = 2，f(x)= 62 mod 9 = 8直到x = 9导致置换.
For x=2, f(x) = 62 mod 9 = 8 till x = 9 results in permute.
permute = [7 8 3 1 2 6 4 5 9];
置换向量给出位置. 使用矩阵索引，根据置换向量排列行向量B中元素的位置，从而产生enc.
permute vector gives positions. Using matrix indexing, the positions of elements in row vector B are arranged according to permute vector resulting in enc.
enc = B(permute);
%enc = [3 6 7 1 4 8 2 5 9]
因此，元素A中元素的原始位置已经改组，由new_A表示.
Thus, the original position of elements in A has been shuffled represented by new_A.
new_A = [3 1 2;6 4 5;7 8 9]; %reshaping new_A = (enc,3,3)
要获得原始矩阵，请再次将new_A重塑为行向量'dec'.
To get original matrix back, new_A is reshaped into a row vector 'dec' again.
dec = [3 6 7 1 4 8 2 5 9];
dec(permute) = dec;
dec = [1 4 7 2 5 8 3 6 9];
org_mat= reshape(dec,3,3)
org_mat = [1 2 3; 4 5 6; 7 8 9];
dec(permute)= dec如何在其中工作?
How does dec(permute)= dec works in this?
推荐答案
之所以起作用，是因为dec = enc = B(permute).
The reason it works is because dec = enc = B(permute).
如果仅将其替换为dec(permute) = dec;，则会得到dec(permute) = B(permute)(仅替换第二个dec.)这将为您提供dec=B.
If you simply replace this into dec(permute) = dec; you get dec(permute) = B(permute) (only replace the second dec.) This gives you dec=B.
这是一般结果.例如，对于任何排列向量p以及向量X和Y，则如果设置X(p)=Y(p)则X=Y，因为将Y中的第p个元素放入<中的第p个元素c6>因此完全保留了Y.
This is a general result. For example, for any permutation vector p and vectors X and Y then if you set X(p)=Y(p) then X=Y because your placing the p'th element from Y into the p'th element in X thus exactly preserving Y.
最后，由于dec=B是您使用B=reshape(A,1,9)创建的B，所以reshape(dec,3,3)当然会返回A，因为这等效于reshape(B,3,3)，只是撤消了原始的重塑.
Finally, since dec=B and you created B using B=reshape(A,1,9) then of course, reshape(dec,3,3) gives you back A as this is equivalent to reshape(B,3,3) which just undoes the original reshape.
我希望这会有所帮助.
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