转化成矩阵沿对角线矢量 [英] transforming a matrix into a vector along its diagonals

问题描述

我不是不是一个程序员，我只需要解决一些数值在MATLAB。 我需要一个函数来进行以下改造为任何方阵：

im not not a programmer, i just need to solve something numerically in matlab. i need a function to make the following transformation for any square matrix:

从

row 1: 1 2 3 
row 2: 4 5 6
row 3: 7 8 9

到

1 4 2 7 5 3 8 6 9

即写矩阵沿其对角线的向量自左右上角。 任何想法吗？

ie write the matrix in a vector along its diagonals from left to top right. any ideas please?

我真的需要多一点帮助，但：

i really need a little more help though:

说，我们已经转化为载体基质，具有记为M（I，J），其中i是行和j列的条目。现在我需要能够从在载体中的位置，在基质中的原来的位置，即找出说，如果在载体中其第三条目，我需要一个函数，会给我I = 1 J = 2。任何想法吗？我真的卡在这个:(谢谢

say the matrix that we have transformed into the vector, has entries denoted by M(i,j), where i are rows and j columns. now i need to be able to find out from a position in the vector, the original position in the matrix, i.e say if its 3rd entry in the vector, i need a function that would give me i=1 j=2. any ideas please? im really stuck on this:( thanks

推荐答案

这是相当类似于 previous 的问题上遍历矩阵Z字形顺序。随着轻微的修改，我们得到：

This is quite similar to a previous question on traversing the matrix in a zigzag order. With slight modification we get:

A = rand(3);                        %# input matrix

ind = reshape(1:numel(A), size(A)); %# indices of elements
ind = spdiags(fliplr(ind));         %# get the anti-diagonals
ind = ind(end:-1:1);                %# reverse order
ind = ind(ind~=0);                  %# keep non-zero indices
B = A(ind);                         %# get elements in desired order

使用 SPDIAGS 功能。这样做的好处是，它任意矩阵尺寸（不只是正方形矩阵）对。例如：

using the SPDIAGS function. The advantage of this is that it works for any arbitrary matrix size (not just square matrices). Example:

A =
      0.75127      0.69908      0.54722      0.25751
       0.2551       0.8909      0.13862      0.84072
      0.50596      0.95929      0.14929      0.25428
B =
  Columns 1 through 6
      0.75127       0.2551      0.69908      0.50596       0.8909      0.54722
  Columns 7 through 12
      0.95929      0.13862      0.25751      0.14929      0.84072      0.25428

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