How to convert a monodimensional index to corresponding indices in a multidimensional array?

问题

Say I have a 3x4x5x6 java double array a that I unroll into an ArrayList b of length 360 in the following way:

for (int i = 0; i<a.length; i++){
    for (int j = 0; j<a[0].length; j++){
        for (int k = 0; k<a[0][0].length; k++){
            for (int m = 0; m<a[0][0][0].length; m++){
                b.add(a[i][j][k][m]);
            }
        }
    }
}

Given the index of b, is there an easy way to find the corresponding 4-tuple of indices in a?

回答1:

Assuming that

• b is the index on the monodimensional array
• i,j,k,m are the four resulting indices on the multidimensional array
• si,sj,sk,sm are the size of any dimension

you can use basic math, it should be something like

• m = b % sm
• k = (b / sm) % sk
• j = (b / (sm*sk)) % sj
• i = b / (sm*sk*sj)

Basically you increment every index by one for every size of the contained arrays (by multiplying sizes) and you wrap it on its dimension.

回答2:

In MATLAB you can use ind2sub to convert linear indices to subscripts.

Eg. a 4-dimensional (3 x 3 x 3 x 3) matrix:

#% The dimensions of n-dimensional matrix:
SizeVector = [ 3, 3, 3, 3 ];

#% Example linear index:
LinearIndex = 17;

[i1, i2, i3, i4 ] = ind2sub(SizeVector, LinearIndex);

i1 =
   2

i2 =
   3

i3 =
   2

i4 =
   1

To check this is correct you can compute the original linear address manually from these subscripts:

 (i4-1)*3^3 + (i3-1)*3^2 + (i2-1)*3^1 + (i1-1)*3^0 + 1

ans =
    17

来源：https://stackoverflow.com/questions/12429492/how-to-convert-a-monodimensional-index-to-corresponding-indices-in-a-multidimens