Talk:Row-major order

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How do we locate an item in a 3 dimensional array?

[edit] 2dimensional and 3 dimensional arrays

what is the general formula for locating an item in a 2dimensional and 3dimensional array?

It depends on the row-major or column major storage method and how it is extended to higher dimensions. Math-wise, an three dimensional (x,y,z) coordinate is pretty common, and you can assume (1,2,3) refers to the x=1, y=2, z=3 point. if you were going to serialize this into a set of numbers, you might step through your whole array along x first, then y , then z, in a row-major-ish way, or along z (the right-most dimension) first, then y, then x in a column-major-ish way. If you have nx, ny, and nz slots along each of the dimensions, then row-major wise, x varies fastest, so you 'd locate the (x,y,z)th item at z*ny*nx+y*nx+x -- Column-major-wise z varies fastest and x varies slowest, so (x,y,z) would be at the z+y*nz+x*ny*nz cell. Of course there's lots of opportunity for off-by-one errors depending on whether your arrays are zero or one based. Drf5n 17:49, 25 August 2006 (UTC)

[edit] Multi-dimensional arrays

The bit on multi-dimensional arrays is a little difficult when you start thinking of what 'column' means in a three or higher dimensional tuple. For instance in a three dimensional (x,y,z) array is it clear that 'x' is the row and 'z' (definitely not 'y') is the column? Or for an n-dimensional (d1,d2,d3,...,dn) array is the row-major/column-major distinction better as something like row-major means d1 varying fastest / is the inner loop versus column-major means dn varying fastest / is the inner loop? Beyond 2d, the column-major concept seems a little fuzzy. Drf5n 18:08, 25 August 2006 (UTC)

[edit] What are advantages/disadvantages of row-major vs col-major?

It would be a helpful addition to this article to tell us why it's one way in C and the other in Fortran. Are they different for a reason, or was it a random decision? —The preceding unsigned comment was added by Msouth@gmail.com (talk • contribs) 17:32, 4 January 2007 (UTC).

Row major is the most common representation because it means that the rows of a 2-D array are just sub-arrays within a larger array. In C, for instance, multidimensional arrays are not defined directly, but rather as being arrays of arrays. You can't do this with a column major representation, because the inner-most array is interleaved throughout the outer array. Row major representation is also going to give you better cache locality where you are accessing each sub-array independently, such as an array of fixed-length strings.

An advantage of column major is that it may make more sense for vector operations, which is important for scientific computing. Consider the matrix row operations of adding one row to all other rows. You would proceed by multiplying each element in the first column by the first element of the row, and then the next column, and so on. Since each column is contiguous in a column major representation, you will get better cache locality, and so fewer cache misses and better performance.

Something like this needs to be in the article, but I'm not comfortable adding it without a citation, which I don't have. AaronWL 11:05, 22 March 2007 (UTC)