Followed is the explaination in Randall Hyde's AoA book:
Column major ordering is the other function frequently used to compute the
address of an array element. FORTRAN and various dialects of BASIC (e.g.,
Microsoft) use this method to index arrays.
In row major ordering the rightmost index increased the fastest as you moved
through consecutive memory locations. In column major ordering the leftmost
index increases the fastest. Pictorially, a column major ordered array is
organized as shown in Figure 5.6.
The formulae for computing the address of an array element when using column
major ordering is very similar to that for row major ordering. You simply reverse
the indexes and sizes in the computation:
For a two-dimension column major array:
Element_Address = Base_Address + (rowindex * col_size + colindex) * Element_Size
I am wondering in overhead  formulae whether the  rowindex  and the colindex should be exchanged  each other as follow:
Element_Address=Base_Address +( colindex* col_size + rowindex) * Element_Size

Would you please tell me which one is correct!
Posted on 2007-05-13 00:34:18 by qlmi
Let's start by replacing the term 'Column' with 'X', and 'Row' with 'Y'.
Here are the revised Column-Major formulae:

Address = Base + (Y * col_size + X) * Element_Size (Randy)
Address = Base + (X * col_size + Y) * Element_Size (Yours)

I think Randy is wrong, and you are right, in regards to Column Major Order.

Guys, its late, you may disagree, and you may have reason to, but before you shoot me down, do note that the 'conventional' array addressing scheme is Row Major, and for Row Major, Randy's Col-Maj formula would be correct, if we replaced col_size with row_size.

Posted on 2007-05-13 00:57:59 by Homer
Got it, thanks for you detail explaination. i can proceed to next section confidently.
Posted on 2007-05-13 06:06:24 by qlmi
There's an ambiguity in the meaning of column size:

1) the column dimension of the matrix, which is the number of columns
2) the length of a matrix column, which is the number of rows

=====

Row-major order:

address = (row-index * columns-per-row + column-index) * element-size

C and C++ use row-major order.

=====

Randy is right about Fortran - it uses column-major order:

address = (column-index * rows-per-column + row-index) * element-size
Posted on 2007-05-13 19:14:41 by tenkey